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Maxwell's equations (mid-left) as featured on a monument in front of Warsaw University's Centre of New Technologies

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862.

The equations have two major variants. The "microscopic" set of Maxwell's equations uses total charge and total current, including the complicated charges and currents in materials at the atomic scale; it has universal applicability but may be infeasible to calculate. The "macroscopic" set of Maxwell's equations defines two new auxiliary fields that describe large-scale behaviour without having to consider these atomic scale details, but it requires the use of parameters characterizing the electromagnetic properties of the relevant materials.

The term "Maxwell's equations" is often used for other forms of Maxwell's equations. For example, space-time formulations are commonly used in high energy and gravitational physics. These formulations, defined on space-time rather than space and time separately, are manifestly[note 1] compatible with special and general relativity. In quantum mechanics and analytical mechanics, versions of Maxwell's equations based on the electric and magnetic potentials are preferred.

Since the mid-20th century, it has been understood that Maxwell's equations are not exact but are a classical field theory approximation to the more accurate and fundamental theory of quantum electrodynamics. In many situations, though, deviations from Maxwell's equations are immeasurably small. Exceptions include nonclassical light, photon-photon scattering, quantum optics, and many other phenomena related to photons or virtual photons.

Contents

Formulation in terms of electric and magnetic fieldsEdit

As a major contributor to the mathematics of vector calculus, Oliver Heaviside was able to rewrite Maxwell's original 20 equations into a mathematically equivalent four equation form. For Maxwell's equations, vector calculus formulations are much more mathematically convenient, and have become the standard formulation to use.[1]

In the electric and magnetic field formulation there are four equations. Two of them describe how the fields vary in space due to sources, if any; electric fields emanating from electric charges in Gauss's law, and magnetic fields as closed field lines not due to magnetic monopoles in Gauss's law for magnetism. The other two describe how the fields "circulate" around their respective sources; the magnetic field "circulates" around electric currents and time varying electric fields in Ampère's law with Maxwell's addition, while the electric field "circulates" around time varying magnetic fields in Faraday's law. A separate law of nature, the Lorentz force law, describes how the electric and magnetic field act on charged particles and currents. A version of this law was included in the original equations by Maxwell but, by convention, is no longer.

The precise formulation of Maxwell's equations depends on the precise definition of the quantities involved. Conventions differ with the unit systems, because various definitions and dimensions are changed by absorbing dimensionful factors like the speed of light c. This makes constants come out differently. The most common form is based on quantities measured using SI units, but other commonly used units include Gaussian units based on the cgs system,[2] Lorentz–Heaviside units (used mainly in particle physics), and Planck units (used in theoretical physics).

Formulation in SI unitsEdit

Name Integral equations Differential equations Meaning
Gauss's law        The electric field leaving a volume is proportional to the charge inside.
Gauss's law for magnetism        There are no magnetic monopoles; the total magnetic flux piercing a closed surface is zero.
Maxwell–Faraday equation (Faraday's law of induction)     The voltage accumulated around a closed circuit is proportional to the time rate of change of the magnetic flux it encloses.
Ampère's circuital law (with Maxwell's addition)     Electric currents and changes in electric fields are proportional to the magnetic field circulating about the area they pierce.

Formulation in Gaussian unitsEdit

Gaussian units are a popular system of units, that are part of the centimetre–gram–second system of units (cgs). When using cgs units it is conventional to use a slightly different definition of electric field Ecgs = c−1 ESI. This implies that the modified electric and magnetic field have the same units (in the SI convention this is not the case: e.g. for EM waves in vacuum, |E|SI, making dimensional analysis of the equations different). Then it uses a unit of charge defined in such a way that the permittivity of the vacuum ε0 = 1/4πc, hence μ0 = /c. These units are sometimes preferred over SI units in the context of special relativity,[3] since when using them, the components of the electromagnetic tensor, the Lorentz covariant object describing the electromagnetic field, have the same unit without constant factors. Using these different conventions, the Maxwell equations become:[4]

Equations in Gaussian units
Name Microscopic equations Macroscopic equations
Gauss's law    
Gauss's law for magnetism  
Maxwell–Faraday equation (Faraday's law of induction)  
Ampère's law (with Maxwell's extension)    

Key for mathematical notationEdit

Symbols in bold represent vector quantities, and symbols in italics represent scalar quantities, unless otherwise indicated.

The equations introduce the electric field, E, a vector field, and the magnetic field, B, a pseudovector field, where each generally have time-dependence.

The universal constants appearing in the equations are

In the differential equations, a local description of the fields,

The sources are taken to be

In the integral equations, a description of the fields within a region of space,

  • Ω is any fixed volume with boundary surface ∂Ω, and
  • Σ is any fixed open surface with boundary curve ∂Σ,
  •    is a surface integral over the surface ∂Ω, (the loop indicates the surface is closed and not open)
  •   is a volume integral over the volume Ω,
  •   is a surface integral over the surface Σ,
  •   is a line integral around the curve ∂Σ (the loop indicates the curve is closed).

Here fixed means the volume or surface do not change in time. Although it is possible to formulate Maxwell's equations with time-dependent surfaces and volumes, this is not actually necessary: the equations are correct and complete with time-independent surfaces. The sources are correspondingly the total amounts of charge and current within these volumes and surfaces, found by integration.

 
where dV is the differential volume element, and
 
where dS denotes the differential vector element of surface area, S, normal to surface, Σ. (Vector area is also denoted by A rather than S, but this conflicts with the magnetic potential, a separate vector field).

The total charge or current refers to including free and bound charges, or free and bound currents. These are used in the macroscopic formulation.

Relationship between differential and integral formulationsEdit

The differential and integral formulations of the equations are mathematically equivalent, by the divergence theorem in the case of Gauss's law and Gauss's law for magnetism, and by the Kelvin–Stokes theorem in the case of Faraday's law and Ampère's law. Both the differential and integral formulations are useful. The integral formulation can often be used to simplify and directly calculate fields from symmetric distributions of charges and currents. On the other hand, the differential formulation is a more natural starting point for calculating the fields in more complicated (less symmetric) situations, for example using finite element analysis.[5]

Flux and divergenceEdit

 
Closed volume Ω and its boundary ∂Ω, enclosing a source (+) and sink (−) of a vector field F. Here, F could be the E field with source electric charges, but not the B field which has no magnetic charges as shown. The outward unit normal is n.

The "fields emanating from the sources" can be inferred from the surface integrals of the fields through the closed surface ∂Ω, defined as the electric flux      and magnetic flux     , as well as their respective divergences ∇ · E and ∇ · B. These surface integrals and divergences are connected by the divergence theorem.

Circulation and curlEdit

 
Open surface Σ and boundary ∂Σ. F could be the E or B fields. Again, n is the unit normal. (The curl of a vector field doesn't literally look like the "circulations", this is a heuristic depiction).

The "circulation of the fields" can be interpreted from the line integrals of the fields around the closed curve ∂Σ:

 

where d is the differential vector element of path length tangential to the path/curve, as well as their curls:

 

These line integrals and curls are connected by Stokes' theorem, and are analogous to quantities in classical fluid dynamics: the circulation of a fluid is the line integral of the fluid's flow velocity field around a closed loop, and the vorticity of the fluid is the curl of the velocity field.

Time evolutionEdit

The "dynamics" or "time evolution of the fields" is due to the partial derivatives of the fields with respect to time:

 

These derivatives are crucial for the prediction of field propagation in the form of electromagnetic waves. Since the surface is taken to be time-independent, we can make the following transition in Faraday's law:

 

see differentiation under the integral sign for more on this result.

Conceptual descriptionsEdit

Gauss's lawEdit

Gauss's law describes the relationship between a static electric field and the electric charges that cause it: The static electric field points away from positive charges and towards negative charges. In the field line description, electric field lines begin only at positive electric charges and end only at negative electric charges. 'Counting' the number of field lines passing through a closed surface, therefore, yields the total charge (including bound charge due to polarization of material) enclosed by that surface divided by dielectricity of free space (the vacuum permittivity). More technically, it relates the electric flux through any hypothetical closed "Gaussian surface" to the enclosed electric charge.

 
Gauss's law for magnetism: magnetic field lines never begin nor end but form loops or extend to infinity as shown here with the magnetic field due to a ring of current.

Gauss's law for magnetismEdit

Gauss's law for magnetism states that there are no "magnetic charges" (also called magnetic monopoles), analogous to electric charges.[6] Instead, the magnetic field due to materials is generated by a configuration called a dipole. Magnetic dipoles are best represented as loops of current but resemble positive and negative 'magnetic charges', inseparably bound together, having no net 'magnetic charge'. In terms of field lines, this equation states that magnetic field lines neither begin nor end but make loops or extend to infinity and back. In other words, any magnetic field line that enters a given volume must somewhere exit that volume. Equivalent technical statements are that the sum total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

Faraday's lawEdit

 
In a geomagnetic storm, a surge in the flux of charged particles temporarily alters Earth's magnetic field, which induces electric fields in Earth's atmosphere, thus causing surges in electrical power grids. Artist's rendition; sizes are not to scale.

The Maxwell-Faraday's equation version of Faraday's law describes how a time varying magnetic field creates ("induces") an electric field.[6] This dynamically induced electric field has closed field lines just as the magnetic field, if not superposed by a static (charge induced) electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators: for example, a rotating bar magnet creates a changing magnetic field, which in turn generates an electric field in a nearby wire.

Ampère's law with Maxwell's additionEdit

 
Magnetic core memory (1954) is an application of Ampère's law. Each core stores one bit of data.

Ampère's law with Maxwell's addition states that magnetic fields can be generated in two ways: by electric current (this was the original "Ampère's law") and by changing electric fields (this was "Maxwell's addition").

Maxwell's addition to Ampère's law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a magnetic field.[6][7] Therefore, these equations allow self-sustaining "electromagnetic waves" to travel through empty space (see electromagnetic wave equation).

The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents,[note 2] exactly matches the speed of light; indeed, light is one form of electromagnetic radiation (as are X-rays, radio waves, and others). Maxwell understood the connection between electromagnetic waves and light in 1861, thereby unifying the theories of electromagnetism and optics.

Vacuum equations, electromagnetic waves and speed of lightEdit

 
This 3D diagram shows a plane linearly polarized wave propagating from left to right with the same wave equations where E = E0 sin(−ωt + kr) and B = B0 sin(−ωt + kr)

In a region with no charges (ρ = 0) and no currents (J = 0), such as in a vacuum, Maxwell's equations reduce to:

 

Taking the curl (∇×) of the curl equations, and using the curl of the curl identity ∇ × (∇ × X) = ∇(∇·X) − ∇2X we obtain the wave equations

 

which identify

 

with the speed of light in free space. In materials with relative permittivity, εr, and relative permeability, μr, the phase velocity of light becomes

 

which is usually[note 3] less than c.

In addition, E and B are mutually perpendicular to each other and the direction of wave propagation, and are in phase with each other. A sinusoidal plane wave is one special solution of these equations. Maxwell's equations explain how these waves can physically propagate through space. The changing magnetic field creates a changing electric field through Faraday's law. In turn, that electric field creates a changing magnetic field through Maxwell's addition to Ampère's law. This perpetual cycle allows these waves, now known as electromagnetic radiation, to move through space at velocity, c.

Macroscopic formulationEdit

The microscopic variant of Maxwell's equation is the version given above. It expresses the electric E field and the magnetic B field in terms of the total charge and total current present, including the charges and currents at the atomic level. The "microscopic" form is sometimes called the "general" form of Maxwell's equations. The macroscopic variant of Maxwell's equation is equally general, however, with the difference being one of bookkeeping.

The "microscopic" variant is sometimes called "Maxwell's equations in a vacuum". This refers to the fact that the material medium is not built into the structure of the equation; it does not mean that space is empty of charge or current.

"Maxwell's macroscopic equations", also known as Maxwell's equations in matter, are more similar to those that Maxwell introduced himself.

Name Integral equations Differential equations
Gauss's law       
Gauss's law for magnetism       
Maxwell–Faraday equation (Faraday's law of induction)    
Ampère's circuital law (with Maxwell's addition)    

Unlike the "microscopic" equations, the "macroscopic" equations separate out the bound charge Qb and bound current Ib to obtain equations that depend only on the free charges Qf and currents If. This factorization can be made by splitting the total electric charge and current as follows:

 
 

Correspondingly, the total current density J splits into free Jf and bound Jb components, and similarly the total charge density ρ splits into free ρf and bound ρb parts.

The cost of this factorization is that additional fields, the displacement field D and the magnetizing field H, are defined and need to be determined. Phenomenological constituent equations relate the additional fields to the electric field E and the magnetic B-field, often through a simple linear relation.

For a detailed description of the differences between the microscopic (total charge and current including material contributes or in air/vacuum)[note 4] and macroscopic (free charge and current; practical to use on materials) variants of Maxwell's equations, see below.

Bound charge and currentEdit

 
Left: A schematic view of how an assembly of microscopic dipoles produces opposite surface charges as shown at top and bottom. Right: How an assembly of microscopic current loops add together to produce a macroscopically circulating current loop. Inside the boundaries, the individual contributions tend to cancel, but at the boundaries no cancelation occurs.

When an electric field is applied to a dielectric material its molecules respond by forming microscopic electric dipoles – their atomic nuclei move a tiny distance in the direction of the field, while their electrons move a tiny distance in the opposite direction. This produces a macroscopic bound charge in the material even though all of the charges involved are bound to individual molecules. For example, if every molecule responds the same, similar to that shown in the figure, these tiny movements of charge combine to produce a layer of positive bound charge on one side of the material and a layer of negative charge on the other side. The bound charge is most conveniently described in terms of the polarization P of the material, its dipole moment per unit volume. If P is uniform, a macroscopic separation of charge is produced only at the surfaces where P enters and leaves the material. For non-uniform P, a charge is also produced in the bulk.[8]

Somewhat similarly, in all materials the constituent atoms exhibit magnetic moments that are intrinsically linked to the angular momentum of the components of the atoms, most notably their electrons. The connection to angular momentum suggests the picture of an assembly of microscopic current loops. Outside the material, an assembly of such microscopic current loops is not different from a macroscopic current circulating around the material's surface, despite the fact that no individual charge is traveling a large distance. These bound currents can be described using the magnetization M.[9]

The very complicated and granular bound charges and bound currents, therefore, can be represented on the macroscopic scale in terms of P and M which average these charges and currents on a sufficiently large scale so as not to see the granularity of individual atoms, but also sufficiently small that they vary with location in the material. As such, Maxwell's macroscopic equations ignore many details on a fine scale that can be unimportant to understanding matters on a gross scale by calculating fields that are averaged over some suitable volume.

Auxiliary fields, polarization and magnetizationEdit

The definitions (not constitutive relations) of the auxiliary fields are:

 

where P is the polarization field and M is the magnetization field which are defined in terms of microscopic bound charges and bound currents respectively. The macroscopic bound charge density ρb and bound current density Jb in terms of polarization P and magnetization M are then defined as

 

If we define the total, bound, and free charge and current density by

 

and use the defining relations above to eliminate D, and H, the "macroscopic" Maxwell's equations reproduce the "microscopic" equations.

Constitutive relationsEdit

In order to apply 'Maxwell's macroscopic equations', it is necessary to specify the relations between displacement field D and the electric field E, as well as the magnetizing field H and the magnetic field B. Equivalently, we have to specify the dependence of the polarisation P (hence the bound charge) and the magnetisation M (hence the bound current) on the applied electric and magnetic field. The equations specifying this response are called constitutive relations. For real-world materials, the constitutive relations are rarely simple, except approximately, and usually determined by experiment. See the main article on constitutive relations for a fuller description.

For materials without polarisation and magnetisation ("vacuum"), the constitutive relations are

 

where ε0 is the permittivity of free space and μ0 the permeability of free space. Since there is no bound charge, the total and the free charge and current are equal.

More generally, for linear materials the constitutive relations are

 

where ε is the permittivity and μ the permeability of the material. Even the linear case can have various complications, however.

  • For homogeneous materials, ε and μ are constant throughout the material, while for inhomogeneous materials they depend on location within the material (and perhaps time).
  • For isotropic materials, ε and μ are scalars, while for anisotropic materials (e.g. due to crystal structure) they are tensors.
  • Materials are generally dispersive, so ε and μ depend on the frequency of any incident EM waves.

Even more generally, in the case of non-linear materials (see for example nonlinear optics), D and P are not necessarily proportional to E, similarly B is not necessarily proportional to H or M. In general D and H depend on both E and B, on location and time, and possibly other physical quantities.

In applications one also has to describe how the free currents and charge density behave in terms of E and B possibly coupled to other physical quantities like pressure, and the mass, number density, and velocity of charge-carrying particles. E.g., the original equations given by Maxwell (see History of Maxwell's equations) included Ohms law in the form

 

Alternative formulationsEdit

Following is a summary of some of the numerous other ways to write the microscopic Maxwell's equations, showing they can be formulated using different points of view and mathematical formalisms that describe the same physics. Often, they are also called the Maxwell equations. The direct space–time formulations make manifest that the Maxwell equations are relativistically invariant (in fact studying the hidden symmetry of the vector calculus formulation was a major source of inspiration for relativity theory). In addition, the formulation using potentials was originally introduced as a convenient way to solve the equations but with all the observable physics contained in the fields. The potentials play a central role in quantum mechanics, however, and act quantum mechanically with observable consequences even when the fields vanish (Aharonov–Bohm effect). See the main articles for the details of each formulation. SI units are used throughout.

Formalism Formulation Homogeneous equations Non-homogeneous equations
Vector calculus Fields

3D Euclidean space + time

   
Potentials (any gauge)

3D Euclidean space + time

   
Potentials (Lorenz gauge)

3D Euclidean space + time

   
Tensor calculus Fields

Minkowski space

   
Potentials (any gauge)

Minkowski space

   
Potentials (Lorenz gauge)

Minkowski space

   
Fields

Any space–time

   
Potentials (any gauge)

Any space–time

   
Potentials (Lorenz gauge)

Any space–time

   
Differential forms Fields

Any space–time

   
Potentials (any gauge)

Any space–time

   
Potentials (Lorenz gauge)

Any space–time

   

where

  • In the vector formulation on Euclidean space + time, φ is the electrical potential, A is the vector potential and ◻ = 1/c2 2/t2 − ∇2 is the d'Alembert operator.
  • In the tensor calculus formulation, the electromagnetic tensor Fαβ is an antisymmetric covariant rank 2 tensor; the four-potential, Aα, is a covariant vector; the current, Jα, is a vector; the square brackets, [ ], denote antisymmetrization of indices; α is the derivative with respect to the coordinate, xα. In Minkowski space coordinates are chosen with respect to an inertial frame; (xα) = (ct,x,y,z), so that the metric tensor used to raise and lower indices is ηαβ = diag(1,−1,−1,−1). The d'Alembert operator on Minkowski space is ◻ = ∂αα as in the vector formulation. In general spacetimes, the coordinate system xα is arbitrary, the covariant derivative α, the Ricci tensor, Rαβ and raising and lowering of indices are defined by the Lorentzian metric, gαβ and the d'Alembert operator is defined as ◻ = ∇αα.
  • In the differential form formulation on arbitrary space times, F = Fαβdxα ∧ dxβ is the electromagnetic tensor considered as a 2-form, A = Aαdxα is the potential 1-form, J is the current 3-form, d is the exterior derivative, and   is the Hodge star on forms defined by the Lorentzian metric of space–time. Note that in the special case of 2-forms such as F, the Hodge star   only depends on the metric up to a local scale . This means that, as formulated, the differential form field equations are conformally invariant, but the Lorenz gauge condition breaks conformal invariance. The operator   is the d'Alembert–Laplace–Beltrami operator on 1-forms on an arbitrary Lorentzian space–time.

Other formulations include the geometric algebra formulation and a matrix representation of Maxwell's equations. Historically, a quaternionic formulation[10][11] was used.

SolutionsEdit

Maxwell's equations are partial differential equations that relate the electric and magnetic fields to each other and to the electric charges and currents. Often, the charges and currents are themselves dependent on the electric and magnetic fields via the Lorentz force equation and the constitutive relations. These all form a set of coupled partial differential equations, which are often very difficult to solve. In fact, the solutions of these equations encompass all the diverse phenomena in the entire field of classical electromagnetism. A thorough discussion is far beyond the scope of the article, but some general notes follow.

Like any differential equation, boundary conditions[12][13][14] and initial conditions[15] are necessary for a unique solution. For example, even with no charges and no currents anywhere in spacetime, many solutions to Maxwell's equations are possible, not just the obvious solution E = B = 0. Another solution is E = constant, B = constant, while yet other solutions have electromagnetic waves filling spacetime. In some cases, Maxwell's equations are solved through infinite space, and boundary conditions are given as asymptotic limits at infinity.[16] In other cases, Maxwell's equations are solved in just a finite region of space, with appropriate boundary conditions on that region: For example, the boundary could be an artificial absorbing boundary representing the rest of the universe,[17][18] or periodic boundary conditions, or (as with a waveguide or cavity resonator) the boundary conditions may describe the walls that isolate a small region from the outside world.[19]

Jefimenko's equations (or the closely related Liénard–Wiechert potentials) are the explicit solution to Maxwell's equations for the electric and magnetic fields created by any given distribution of charges and currents. It assumes specific initial conditions to obtain the so-called "retarded solution", where the only fields present are the ones created by the charges. Jefimenko's equations are not so helpful in situations when the charges and currents are themselves affected by the fields they create.

Numerical methods for differential equations can be used to approximately solve Maxwell's equations when an exact solution is impossible. These methods usually require a computer, and include the finite element method and finite-difference time-domain method.[12][14][20][21][22] For more details, see Computational electromagnetics.

Maxwell's equations seem overdetermined, in that they involve six unknowns (the three components of E and B) but eight equations (one for each of the two Gauss's laws, three vector components each for Faraday's and Ampere's laws). (The currents and charges are not unknowns, being freely specifiable subject to charge conservation.) This is related to a certain limited kind of redundancy in Maxwell's equations: It can be proven that any system satisfying Faraday's law and Ampere's law automatically also satisfies the two Gauss's laws, as long as the system's initial condition does.[23][24] This explanation was first introduced by Julius Adams Stratton in 1941.[25] Although it is possible to simply ignore the two Gauss's laws in a numerical algorithm (apart from the initial conditions), the imperfect precision of the calculations can lead to ever-increasing violations of those laws. By introducing dummy variables characterizing these violations, the four equations become not overdetermined after all. The resulting formulation can lead to more accurate algorithms that take all four laws into account.[26]

Limitations of the Maxwell equations as a theory of electromagnetismEdit

While Maxwell's equations (along with the rest of classical electromagnetism) are extraordinarily successful at explaining and predicting a variety of phenomena, they are not exact, but approximations. In some special situations, they can be noticeably inaccurate. Examples include extremely strong fields (see Euler–Heisenberg Lagrangian) and extremely short distances (see vacuum polarization). Moreover, various phenomena occur in the world even though Maxwell's equations predict them to be impossible, such as "nonclassical light" and quantum entanglement of electromagnetic fields (see quantum optics). Finally, any phenomenon involving individual photons, such as the photoelectric effect, Planck's law, the Duane–Hunt law, single-photon light detectors, etc., would be difficult or impossible to explain if Maxwell's equations were exactly true, as Maxwell's equations do not involve photons. For the most accurate predictions in all situations, Maxwell's equations have been superseded by quantum electrodynamics.

VariationsEdit

Popular variations on the Maxwell equations as a classical theory of electromagnetic fields are relatively scarce because the standard equations have stood the test of time remarkably well.

Magnetic monopolesEdit

Maxwell's equations posit that there is electric charge, but no magnetic charge (also called magnetic monopoles), in the universe. Indeed, magnetic charge has never been observed (despite extensive searches)[note 5] and may not exist. If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields.[27][28]

See alsoEdit

NotesEdit

  1. ^ Maxwell's equations in any form are compatible with relativity. These space-time formulations, though, make that compatibility more readily apparent.
  2. ^ The quantity we would now call 1ε0μ0, with units of velocity, was directly measured before Maxwell's equations, in an 1855 experiment by Wilhelm Eduard Weber and Rudolf Kohlrausch. They charged a leyden jar (a kind of capacitor), and measured the electrostatic force associated with the potential; then, they discharged it while measuring the magnetic force from the current in the discharge wire. Their result was 3.107×108 m/s, remarkably close to the speed of light. See The story of electrical and magnetic measurements: from 500 B.C. to the 1940s, by Joseph F. Keithley, p115
  3. ^ There are cases (anomalous dispersion) where the phase velocity can exceed c, but the "signal velocity" will still be < c
  4. ^ In some books—e.g., in U. Krey and A. Owen's Basic Theoretical Physics (Springer 2007)—the term effective charge is used instead of total charge, while free charge is simply called charge.
  5. ^ See magnetic monopole for a discussion of monopole searches. Recently, scientists have discovered that some types of condensed matter, including spin ice and topological insulators, which display emergent behavior resembling magnetic monopoles. (See [1] and [2].) Although these were described in the popular press as the long-awaited discovery of magnetic monopoles, they are only superficially related. A "true" magnetic monopole is something where ∇ ⋅ B ≠ 0, whereas in these condensed-matter systems, ∇ ⋅ B = 0 while only ∇ ⋅ H ≠ 0.

ReferencesEdit

  1. ^ Bruce J. Hunt (1991) The Maxwellians, chapter 5 and appendix, Cornell University Press
  2. ^ David J Griffiths (1999). Introduction to electrodynamics (Third ed.). Prentice Hall. pp. 559–562. ISBN 0-13-805326-X.
  3. ^ J.D. Jackson. "Preface". Classical Electrodynamics (3rd ed.). ISBN 0-471-43132-X.
  4. ^ Littlejohn, Robert (Fall 2007). "Gaussian, SI and Other Systems of Units in Electromagnetic Theory" (PDF). Physics 221A, University of California, Berkeley lecture notes. Retrieved 2008-05-06.
  5. ^ Šolín, Pavel (2006). Partial differential equations and the finite element method. John Wiley and Sons. p. 273. ISBN 0-471-72070-4.
  6. ^ a b c J.D. Jackson, "Maxwell's Equations" video glossary entry
  7. ^ Principles of physics: a calculus-based text, by R.A. Serway, J.W. Jewett, page 809.
  8. ^ See David J. Griffiths (1999). "4.2.2". Introduction to Electrodynamics (third ed.). Prentice Hall. for a good description of how P relates to the bound charge.
  9. ^ See David J. Griffiths (1999). "6.2.2". Introduction to Electrodynamics (third ed.). Prentice Hall. for a good description of how M relates to the bound current.
  10. ^ P.M. Jack (2003). "Physical Space as a Quaternion Structure I: Maxwell Equations. A Brief Note". Toronto, Canada. arXiv:math-ph/0307038.
  11. ^ A. Waser (2000). "On the Notation of Maxwell's Field Equations" (PDF). AW-Verlag.
  12. ^ a b Peter Monk (2003). Finite Element Methods for Maxwell's Equations. Oxford UK: Oxford University Press. p. 1 ff. ISBN 0-19-850888-3.
  13. ^ Thomas B. A. Senior & John Leonidas Volakis (1995-03-01). Approximate Boundary Conditions in Electromagnetics. London UK: Institution of Electrical Engineers. p. 261 ff. ISBN 0-85296-849-3.
  14. ^ a b T Hagstrom (Björn Engquist & Gregory A. Kriegsmann, Eds.) (1997). Computational Wave Propagation. Berlin: Springer. p. 1 ff. ISBN 0-387-94874-0.
  15. ^ Henning F. Harmuth & Malek G. M. Hussain (1994). Propagation of Electromagnetic Signals. Singapore: World Scientific. p. 17. ISBN 981-02-1689-0.
  16. ^ David M Cook (2002). The Theory of the Electromagnetic Field. Mineola NY: Courier Dover Publications. p. 335 ff. ISBN 0-486-42567-3.
  17. ^ Jean-Michel Lourtioz (2005-05-23). Photonic Crystals: Towards Nanoscale Photonic Devices. Berlin: Springer. p. 84. ISBN 3-540-24431-X.
  18. ^ S. G. Johnson, Notes on Perfectly Matched Layers, online MIT course notes (Aug. 2007).
  19. ^ S. F. Mahmoud (1991). Electromagnetic Waveguides: Theory and Applications. London UK: Institution of Electrical Engineers. Chapter 2. ISBN 0-86341-232-7.
  20. ^ John Leonidas Volakis, Arindam Chatterjee & Leo C. Kempel (1998). Finite element method for electromagnetics : antennas, microwave circuits, and scattering applications. New York: Wiley IEEE. p. 79 ff. ISBN 0-7803-3425-6.
  21. ^ Bernard Friedman (1990). Principles and Techniques of Applied Mathematics. Mineola NY: Dover Publications. ISBN 0-486-66444-9.
  22. ^ Taflove A & Hagness S C (2005). Computational Electrodynamics: The Finite-difference Time-domain Method. Boston MA: Artech House. Chapters 6 & 7. ISBN 1-58053-832-0.
  23. ^ H Freistühler & G Warnecke (2001). Hyperbolic Problems: Theory, Numerics, Applications. p. 605.
  24. ^ J Rosen. "Redundancy and superfluity for electromagnetic fields and potentials". American Journal of Physics. 48 (12): 1071. Bibcode:1980AmJPh..48.1071R. doi:10.1119/1.12289.
  25. ^ J.A. Stratton (1941). Electromagnetic Theory. McGraw-Hill Book Company. pp. 1–6.
  26. ^ B Jiang & J Wu & L.A. Povinelli (1996). "The Origin of Spurious Solutions in Computational Electromagnetics". Journal of Computational Physics. 125 (1): 104. Bibcode:1996JCoPh.125..104J. doi:10.1006/jcph.1996.0082.
  27. ^ J.D. Jackson. "6.11". Classical Electrodynamics (3rd ed.). ISBN 0-471-43132-X.
  28. ^ "IEEEGHN: Maxwell's Equations". Ieeeghn.org. Retrieved 2008-10-19.
Further reading can be found in list of textbooks in electromagnetism

Historical publicationsEdit

The developments before relativity:

External linksEdit

Modern treatmentsEdit

OtherEdit


{{DEFAULTSORT:Maxwell's Equations}} Category:Electromagnetism Category:Equations of physics Category:Partial differential equations Category:James Clerk Maxwell


In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

  1. that the laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference).
  2. that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".[1] The inconsistency of Newtonian mechanics with Maxwell’s equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving motions nearing the speed of light. As of today, special relativity is the most accurate model of motion at any speed. Even so, the Newtonian mechanics model is still useful (due to its simplicity and high accuracy) as an approximation at small velocities relative to the speed of light.

Special relativity implies a wide range of consequences, which have been experimentally verified,[2] including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in a vacuum.[3][4]

A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer can occur at different times for another.

The theory is "special" in that it only applies in the special case where the curvature of spacetime due to gravity is negligible.[5][6] In order to include gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerated frames of reference.[7]

As Galilean relativity is now considered an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, i.e. at a sufficiently small scale and in conditions of free fall. Whereas general relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space. A locally Lorentz-invariant frame that abides by special relativity can be defined at sufficiently small scales, even in curved spacetime.

Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light,[8] a phenomenon that had been recently observed in the Michelson–Morley experiment. He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.[9]

 
Albert Einstein around 1905, the year his "Annus Mirabilis papers" – which included Zur Elektrodynamik bewegter Körper, the paper founding special relativity – were published.

PostulatesEdit

Einstein discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the (then) known laws of either mechanics or electrodynamics. These propositions were the constancy of the speed of light and the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as:[1]

  • The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.[1]
  • The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body" (from the preface).[1] That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.

The derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions (made in almost all theories of physics), including the isotropy and homogeneity of space and the independence of measuring rods and clocks from their past history.[11]

Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations.[12] However, the most common set of postulates remains those employed by Einstein in his original paper. A more mathematical statement of the Principle of Relativity made later by Einstein, which introduces the concept of simplicity not mentioned above is:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.[13]

Henri Poincaré provided the mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincaré group of symmetry transformations. Einstein later derived these transformations from his axioms.

Many of Einstein's papers present derivations of the Lorentz transformation based upon these two principles.[14]

Einstein consistently based the derivation of Lorentz invariance (the essential core of special relativity) on just the two basic principles of relativity and light-speed invariance. He wrote:

The insight fundamental for the special theory of relativity is this: The assumptions relativity and light speed invariance are compatible if relations of a new type ("Lorentz transformation") are postulated for the conversion of coordinates and times of events... The universal principle of the special theory of relativity is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations (for the transition from one inertial system to any other arbitrarily chosen inertial system). This is a restricting principle for natural laws...[10]

Thus many modern treatments of special relativity base it on the single postulate of universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime.[15][16]

From the principle of relativity alone without assuming the constancy of the speed of light (i.e. using the isotropy of space and the symmetry implied by the principle of special relativity) one can show that the spacetime transformations between inertial frames are either Euclidean, Galilean, or Lorentzian. In the Lorentzian case, one can then obtain relativistic interval conservation and a certain finite limiting speed. Experiments suggest that this speed is the speed of light in vacuum.[17][18]

The constancy of the speed of light was motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether. There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment.[19][20] In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.

Lack of an absolute reference frameEdit

The principle of relativity, which states that there is no preferred inertial reference frame, dates back to Galileo, and was incorporated into Newtonian physics. However, in the late 19th century, the existence of electromagnetic waves led physicists to suggest that the universe was filled with a substance that they called "aether", which would act as the medium through which these waves, or vibrations travelled. The aether was thought to constitute an absolute reference frame against which speeds could be measured, and could be considered fixed and motionless. Aether supposedly possessed some wonderful properties: it was sufficiently elastic to support electromagnetic waves, and those waves could interact with matter, yet it offered no resistance to bodies passing through it. The results of various experiments, including the Michelson–Morley experiment, led to the theory of special relativity, by showing that there was no aether.[21] Einstein's solution was to discard the notion of an aether and the absolute state of rest. In relativity, any reference frame moving with uniform motion will observe the same laws of physics. In particular, the speed of light in vacuum is always measured to be c, even when measured by multiple systems that are moving at different (but constant) velocities.

Reference frames, coordinates, and the Lorentz transformationEdit

 
The primed system is in motion relative to the unprimed system with constant velocity v only along the x-axis, from the perspective of an observer stationary in the unprimed system. By the principle of relativity, an observer stationary in the primed system will view a likewise construction except that the velocity they record will be −v. The changing of the speed of propagation of interaction from infinite in non-relativistic mechanics to a finite value will require a modification of the transformation equations mapping events in one frame to another.

Reference frames play a crucial role in relativity theory. The term reference frame as used here is an observational perspective in space which is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes. In addition, a reference frame has the ability to determine measurements of the time of events using a 'clock' (any reference device with uniform periodicity).

An event is an occurrence that can be assigned a single unique time and location in space relative to a reference frame: it is a "point" in spacetime. Since the speed of light is constant in relativity in each and every reference frame, pulses of light can be used to unambiguously measure distances and refer back the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired.

For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four spacetime coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S.

In relativity theory we often want to calculate the position of a point from a different reference point.

Suppose we have a second reference frame S′, whose spatial axes and clock exactly coincide with that of S at time zero, but it is moving at a constant velocity v with respect to S along the x-axis.

Since there is no absolute reference frame in relativity theory, a concept of 'moving' doesn't strictly exist, as everything is always moving with respect to some other reference frame. Instead, any two frames that move at the same speed in the same direction are said to be comoving. Therefore, S and S′ are not comoving.

Define the event to have spacetime coordinates (t,x,y,z) in system S and (t′,x′,y′,z′) in S′. Then the Lorentz transformation specifies that these coordinates are related in the following way:

 

where

 

is the Lorentz factor and c is the speed of light in vacuum, and the velocity v of S′ is parallel to the x-axis. The y and z coordinates are unaffected; only the x and t coordinates are transformed. These Lorentz transformations form a one-parameter group of linear mappings, that parameter being called rapidity.

There is nothing special about the x-axis, the transformation can apply to the y or z axes, or indeed in any direction, which can be done by directions parallel to the motion (which are warped by the γ factor) and perpendicular; see main article for details.

A quantity invariant under Lorentz transformations is known as a Lorentz scalar.

Writing the Lorentz transformation and its inverse in terms of coordinate differences, where for instance one event has coordinates (x1, t1) and (x1, t1), another event has coordinates (x2, t2) and (x2, t2), and the differences are defined as

 

we get

 

These effects are not merely appearances; they are explicitly related to our way of measuring time intervals between events which occur at the same place in a given coordinate system (called "co-local" events). These time intervals will be different in another coordinate system moving with respect to the first, unless the events are also simultaneous. Similarly, these effects also relate to our measured distances between separated but simultaneous events in a given coordinate system of choice. If these events are not co-local, but are separated by distance (space), they will not occur at the same spatial distance from each other when seen from another moving coordinate system. However, the spacetime interval will be the same for all observers. The underlying reality remains the same. Only our perspective changes.

Consequences derived from the Lorentz transformationEdit

The consequences of special relativity can be derived from the Lorentz transformation equations.[22] These transformations, and hence special relativity, lead to different physical predictions than those of Newtonian mechanics when relative velocities become comparable to the speed of light. The speed of light is so much larger than anything humans encounter that some of the effects predicted by relativity are initially counterintuitive.

Relativity of simultaneityEdit

 
Event B is simultaneous with A in the green reference frame, but it occurs before A in the blue frame, and occurs after A in the red frame.

Two events happening in two different locations that occur simultaneously in the reference frame of one inertial observer, may occur non-simultaneously in the reference frame of another inertial observer (lack of absolute simultaneity).

From the first equation of the Lorentz transformation in terms of coordinate differences

 

it is clear that two events that are simultaneous in frame S (satisfying Δt = 0), are not necessarily simultaneous in another inertial frame S′ (satisfying Δt′ = 0). Only if these events are additionally co-local in frame S (satisfying Δx = 0), will they be simultaneous in another frame S′.

Time dilationEdit

The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames (e.g., the twin paradox which concerns a twin who flies off in a spaceship traveling near the speed of light and returns to discover that his or her twin sibling has aged much more).

Suppose a clock is at rest in the unprimed system S. The location of the clock on two different ticks is then characterized by Δx = 0. To find the relation between the times between these ticks as measured in both systems, the first equation can be used to find:

     for events satisfying     

This shows that the time (Δt′) between the two ticks as seen in the frame in which the clock is moving (S′), is longer than the time (Δt) between these ticks as measured in the rest frame of the clock (S). Time dilation explains a number of physical phenomena; for example, the lifetime of muons produced by cosmic rays impinging on the Earth's atmosphere is measured to be greater than the lifetimes of muons measured in the laboratory.[23]

Length contractionEdit

The dimensions (e.g., length) of an object as measured by one observer may be smaller than the results of measurements of the same object made by another observer (e.g., the ladder paradox involves a long ladder traveling near the speed of light and being contained within a smaller garage).

Similarly, suppose a measuring rod is at rest and aligned along the x-axis in the unprimed system S. In this system, the length of this rod is written as Δx. To measure the length of this rod in the system S′, in which the clock is moving, the distances x′ to the end points of the rod must be measured simultaneously in that system S′. In other words, the measurement is characterized by Δt′ = 0, which can be combined with the fourth equation to find the relation between the lengths Δx and Δx′:

     for events satisfying     

This shows that the length (Δx′) of the rod as measured in the frame in which it is moving (S′), is shorter than its length (Δx) in its own rest frame (S).

Composition of velocitiesEdit

Velocities (speeds) do not simply add. If the observer in S measures an object moving along the x axis at velocity u, then the observer in the S′ system, a frame of reference moving at velocity v in the x direction with respect to S, will measure the object moving with velocity u′ where (from the Lorentz transformations above):

 

The other frame S will measure:

 

Notice that if the object were moving at the speed of light in the S system (i.e. u = c), then it would also be moving at the speed of light in the S′ system. Also, if both u and v are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities

 

The usual example given is that of a train (frame S′ above) traveling due east with a velocity v with respect to the tracks (frame S). A child inside the train throws a baseball due east with a velocity u′ with respect to the train. In nonrelativistic physics, an observer at rest on the tracks will measure the velocity of the baseball (due east) as u = u′ + v, while in special relativity this is no longer true; instead the velocity of the baseball (due east) is given by the second equation: u = (u′ + v)/(1 + uv/c2). Again, there is nothing special about the x or east directions. This formalism applies to any direction by considering parallel and perpendicular components of motion to the direction of relative velocity v, see main article for details.

Other consequencesEdit

Thomas rotationEdit

The orientation of an object (i.e. the alignment of its axes with the observer's axes) may be different for different observers. Unlike other relativistic effects, this effect becomes quite significant at fairly low velocities as can be seen in the spin of moving particles.

Equivalence of mass and energyEdit

As an object's speed approaches the speed of light from an observer's point of view, its relativistic mass increases thereby making it more and more difficult to accelerate it from within the observer's frame of reference.

The energy content of an object at rest with mass m equals mc2. Conservation of energy implies that, in any reaction, a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic energies of the particles after the reaction. Similarly, the mass of an object can be increased by taking in kinetic energies.

In addition to the papers referenced above—which give derivations of the Lorentz transformation and describe the foundations of special relativity—Einstein also wrote at least four papers giving heuristic arguments for the equivalence (and transmutability) of mass and energy, for E = mc2.

Mass–energy equivalence is a consequence of special relativity. The energy and momentum, which are separate in Newtonian mechanics, form a four-vector in relativity, and this relates the time component (the energy) to the space components (the momentum) in a non-trivial way. For an object at rest, the energy–momentum four-vector is (E/c, 0, 0, 0): it has a time component which is the energy, and three space components which are zero. By changing frames with a Lorentz transformation in the x direction with a small value of the velocity v, the energy momentum four-vector becomes (E/c, Ev/c2, 0, 0). The momentum is equal to the energy multiplied by the velocity divided by c2. As such, the Newtonian mass of an object, which is the ratio of the momentum to the velocity for slow velocities, is equal to E/c2.

The energy and momentum are properties of matter and radiation, and it is impossible to deduce that they form a four-vector just from the two basic postulates of special relativity by themselves, because these don't talk about matter or radiation, they only talk about space and time. The derivation therefore requires some additional physical reasoning. In his 1905 paper, Einstein used the additional principles that Newtonian mechanics should hold for slow velocities, so that there is one energy scalar and one three-vector momentum at slow velocities, and that the conservation law for energy and momentum is exactly true in relativity. Furthermore, he assumed that the energy of light is transformed by the same Doppler-shift factor as its frequency, which he had previously shown to be true based on Maxwell's equations.[1] The first of Einstein's papers on this subject was "Does the Inertia of a Body Depend upon its Energy Content?" in 1905.[24] Although Einstein's argument in this paper is nearly universally accepted by physicists as correct, even self-evident, many authors over the years have suggested that it is wrong.[25] Other authors suggest that the argument was merely inconclusive because it relied on some implicit assumptions.[26]

Einstein acknowledged the controversy over his derivation in his 1907 survey paper on special relativity. There he notes that it is problematic to rely on Maxwell's equations for the heuristic mass–energy argument. The argument in his 1905 paper can be carried out with the emission of any massless particles, but the Maxwell equations are implicitly used to make it obvious that the emission of light in particular can be achieved only by doing work. To emit electromagnetic waves, all you have to do is shake a charged particle, and this is clearly doing work, so that the emission is of energy.[27][28]

How far can one travel from the Earth?Edit

Since one can not travel faster than light, one might conclude that a human can never travel farther from Earth than 40 light years if the traveller is active between the ages of 20 and 60. One would easily think that a traveller would never be able to reach more than the very few solar systems which exist within the limit of 20–40 light years from the earth. But that would be a mistaken conclusion. Because of time dilation, a hypothetical spaceship can travel thousands of light years during the pilot's 40 active years. If a spaceship could be built that accelerates at a constant 1 g, it will, after a little less than a year, be travelling at almost the speed of light as seen from Earth. This is described by:

 

where v(t) it the velocity at a time, t, a is the acceleration of 1g and t is the time as measured by people on Earth.[29] Therefore, after 1 year of accelerating at 9.81m/s2, the spaceship will be travelling at v = 0.77c relative to Earth. Time dilation will increase the travellers life span as seen from the reference frame of the Earth to 2.7 years, but his lifespan measured by a clock travelling with him will not change. During his journey, people on Earth will experience more time than he does. A 5-year round trip for him will take 6½ Earth years and cover a distance of over 6 light-years. A 20-year round trip for him (5 years accelerating, 5 decelerating, twice each) will land him back on Earth having travelled for 335 Earth years and a distance of 331 light years.[30] A full 40-year trip at 1 g will appear on Earth to last 58,000 years and cover a distance of 55,000 light years. A 40-year trip at 1.1 g will take 148,000 Earth years and cover about 140,000 light years. A one-way 28 year (14 years accelerating, 14 decelerating as measured with the cosmonaut's clock) trip at 1 g acceleration could reach 2,000,000 light-years to the Andromeda Galaxy.[31] This same time dilation is why a muon travelling close to c is observed to travel much further than c times its half-life (when at rest).[32]

Causality and prohibition of motion faster than lightEdit

 
Diagram 2. Light cone

In diagram 2 the interval AB is 'time-like'; i.e., there is a frame of reference in which events A and B occur at the same location in space, separated only by occurring at different times. If A precedes B in that frame, then A precedes B in all frames. It is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the cause and B the effect).

The interval AC in the diagram is 'space-like'; i.e., there is a frame of reference in which events A and C occur simultaneously, separated only in space. There are also frames in which A precedes C (as shown) and frames in which C precedes A. If it were possible for a cause-and-effect relationship to exist between events A and C, then paradoxes of causality would result. For example, if A was the cause, and C the effect, then there would be frames of reference in which the effect preceded the cause. Although this in itself won't give rise to a paradox, one can show[33][34] that faster than light signals can be sent back into one's own past. A causal paradox can then be constructed by sending the signal if and only if no signal was received previously.

Therefore, if causality is to be preserved, one of the consequences of special relativity is that no information signal or material object can travel faster than light in vacuum. However, some "things" can still move faster than light. For example, the location where the beam of a search light hits the bottom of a cloud can move faster than light when the search light is turned rapidly.[35]

Even without considerations of causality, there are other strong reasons why faster-than-light travel is forbidden by special relativity. For example, if a constant force is applied to an object for a limitless amount of time, then integrating F = dp/dt gives a momentum that grows without bound, but this is simply because   approaches infinity as   approaches c. To an observer who is not accelerating, it appears as though the object's inertia is increasing, so as to produce a smaller acceleration in response to the same force. This behavior is observed in particle accelerators, where each charged particle is accelerated by the electromagnetic force.

Geometry of spacetimeEdit

Comparison between flat Euclidean space and Minkowski spaceEdit

 
Orthogonality and rotation of coordinate systems compared between left: Euclidean space through circular angle φ, right: in Minkowski spacetime through hyperbolic angle φ (red lines labelled c denote the worldlines of a light signal, a vector is orthogonal to itself if it lies on this line).[36]

Special relativity uses a 'flat' 4-dimensional Minkowski space – an example of a spacetime. Minkowski spacetime appears to be very similar to the standard 3-dimensional Euclidean space, but there is a crucial difference with respect to time.

In 3D space, the differential of distance (line element) ds is defined by

 

where dx = (dx1, dx2, dx3) are the differentials of the three spatial dimensions. In Minkowski geometry, there is an extra dimension with coordinate X0 derived from time, such that the distance differential fulfills

 

where dX = (dX0, dX1, dX2, dX3) are the differentials of the four spacetime dimensions. This suggests a deep theoretical insight: special relativity is simply a rotational symmetry of our spacetime, analogous to the rotational symmetry of Euclidean space (see image right).[37] Just as Euclidean space uses a Euclidean metric, so spacetime uses a Minkowski metric. Basically, special relativity can be stated as the invariance of any spacetime interval (that is the 4D distance between any two events) when viewed from any inertial reference frame. All equations and effects of special relativity can be derived from this rotational symmetry (the Poincaré group) of Minkowski spacetime.

The actual form of ds above depends on the metric and on the choices for the X0 coordinate. To make the time coordinate look like the space coordinates, it can be treated as imaginary: X0 = ict (this is called a Wick rotation). According to Misner, Thorne and Wheeler (1971, §2.3), ultimately the deeper understanding of both special and general relativity will come from the study of the Minkowski metric (described below) and to take X0 = ct, rather than a "disguised" Euclidean metric using ict as the time coordinate.

Some authors use X0 = t, with factors of c elsewhere to compensate; for instance, spatial coordinates are divided by c or factors of c±2 are included in the metric tensor.[38] These numerous conventions can be superseded by using natural units where c = 1. Then space and time have equivalent units, and no factors of c appear anywhere.

3D spacetimeEdit

 
Three-dimensional dual-cone.
 
Null spherical space.

If we reduce the spatial dimensions to 2, so that we can represent the physics in a 3D space

 

we see that the null geodesics lie along a dual-cone (see image right) defined by the equation;

 

or simply

 

 which is the equation of a circle of radius c dt.

4D spacetimeEdit

If we extend this to three spatial dimensions, the null geodesics are the 4-dimensional cone:

 

so

 

This null dual-cone represents the "line of sight" of a point in space. That is, when we look at the stars and say "The light from that star which I am receiving is X years old", we are looking down this line of sight: a null geodesic. We are looking at an event a distance   away and a time d/c in the past. For this reason the null dual cone is also known as the 'light cone'. (The point in the lower left of the picture above right represents the star, the origin represents the observer, and the line represents the null geodesic "line of sight".)

The cone in the −t region is the information that the point is 'receiving', while the cone in the +t section is the information that the point is 'sending'.

The geometry of Minkowski space can be depicted using Minkowski diagrams, which are useful also in understanding many of the thought-experiments in special relativity.

Note that, in 4d spacetime, the concept of the center of mass becomes more complicated, see center of mass (relativistic).

Physics in spacetimeEdit

Transformations of physical quantities between reference framesEdit

Above, the Lorentz transformation for the time coordinate and three space coordinates illustrates that they are intertwined. This is true more generally: certain pairs of "timelike" and "spacelike" quantities naturally combine on equal footing under the same Lorentz transformation.

The Lorentz transformation in standard configuration above, i.e. for a boost in the x direction, can be recast into matrix form as follows:

 

In Newtonian mechanics, quantities which have magnitude and direction are mathematically described as 3d vectors in Euclidean space, and in general they are parametrized by time. In special relativity, this notion is extended by adding the appropriate timelike quantity to a spacelike vector quantity, and we have 4d vectors, or "four vectors", in Minkowski spacetime. The components of vectors are written using tensor index notation, as this has numerous advantages. The notation makes it clear the equations are manifestly covariant under the Poincaré group, thus bypassing the tedious calculations to check this fact. In constructing such equations, we often find that equations previously thought to be unrelated are, in fact, closely connected being part of the same tensor equation. Recognizing other physical quantities as tensors simplifies their transformation laws. Throughout, upper indices (superscripts) are contravariant indices rather than exponents except when they indicate a square (this is should be clear from the context), and lower indices (subscripts) are covariant indices. For simplicity and consistency with the earlier equations, Cartesian coordinates will be used.

The simplest example of a four-vector is the position of an event in spacetime, which constitutes a timelike component ct and spacelike component x = (x, y, z), in a contravariant position four vector with components:

 

where we define X0 = ct so that the time coordinate has the same dimension of distance as the other spatial dimensions; so that space and time are treated equally.[39][40][41] Now the transformation of the contravariant components of the position 4-vector can be compactly written as:

 

where there is an implied summation on   from 0 to 3, and   is a matrix.

More generally, all contravariant components of a four-vector   transform from one frame to another frame by a Lorentz transformation:

 

Examples of other 4-vectors include the four-velocity Uμ, defined as the derivative of the position 4-vector with respect to proper time:

 

where the Lorentz factor is:

 

The relativistic energy   and relativistic momentum   of an object are respectively the timelike and spacelike components of a contravariant four momentum vector:

 

where m is the invariant mass.

The four-acceleration is the proper time derivative of 4-velocity:

 

The transformation rules for three-dimensional velocities and accelerations are very awkward; even above in standard configuration the velocity equations are quite complicated owing to their non-linearity. On the other hand, the transformation of four-velocity and four-acceleration are simpler by means of the Lorentz transformation matrix.

The four-gradient of a scalar field φ transforms covariantly rather than contravariantly:

 

that is:

 

only in Cartesian coordinates. It's the covariant derivative which transforms in manifest covariance, in Cartesian coordinates this happens to reduce to the partial derivatives, but not in other coordinates.

More generally, the covariant components of a 4-vector transform according to the inverse Lorentz transformation:

 

where   is the reciprocal matrix of  .

The postulates of special relativity constrain the exact form the Lorentz transformation matrices take.

More generally, most physical quantities are best described as (components of) tensors. So to transform from one frame to another, we use the well-known tensor transformation law[42]

 

where   is the reciprocal matrix of  . All tensors transform by this rule.

An example of a four dimensional second order antisymmetric tensor is the relativistic angular momentum, which has six components: three are the classical angular momentum, and the other three are related to the boost of the center of mass of the system. The derivative of the relativistic angular momentum with respect to proper time is the relativistic torque, also second order antisymmetric tensor.

The electromagnetic field tensor is another second order antisymmetric tensor field, with six components: three for the electric field and another three for the magnetic field. There is also the stress–energy tensor for the electromagnetic field, namely the electromagnetic stress–energy tensor.

MetricEdit

The metric tensor allows one to define the inner product of two vectors, which in turn allows one to assign a magnitude to the vector. Given the four-dimensional nature of spacetime the Minkowski metric η has components (valid in any inertial reference frame) which can be arranged in a 4 × 4 matrix:

 

which is equal to its reciprocal,  , in those frames. Throughout we use the signs as above, different authors use different conventions – see Minkowski metric alternative signs.

The Poincaré group is the most general group of transformations which preserves the Minkowski metric:

 

and this is the physical symmetry underlying special relativity.

The metric can be used for raising and lowering indices on vectors and tensors. Invariants can be constructed using the metric, the inner product of a 4-vector T with another 4-vector S is:

 

Invariant means that it takes the same value in all inertial frames, because it is a scalar (0 rank tensor), and so no Λ appears in its trivial transformation. The magnitude of the 4-vector T is the positive square root of the inner product with itself:

 

One can extend this idea to tensors of higher order, for a second order tensor we can form the invariants:

 

similarly for higher order tensors. Invariant expressions, particularly inner products of 4-vectors with themselves, provide equations that are useful for calculations, because one doesn't need to perform Lorentz transformations to determine the invariants.

Relativistic kinematics and invarianceEdit

The coordinate differentials transform also contravariantly:

 

so the squared length of the differential of the position four-vector dXμ constructed using

 

is an invariant. Notice that when the line element dX2 is negative that dX2 is the differential of proper time, while when dX2 is positive, dX2 is differential of the proper distance.

The 4-velocity Uμ has an invariant form:

 

which means all velocity four-vectors have a magnitude of c. This is an expression of the fact that there is no such thing as being at coordinate rest in relativity: at the least, you are always moving forward through time. Differentiating the above equation by τ produces:

 

So in special relativity, the acceleration four-vector and the velocity four-vector are orthogonal.

Relativistic dynamics and invarianceEdit

The invariant magnitude of the momentum 4-vector generates the energy–momentum relation:

 

We can work out what this invariant is by first arguing that, since it is a scalar, it doesn't matter in which reference frame we calculate it, and then by transforming to a frame where the total momentum is zero.

 

We see that the rest energy is an independent invariant. A rest energy can be calculated even for particles and systems in motion, by translating to a frame in which momentum is zero.

The rest energy is related to the mass according to the celebrated equation discussed above:

 

Note that the mass of systems measured in their center of momentum frame (where total momentum is zero) is given by the total energy of the system in this frame. It may not be equal to the sum of individual system masses measured in other frames.

To use Newton's third law of motion, both forces must be defined as the rate of change of momentum with respect to the same time coordinate. That is, it requires the 3D force defined above. Unfortunately, there is no tensor in 4D which contains the components of the 3D force vector among its components.

If a particle is not traveling at c, one can transform the 3D force from the particle's co-moving reference frame into the observer's reference frame. This yields a 4-vector called the four-force. It is the rate of change of the above energy momentum four-vector with respect to proper time. The covariant version of the four-force is:

 

In the rest frame of the object, the time component of the four force is zero unless the "invariant mass" of the object is changing (this requires a non-closed system in which energy/mass is being directly added or removed from the object) in which case it is the negative of that rate of change of mass, times c. In general, though, the components of the four force are not equal to the components of the three-force, because the three force is defined by the rate of change of momentum with respect to coordinate time, i.e. dp/dt while the four force is defined by the rate of change of momentum with respect to proper time, i.e. dp/dτ.

In a continuous medium, the 3D density of force combines with the density of power to form a covariant 4-vector. The spatial part is the result of dividing the force on a small cell (in 3-space) by the volume of that cell. The time component is −1/c times the power transferred to that cell divided by the volume of the cell. This will be used below in the section on electromagnetism.

Relativity and unifying electromagnetismEdit

Theoretical investigation in classical electromagnetism led to the discovery of wave propagation. Equations generalizing the electromagnetic effects found that finite propagation speed of the E and B fields required certain behaviors on charged particles. The general study of moving charges forms the Liénard–Wiechert potential, which is a step towards special relativity.

The Lorentz transformation of the electric field of a moving charge into a non-moving observer's reference frame results in the appearance of a mathematical term commonly called the magnetic field. Conversely, the magnetic field generated by a moving charge disappears and becomes a purely electrostatic field in a comoving frame of reference. Maxwell's equations are thus simply an empirical fit to special relativistic effects in a classical model of the Universe. As electric and magnetic fields are reference frame dependent and thus intertwined, one speaks of electromagnetic fields. Special relativity provides the transformation rules for how an electromagnetic field in one inertial frame appears in another inertial frame.

Maxwell's equations in the 3D form are already consistent with the physical content of special relativity, although they are easier to manipulate in a manifestly covariant form, i.e. in the language of tensor calculus.[43] See main links for more detail.

StatusEdit

Special relativity in its Minkowski spacetime is accurate only when the absolute value of the gravitational potential is much less than c2 in the region of interest.[44] In a strong gravitational field, one must use general relativity. General relativity becomes special relativity at the limit of a weak field. At very small scales, such as at the Planck length and below, quantum effects must be taken into consideration resulting in quantum gravity. However, at macroscopic scales and in the absence of strong gravitational fields, special relativity is experimentally tested to extremely high degree of accuracy (10−20)[45] and thus accepted by the physics community. Experimental results which appear to contradict it are not reproducible and are thus widely believed to be due to experimental errors.

Special relativity is mathematically self-consistent, and it is an organic part of all modern physical theories, most notably quantum field theory, string theory, and general relativity (in the limiting case of negligible gravitational fields).

Newtonian mechanics mathematically follows from special relativity at small velocities (compared to the speed of light) – thus Newtonian mechanics can be considered as a special relativity of slow moving bodies. See classical mechanics for a more detailed discussion.

Several experiments predating Einstein's 1905 paper are now interpreted as evidence for relativity. Of these it is known Einstein was aware of the Fizeau experiment before 1905,[46] and historians have concluded that Einstein was at least aware of the Michelson–Morley experiment as early as 1899 despite claims he made in his later years that it played no role in his development of the theory.[20]

  • The Fizeau experiment (1851, repeated by Michelson and Morley in 1886) measured the speed of light in moving media, with results that are consistent with relativistic addition of colinear velocities.
  • The famous Michelson–Morley experiment (1881, 1887) gave further support to the postulate that detecting an absolute reference velocity was not achievable. It should be stated here that, contrary to many alternative claims, it said little about the invariance of the speed of light with respect to the source and observer's velocity, as both source and observer were travelling together at the same velocity at all times.
  • The Trouton–Noble experiment (1903) showed that the torque on a capacitor is independent of position and inertial reference frame.
  • The Experiments of Rayleigh and Brace (1902, 1904) showed that length contraction doesn't lead to birefringence for a co-moving observer, in accordance with the relativity principle.

Particle accelerators routinely accelerate and measure the properties of particles moving at near the speed of light, where their behavior is completely consistent with relativity theory and inconsistent with the earlier Newtonian mechanics. These machines would simply not work if they were not engineered according to relativistic principles. In addition, a considerable number of modern experiments have been conducted to test special relativity. Some examples:

Theories of relativity and quantum mechanicsEdit

Special relativity can be combined with quantum mechanics to form relativistic quantum mechanics. It is an unsolved problem in physics how general relativity and quantum mechanics can be unified; quantum gravity and a "theory of everything", which require such a unification, are active and ongoing areas in theoretical research.

The early Bohr–Sommerfeld atomic model explained the fine structure of alkali metal atoms using both special relativity and the preliminary knowledge on quantum mechanics of the time.[47]

In 1928, Paul Dirac constructed an influential relativistic wave equation, now known as the Dirac equation in his honour,[48] that is fully compatible both with special relativity and with the final version of quantum theory existing after 1926. This equation explained not only the intrinsic angular momentum of the electrons called spin, it also led to the prediction of the antiparticle of the electron (the positron),[48][49] and fine structure could only be fully explained with special relativity. It was the first foundation of relativistic quantum mechanics. In non-relativistic quantum mechanics, spin is phenomenological and cannot be explained.

On the other hand, the existence of antiparticles leads to the conclusion that relativistic quantum mechanics is not enough for a more accurate and complete theory of particle interactions. Instead, a theory of particles interpreted as quantized fields, called quantum field theory, becomes necessary; in which particles can be created and destroyed throughout space and time.

See alsoEdit

People: Hendrik Lorentz | Henri Poincaré | Albert Einstein | Max Planck | Hermann Minkowski | Max von Laue | Arnold Sommerfeld | Max Born | Gustav Herglotz | Richard C. Tolman
Relativity: Theory of relativity | History of special relativity | Principle of relativity | General relativity | Frame of reference | Inertial frame of reference | Lorentz transformations | Bondi k-calculus | Einstein synchronisation | Rietdijk–Putnam argument | Special relativity (alternative formulations) | Criticism of relativity theory | Relativity priority dispute
Physics: Newtonian Mechanics | spacetime | speed of light | simultaneity | center of mass (relativistic) | physical cosmology | Doppler effect | relativistic Euler equations | Aether drag hypothesis | Lorentz ether theory | Moving magnet and conductor problem | Shape waves | Relativistic heat conduction | Relativistic disk | Thomas precession | Born rigidity | Born coordinates
Mathematics: Derivations of the Lorentz transformations | Minkowski space | four-vector | world line | light cone | Lorentz group | Poincaré group | geometry | tensors | split-complex number | Relativity in the APS formalism
Philosophy: actualism | conventionalism | formalism
Paradoxes: Twin paradox | Ehrenfest paradox | Ladder paradox | Bell's spaceship paradox | Velocity composition paradox

ReferencesEdit

  1. ^ a b c d e Albert Einstein (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik 17: 891; English translation On the Electrodynamics of Moving Bodies by George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920).
  2. ^ Tom Roberts and Siegmar Schleif (October 2007). "What is the experimental basis of Special Relativity?". Usenet Physics FAQ. Retrieved 2008-09-17.
  3. ^ Albert Einstein (2001). Relativity: The Special and the General Theory (Reprint of 1920 translation by Robert W. Lawson ed.). Routledge. p. 48. ISBN 0-415-25384-5.
  4. ^ Richard Phillips Feynman (1998). Six Not-so-easy Pieces: Einstein's relativity, symmetry, and space–time (Reprint of 1995 ed.). Basic Books. p. 68. ISBN 0-201-32842-9.
  5. ^ Sean Carroll, Lecture Notes on General Relativity, ch. 1, "Special relativity and flat spacetime," http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll1.html
  6. ^ Wald, General Relativity, p. 60: "...the special theory of relativity asserts that spacetime is the manifold ℝ4 with a flat metric of Lorentz signature defined on it. Conversely, the entire content of special relativity ... is contained in this statement ..."
  7. ^ Rindler, W., 1969, Essential Relativity: Special, General, and Cosmological
  8. ^ Edwin F. Taylor and John Archibald Wheeler (1992). Spacetime Physics: Introduction to Special Relativity. W. H. Freeman. ISBN 0-7167-2327-1.
  9. ^ Wolfgang Rindler (1977). Essential Relativity. Birkhäuser. p. §1,11 p. 7. ISBN 3-540-07970-X.
  10. ^ a b Einstein, Autobiographical Notes, 1949.
  11. ^ Einstein, "Fundamental Ideas and Methods of the Theory of Relativity", 1920
  12. ^ For a survey of such derivations, see Lucas and Hodgson, Spacetime and Electromagnetism, 1990
  13. ^ Einstein, A., Lorentz, H. A., Minkowski, H., & Weyl, H. (1952). The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity. Courier Dover Publications. p. 111. ISBN 0-486-60081-5.CS1 maint: multiple names: authors list (link)
  14. ^ Einstein, On the Relativity Principle and the Conclusions Drawn from It, 1907; "The Principle of Relativity and Its Consequences in Modern Physics", 1910; "The Theory of Relativity", 1911; Manuscript on the Special Theory of Relativity, 1912; Theory of Relativity, 1913; Einstein, Relativity, the Special and General Theory, 1916; The Principle Ideas of the Theory of Relativity, 1916; What Is The Theory of Relativity?, 1919; The Principle of Relativity (Princeton Lectures), 1921; Physics and Reality, 1936; The Theory of Relativity, 1949.
  15. ^ Das, A. (1993) The Special Theory of Relativity, A Mathematical Exposition, Springer, ISBN 0-387-94042-1.
  16. ^ Schutz, J. (1997) Independent Axioms for Minkowski Spacetime, Addison Wesley Longman Limited, ISBN 0-582-31760-6.
  17. ^ Yaakov Friedman (2004). Physical Applications of Homogeneous Balls. Progress in Mathematical Physics. 40. pp. 1–21. ISBN 0-8176-3339-1.
  18. ^ David Morin (2007) Introduction to Classical Mechanics, Cambridge University Press, Cambridge, chapter 11, Appendix I, ISBN 1-139-46837-5.
  19. ^ Michael Polanyi (1974) Personal Knowledge: Towards a Post-Critical Philosophy, ISBN 0-226-67288-3, footnote page 10–11: Einstein reports, via Dr N Balzas in response to Polanyi's query, that "The Michelson–Morley experiment had no role in the foundation of the theory." and "..the theory of relativity was not founded to explain its outcome at all." [3]
  20. ^ a b Jeroen van Dongen (2009). "On the role of the Michelson–Morley experiment: Einstein in Chicago" (PDF). Eprint arXiv:0908.1545. 0908: 1545. arXiv:0908.1545. Bibcode:2009arXiv0908.1545V.
  21. ^ Staley, Richard (2009), "Albert Michelson, the Velocity of Light, and the Ether Drift", Einstein's generation. The origins of the relativity revolution, Chicago: University of Chicago Press, ISBN 0-226-77057-5
  22. ^ Robert Resnick (1968). Introduction to special relativity. Wiley. pp. 62–63.
  23. ^ Daniel Kleppner and David Kolenkow (1973). An Introduction to Mechanics. pp. 468–70. ISBN 0-07-035048-5.
  24. ^ Does the inertia of a body depend upon its energy content? A. Einstein, Annalen der Physik. 18:639, 1905 (English translation by W. Perrett and G.B. Jeffery)
  25. ^ Max Jammer (1997). Concepts of Mass in Classical and Modern Physics. Courier Dover Publications. pp. 177–178. ISBN 0-486-29998-8.
  26. ^ John J. Stachel (2002). Einstein from B to Z. Springer. p. 221. ISBN 0-8176-4143-2.
  27. ^ On the Inertia of Energy Required by the Relativity Principle, A. Einstein, Annalen der Physik 23 (1907): 371–384
  28. ^ In a letter to Carl Seelig in 1955, Einstein wrote "I had already previously found that Maxwell's theory did not account for the micro-structure of radiation and could therefore have no general validity.", Einstein letter to Carl Seelig, 1955.
  29. ^ Baglio, Julien (26 May 2007). "Acceleration in special relativity: What is the meaning of "uniformly accelerated movement" ?" (PDF). Physics Department, ENS Cachan. Retrieved 22 January 2016.
  30. ^ Philip Gibbs and Don Koks. "The Relativistic Rocket". Retrieved 30 August 2012.
  31. ^ Philip Gibbs and Don Koks. "The Relativistic Rocket". Retrieved 13 October 2013.
  32. ^ The special theory of relativity shows that time and space are affected by motion. Library.thinkquest.org. Retrieved on 2013-04-24.
  33. ^ R. C. Tolman, The theory of the Relativity of Motion, (Berkeley 1917), p. 54
  34. ^ G. A. Benford, D. L. Book, and W. A. Newcomb (1970). "The Tachyonic Antitelephone". Physical Review D. 2 (2): 263. Bibcode:1970PhRvD...2..263B. doi:10.1103/PhysRevD.2.263.CS1 maint: multiple names: authors list (link)
  35. ^ Wesley C. Salmon (2006). Four Decades of Scientific Explanation. University of Pittsburgh. p. 107. ISBN 0-8229-5926-7., Section 3.7 page 107
  36. ^ J.A. Wheeler, C. Misner, K.S. Thorne (1973). Gravitation. W.H. Freeman & Co. p. 58. ISBN 0-7167-0344-0.CS1 maint: multiple names: authors list (link)
  37. ^ J.R. Forshaw, A.G. Smith (2009). Dynamics and Relativity. Wiley. p. 247. ISBN 978-0-470-01460-8.
  38. ^ R. Penrose (2007). The Road to Reality. Vintage books. ISBN 0-679-77631-1.
  39. ^ Jean-Bernard Zuber & Claude Itzykson, Quantum Field Theory, pg 5, ISBN 0-07-032071-3
  40. ^ Charles W. Misner, Kip S. Thorne & John A. Wheeler, Gravitation, pg 51, ISBN 0-7167-0344-0
  41. ^ George Sterman, An Introduction to Quantum Field Theory, pg 4 , ISBN 0-521-31132-2
  42. ^ Sean M. Carroll (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesley. p. 22. ISBN 0-8053-8732-3.
  43. ^ E. J. Post (1962). Formal Structure of Electromagnetics: General Covariance and Electromagnetics. Dover Publications Inc. ISBN 0-486-65427-3.
  44. ^ Øyvind Grøn and Sigbjørn Hervik (2007). Einstein's general theory of relativity: with modern applications in cosmology. Springer. p. 195. ISBN 0-387-69199-5. Extract of page 195 (with units where c=1)
  45. ^ The number of works is vast, see as example:
    Sidney Coleman, Sheldon L. Glashow (1997). "Cosmic Ray and Neutrino Tests of Special Relativity". Phys. Lett. B405 (3–4): 249–252. arXiv:hep-ph/9703240. Bibcode:1997PhLB..405..249C. doi:10.1016/S0370-2693(97)00638-2.
    An overview can be found on this page
  46. ^ John D. Norton, John D. (2004). "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905". Archive for History of Exact Sciences. 59: 45–105. Bibcode:2004AHES...59...45N. doi:10.1007/s00407-004-0085-6.
  47. ^ R. Resnick, R. Eisberg (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles (2nd ed.). John Wiley & Sons. pp. 114–116. ISBN 978-0-471-87373-0.
  48. ^ a b P.A.M. Dirac (1930). "A Theory of Electrons and Protons". Proceedings of the Royal Society. A126 (801): 360. Bibcode:1930RSPSA.126..360D. doi:10.1098/rspa.1930.0013. JSTOR 95359.
  49. ^ C.D. Anderson (1933). "The Positive Electron". Phys. Rev. 43 (6): 491–494. Bibcode:1933PhRv...43..491A. doi:10.1103/PhysRev.43.491.

TextbooksEdit

Journal articlesEdit

External linksEdit

Original worksEdit

Special relativity for a general audience (no mathematical knowledge required)Edit

  • Einstein Light An award-winning, non-technical introduction (film clips and demonstrations) supported by dozens of pages of further explanations and animations, at levels with or without mathematics.
  • Einstein Online Introduction to relativity theory, from the Max Planck Institute for Gravitational Physics.
  • Audio: Cain/Gay (2006) – Astronomy Cast. Einstein's Theory of Special Relativity

Special relativity explained (using simple or more advanced mathematics)Edit

VisualizationEdit


{{DEFAULTSORT:Special Relativity}} Category:Concepts in physics Category:Albert Einstein



TABLE OF CONTENT


§ 1. Introduction

§ 2. Huygens

§ 3. Fresnel

§ 4. Maxwell

§ 5. Michelson

§ 6. Kirchhoff

§ 7. Poynting

§ 8. Lorentz

§ 9. Lenard

§ 10. Planck

§ 11. Einstein's Energy Quanta

§ 12. Einstein Electrodynamics

§ 13. Einstein Electron Inertial Mass

§ 14. Minkowski

§ 15. Einstein's Electromagnetic Ether

§ 16. General Relativity

§ 17. Relativity: Special and General Theory

§ 18. Einstein's Ether

§ 19. Quantum Mechanics

§ 20. Heisenberg

§ 21. Quantum Electrodynamics






________________________________________________________________________________________________________________________________________






The Wave Theory of Light and its affect on Modern Physics and Astronomy

Ben T. Ito

September 27, 2015




This paper will analyze the wave theory of light and its consequence upon modern physics and astronomy. Huygens describes the propagation of light using light waves formed by the motion of an Ethereal matter. Huygens' ether particles possess a hardness that produces a springiness used to transmit light energy through the optical ether, forming propagating light waves. Fresnel describes diffraction using interfering light-waves produced by the vibration of an elastic fluid yet diffraction forms in vacuum, void of an elastic fluid, composed of matter; consequently, Maxwell introduces an electromagnetic theory of light, based on Faraday's induction experiment, since Faraday's induction effect forms in vacuum, but induction is not luminous. Hertz's spark gap experiment is used to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. In Einstein's (1905) electrodynamics (special relativity), Einstein alters the dimensions of Maxwell's equations to justify light propagating in vacuum but manipulating the coordinate system (inertial frame), of Maxwell's equations, does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous; therefore, Maxwell's equations cannot be used to justify light propagating in vacuum (empty space). In addition, the velocity of light is used to justify Maxwell's theory but Roemer's ten minute time delay is caused by numerous factors, such as, Roemer's assumption the Earth and Jupiter have circular orbits that rotate on the same plane, and Jupiter being stationary during the propagation of the Earth from L to K (fig 22), during Io's completion of a cycle of rotation, around Jupiter. Roemer's experiment is an extremely crude and inaccurate attempt at measuring the velocity of light and has absolutely no scientific merit. Fizeau (1849) and Foucault (1850) velocity of light experiments attempt to measure the velocity of light use rotating devices that continue to emit light, after the signal is produced, since an individual signal cannot form an intensity, after propagating a distance of 8km. In modern physics, a pulse beam is used to measure the velocity of light since a single pulse of light produced by a Kerr shutter (nanoseconds) cannot form a measurable intensity, after propagating 50km which proves the velocity of light has not been measured and cannot be used to justify Maxwell's theory. In addition, Maxwell's equations, describe a disturbance within a three dimensional volume, that represent the formation of a spherical wave that produces a longitudinal wave which conflicts with Maxwell's transverse waves; consequently, the electromagnetic transverse wave equations of light cannot be derived using Maxwell's equations (equ 85 - 111). Quantum mechanics, quantum electrodynamics, string theory and particle physics use the gauge transformation of Maxwell's equations but representing Maxwell's equations with a potential does not change the fact that Maxwell's equations are derived using Faraday's induction experiment that is not luminous, nor can the potential of a massless electromagnetic induction field represent the structure of an electron, proton, nuclei or subatomic particle that has a mass. In particle physics, subatomic particles are described using tracks formed in liquid hydrogen, within a bubble chamber. An accelerated electron beam is incident to an external metallic target that collision produces the alleged subatomic particles, that have a mass, which propagate through the steel enclosure (more than an inch thick), of the bubble chamber, to form tracks in the liquid hydrogen but subatomic particles, that have a mass, cannot propagate through the steel enclosure of the bubble chamber without forming a hole, in the steel enclosure, and causing an explosion of the liquid hydrogen. In gravitational physics, Weber (1970) detected gravity waves that have the frequency of sound (1662 Hz) yet the vacuum of celestial space does not transmit sound. Wheeler describes electromagnetic gravity waves. Thorne, Ohanian and Gertsenshtein describe electromagnetic gravity waves that propagate at the velocity of light. Experimentally, the European pulsar timing array (EPTA), detected a gravity wave with the frequency of 10-8 Hz which forms a wavelength of λ = 1016 m which is more than a light year in length!! Furthermore, electromagnetic shielding proves gravity is not an electromagnetic phenomenon. Particle and gravitational physics are the result of the deception and manipulation that originate from the wave theory of light.




________________________________________________________________________________________________________________________________________




§ 1. Introduction




The ancient Greeks believed the eye sent out feelers that emanated from the eye and felt the object being observed. Most, if not all, of the ancient Greek writings were translated from Arabic since the Roman conquerors attempted to destroyed the ancient Greek writings. In the 9th century AD, Middle East, Iraqi scholars studying the translations of the ancient Greek writings resulted in the advent of the light ray theory. In Kindi's (b. 801 AD) paper "De Aspectibus", Kindi introduced the theory of vision, where light rays, interacting with the eye, formed vision. In Haytham's (b. 965) paper "Opticae Thesaurus", Haytham enhanced Kindi's theory, by dissecting the eye and analyzing the anatomy of the eye, resulting in the invention of the two lens magnifier that Syrian scholar Shatir (b. 1304) used to form the theory that planets revolved around the sun, described in Shatir's paper "The Final Quest Concerning the Rectification of Principles". Copernicus (1474) used Shatir's diagrams and calculations to describe planets revolving around the sun. Galileo (b. 1564) used the design of the two lens Arabian magnifier in the construction of the astronomic telescope. In 1610, Galileo discovered the rings of Saturn, and supported Shatir's theory which, at the time, was highly controversial; consequently, Galileo was punished with a life sentence, of home incarceration, for his outspoken criticism of the Ptolemy model. Leibniz (b. 1646) studied the area problem of a planetary orbital ellipse, and discovered the mathematical derivative and integration. Newton's (b. 1643) equations of motion are based on Leibniz's derivative.


Huygens (1690) describes a propagation mechanism of light using light waves formed by the motion of an Ethereal matter where the particles of the ether possess a hardness that produces a springiness used to form light waves which propagate through the optical ether, composed of matter (solid, liquid or gas). Fresnel (1819) describes diffraction using interfering light-waves created by the vibration of an elastic fluid where the light waves interfere, at the diffraction screen, forming the intensity of the diffraction pattern. Maxwell (1864) depicts polarization using transverse light waves, formed by the motion, of an elastic medium yet the propagation, diffraction and polarization effects of light form in vacuum, that is void of an optical ether, composed of matter. Michelson (1881) tests for the existence of Fresnel's optical ether, composed of matter, but the result was negative. Lorentz (1899) reverses the negative result of Michelson's experiment to justify the existence of Fresnel's optical ether but light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical ether does not physically exist; Lorentz's transformation is based on the constant magnitude of the earth yearly motion's tangential velocity vector px but, as time increases, px is not constant. The same method of deception, based on the earth's daily and yearly rotational motions, that ancient scientists used to justify the theory that the earth is the center of the Universe is used to justify the existence of the optical aether. In Einstein's (1905) electrodynamics (special relativity), Einstein alters the dimensions of Maxwell's equations to justify light propagating in vacuum but altering the coordinate system (inertial frame) of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous; consequently, Maxwell's equations cannot be used to justify light propagating in vacuum (empty space). In Einstein's paper "Relativity: Special and General Theory" (1917), Einstein uses the reversal of the negative result of Michelson-Morley experiment, based on Lorentz's transformation, to justify the existence of Fresnel's optical ether, composed of matter.


"More artificial theories have been tried out, assuming that the real truth lies somewhere between these two limiting cases: that the ether is only partially carried by the moving bodies. But they all failed! Every attempt to explain the electromagnetic phenomena in moving CS with the help of the motion of the ether, motion through the ether, or both these motions, proved unsuccessful. Thus arose one of the most dramatic situations in the history of science. All assumptions concerning ether led nowhere! The experimental verdict was always negative." (Weaver, p. 145).


Maxwell's (1864) electromagnetic theory of light, based on Faraday induction experiment, was introduced since induction forms in vacuum but induction is not luminous; consequently, Poynting (1884) derived an electromagnetic energy equation of light but Poynting's current wire is not emitting light; therefore, Poynting's energy equation cannot be used to represent the energy of light. Hertz's (1887) attempts to structurally unite light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap emits electrons yet Faraday's induction experiment is also not an ionization effect which contradicts Maxwell's theory. Furthermore, in 1902, Lenard proves light is composed of particles that energy is dependent on only the frequency which conflicts with Fresnel's light waves' energy that is dependent on the wave amplitude which is used to form the intensity of the diffraction pattern. Also, Lenard's optic particles contradict the continuity of Maxwell's electromagnetic field. Planck (1901) seeks to structurally unify light with induction and quantizes Maxwell's electromagnetic field, using the blackbody radiation effect, that emits light and the radio induction effect, in the derivation of the energy element (hv) that represents the energies of both the blackbody light and radio induction effect emissions but the blackbody emits electrons yet Faraday's induction effect is not an ionization effect that contradicts Planck's unification and quantization of Maxwell's electromagnetic field. In Einstein's (1905) electrodynamics (special relativity), Einstein alters the dimensions of Maxwell's equations to justify Maxwell's theory but manipulating the coordinate system of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday's induction experiment that is not luminous. In addition, the velocity of light is used to justify Maxwell's theory but Roemer's ten minute time delay is caused by numerous factors, such as, Roemer's assumption the Earth and Jupiter have circular orbits that rotate on the same plane, and Jupiter being stationary during the propagation of the Earth from L to K (fig 22), during Io's completion of a cycle of rotation, around Jupiter. Furthermore, Roemer ignores the measurement uncertainty, using a 1675 astronomic telescope and pendulum clock, in the determination of the time Io enters and exists the ellipse. Roemer's experiment is an extremely crude and inaccurate attempt at measuring the velocity of light and has absolutely no scientific merit. Fizeau (1849) and Foucault (1850) velocity of light experiments attempt to measure the velocity of light use rotating devices that continue to emit light, after the signal is produced, since an individual signal cannot form an intensity, after propagating a distance of 8km. In modern physics, a pulse beam is used to measure the velocity of light since a single pulse of light produced by a Kerr shutter (nanoseconds) cannot produce a measurable intensity, after propagating 50km which proves the velocity of light has not been measured and cannot be used to justify Maxwell's theory.


Einstein uses the aberration effect of light, based on the Doppler effect (Einstein2, § 7), to explain the stellar red and blue shifts that is used to justify the existence of Maxwell's electromagnetic light wave but the aberration of light does not alter the fact that Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. Einstein (1910) describes an electromagnetic ether that forms light waves in vacuum but the electromagnetic ether's electromagnetic field originates from Faraday's induction effect. Furthermore, Einstein (1917) uses the increase of an electron's inertia after absorbing an electromagnetic photon to justify Maxwell's electromagnetic theory of light but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. The analysis of the wave theory of light begins with Huygens' principle.




________________________________________________________________________________________________________________________________________




§ 2. Huygens




In Huygens' paper, "Treatise on Light" (1690), Huygens' describes light, using spherical waves, based on a sound wave analogy.


"We know that by means of the air, which is an invisible and impalpable body, Sound spreads around the spot where it has been produced, by a movement which is passed on successively from one part of the air to another; and that the spreading of this movement, taking place equally rapidly on all sides, ought to form spherical surfaces ever enlarging and which strike our ears. Now there is no doubt at all that light also comes from the luminous body to our eyes by some movement impressed on the matter which is between the two; since, as we have already seen, it cannot be by the transport of a body which passes from one to the other. If, in addition, light takes time for its passage—which we are now going to examine—it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as Sound does, by spherical surfaces and waves" (Huygens, p. 5).


"It is true that we are here supposing a strange velocity that would be a hundred thousand times greater than that of Sound. For Sound, according to what I have observed, travels about 180 Toises in the time of one Second, or in about one beat of the pulse. But this supposition ought not to seem to be an impossibility; since it is not a question of the transport of a body with so great a speed, but of a successive movement which is passed on from some bodies to others. I have then made no difficulty, in meditating on these things, in supposing that the emanation of light is accomplished with time, seeing that in this way all its phenomena can be explained, and that in following the contrary opinion everything is incomprehensible. For it has always seemed tome that even Mr. Des Cartes, whose aim has been to treat all the subjects of Physics intelligibly, and who assuredly has succeeded in this better than any one before him, has said nothing that is not full of difficulties, or even inconceivable, in dealing with Light and its properties." (Huygens, p. 7).


"the velocity of Light is more than six hundred thousand times greater than that of Sound. This, however, is quite another thing from being instantaneous, since there is all the difference between a finite thing and an infinite. Now the successive movement of Light being confirmed in this way, it follows, as I have said, that it spreads by spherical waves, like the movement of Sound." (Huygens, p. 10).


Huygens' spherical waves are formed by the motion of an ether, composed of matter, yet light propagates in vacuum that is void of matter which contradicts the existence of Huygens' spherical waves, formed by the motion of an ether. A wave is a mechanical entity that is formed by the motion of a medium, composed of matter (solid, liquid or gas). A force that acts on a medium, composed of matter, produces a wave. Air is the medium that forms sound waves but sound cannot propagate in a vacuum since vacuum is void of air molecules required in forming sound waves yet Huygens is using a sound wave analogy to represent the propagation of light. One of the most important physical characteristic of sound is not applicable to light since light propagates in vacuum that is void of an optical medium, composed of matter, which is experimental proof Huygens' sound wave analogy cannot be applied to light.




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Huygens is describing the formation of light waves produced by the motion of an Ethereal matter.


"Now if one examines what this matter may be in which the movement coming from the luminous body is propagated, which I call Ethereal matter" (Huygens, p. 11).


"But the extreme velocity of Light, and other properties which it has, cannot admit of such a propagation of motion, and I am about to show here the way in which I conceive it must occur. For this, it is needful to explain the property which hard bodies must possess to transmit movement from one to another." (Huygens, p. 13).


"But it is still certain that this progression of motion is not instantaneous, but successive, and therefore must take time. For if the movement, or the disposition to movement, if you will have it so, did not pass successively through all these spheres, they would all acquire the movement at the same time, and hence would all advance together; which does not happen. For the last one leaves the whole row and acquires the speed of the one which was pushed. Moreover there are experiments which demonstrate that all the bodies which we reckon of the hardest kind, such as quenched steel, glass, and agate, act as springs and bend somehow, not only when extended as rods but also when they are in the form of spheres or of other shapes." (Huygens, p. 13).


"Now in applying this kind of movement to that which produces Light there is nothing to hinder us from estimating the particles of the ether to be of a substance as nearly approaching to perfect hardness and possessing a springiness as prompt as we choose. It is not necessary to examine here the causes of this hardness, or of that springiness, the consideration of which would lead us too far from our subject. I will say, however, in passing that we may conceive that the particles of the ether" (Huygens, p. 14).


"But though we shall ignore the true cause of springiness we still see that there are many bodies which possess this property; and thus there is nothing strange in supposing that it exists also in little invisible bodies like the particles of the Ether. Also if one wishes to seek for any other way in which the movement of Light is successively communicated, one will find none which agrees better, with uniform progression, as seems to be necessary, than the property of springiness; because if this movement should grow slower in proportion as it is shared over a greater quantity of matter, in moving away from the source of the light, it could not conserve this great velocity over great distances. But by supposing springiness in the ethereal matter, its particles will have the property of equally rapid restitution whether they are pushed strongly or feebly; and thus the propagation of Light will always go on with an equal velocity." (Huygens, p. 15).


Light propagates through a glass vacuum tube that is void of an optical ether, composed of matter (solid, liquid or gas), which is experimental proof the propagation of light does not involve Huygens' optical ether or light waves.




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Huygens states optical ether, composed of matter, penetrates glass and exists in vacuum.


"This may be proved by shutting up a sounding body in a glass vessel from which the air is withdrawn by the machine which Mr. Boyle has given us, and with which he has performed so many beautiful experiments. But in doing this of which I speak, care must be taken to place the sounding body on cotton or on feathers, in such a way that it cannot communicate its tremors either to the glass vessel which encloses it, or to the machine; a precaution which has hitherto been neglected. For then after having exhausted all the air one hears no Sound from the metal, though it is struck. One sees here not only that our air, which does not penetrate through glass, is the matter by which Sound spreads; but also that it is not the same air but another kind of matter in which Light spreads; since if the air is removed from the vessel the Light does not cease to traverse it as before. And this last point is demonstrated even more clearly by the celebrated experiment of Torricelli, in which the tube of glass from which the quicksilver has withdrawn itself, remaining void of air, transmits Light just the same as when air is in it. For this proves that a matter different from air exists in this tube, and that this matter must have penetrated the glass or the quicksilver, either one or the other, though they are both impenetrable to the air. And when, in the same experiment, one makes the vacuum after putting a little water above the quicksilver, one concludes equally that the said matter passes through glass or water, or through both." (Huygens, p. 11 & 12).


Huygens' optical ether, composed of matter, propagating through glass would produce a hole, in the glass, or shatter the glass, which would eliminate the vacuum. Vacuum is void of matter (solid, liquid or gas). Light propagating through a glass vacuum tube proves the propagation of light does not involve an optical ether or light waves.




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Huygens represents the propagation of light with partial waves (spherical waves) that are used to construct the wave DCF (fig 1).


"There is the further consideration in the emanation of these waves, that each particle of matter in which a wave spreads, ought not to communicate its motion only to the next particle which is in the straight line drawn from the luminous point, but that it also imparts some of it necessarily to all the others which touch it and which oppose themselves to its movement. So it arises that around each particle there is made a wave of which that particle is the centre. Thus if DCF is a wave emanating from the luminous point A, which is its centre, the particle B, one of those comprised within the sphere DCF, will have made its particular or partial wave KCL, which will touch the wave DCF at C at the same moment that the principal wave emanating from the point A has arrived at DCF; and it is clear that it will be only the region C of the wave KCL which will touch the wave DCF, to wit, that which is in the straight line drawn through AB. Similarly the other particles of the sphere DCF, such as bb, dd, etc., will each make its own wave. But each of these waves can be infinitely feeble only as compared with the wave DCF, to the composition of which all the others contribute by the part of their surface which is most distant from the centre A." (Huygens, p. 19).


Huygens' partial waves KCL originate from points b, b, b, along the wave HI. The far points C, C, C, of the partial waves KCL, are used to construct the wave DCF which represents Huygens' propagation mechanism of light but Huygens' wave HI is arbitrary creating energy (partial waves), from points b, b, b, along the wave HI, away from the light source, which violates energy conservation. In addition, only the far points C, C, C, of the partial waves KCL, are used to construct the wave DCF, the partial waves' structures between K and C, and between C and L, are destroyed, after the wave DCF is constructed. An enormous amount of energy (partial waves) is created then destroyed in Huygens' propagation mechanism of light.




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Huygens describes the transmission and reflection effects of light (fig 2 & 3) using spherical waves generated by the transmission and reflection surface.


"If one considers further the other pieces H of the wave AC, it appears that they will not only have reached the surface AB by straight lines HK parallel to CB, but that in addition they will have generated in the transparent air, from the centres K, K, K, particular spherical waves, represented here by circumferences the semi-diameters of which are equal to KM, that is to say to the continuations of HK as far as the line BG parallel to AC." (Huygens, p. 24).


Huygens' spherical waves originate from points K, K, K, along the transmission and reflection surface AB. The generation of spherical waves, by the transmission and reflection surface, represents the arbitrary creation of energy, away from the physical light source, which violates energy conservation. In addition, the spherical waves, used to construct the transmission and reflection waves (fig 2 & 3), have varying circumferences which would form inconsistent amplitudes along the transmission and reflection waves.




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§ 3. Fresnel




In Fresnel's paper, "Memorie su la Diffraction de la Lumiere" (1819), Fresnel describes diffraction using interfering light waves formed by the vibration of the elastic fluid.


"21. If we call λ the length of a light-wave, that is to say, the distance between two points in the ether where vibrations of the same kind are occurring at the same time" (Fresnel, § 21).


"Admitting that light consists in vibrations of the ether similar to sound-waves, we can easily account for the inflection of rays of light at sensible distances from the diffraction body." (Fresnel, § 33).


"To understand how a single luminous particle may perform a large series of oscillations all of which are nearly equal, we have only to imagine that its density is much greater than that of the fluid in which it vibrates---and, indeed, this is only what has already been inferred from the uniformity of the motions of the planets through this same fluid which fills planetary space." (Fresnel, § 33).


"APPLICATIONS OF HUYGENS'S PRINCIPLE TO THE PHENOMENA OF DIFFRACTION

43. Having determined the resultant of any number of trains of light-waves. I shall now show how by the aid of these interference formulae and by the principle of Huygens alone it is possible to explain, and even to compute, all the phenomena of diffraction. This principle, which I consider as a rigorous deduction from the basal hypothesis, may be expressed thus: The vibrations at each point in the wave-front may be considered as the sum of the elementary motions which at any one instant are sent to that point from all parts of this same wave in any one of its pervious* positions, each of these parts acting independently the one of the other. It follows from the principle of the superposition of small motions that the vibrations produced at any point in an elastic fluid" (Fresnel, § 43).


The motion of an optical fluid, composed of matter, forms Fresnel's interfering light waves that produce the diffraction effect of light yet diffraction forms in vacuum that is void of an elastic fluid, composed of matter, which is experimental proof Fresnel's diffraction mechanism of light is physically invalid.




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Fresnel describes diffraction using interfering light waves that resultant amplitudes are used to form the intensity and dark fringes of the diffraction pattern (fig 4).


"In order to compute the total effect, I refer these partial resultants to the wave emitted by the point M on the straight line CP, and to another wave displaced a quarter of a wave-length with reference to the preceding. This is the process already employed (p. 101) in the general solution of the interference problem. We shall consider only a section of the wave made by the plane perpendicular to the edge of the screen, and shall indicate by dz an element, nn', of the primary wave, and by z its distance from the point M. These, as I have shown, suffice to determine the position and the relative intensities of the bright and dark bands." (Fresnel, § 53).


Fresnel's wave AMI forms expanding secondary waves, at the diffraction object. The expanding secondary waves propagate to the diffraction screen and interfere, forming the diffraction pattern. The formation of expanding secondary waves, from points along the wave AMI, represents the arbitrary generation of energy, away from the light source, which violates energy conservation.




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Fresnel derives a diffraction intensity equation by summating the interfering light waves' amplitudes, at the diffraction screen, using a line integral (equ 1).


"Hence the intensity of the vibration at P resulting from all these small disturbances is




{ [ ʃ dz cos (π z2 (a + b) / abλ) ]2 + [ ʃ dz sin (π z2 (a + b) / abλ)]2 }1/2 "..................................1




(Fresnel, § 53). Fresnel is using a line integral to summate the interfering light waves' amplitudes, at the diffraction screen, but a line integral represents a length. Fresnel is violating the definition of a line integral in the derivation of the diffraction intensity equations of light (equ 1) which proves Fresnel's derivation is mathematically invalid.


During the diffraction effect, as time increases, the crests and nodes, of the propagating light waves, move in the forward direction. At a point P, on the diffraction screen, the propagating light waves' amplitudes oscillate, forming an average resultant amplitude of zero, which would eliminate the interference effect; consequently, Fresnel omits the time from his derivation. One of the most important physical property of light is omitted in Fresnel's derivation since propagating light waves eliminate the diffraction pattern. In addition, Fresnel's light waves' amplitudes, that produce the intensity (energy) of the diffraction pattern, represent a light energy that is dependent on the wave amplitude which conflicts with Lenard's photoelectric effect that proves light is composed of particles that energy is dependent on only the frequency (Lenard, Intro).


The formation of the small circular aperture's diffraction pattern (fig 5) is represented using wave interference but the destructive interference of Fresnel's light waves' amplitudes, to form the dark fringes of the diffraction pattern, would result in a measurable reduction in the total light intensity of the diffraction pattern since the destroyed light waves' amplitudes (intensities) do not contribute to the total light intensity of the diffraction pattern yet, experimentally, more than 10%, of the diffraction pattern is composed of dark areas which would result in at least a 10% reduction of the total light intensity of the diffraction pattern yet the total light intensity, that enters a small circular aperture (dt = 1s), equals the total light intensity that forms the diffraction pattern (dt = 1s) which is experimental proof the aperture diffraction effect of light is not formed by Fresnel's wave interference mechanism.




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§ 4. Maxwell




In Maxwell's paper, "On Physical Lines of Force" (1861), Maxwell describes a varying electric current formed in a dielectric.


"The effect of this action on the dielectric mass is to produce a general displacement of the electricity in a certain direction. This displacement does not amount to a current, because when it has attained a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or negative direction, according as the displacement is increasing or diminishing. The amount of the displacement depends on the nature of the body, and on the electromotive force; so that if h is the displacement, R the electromotive force, and E a coefficient depending of the nature of the dielectric,




R = - 4π E2 h,........................2




and if r is the value of the electric current due to displacement,




r = dh/dt"..................................3




(Maxwell1, Part III). Maxwell's varying electric current (equ 3) is formed by the displacement of a dielectric.




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In Maxwell's paper, "Dynamical Theory of the Electromagnetic Field" (1864), Maxwell states the optical aether, composed of matter, exists within Geissler's glass vacuum tube.


"It may be filled with any kind of matter, or we may endeavour to render it empty of all gross matter, as in the case of Geissler’s tubes and other so called vacua. There is always, however, enough of matter left to receive and transmit the undulations of light and heat, and it is because the transmission of these radiations is not greatly altered when transparent bodies of measurable density are substituted for the so-called vacuum, that we are obliged to admit that the undulations are those of an ethereal substance, and not of the gross matter, the presence of which merely modifies in some way the motion of the ether." (Maxwell2, Intro).


Maxwell is stating that the optical ether, composed of matter, exists within a glass vacuum tube but vacuum is void of matter. Light propagating through a glass vacuum tube is definitive and irreversible experimental proof the propagation of light does not involve an optical ether, composed of matter.




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Maxwell's electric current is formed by the displacement of the molecules of the dielectric.


"In a dielectric under the action of electromotive force, we may conceive that the electricity in each molecule is so displaced that one side is rendered positively and the other negatively electrical, but that the electricity remains entirely connected with the molecule, and does not pass from one molecule to another. The effect of this action on the whole dielectric mass is to produce a general displacement of electricity in a certain direction. This displacement does not amount to a current, because when it has attained to a certain value it remains constant, but it is the commencement of a current, and its variations constitute currents in the positive or the negative direction according as the displacement is increasing or decreasing. In the interior of the dielectric there is no indication of electrification, because the electrification of the surface of any molecule is neutralized by the opposite electrification of the surface of the molecules in contact with it; but at the bounding surface of the dielectric, where the electrification is not neutralized, we find the phenomena which indicate positive or negative electrification.

The relation between the electromotive force and the amount of electric displacement it produces depends on the nature of the dielectric, the same electromotive force producing generally a greater electric displacement in solid dielectrics, such as glass or sulphur, than in air." (Maxwell2, Part I).


The motion of the molecules of the dielectric, that is composed of matter (solid, liquid or gas), forms Maxwell's electric current yet light propagates in vacuum that is void of matter which is experimental proof Maxwell's electric current does not physically exist.




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Maxwell's equations are derived using Faraday's induction experiment and Maxwell's electric current.


"ON ELECTROMAGNETIC INDUCTION" (Maxwell2, Part II).


"If, therefore, the phenomena described by Faraday in the Ninth Series of his Experimental Researches were the only known facts about electric currents, the laws of Ampere relating to the attraction of conductors carrying currents as well as those of Faraday about the mutual induction of currents, might be deduced by mechanical reasoning." (Maxwell2, Part II).


"Equations of Magnetic Force.


uα = dH/dy - dG/dz............................................4


uβ = dF/dz - dH/dx.............................................5


uλ = dG/dx - dF/dy.............................................6


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Equations of Currents...


dλ/dy - dβ/dz = 4πp'............................................7


dα/dz - dλ/dx = 4πq'............................................8


dβ/dx - dα/dy = 4πr'............................................9


We may call these the Equations of Currents." (Maxwell2, Part III).


Maxwell's equations are derived using Faraday's induction experiment and Maxwell's electric current but Faraday's induction experiment is not luminous. Furthermore, Maxwell's electric current is formed by the motion of the molecules of a dielectric yet light propagates in vacuum that is void of a dielectric, composed of matter, which is experimental proof Maxwell's electric current does not physically exist. Also, Maxwell's equations represent a disturbance within a three dimensional volume (x,y,z) that produces a spherical wave that forms a longitudinal wave that conflicts with Maxwell's transverse waves. Maxwell's equations are the most important equations of physics yet, in Part III, Maxwell does not use any figures, in the derivation of Maxwell's equations (equ 4-9).




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Maxwell's electric current is formed within a dielectric, of a varying capacitor.


"PART V. — THEORY OF CONDENSERS.


Capacity of a Condenser.


(83) The simplest form of condenser consists of a uniform layer of insulating matter bounded by two conducting surfaces, and its capacity is measured by the quantity of electricity on either surface when the difference of potentials is unity.

Let S be the area of either surface, a the thickness of the dielectric, and k its coefficient of electric elasticity; then on one side of the condenser the potential is Y1 and on the other side Y1 + 1, and within its substance" (Maxwell2, Part V).


"(85) When the dielectric of which the condenser is formed is not a perfect insulator, the phenomena of conduction are combined with those of electric displacement. The condenser, when left charged, gradually loses its charge, and in some cases, after being discharged completely, it gradually acquires a new charge of the same sign as the original charge, and this finally disappears. These phenomena have been described by Professor Faraday (Experimental Researches, Series XI.) and by Mr. F. Jenkin (Report of Committee of Board of Trade on Submarine Cables), and may be classed under the name of "Electric Absorption." (Maxwell2, Part V).


Maxwell's varying capacitor induction effect is formed by an electric current that is produced by the motion of a dielectric yet the varying capacitor induction effect forms using vacuum in the space between the capacitor plates which is experimental proof the varying capacitor induction effect is not formed by Maxwell's electric current.




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Maxwell's describes an electromagnetic theory of light based on Faraday induction experiment.


"ELECTROMAGNETIC THEORY OF LIGHT" (Maxwell2, Part VI).


"We then examine electromagnetic phenomena, seeking for their explanation in the properties of the field which surrounds the electrified or magnetic bodies." (Maxwell2, Part VI).


Maxwell's (1864) electromagnetic theory of light is based on Faraday induction experiment that is not luminous; therefore, Poynting (1884) derived an electromagnetic energy equation of light but Poynting's current wire is not emitting light; consequently, Poynting's energy equation of light cannot be used to represent the energy of light or justify Maxwell's theory. Hertz (1887) attempts to structurally unite light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect. Planck (1901) uses the blackbody radiation effect, that emits light and the radio induction effect, to structurally unite light with induction, by deriving an energy element (hv) that is used to represent the energies of the blackbody light and radio emissions. The representation of the energies of both the blackbody light and radio induction effect emissions with Planck's energy element (hv) structurally unites light with induction and also quantizes Maxwell's electromagnetic field since light is composed of particles but the blackbody also emits electrons. The production of light is always accompanied by the emission of electrons yet Faraday's induction experiment is not emitting electrons and is therefore not an ionization effect; consequently, Planck's blackbody radiation effect cannot be used to structurally unite, light with induction, which is experimental proof light is not an electromagnetic phenomenon. Einstein's (1905) derivation of the energy quanta (RBv/N) is also based on the blackbody radiation effect. Planck's blackbody derivation is the foundation of modern theoretical physics that deception and manipulation is supported by Einstein. To justify Maxwell's theory requires the production of light without the emission of electrons since Faraday's induction experiment is not an ionization effect but when light is generated, electrons are always emitted which contradicts Maxwell's theory. In addition, Lenard's photoelectric effect (1902) proves light is composed of particles that energy is dependent on only the frequency which contradicts the continuity of Maxwell's electromagnetic field, and Fresnel's wave amplitude energy used to form the intensity (energy) of the diffraction pattern. In addition, the velocity of light is used to justify Maxwell's theory but Roemer's ten minute time delay is caused by numerous factors, such as, Roemer's assumption the Earth and Jupiter have circular orbits that rotate on the same plane, and Jupiter being stationary during the propagation of the Earth from L to K (fig 22), during Io's completion of a cycle of rotation, around Jupiter. Furthermore, Roemer ignores the measurement uncertainty, using a 1675 astronomic telescope and pendulum clock (10 seconds for 24 hours). Roemer's experiment is an extremely crude and inaccurate attempt at measuring the velocity of light and has absolutely no scientific merit. Fizeau (1849) and Foucault (1850) velocity of light experiments attempt to measure the velocity of light use rotating devices that do not stop the emission of light, after the signal is emitted. In the modern physics method of measuring the velocity of light, a pulse beam is used since a single pulse of light produced by a Kerr shutter (nanoseconds) cannot produce a measurable intensity; therefore, the pulse beam and rotating device velocity of light experiments are arbitrary which proves the velocity of light has not been measured and cannot be used to justify Maxwell's theory. Faraday's induction effect, Lenard's photoelectric effect, the velocity of light, and the aether, produce difficulties regarding the validity of Maxwell's electromagnetic theory of light.




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"Maxwell's electrodynamics proceeds in the same unusual way already analyzed in studying his electrostatics. Under the influence of hypotheses which remain vague and undefined in his mind, Maxwell sketches a theory which he never completes, he does not even bother to remove contradictions from it; then he starts changing this theory, he imposes on it essential modifications which he does not notify to his reader; the latter tries in vain to fix the fugitive and intangible thought of the author; just when he thinks he has got it, even the parts of the doctrine dealing with the best studied phenomena are seen to vanish. And yet this strange and disconcerting method led Maxwell to the electromagnetic theory of light!" (Duhem, 1902).


"Laudan recalls, with considerable rhetorical effect, James Clerk Maxwell's remark that "the aether was better confirmed than any other theoretical entity in natural philosophy" (Laudan 1984 114; the formulation is Laudan's not Maxwell's). Although we can understand his claim, based as it was on the multiplicity of phenomena to which schemata appealing to wave propagation had been successfully applied, Maxwell was wrong. The entire confirmation of the existence of the ether rested on a series of paths, each sharing a common link. The success of the optical and electromagnetic schemata, employing the mathematical account of wave propagation begun by Fresnel and extended by his successors (including, or course, Maxwell), gave scientists good reason for believing that electromagnetic waves were propagated according to Maxwell's equations. From that conclusion they could derive the existence of the ether---but only supposing in every case that wave propagation requires a medium. Thus the confirmation of the existence of the ether was no better than the evidence for that supposition." (Kitcher, p. 149).


"But Maxwell's theory added to what Hermann von Helmholtz [see Hertz (1894)] described as "the pathless wilderness" of electromagnetic theories: Maxwell's theory contained twenty equations in twenty unknowns (they included potentials and fields); it did not clearly define electricity; electrical disturbances were supposed to propagate as stresses and strains in an all-pervasive dielectric medium." (Miller, p. 92).


"Heisenberg wrote in (1929), that "the existence of the electron" is as unintelligible to the wave mechanical theory as the "existence of the light quantum" to Maxwell's theory." (Miller, p. 18).


"Maxwell jumped to a conclusion. He concluded that light is one form of electromagnetic wave. He had no real evidence for this, but he felt that the coincidence of that tremendous speed was not a coincidence at all." (Bova, p. 159).




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Maxwell's describes the electric field as the optical ether that motion forms transverse light waves.


"(100) The equations of the electromagnetic field, deduced from purely experimental evidence, show that transversal vibrations only can be propagated. If we were to go beyond our experimental knowledge and to assign a definite density to a substance which we should call the electric fluid, and select either vitreous or resinous electricity as the representative of that fluid, then we might have normal vibrations propagated with a velocity depending on this density. We have, however, no evidence as to the density of electricity, as we do not even know whether to consider vitreous electricity as a substance or as the absence of a substance.

Hence electromagnetic science leads to exactly the same conclusions as optical science with respect to the direction of the disturbances which can be propagated through the field; both affirm the propagation of transverse vibrations, and both give the same velocity of propagation. On the other hand, both sciences are at a loss when called on to affirm or deny the existence of normal vibrations." (Maxwell2, Part VI).


Maxwell's electromagnetic theory of light is based on Faraday's induction effect that is not luminous; therefore, Maxwell's electric field cannot be used to represent the optical ether. In addition, Maxwell's describes an optical aether, composed of matter (Maxwell, Intro), that produces a contradiction since Maxwell's massless electric field is incompatible with Maxwell's aether, composed of matter.




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Maxwell represents polarization using transverse waves formed by the motion of the elastic medium.


"(91) At the commencement of this paper we made use of the optical hypothesis of an elastic medium through which the vibrations of light are propagated" (Maxwell2, Part VI).


"the disturbance at any point is transverse to the direction of propagation, and such waves may have all the properties of polarized light." (Maxwell2, Part VI).


Polarized light propagates in vacuum that is void of an elastic medium, composed of matter, which contradicts the existence of Maxwell's transverse light waves that are used to represent polarization. In addition, a transverse wave is a surface wave that cannot form within a volume since a disturbance within a volume represents a spherical wave that forms a longitudinal wave.




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Maxwell derives a wave propagation equation of light using Maxwell's equations.


"(93) If we combine the equations of Magnetic Force (B) with those of Electric Currents (C)...........


Absolute Values of the Electromotive and Magnetic Forces called into play in the Propagation of Light.


(108) If the equation of propagation of light is




F = A cos [(2π/λ)(z - Vt)]"...................................................10




(Maxwell2, Part VI). Maxwell's propagation equation of light is derived using Maxwell's equations (equ 4-9) that are not luminous; consequently, the derivation of Maxwell's propagation equation of light is physically invalid.




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§ 5. Michelson




In Michelson's paper, "The Relative Motion of the Earth and the Lumiferous Ether" (1881), Michelson tests for Fresnel's optical ether, composed of matter (Fresnel, § 43).


"The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space. According to Fresnel, the ether, which is enclosed in optical media, partakes of the motion of these media, to an extent depending on their indices of refraction. For air, this motion would be but a small fraction of that of the air itself and will be neglected." (Michelson, p. 120).


"Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth's surface, would depend on the direction in which it travels." (Michelson, p. 120).


The incident light beam, of Michelson's experiment, is split into two light rays. One light ray propagates parallel to the direction of the ether wind (drift). The second light ray propagates perpendicular to the ether drift. Both light rays propagate towards two separate mirrors then are reflected back and recombined to form an interference pattern. Rotating Michelson's experimental apparatus does not affect the diffraction pattern which represents the negative result of Michelson's experiment. Michelson-Morley experiment (1887) is also testing for Fresnel's optical ether (Michelson-Morley, p. 334) but both Michelson and Michelson-Morley experiments are unnecessary since light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical ether, composed of matter, does not physically exist. Also, in Michelson's experiment, the parallel light ray is propagating in the direction of the ether wind (drift) then is reflected, by the mirror, and propagates in the opposite direction, which cancels the test of the ether drift. In Michelson-Morley experiment, numerous reflections are used to cover up the cancelation problem formed by the reflection. Not only is Michelson, and Michelson-Morley experiments unnecessary, both experiments are not testing for the ether.




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§ 6. Kirchhoff




The Huygens-Fresnel wave theory of light is based on spherical waves, based on a sound wave analogy.


"10-4. Defects of Fresnel's Theory...


3. To these difficulties regarding the nature of the secondary sources there is added the difficulty of explaining the existence of the obliquity factor and, in particular, why the sources do not radiate backwards....In addition, one can easily "forget" the backwave." (Longhurst, p. 188).


Light does not produce a retrogressive wave formed by a spherical wave's uniform and radial structure. A light beam propagating in the forward direction does not form a backwards intensity, propagating towards the light source, which contradicts Huygens' propagation and Fresnel's diffraction mechanisms of light.




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In Kirchhoff's formulation of Huygens' Principle (1883), Kirchhoff eliminates the retrogressive wave, using Green's theorem,


"8.3 Kirchhoff's diffraction theory


8.3.1 The integral theorem of Kirchhoff


The basic idea of the Huygens-Fresnel theory is that the light disturbance at a point P arises from the superposition of secondary waves that proceed from a surface situated between this point and the light source. This idea was put on a sounder mathematical basis by Kirchhoff†....................If U' is any other function which satisfies the same continuity requirements as U, we have by Green's theorem" (Born and Wolf, p. 417-418).




"∭(ψ2 ∇2ψ1 - ψ1 ∇2 ψ2) dV = ∬(ψ2 [dψ1/dn] - ψ1[dψ2/dn])dS" ..............................11




Longhurst, p. 190). In Green's theorem (equ 11), a volume integral is equated to a surface integral which is physically invalid and proves Kirchhoff's elimination of the retrogressive wave, using Green's theorem, is mathematically invalid.




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Kirchhoff uses equation 11 to derive an obliquity factor that eliminates the retrogressive wave, formed by a spherical wave.


"10-7. Application to Spherical Waves


Equation (10-15) was derived for a surface S which enclosed the point P but not the source (since it was assumed in applying Green's theorem that ψ remains finite throughout the volume of integration). It can be shown that the same result follows if S encloses the source but not the point P. Thus in the case of a single point source the closed surface S may be taken as a spherical wavefront." (Longhurst, p. 192).


"1. The integrand includes an obliquity factor ½(1 + cos θ) which is unity in the forward direction (θ = 0) and zero in the reverse direction (θ = π). The amplitude factor a/λ is also present as was seen to be necessary." (Longhurst, p. 193).


Kirchhoff is mathematically eliminating the unwanted structure of the retrogressive wave that propagates in the reverse (backwards) direction, using Green's theorem, but a spherical wave's uniform and radial structure forms a retrogressive wave that is not experimentally observed. Kirchhoff's mathematical elimination of the retrogressive wave, based on Green theorem, is destroying mathematical physics.




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§ 7. Poynting




In Poynting's paper, "On the Transfer of Energy in the Electromagnetic Field" (1884), Poynting's current wire forms electric and magnetic fields, in free space surrounding the current wire (fig 6).


"Applications of the Law of Transfer of Energy.


(1) A straight wire conveying a current.


In this case very near the wire, and within it, the lines of magnetic force are circles round the axis of the wire. The lines of electric force are along the wire, if we take it as proved that the flow across equal areas of the cross section is the same at all parts of the section. If AB, fig. 1, represents the wire, and the current is from A to B, then a tangent plane to the surface at any point contains the directions of both the electromotive and magnetic intensities (we shall write E.M.I. and M.I. for these respectively in what follows), and energy is therefore flowing in perpendicularly through the surface, that is, along the radius towards the axis." (Poynting, p. 350).


A current is flowing through Poynting's conduction wire that forms electric and magnetic fields (E.M.I and M.I), in the free space, that surrounds the current wire, which conflicts with Faraday and Ampere laws that only represents an external magnetic field.




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Poynting uses the electric and magnetic fields, formed by a current wire, in an energy equation of light.


"(7) The electromagnetic theory of light.


The velocity of plane waves of polarized light on the electromagnetic theory may be deduced fromthe consideration of the flow of energy.......If E the E.M.I and B the M.I within the volume, supposed so small that the energy within is




KE2 / 8π + uB2 / 8π..................................................................12




(Poynting, p. 190). Poynting's electromagnetic field originates from Poynting's current wire that is not luminous which is experimental proof Poynting's energy equation (equ 12) cannot be used to represent the energy of light.




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§ 8. Lorentz




In Lorentz's paper "Simplified Theory of Electrical and Optical Phenomena in Moving Systems" (1899), Lorentz represents the optical aether, with Maxwell's equations,


"The ions were supposed to be perfectly permeable to the aether, so that they can move while the aether remains at rest. I applied to the aether the ordinary electromagnetic equations, and to the ions certain other equations which seemed to present themselves rather naturally." (Lorentz, § 1).


"If, now, V be the velocity of light in the aether, the fundamental equations will be" (Lorentz, § 2).


Maxwell's equations, represent a massless electromagnetic induction field, that originates from Faraday's induction effect that is not luminous.




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Lorentz is representing the optical aether with Maxwell's equations.


"If, now, V be the velocity of light in the aether, the fundamental equations will be






Div E = q.....................................................................13






Div B = 0......................................................................14






dBz /dy - dBy /dz = 4πq(px + vx) + 4π(d/dt - px d/dx) Ex..............................................15








dBx /dz - dBz /dx = 4πpqvy + 4π(d/dt - px d/dx) Ey......................................................16








dBy /dx - dBx /dy = 4πqvz + 4π(d/dt - px d/dx) Ez........................................................17






..............................................................................................................






4πV2(dEz /dy - dEy /dz) = - (d/dt - px d/dx) Bx..............................................................18






4πV2(dEx /dz - dEz /dx) = - (d/dt - px d/dx) By..............................................................19






4πV2(dEy /dx - dEx /dy) = - (d/dt - px d/dx) Bx..............................................................20






...In most applications p would be the velocity of the earth in its yearly motion." (Lorentz, § 3).







Maxwell's equations are derived using Faraday's induction experiment that is not luminous; consequently, Maxwell's equations cannot be used to represent the electromagnetic aether.




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Lorentz transforms the dimensions of Michelson's experimental apparatus to reverse the negative result of Michelson's experiment to justify the existence of Fresnel's optical ether (Michelson, p. 120), composed of matter (Fresnel, § § 33 & 43).


"§ 9. Hitherto all quantities of the order p2x /V2 have been neglected. As is well known, these must be taken into account in the discussion of Michelson's experiment, in which two rays of light interfered after having traversed rather long paths, the one parallel to the direction of the earth's motion, and the other perpendicular to it. In order to explain the negative result of this experiment Fitzgerald and myself have supposed that, in consequence of the translation, the dimensions of the solid bodies serving to support the optical apparatus, are altered in a certain ratio." (Lorentz, § 9).


Lorentz uses the earth yearly motion's tangential velocity vector px to reverse the negative result of Michelson's experiment yet, as time increases, px is not constant. Example, near sunset, at the surface of the earth, the magnitude of px is zero (fig 7) but at midnight, the magnitude of px is equal to p; consequently, because of the affect of the earth's daily rotational motion, Lorentz's earth yearly motion's tangential velocity vector px varies from zero to over 1000 mph yet Lorentz's transformation is based on a constant value of px . The same method of deception, based on the earth's daily and yearly rotational motions, that ancient scientists used to justify the theory that the earth is the center of the Universe is used to justify the existence of the aether. In addition, Lorentz's transformation is unnecessary since light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical ether, composed of matter, does not physically exist.




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§ 9. Lenard




In Lenard's (1902) photoelectric effect experiment, the change in the intensity, of a monochromatic incident light beam, that is past the threshold intensity, does not affect the emitted photoelectrons' maximum kinetic energy (Lenard, Intro). Only the change in the frequency, of the incident beam, affects the emitted photoelectrons' maximum kinetic energy which is experimental proof light is composed of particles that energy is dependent on only the frequency.


"The first investigator to show that the energy of emission of the photoelectron is independent of the intensity of the light was Lenard1, who found that a seventy fold change in the intensity of the light did not alter the maximum energy of emission of the photoelectron by as much as 1 per cent." (Hughes, p. 27).


"The maximum energy of the electrons released at a photoelectric surface is independent of the intensity of the incident light, but increases linearly with the frequency of light.....The basic theory of the photoelectric effect, which conforms to these laws---both of which are based on experiments by Lenard" (Zworykin, p. 8).


"Heisenberg wrote in (1929), that "the existence of the electron" is as unintelligible to the wave mechanical theory as the "existence of the light quantum" to Maxwell's theory." (Miller, p. 18).


Lenard's photoelectric effect proves light is composed of particles which conflicts with the continuity of Maxwell's electromagnetic field and the wave amplitude energy of Fresnel's diffraction mechanism. Lenard's photoelectric effect proves the wave theory of light is physically invalid.




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§ 10. Planck




In Planck's paper, "On the Law of Distribution of Energy in the Normal Spectrum" (1901), Planck is supporting Maxwell's electromagnetic theory of light by structurally unifying light with the radio induction effect and quantizing Maxwell's electromagnetic field, using the blackbody radiation effect.


"In any case the theory requires a correction, and I shall attempt in the following to accomplish this on the basis of the theory of electromagnetic radiation which I developed." (Planck, Intro).


"In my last article4 I showed that the physical foundations of the electromagnetic radiation theory, including the hypothesis of "natural radiation", withstand the most severe criticism" (Planck, Intro).


Planck is supporting Maxwell's theory that is based on Faraday's induction experiment that is not luminous, nor does induction represent a particle structure (photoelectric effect); consequently, Planck structurally unifies light with induction and quantizes Maxwell's electromagnetic field, using the blackbody radiation effect, that emits light and the radio induction effect but the blackbody radiation effect also emits electrons yet Faraday's induction experiment is not an ionization effect which contradicts Planck's justification of Maxwell's theory.




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Planck's blackbody derivation is based on the blackbody surface electrons, oscillating a diathermic medium (optical ether), at the frequency of light, forming electromagnetic photons, that energy is represented with Planck's energy element (hv).


"§ 7. We now want to examine what Wien's displacement law states about the dependence of the entropy S of our resonator on its energy U and its characteristic, particularly in the general case where the resonator is situated in an arbitrary diathermic medium. For this purpose we next generalize Thiesen's form of the law for the radiation in an arbitrary diathermic medium with the velocity of light c. Since we do not have to consider the total radiation, but only the monochromatic radiation, it becomes necessary in order to compare different diathermic media to introduce the frequency v instead of the wavelength λ." (Planck, Part 1, § 7).


"Now according to the well-known Kirchoff-Clausius law, the energy emitted per unit time at the frequency v and temperature T from a black surface in a diathermic medium is inversely proportional to the square of the velocity of propagation c2; hence the energy density U is inversely proportional to c3 and we have:" (Planck, Part 1, § 7).


"the entropy of a resonator vibrating in an arbitrary diathermic medium depends only on the variable U/v, containing besides this only universal constants. This is the simplest form of Wien's displacement law known to me." (Planck, Part 1, § 9).


The blackbody radiation effect forms in vacuum that is void of a diathermic medium, composed of matter, which contradicts Planck's blackbody derivation that electromagnetic photons are formed by the motion of a diathermic medium.




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Planck's energy element (hv) is derived using Boltzmann's thermodynamic entropy equation,




S = k log R..................................................................................................21




that is used with Planck's blackbody electron (resonator) kinetic energy distribution ratio (Planck, § 3),




R = (N + P)N + P / NN · PP...........................................................................22




to form (Planck, § 5)




SN = k{N + P) log (N + P) - N log N - P log P)............................................23




Using UN = NU and UN = Pe, equation 23 becomes,




S = k{(1 + U/e) log (1 + U/e) - U/e log U/e}.................................................24




Equation 24 is represented as,




S = f(U/e)....................................................................................................25




The second entropy equation is derived using (Planck, § 8),




T = v · f(U/v)......................................................................26




The following equation (Planck, § 9),




1/T = dS/dU..........................................................................27




and equations 26 are used to form,




dS/dU = 1/v · f(U/v)...........................................................28




Integrating equation 28,




S = f(U/v)...............................................................................29




Using equations 25 and 29, a proportionality is formed,




e α v......................................................................................30




Planck's energy element is derived using equation 30.


"§10. If we apply Wien's displacement law in the latter form to equation (6) for the entropy S, we then find that the energy element e must be proportional to the frequency v, thus:




e = hv"....................................................................................31




(Planck, § 10). Planck's derivation of the energy element (equ 31) is based on Boltzmann's thermodynamic entropy (equ 21) that represents the closed initial and final volumes (V/Vo) that contain a gas in thermodynamic equilibrium. Planck replaces Boltzmann's volume ratio (V/Vo) with a blackbody surface electron kinetic energy distribution ratio (equ 22) which violates Boltzmann's entropy equation.


The glowing hot blackbody surface's electrons dissipate energy, in the form of the blackbody emissions, which forms the constant total energy of the blackbody surface electrons, that entropy is represented with S = f(U/e) but Planck's emission entropy S = f(U/v), (equ 29) total energy and volume increases, as time increases, since the blackbody is emitting radiation, outside the blackbody, in an every increasing volume that total energy increases, as time increases, consequently, S = f(U/v), cannot produce an equilibrium required in forming an entropy which proves the derivation of Planck's energy element, using S = f(U/v), is physically invalid.




..........................................................................................................




Planck's blackbody intensity equation is derived using Planck's energy element (hv) in equation 24,




S = k{(1 + U/hv)log(1 + U/hv) - U/hv log U/hv}.....................................32




Differentiating equation 32 with respect to U using,




1/T = dS/dU.........................................................................................33




forms,




U_\nu(T) = \frac{hv}{e^\frac{h\nu}{k_\mathrm{}T} - 1}.............................................................34




Equation 34 is used to derive Planck's blackbody intensity equation,




u_\nu(T) = \frac{ 2 h \nu^3}{c^2} \frac{1}{e^\frac{h\nu}{k_\mathrm{}T} - 1}.................................................35




In the derivation of equation 32, that is used in the derivation of Planck's blackbody intensity equation (equ 35), Planck's energy element (hv) is used in equation 24 that represents the equating of the kinetic energy (ke = ½mv2) of the blackbody surface electrons (resonators), with the energy (hv) of massless electromagnetic photons which is physically invalid. According to Planck, the blackbody surface electrons oscillate a diathermic medium (optical ether), composed of matter, that kinetic motion forms electromagnetic photons but the blackbody radiation effect forms in vacuum that is void of matter which proves Planck's derivation of the blackbody intensity equation, based on the vibration of a diathermic medium, is physically invalid.




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§ 12. Einstein Electrodynamics




In Einstein's paper, "On the Electrodynamics of Moving Bodies" (1905), Einstein states the luminiferous ether is superfluous.


"The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place." (Einstein2, Intro).


Einstein states the luminiferous ether is superfluous yet Einstein uses the reversal of Michelson-Morley experiment (Einstein6, § 16), to justify the existence of Fresnel's optical ether (Michelson-Morley, p. 334), composed of matter (Fresnel, § § 33 & 43) which produces a contradiction.




..................................................................................................................




Einstein transforms (alters) the coordinate system of Maxwell's equations to justify light propagating in vacuum (empty space).


"§ 6. Transformation of the Maxwell-Hertz equations for empty space. On the nature of the electromotive forces that arise upon motion in a magnetic field.


Let the Maxwell-Hertz equations for empty space be valid for the system at rest K, so that we have






dX/dt = dN/dy - dM/dz.................................................40






dY/dt = dL/dz - dN/dx..................................................41




dZ/dt = dM/dx - dL/dy..................................................42






.......................................................................................




dL/dt = dY/dz - dZ/dy...................................................43




dM/dt = dZ/dx - dX/dz..................................................44






dN/dt = dX/dy - dY/dx...................................................45






where (X,Y,Z) denotes the vector of the electric force, and (L,M,N) that of the magnetic force." (Einstein2, § 6).








β = 1/(1 - v2/c2)1/2............................................................46








Applying equation 46 to the coordinate system of Maxwell's equations,






"X' = X............................ L' = L......................................47a,b




Y' = β[Y - (v/c)N]............. M'= β[M + (v/c)Z]....................48a,b






Z' = β[Z + (v/c)M],.............N' = β[N - (v/c)Y]"..................49a,b





(Einstein2, § 6). Altering the coordinates system (inertial frame), of Maxwell's equations, does not change the fact that Maxwell's equations are derived using Faraday's induction experiment that is not luminous; consequently, the manipulation of the coordinate system, of Maxwell's equations, cannot be used to justify light propagating in vacuum. Also, the electromagnetic transverse wave equations of light cannot be derived using Maxwell's equations (equ 85 - 111) since Maxwell's equations represent a disturbance within a three dimensional volume that produces a spherical wave which forms a longitudinal wave that conflicts with Maxwell's transverse waves.




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Einstein states that relativity is based on Lorentz theory.


"the electrodynamic foundation of Lorentz's theory of the electrodynamics of moving bodies is in agreement with the principle of relativity." (Einstein2, § 9).


Lorentz uses Maxwell's equations to represent the optical ether; in addition, in the same paper, Lorentz reverses the negative result of Michelson's experiment to justify the existence of Fresnel's optical ether, composed of matter (Lorentz, §§ 3 & 9) which produces a contradiction since Maxwell's massless electromagnetic field cannot be used to represent the optical ether, composed of matter. Einstein (1910) describes an electromagnetic ether that forms light waves in vacuum (Einstein4, § 1) and, in 1917, Einstein uses the reversal of Michelson-Morley experiment to justify the existence of Fresnel's optical ether, composed of matter (Einstein6, § 16) that corresponds with Lorentz's contradiction.


"experimental contradiction does not have the power to transform a physical hypothesis into an indisputable truth;" (Duhem*, p. 190).




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§ 13. Einstein's Inertia




In Einstein's paper, "Does the Inertia of a Body depend upon its Energy Content?" (1905), Einstein describes the decrease in the inertia, of an electron, after emitting a photon.


"There I based myself upon the Maxwell-Hertz equations for empty space along with Maxwell's expression for the electromagnetic energy" (Einstein3, p. 639).


"Let this body simultaneously emit plane waves of light of energy L/2" (Einstein3, p. 640).


"The kinetic energy of the body with respect to (ξ,η,ς) decreases as a result of the emission of light..... If a body releases the energy L in the form of radiation, its mass decreases by L/V2." (Einstein3, p. 641).


Einstein's term L/V2 represents the decrease in the inertia of an electron after emitting an electromagnetic photon but Maxwell's electromagnetic field originates from Faraday's induction experiment that is not luminous.




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§ 14. Minkowski




In Minkowski's paper, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies" (1908), Minkowski represents the aether with Maxwell's equations.


"§ 2. The Fundamental Equations for Æther.



curl m - dE/dt = pm........................................50


div e = p.........................................................51


curl e + dm/dt = 0...........................................52



div m = 0........................................................53



(Minkowski, Part 1, § 2). Minkowski is representing the optical aether with Maxwell's equations but Maxwell's equations are derived using Faraday's induction experiment that is not luminous; consequently, Maxwell's equations cannot be used to represent the electromagnetic aether.




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§ 15. Einstein's Electromagnetic Ether




In Einstein's paper, "The Principle of Relativity and Its Consequences in Modern Physics" (1910), Einstein describes an electromagnetic ether.


"When it was realized that a profound analogy exists between the elastic vibrations of ponderable matter and the phenomena of interference and diffraction of light, it could not be doubted that light must be considered as a vibratory state of a special kind of matter. Since, moreover, light can propagate in places devoid of ponderable matter, one was forced to assume for the propagation of light a special kind of matter that is different from ponderable matter, and that was given the name "ether." (Einstein4, § 1).


"The introduction of the electromagnetic theory of light brought about a certain modification of the ether hypothesis. At first the physicists did not doubt that the electromagnetic phenomena must be reduced to the modes of motion of this medium. But as they gradually became convinced that none of the mechanical theories of ether provided a particularly impressive picture of electromagnetic phenomena, they got accustomed to considering the electric and magnetic fields as entities whose mechanical interpretation is superfluous. Thus, they have come to view theses fields in the vacuum as special states of the ether" (Einstein4, § 1).


Einstein's electromagnetic ether's electromagnetic field originates from Faraday's induction effect that is not luminous which is experimental proof Maxwell's electromagnetic field cannot be used to represent the electromagnetic ether.




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§ 16. General Relativity




In Einstein's paper, "The Foundation of the Generalised Theory of Relativity" (1916), Einstein uses Maxwell's equations,



dh/dt + rot e = 0................................................54



div h = 0...........................................................55



.....................................................................................................



rot h - de'/dt = i................................................56



div e' = p..........................................................57




(Einstein5, § 20). Maxwell's equations are derived using Faraday's induction effect that is not luminous. Also, the electromagnetic transverse wave equations of light (equ 85 - 111) cannot be derived using Maxwell's equations since a disturbance within a volume forms a longitudinal wave.




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§ 17. Relativity: Special and General Theory




In Einstein paper, "Relativity: Special and General Theory" (1917), Einstein alters the coordinate system to justify light propagating in vacuum, using Lorentz's theory.


"The relations must be so chosen that the law of transmission of light in vacuo is satisfied for one and the same ray of light (and of course for every ray) with respect to K and K'. For the relative orientation in space of the co-ordinate systems indicated in the diagram (Fig. 2), this problem is solved by means of the equations:



x' = (x - vt)/(1 - v2/c2)1/2)...................................................58



y' = y............................................ ..................................59



z' = z ..............................................................................60



t' = (t - v/c2)/(1 - v2/c2)1/2..................................................61



This system of equations is known as the "Lorentz transformation" (Einstein6, § 11).


Einstein's relativity is based Lorentz's transformation where Lorentz transforms the dimensions of Maxwell's equations, using the earth's tangential velocity vector px, in the representon of the electromagnetic aether (Lorentz, § 3). Also, Lorentz transformation is used to reverse the negative results of Michelson's experiment to justify the existence of Fresnel's optical ether, composed of matter (Lorentz, § 9) which produces a contradiction since Maxwell's equations represent a massless electromagnetic field that conflicts with Fresnel's optical ether, composed of matter. Furthermore, Lorentz and Einstein transformation of the coordinate system (inertial frame) does not change the fact that Maxwell's theory is based on Faraday's induction experiment that is not luminous.




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Einstein is justifying the existence of Fresnel's optical ether (Michelson-Morley, p. 333), composed of matter, using the reversal of the negative result of Michelson-Morley experiment.


"On the other hand, all coordinate systems moving relatively were to be regarded as in motion with respect to the æther. To this motion against the æther ("æther-drift") were attributed more complicated laws which were supposed to hold relative to. Strictly speaking, such an æther-drift ought also to be assumed relative to the earth, and for a long time the efforts of physicists were devoted to attempts to detect the existence of an æther-drift at the earth's surface....Although the estimated difference between these two times is exceedingly small, Michelson and Morley performed an experiment involving interference in which this difference should have been clearly detectable. But the experiment gave a negative result — a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the æther produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the difference in time mentioned above." (Einstein6, § 16).


Einstein is using the reversal of Michelson-Morley experiment, based on Lorentz's transformation, to justify the existence of the optical ether, composed of matter, where Lorentz uses the earth yearly motion's tangential velocity vector px, to reverse the negative result of Michelson's experiment yet px is not constant, as time increases. Example, near sunset, at the surface of the earth, the magnitude of px is zero (fig 7) but at midnight, the magnitude of px is equal to p; consequently, because of the earth's daily motion, the earth yearly motion's tangential velocity vector px varies from zero to well over 1000 mph which conflicts with Einstein's constant magnitude translational velocity (v) that is used in equations 58 and 61. Furthermore, light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical aether, composed of matter, does not physically exist.




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Einstein describes the increase in the inertia of the electron after absorbing a photon.


"XV. General Results of the Theory


IT is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, i.e. the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favor." (Einstein6, § 15).


"Hence we can say: If a body takes up an amount of energy Eo, then its inertial mass increases by an amount




Eo/c2.......................................................................................................62




the inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form




mc2 + Eo/ (1 - v2/c2)1/2.................................................................................63




we see that the term mc2, which has hitherto attracted our attention, is nothing else than the energy possessed by the body before it absorbed the energy Eo." (Einstein6, § 15).


Einstein's term Eo/c2 (equ 62) represents the increase in the inertia of an electron after absorbing an electromagnetic photon but Maxwell's electromagnetic field originates from Faraday's induction experiment that is not luminous. In addition, the discontinuous structure of Einstein's electromagnetic photon conflicts with the continuity of Maxwell's electromagnetic induction field. Also, Einstein's term Eo represents the energy of an electromagnetic photon; consequently, the inertia (m), that is represented with Eo/c2 (equ 62), is massless. Einstein is attempting to structurally unify Maxwell's electromagnetic field with Fresnel's optical ether, composed of matter, using an energy equation Eo = mc2 but the inertial (m) of Einstein's energy equation is massless which proves Einstein's structural unification is physically invalid.




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§ 18. Einstein's Ether




In a lecture, by Einstein, on May 5th 1920, at the University of Leyden, Einstein is justifying the optical ether, using Lorentz's theory and Einstein relativity.


"Such was the state of things when H. A. Lorentz entered upon the scene. He brought theory into harmony with experience by means of a wonderful simplification of theoretical principles. He achieved this, the most important advance in the theory of electricity since Maxwell, by taking from ether its mechanical, and from matter its electromagnetic qualities. As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements; their electromagnetic activity is entirely confined to the carrying of electric charges. Thus Lorentz succeeded in reducing all electromagnetic happenings to Maxwell's equations for free space.

As to the mechanical nature of the Lorentzian ether, it may be said of it, in a somewhat playful spirit, that immobility is the only mechanical property of which it has not been deprived by H. A. Lorentz. It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility. How this is to be understood will forthwith be expounded...

More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it. We shall see later that this point of view, the conceivability of which I shall at once endeavour to make more intelligible by a somewhat halting comparison, is justified by the results of the general theory of relativity." (Einstein7, Lecture).


Lorentz uses Maxwell's equations to represent the electromagnetic aether (Lorentz, § 3) then Lorentz reverses the negative result of Michelson's experiment (Lorentz, § 9) to justify the existence of Fresnel optical ether (Michelson, p. 120), composed of matter (Fresnel, § § 33 & 43) which produces a contradiction since Maxwell's massless electromagnetic field cannot be used to represent Fresnel's ether, composed of matter; consequently, Lorentz does not bring harmony to the ether problem. In Einstein's (1905) electrodynamics (special relativity), Einstein alters (transforms) the dimensions of Maxwell's equations to justify light propagating in vacuum but altering the coordinate system (inertial frame) of Maxwell's equations does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous; consequently, Maxwell's equations cannot be used to justify light propagating in vacuum (empty space). Furthermore, in Einstein's paper, "Relativity: Special and General Theory" (1917), Einstein uses the reversal of Michelson-Morley experiment (Einstein6, § 15), to justify the existence of Fresnel's optical ether (Michelson-Morley, p. 334), composed of matter (Fresnel, § § 33 & 43) yet light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical ether, composed of matter, does not physically exist which proves Einstein's justification of the optical ether is physically invalid.




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§ 19. Quantum Mechanics




Quantum mechanics is based on Planck's blackbody quantization of Maxwell's electromagnetic field. Planck uses the blackbody radiation effect, that emits light and the radio induction effect, to quantize Maxwell's electromagnetic field, by deriving an energy element, that represents the energy of the blackbody light and radio induction effect emissions but the blackbody emits electrons yet Faraday's induction effect is not an ionization effect which contradicts Planck's quantization of Maxwell's electromagnetic field. Davisson–Germer (1927) electron scattering experiment is used to justify wave interference but the destructive interference of electrons to form the non-electron fringes of Davission-Germer electron scattering pattern, violates energy conservation.




....................................................................................................................................................................




de Broglie electron matter waves when used to represent an atomic electron (fig 8) does not function in the three dimensional representation of a spherical shape atom since, in the direction perpendicular to the atomic electron matter wave, a constant amplitude or zero is formed. Nonetheless, the atomic electron matter wave is transformed into a particle-in-a-box (fig 9) and represented in a rectangular coordinate system (x,y,z),




-(h2/2u)∇"Ψ(x,y,z) + V(x,y,z) + V(x,y,z)Ψ(x,y,z) = EΨ(x,y,z)..................64




Schrödinger transforms the particle-in-a-box electron matter wave, of equation 64, into a probability wave, that is represented in spherical coordinate system (r,Θ,φ,),




-(h2/2u)∇"Ψ(r,Θ,φ) + V(r,Θ,φ) + V(r,Θ,φ)Ψ(r,Θ,φ) = EΨ(r,Θ,φ)..................65




"As an alternative, in 1926 German physicist Max Born sharply refined Schrodinger's interpretation of an electron wave, and it is his interpretation--amplified by Bohr and his colleagues--that is still with us today......He asserted that an electron wave must be interpreted from the standpoint of probability." (Greene, p. 105).


"Just a few months after de Broglie's suggestion, Schrodinger took the decisive step toward this end by determining an equation that governs the shape and the evolution of probability waves, or as they came to be known, wave functions." (Greene, p. 107).


"Schrodinger, de Broglie, and Born explained this phenomenon by associating a probability wave to each electron." (Greene, p. 109).


Schrodinger's (probability) wave equation (equ 65), using multiple electrons, and a spherical coordinate system, is used to derive the atomic orbital equations but Schrodinger's electron probability wave represents the position probability of electrons; consequently, Schrodinger's electron probability wave cannot form a negative value required in producing destructive wave interference that is used in the formation of the atomic orbitals. Also, the atomic orbitals (fig 10) are not spheres, centered around the origin, that is required in using a spherical coordinate system.




_________________________________________________________________________________________________________________________________________________________________




Quantum mechanics uses a gauge transformation of Maxwell's equations.


"A similar, but more subtle and deep, situation arises in electrodynamics where one can express the (physical) electric and magnetic fields in terms of scalar (ɸ(r,t)) and vector (A(r,t)) potentials via




B(r,t) = ∇ x A(r,t)......................................................................................66




E(r,t) = - ∇ɸ(r,t) - d/dtA(r,t).......................................................................67




....Such a change in potentials is called a gauge transformation, and will be seen to play and important role in the quantum mechanical treatment of charged particle interactions." (Robinett, p.447); (Cohen-Tannoudji, p. 315).


The gauge transformation is based on Maxwell's equations but representing Maxwell's equations with a potential does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor does the gauge transformation alter the fact that the particle structure of a photon conflicts with the continuity of Maxwell's electromagnetic induction field. Also, Maxwell's equations represent a massless electromagnetic field that cannot be used to represent the structure of an electron, proton or nuclei that has a mass.




_________________________________________________________________________________________________________________________________________________________________




§ 20. Heisenberg




In Heisenberg's paper, "The Self-energy of the Electron" (1930), Heisenberg describes an energy divergence, of an electron point source, near the surface of the electron.


"In classical theory, the field strengths E and H become arbitrarily large in the neighborhood of the point-charge e, so that the integral over the energy density 1/8π (E2 + H2) diverges. To overcome this difficulty, one therefore assumes a finite radius ro for the electron in classical electron theory." (Heisenberg, Intro).


Heisenberg uses a finite electron radius ro to solve the energy problem of an electron point source but Heisenberg's electron point source is radiating an electromagnetic field (energy), in free space, as time increases, which represents an electron, as a physical source, that is generating its own self-energy which violates energy conservation. Also, a finite volume contains an infinite number of positions. When an infinite number of positions is represented with electromagnetic field vectors (energy), an infinite energy is formed. The ether, composed of matter, limits the number of positions forming a finite energy but the ether does not physically exist (vacuum) which proves Heisenberg's electromagnetic fields do not physically exist.




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§ 21. Quantum Electrodynamics




Quantum electrodynamics is based on the quantization of Maxwell's electromagnetic field that is used to represent the structure of an electromagnetic photon.


"2.2 Dirac's quantization of the electromagnetic field"(Miller, p. 20).


"Toward future considerations in quantum field theory another noteworthy point about Dirac's paper is his description of photon absorption and emission." (Miller, p. 23).


Maxwell's electromagnetic theory of light is based on Faraday's induction experiment that is not luminous. Hertz spark gap is used to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is not an ionization effect. Furthermore, the quantum electrodynamics photon conflicts with the continuity of Maxwell's electromagnetic field.




................................................................




In Feynman's paper, "Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction" (1950), Feynman's quantum electrodynamics is based on Maxwell's theory.


"This separation is especially useful in quantum electrodynamics which represents the interaction of matter with the electromagnetic field. The electromagnetic field is an especially simple system and its behavior can be analyzed completely." (Feynman, Intro).


"The secret to the success of QED lies in the fact that the QED Lagrangian is invariant under a gauge transformation; that is, the equations of motion are unaffected by the following transformation of the photon field: (Cheng, p. 237).


Feynman's quantum electrodynamics uses Maxwell's electromagnetic theory of light that is based on Faraday's induction experiment that is not luminous. Hertz's spark gap experiment is used to justify Maxwell's theory but Hertz's spark gap emits electrons yet Faraday's induction effect is also not an ionization effect which contradicts Feynman's QED.




....................................................................................................................................................................................




In Feynman's book, "QED: The Strange Theory of Light and Matter" (1985), Feynman states:


"Nature has got it cooked up so we'll never be able to figure out how She does it: if we put instruments in to find out which way the light goes, we can find out, all right, but the wonderful interference effects disappear." (Feynman, p. 81).


Feynman cannot describe interference using QED photons since the formation of the dark fringes of the diffraction pattern (fig 11) would represent the destruction of QED photons (energy) that violates energy conservation. Also, the destroyed QED photons do not contribute to the total light intensity of the diffraction pattern which would result in a measurable reduction in the total light intensity of the diffraction pattern yet experimentally, the total light intensity (dt = 1s), that enters a small aperture, equals the total light intensity of the diffraction pattern which is experimental proof the aperture diffraction effect of light is not formed by interfering QED photons.




_________________________________________________________________________________________________________________________________________________________________




QED use the Gauge transformation of Maxwell's equations.


"2.1.3 Local gauge invariance of QED...


The electromagnetic field strengths...do not uniquely define the potential Au(x) by the equation




Fuv(x) = duAv(x) = dvAu(x)...........................................68




The gauge transformation




A'u(x) = Au(x) + duθ(x)...........................................69




The gauge transformation is based on Maxwell's equations that are derived using Faraday's induction experiment that is not luminous. Hertz's spark gap experiment is used to structurally unite light with induction but Hertz's spark gap is emitting electrons yet Faraday's induction effect is also not an ionization effect which contradicts Feynman's QED.




_________________________________________________________________________________________________________________________________________________________________




§ 22. String Theory




String theory is based on Maxwell's electromagnetic theory of light.


"The electromagnetic fields are, in fact, themselves associated with particles called photons. These photons, again, are a different mode of oscillation of the string, in just the same way that the electron is some mode of oscillation of the string. So what we think of as electric charge is really a coupling together of different pieces of string which are oscillating in slightly different ways, and the photon is neither more elementary nor less elementary than the electron." by John Ellis (Davies, p. 154 - 156).


"The theoretical status of the four fundamental interactions was very uneven in the mid-Sixties: only the electromagnetic interaction could afford an (almost1) entirely satisfactory description (hence a 3-star status) according to quantum electrodynamics (QED), the quantum-relativistic extension of Maxwell's theory." by Gabriele Veneziano (Cappelli, p. 17).


"In four-dimensional spacetime, Maxwell theory gives rise to D - 2 = 2 single-photon states for any fixed spatial momentum. This is indeed familiar to you, at least classically. An electromagnetic plane wave which propagates in a fixed direction and has some fixed wavelength (i.e., fixed momentum), can be written as a superposition of two plane waves that represent independent polarization states." (Zwiebach, p. 180).


"The captivating thing about the early string theories was that although they had this apparent problem in fact they avoid it in a way that is avoided in Maxwell's theory of electromagnetism. But they avoid it in an infinitely more subtle way, because the problem is infinitely bigger. The fact that it can be avoided at all is remarkable." (Davies, p. 110).


An oscillating string is used to represent the structure of an electromagnetic string photon but Maxwell's electromagnetic theory of light is based on Faraday's induction effect that is not luminous; Hertz's spark gap is used to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is not an ionization effect; therefore, electromagnetic string photons, based on Maxwell's theory, cannot be used to represent light.




_________________________________________________________________________________________________________________________________________________________________




String theory uses the gauge transformation of Maxwell's equations.


"We can write the gauge transformations more explicitly in component form. Using (3.19) and (3.12), we find




Φ --> Φ' - 1/c (dε/dt)...........................70




A --> A + ∇ε.......................................71




The gauge transformation of a gradient to a vector does not change its curl, so B = ∇ x A is unchanged. The scalar potential Φ also changes under gauge transformations. This is necessary to keep E unchanged." (Zwiebach, 43).


Representing Maxwell's equations with a potential does not change the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous. Hertz's spark gap is used to structurally unite light with induction but Hertz's spark gap emits electrons yet Faraday's induction effect is not an ionization effect.




_________________________________________________________________________________________________________________________________________________________________




§ 23. Particle Physics




Particle physics is based on Maxwell's electromagnetic theory.


"Each of these particles, called a fermion, spins and exists in two spin (or polarization) states called left-handed (i.e. appears to be spinning clockwise as viewed by and observer that it is approaching) and right-handed (i.e. spinning anti-clockwise) spin states. One may add a fifth particle, the photon to this list. The photon is a quantum of electromagnetic field. It is a boson and carries spin 1, is electrically neutral and has zero mass" (Fayyazuddin, p. 1).


A photon's (boson) electromagnetic field is represented with the gauge transformation of Maxwell's equations but representing Maxwell's equations with a potential does not chance the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous. Also, a particle structure of light conflicts with the continuity of Maxwell's electromagnetic field. In addition, a fermion, that has a mass, cannot be represented with the gauge transformation since Maxwell's equations represent a massless electromagnetic field. Also, the existence of subatomic particles is justified using liquid hydrogen tracks formed within a bubble chamber. The accelerated electron beam is incident to an external metallic target that interaction produces subatomic particles that propagate through the steel enclosure (more than an inch of steel), of the bubble chamber, to form the liquid hydrogen tracks but the subatomic particles, that have a mass, cannot propagate through the steel container of a bubble chamber without producing a hole, and causing an explosion of the liquid hydrogen.




.....................................................................................




Particle physics is based on the gauge transformation of Maxwell's equations.


"2.3 Electromagnetic Field" (Leon, p. 29).




E = - (dA/dt) - ∇φ,........................B = ∇ x A".......................72a,b




(Leon, p. 29); (Martin, p. 290), (Roe, p. 71). Representing Maxwell's equations with an electromagnetic potential does not alter the fact that Maxwell's equations are derived using Faraday's induction effect that is not luminous, nor can the massless induction effect represent the structure of a subatomic particle that has a mass.




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§ 24. Gravitation




Newton's gravity equation F = (G m1 m2)/r2 is verified by Cavendish using lead spheres that gravitational force is measured using a torsion mechanism which is an extremely crude and inaccurate experiment since Cavendish is measuring a force of one µg. In an alternative experiment, a lead sphere (2 kg) is suspended using a thin titanium wire (1.5 m), and placed at the center, of the outer surface, of a moveable 2000 kg lead block (fig 12). The angle of the wire is monitored, using two lasers beams. The lead sphere is initially situated .001 mm from the outer surface, near the center, of the lead block, then the lead block is moved away from the suspended lead sphere. After the lead block is moved 1 cm from the suspended lead sphere, there is no measurable change in the angle of the wire, that is suspending the lead sphere, which contradicts Cavendish's experiment and Newton's gravity equation.




.................................................................................................................................................................




In Einstein paper, "The Foundation of the Generalised Theory of Relativity" (1916), Einstein describes gravity with Maxwell's electromagnetic field.


"In the following, we differentiate "gravitation-field" from "matter", in the sense that everything besides the gravitation-field will be signified as matter; therefore, the term includes not only "matter" in the usual sense, but also the electro-dynamic field." (Einstein5, § 14).


"On account of (30) the equation (66) becomes equivalent to (57) and (57a) when \varkappa_{\sigma} vanishes. Thus T_{\sigma}^{\nu} are the energy-components of the electro-magnetic field. With the help of (61) and (64) we can easily show that the energy-components of the electro-magnetic field, in the case of the special relativity theory, give rise to the well-known maxwell-poynting expressions.


We have now deduced the most general laws which the gravitation-field and matter satisfy when we use a co-ordinate system for which \sqrt{-g}=1." (Einstein5, § 20).


Maxwell's theory is based on Faraday's induction effect yet a magnet does not affect glass or wood which is experimental proof gravity is not an electromagnetic phenomenon.




_________________________________________________________________________________________________________________________________________________________________




Gravitation physics is based on Maxwell's theory.


"Although in some sense the preceding arguments may be regarded as a derivation of Maxwell's equations, the limitations of this approach should be kept in mind. Clearly, we have had to make quite a few assumptions to reach Eq. [14]. The objective of our game with electrodynamics was to obtain a prescription for finding the field equations in the hope that an analogous prescription will lead us to the filed equation for gravitation." (Ohanian, p. 135).


"§35.11. CONPARISON OF AN EXACT ELECTROMAGNETIC PLANE WAVE WITH THE GRAVITATIONAL PLANE WAVE." (Misner, Thorne, Wheeler, p. 961).


"It represents an electromagnetic plane wave analogous to the gravitational plane wave of the last few sections." (Misner, Thorne, Wheeler, p. 961).


Maxwell's theory is based on Faraday's induction experiment yet glass or wood, are unaffected by a magnet, which is experimental proof gravity is not an electromagnetic phenomenon. Furthermore, electromagnetic shielding is experimental proof gravity is not an electromagnetic phenomenon.




..........................................................................................................................................




Thorne describes gravity waves that propagates at the velocity of light.


"9.2 The physical and mathematical description of a gravitational wave" by Thorne. (Hawking, p. 338).


"General relativistic gravitational waves are ripples in the curvature of space time that propagates with the speed of light." by Thorne (Hawking, p. 338).


"Because gravitational and electromagnetic waves should propagate with the same speed, they can interact in a coherent way (Gertsenshtein, 1962)." by Thorne (Hawking, p. 361).


"Gravitational effects cannot propagate with infinite speed. This is obvious both from the lack of Lorentz invariance of infinite speed and from the causality violations that are associated with signal speeds in excess of the speed of light. Since the speed of light is the only Lorentz-invariant speed, we expect that gravitational effects propagate in the form of waves at the speed of light." (Ohanian, p. 241).


According to Thorne, Ohanian and Gertsenshtein, gravity waves propagating at the velocity of light.




_________________________________________________________________________________________________________________________________________________________________




Weber experimentally detected gravity waves that have the frequency of sound (1662 Hz).


"Further advances are necessary in order to generate and detect gravitational waves in the laboratory." (Weber, Conclusion, 1960).


"A description is given of the gravitational radiation experiments involving detectors at opposite ends of a 1000 kilometer baseline, at Argonne National Laboratory and the University of Maryland. Sudden increases in detector output are observed roughly once in several days, coincident within the resolution time of 0.25 seconds. The statistics rule out an accidental origin and experiments rule out seismic and electromagnetic effects. It is reasonable to conclude that gravitational radiation is being observed." (Weber, Abstract, 1970).


"EXPERIMENTS AT 1662 HERTZ" (Weber, Intro, 1970).


Weber's gravity wave experiment is testing for the frequency of sound waves (1662 Hz) but celestial gravity waves that have a frequency of sound cannot propagate in the vacuum of celestial space.




_________________________________________________________________________________________________________________________________________________________________




The frequencies of the gravitational wave, using a beam detector, was estimated with a range of 200 Hz - 10,000 Hz that includes Munich beam 1980, Caltech beam 1983, Glasgow beam 1987 and LIGO gravitational wave beam detectors.


"Because his best wisdom is so insecure, Fig. 9.4 shows wave strengths based not on these specific models, but rather on the general equation (37) for several possible values of ΔEGW and ro, and for the entire range of characteristic frequencies that have shown up in model calculations 200 Hz < fc < 10 000 Hz." by Thorne (Hawking, p. 375).


According to scientists, at Caltech, celestial electromagnetic gravity waves, that have the frequencies of sound waves (200 Hz - 10,000 Hz), have been experimentally detected, using a Caltech gravity beam, yet the vacuum of celestial space does not allow for the transmission of sound since the vacuum of celestial space is void of the quantity of gas molecules required in forming sound waves.




..............................................................




Gravity waves are represented with the following frequencies and sources.



"TABLE 5.1 FREQUENCY BANDS FOR GRAVIATIONAL WAVES








Designation.........................................Frequency...............................Typical sources


Extremely low frequency.....................10-7 to 10-4 Hz..........................Slow binaries, black hole (>108 Mo)

Very low frequency..............................10-4 to 10-1 Hz..........................Fast binaries, black holes (<108 Mo), white-dwarf vibrations

Low frequency......................................10-1 to 102 Hz..........................Binary pulsars, black holes (<105 Mo)

Medium frequency................................102 to 105 Hz...........................Supernovas, pulsar vibrations

High frequency......................................105 to 108 Hz...........................Man-made?

Very high frequency..............................108 to 1011 Hz..........................Blackbody, cosmological?" (Ohanian, p. 242).








"The most promising frequency band is that of medium frequency, from 102 to 105 Hz. There are several probable sources of gravitational waves in this band and, fortunately, detectors that respond to waves in this band can be built. There is little doubt that gravitational waves are incident on the Earth; the question is, can we build a detector sufficiently sensitive to feel them?" (Ohanian, p. 242).


Gravity waves that have a frequency range between 10-7 to 104 Hz and propagate at the velocity of light proves electromagnetic gravity waves have never been experimentally detected since a gravity wave with the frequency of 10-7 Hz forms a wavelength of 1015 meters!




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Gravitational physics uses the gauge transformation of Maxwell's equations.


"The gauge transformation [3.49] for huv implies the gauge transformation" (Ohanian, p. 244).


"Associated with an electromagnetic disturbance is a mass, the gravitational attraction of which under appropriate circumstances is capable of holding the disturbance together for a time long in comparison with the characteristic periods of the system. Such gravitational-electromagnetic entities, or "geons"; are analyzed via classical relativity theory." (Wheeler, Abstract).


"In electrodynamics, 21 the wave equation describing electromagnetic waves in vacuum is, in the Lorentz gauge....................Similarly, in general relativity, in the weak field limit, the wave equation describing gravitational waves in vacuum is equation (2.10.11)...........A similar analogy is valid for the gravitomagnetic field. 9 In electrodynamics, 21 from the Maxwell equations (2.8.43) and (2.8.44) and in particular from magnetic monopoles, ∇ · B = 0, one can write B = ∇ x A, where A is the vector potential. From Ampere's law for a stationary current distribution: ∇ x B = (4π/c)j, where j is the current density, one has then:" (Ciufolini and Wheeler, p. 317).


"TABLE 21.2 Gauge Transformations in Linearized Gravity and Electromagnetic




A ---> A + ∇Λ....Φ --> Φ - dΛ/dt".......................73




(Hartle, p. 462). The gauge transformation is based on Maxwell's equations that are derived using Faraday's induction experiment yet gravity affects glass and wood which is experimental proof the gauge transformation of Maxwell's equations cannot be used to represent gravity.




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§ 25. Astronomy




Modern astronomy uses parallax to determine the distance to a star. The distance to Alpha Centauri is calculated, using parallax, where the distance of the earth's orbital diameter is used as the reference distance. The change in the angular position of Alpha Centauri, after the observer propagates the distance of half an earth orbit (6 months), is used to determine the distance to Alpha Centauri but since the advent of stellar photography, the stellar universe is stationary since a stellar photographs taken in 2015 can be found to match exactly the stellar photograph taken in 1900; consequently, the calculation of the distance to a star, using the change in the position of a star, cannot be calculated, since the stellar universe is stationary (stellar maps).


The expansion of the universe is justified using a spiral galaxy but the photograph of a spiral galaxy is arbitrarily created, by manipulating the photographic plate. Also, the photograph of the Milky Way spiral galaxy, that contains the sun and the earth, is fiction, since to take this photograph would require that the photographer be many light years away from the earth. In addition, the photograph of the Eagle Nebula, using the Spitzer telescope is also fictitiously created, using computer imaginary, since the photograph represents the view of a celestial gas (fig 13) yet the vacuum of celestial space is void of the quantity of gas molecules implied in the photograph of the Eagle Nebula. Also, modern astronomers are viewing a single point in space (.1 arcseconds), using the Spitzer telescope, in photographing the Eagle Nebula that has a width of more than 70 light years and represents over 8000 stars yet the Spitzer space telescope does not have the resolution power to view the lunar lander on the surface of the moon. Astronomers are assuming that the Spitzer telescope has the power to resolve the stars of the Eagle Nebula that is 7000 light years from the earth. In addition, to determine the resolution, of the Eagle Nebula, requires the distance from the earth to the Eagle Nebula but the stellar universe is stationary; consequently, the distance, from the earth to the Eagle Nebula, necessary to determine the resolution, cannot be determined which is experimental proof the photograph of the Eagle Nebula is fiction. Furthermore, the red shift is used to justify the expansion theory but every star, at different times and positions, forms both red and blue shifts since the stellar universe is stationary. The same method of deception, based on the earth's daily and yearly rotational motions, that ancient scientists used to justify the theory that the earth is the center of the Universe is used to verify the expansion theory.




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§ 26. Maxwell's Equations




The modern physics derivation of Maxwell's electric curl equation is described using Lenz's induction experiment where a propagating magnet induces a varying current in a distant wire loop (fig 14) . The magnetic flux (dB/dt) that is incident normal to the plane formed by a wire loop produces the wire loop emf,




emf = - ʃʃ (dB/dt)· dA...........................................74




A second wire loop emf equation is used that represents the internal electric field E that forms the wire loop emf,




emf = ʃ E · dl.......................................................75




Equating equations 74 and 75,




ʃ E · dl = - ʃʃ (dB/dt)· dA.......................................76




Using Stokes' theorem (Hecht, p. 649),




ʃ E · dl = - ʃʃ (∇ x E)· dA......................................77




Equating equations 76 and 77,




- ʃʃ(dB/dt)· dA = ʃʃ (∇ x E)· dA.............................78




Maxwell electric curl equation is derived using equation 78,




∇ x E = - dB/dt...................................................79




The derivation of Maxwell's electric curl equation (equ 79) is based on Stokes' theorem that is used to form equation 77 but a length integral is equated to the areas integral which is mathematically invalid. On the right side of equation 77, the term (∇ x E) represents a volume that when surface is integrated, forms a surface area, that is not equal to a length. Furthermore, the electric field of equation 75, that forms the wire loop emf, only forms within the conduction wire and cannot be used to represent an external electric field of Maxwell's electric curl equation (equ 79). Also, the magnetic flux (dB/dt) of Maxwell's electric curl equation, that forms the wire loop emf, only forms in the plane of the wire loop, and cannot be used to represent a magnetic field, away from the wire loop.




..................................................................................................................




Maxwell's magnetic curl equation is derived using Ampere's law (Hecht, p. 42),




ʃ B · dl = ui.........................................................80




Maxwell electric current (dE/dt), that forms in the space between a varying capacitor (fig 15), is added to Ampere's law,




ʃ B · dl = ʃʃ (J + ε dE/dt) · dA ..........................81




Using Stokes' theorem, on the left side of equation 81 forms (Hecht, p. 649),




ʃ B · dl = ʃʃ (∇ x B) · dA........................................82




Equating equations 81 and 82, using J = 0,




ʃʃ (ε dE/dt)· dA = ʃʃ (∇ x B) · dA............................83




Maxwell's magnetic curl equation is derived using equation 83,




∇ x B = 1/c (dE/dt)............................................84




In equation 82, the length integral is equated to an area integral which proves the derivation of Maxwell's electric curl equation (equ 84), using equation 82, is mathematically invalid. On the right side of equation 82, the term (∇ x B) represents a volume that when surface is integrated, forms a surface area, that is not equal to a length. In addition, Maxwell's electric current (dE/dt) that forms in free space conflicts with equation 75 that electric field only forms within the conduction wire.


The electric field, of Maxwell's electric current, is formed by the motion of air molecules (Maxwell2, Part I) but the varying capacitor induction effect forms with vacuum in the space between the capacitor plates which is experimental proof Maxwell's electric current does not physically exist. I predict that the varying capacitor induction effect is formed by a capacitor plate surface current that magnetic force induces a surface current on the adjacent capacitor plate. Example, when two radio antennas are place close together (1 meter), a varying surface current on the transmission antenna induces a varying current on the reception antenna; consequently, the two antennas act similar to the varying capacitor induction effect formed by a surface current but the varying capacitor induction effect represented with a surface current conflicts with Maxwell's electric current mechanism.


The derivation of Maxwell's equations (equ 79 & 84), using equations 78 and 83, requires that Maxwell's equations be used in whole since the left and right sides of equations 78 and 83 are compared in the derivation of Maxwell's equations yet in the derivation of the electromagnetic transverse wave equations of light (equ 98 & 99), 14 of the 18 differential components, that form the expansion of Maxwell's equations, are eliminated which violates equations 78 and 83.




____________________________________________________________________________________________________________________________________________________________________

Part B




In an alternative method, the electromagnetic transverse wave equations of light are derived using Maxwell's equations,




∇ x E = - dB/dt..............∇ x B = 1/c (dE/dt)...................102a,b


∇ · E = 0........................∇ · B = 0.................................103a,b




Applying a curl operator to Maxwell's electric curl equation (equ 102a) forms,




∇ x (∇ x E) = - d/dt (∇ x B)...................................................104




Using equation 102b, in equation 104, then rearranging,




∇ x (∇ x E) = - 1/c (d2E/d2t)....................................................105




....................................................................................................................................




A second equation is derived using the gradient identity (Klein, p. 523),




∇ x (∇ x E) = E(∇ · E) - ∇2 E........................................106




and ∇ · E = 0 (equ 103a) to form,




∇ x (∇ x E) = ∇2 E...........................................................107




....................................................................................................................................




Equating equations 105 and 107 (Hobson, p. 23),




d2E/d2t - c2 ∇2 E = 0.......................................................108




A similar equation is derived for the magnetic field,




d2B/d2t - c2 ∇2 B = 0........................................................109




The r-direction electromagnetic wave equations of light (fig 15) are derived using equations 108 and 109,




E = Eo ei(kr - wt) ............................................................110



B = Bo ei(kr - wt) ............................................................111




The second order gradients, ∇2 E and ∇2 B, of equations 108 and 109, represent the disturbance within a volume that forms the electromagnetic longitudinal wave equations (equ 110 & 111) that conflicts with Maxwell's transverse waves.




______________________________________________________________________________________________________________________________________________________________




The electromagnetic wave equations (equ 98 & 99) contain the term (kz - wt). Using k = 2π/λ, and ct = z in kz forms,




kz = (2π/λ)(ct).................................................................................................112




Simplifying equation 112 using λf = c and w = 2πf forms,




kz = (2π/λ)(λf)t = (2πf)t = wt...........................................................................113




rearranging equation 113 forms,




kz - wt = 0..........................................................................................................114




Equation 114 proves the derivation of the electromagnetic wave equations of light (equ 98 & 99), using Maxwell's equations, is physically invalid. Using the same method, the variables kr - wt = 0, of equations 110 and 111, produce the same result.




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§ 28. Transmission and Reflection Equations




The transmission and reflection equations of light are derived using light waves represented with (Hecht, p. 111),




I = Io cos(k1x - wt) ĵ,.................................................115



R = Io cos(k1x - wt) ĵ,................................................116

T = Io cos(-k2x - wt) ĵ,...............................................117






The incident I, transmission T and reflection R light waves' (equ 115 - 117) interaction, at the transmission and reflection surface (fig 16), is represented with,




Io cos(k1x - wt) j + Ro cos(k1x - wt) j = To cos(- k2x + wt) j......................118




Using t = 0 and x = 0, equation 118 forms (Hecht, p. 113), (Klein, p. 570),




Io + Ro = To............................................................119




The following equation (Hecht, p. 114),




n1Io - n1Ro = n2To.................................................120




and equation 119 are used to derive the transmission and reflection equations,




t = 2n1 / (n1 + n2).................................................121



r = (n2 - n1) / (n1 + n2).........................................122




Using an air glass surface, n1 = 1 and n2 = 1.5, equation 120 forms,




Io - Ro = 1.5To.....................................................123




The difference of the incident (Io) and reflection (Ro) maximum amplitudes, derived using equation 120, forms a value that is greater than the sum (equ 119) which proves the derivation of the transmission and reflection equations of light, using equations 119 and 120, is mathematically invalid.




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The quantum mechanic step potential method is used to derive the transmission and reflection equations (Eisberg, p. 211), (McGervey, p. 102). The interaction of the incident, reflection and transmission light waves, at the surface interface (x = 0), is represented with,




Ioe ikx + Roe -ikx = Toeikx ...................................124




Using x = 0, in equation 124, the following equation is formed,




Io + Ro = To............................................................125




Differentiating equations 124 with respect to x forms,




k1(Io - Ro) = k2To....................................................126




Replacing k with n since k is proportional to n, equation 126 forms,




n1Io - n1Ro = n2To..................................................127




Equations 125 and 127 are used in the derivation of the transmission and reflection equations.




t = 2n1 / (n1 + n2) .................................................128


r = (n2 - n1) / (n1 + n2) .........................................129




Using n1 = 1 and n2 = 1.5 in equation 127 forms,




Io - Ro = (1.5)To ...................................................130




Using a air/glass interface, the difference of the incident and reflection light waves' maximum amplitudes (equ 130) is greater then the sum (equ 125) which proves the quantum mechanics step potential derivation of the transmission and reflection equations (equ 128 & 129) is mathematically invalid.




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§ 29. Polarization




Polarized light is represented using two adjacent electric transverse waves that phase difference forms linear, elliptical and circular polarized light (Hecht, p. 325-328), (fig 17) but the electric field of polarized light originates from Faraday's induction experiment that is not luminous. Also, a wave is a mechanical entity that requires a medium, composed of matter, yet polarized light propagates in vacuum that is void of matter which contradicts Maxwell's polarization mechanism. Furthermore, a transverse wave is a surface wave that cannot form in a volume since the disturbance within a volume forms a longitudinal wave.


In the polarization mechanism, non-polarized light interacts with a linear polarization filter forming linear polarized light. Non-polarized light (natural light) is represented with numerous transverse waves on the same axis (fig 18). The transverse waves of non-polarized light represent the possible angles of the linear polarization filter; therefore, the transverse waves of non-polarized represent more than 100 transverse waves on the same axis but a transverse wave is a surface wave that cannot form within a volume.




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§ 30. Aperture Diffraction Effect of Light




The rectangular aperture diffraction effect of light is described where the aperture emits electric spherical waves represented with (Hecht, p. 464),




dE = (Eo/r) ei(wt - kr) dS................................................131




The distances from the points in the aperture (y,z) to the diffraction screen point (Y,Z) is represented with (fig 19),




r = R[1 - (Yy + Zz)/R2]................................................132




Simplifying equation 132, using the binomic expansion, then inserting the result in equation 131, using t = 0, and integrating forms,




E = ʃʃ eik(Yy + Zz)/R dS......................................133




Equation 133 is used to derive the aperture diffraction intensity equation of light,




I = [(sin A)/A]2 [(sin B)/B]2.........................134




Hecht is using a surface integral (equ 133) to derive the aperture diffraction intensity equation of light but a surface integral only represents an area, described by the limits of the aperture, and cannot be used to summate the interfering light waves amplitudes, at the diffraction screen, which proves Hecht's derivation of the aperture diffraction intensity equation of light (equ 134) is mathematically invalid. In addition, the light waves' amplitudes, that form the intensity (energy) of the diffraction pattern, represents a light energy that is dependent on the wave amplitude, which conflicts with Lenard's photoelectric effect that proves light is composed of particles that energy is dependent on only the frequency (Lenard, Intro).


During the diffraction effect, the crests and nodes, of the light waves, propagate in the forward direction. At a point (Y,Z) on the diffraction screen, as time increases, the propagating light waves' amplitudes oscillate, forming an average resultant amplitude of zero, which would eliminate the interference effect; consequently, Hecht uses t = 0 that eliminates the propagation of the light waves.


In an experiment, a small circular aperture forms a diffraction pattern (fig 5). The destructive interference of the light waves' amplitudes are used to form the dark fringes of the diffraction pattern which would result in a measurable reduction in the total light intensity of the diffraction pattern since the destroyed light waves amplitudes (intensities) do not contribute to the total light intensity of the diffraction pattern. More than 10% of the diffraction pattern is composed of dark areas which would result in at least a 10% reduction in the total light intensity of the diffraction pattern yet the total light intensity that enters the aperture (dt = 1s) equals the total light intensity of the diffraction pattern which is experimental proof diffraction is not formed by wave interference that is used in the derivation of the aperture diffraction intensity equation of light (equ 134).




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§ 31. Optic Particle Theory




The wave theory of light is based on an optical ether, composed of matter, yet light propagates in vacuum that is void of matter. Einstein describes an electromagnetic ether that forms light waves in vacuum but Einstein's electromagnetic ether's electromagnetic field originates from Faraday's induction effect that is not luminous. In addition, Lenard's photoelectric effect proves light is composed of particles that energy is dependent on only the frequency which conflicts with Fresnel's light waves' amplitudes that are used to form the intensity (energy) of the diffraction pattern. I predicts that the aperture diffraction effect of light is formed by the optic particles that enter an aperture and are redirected, by the aperture, to only the intensity areas of the diffraction pattern (fig 20) without involving an optical ether, light waves or wave interference. The scalar energy of the redirected optic particles forms the intensity of the diffraction pattern. Furthermore, Maxwell describes the polarization effect of light using transverse waves but a transverse wave is a surface wave that cannot form within a volume since the disturbance, within a volume, forms a longitudinal wave. In the grid polarization effect, a fine wire grid is used to form linear polarized light. I predict, that the spaces between the wires, that form the wire grid, aligns the optic particles, that interact with the polarization wire grid, forming linear polarized light (fig 21).




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§ 32. Velocity of Light




Roemer (1676) attempts to measure the velocity of light, using Io, the satellite moon of Jupiter, as a clock.


"17. As we have remarked in S 2, ROEMER predicted in September of I676 that the eclipse of the first satellite of Jupiter which was supposed to take place on the following November 9 at 5 h. 25 m. 45s. would be 10 minutes late. On November 9, this eclipse was observed at the Observatoire Royal at 5h. 35m. 45s., in perfect confirmation of his prognosis." (Cohen, § 17).


Roemer's ten minute time delay is caused by numerous factors, such as, Roemer's assumption the Earth and Jupiter have circular orbits that rotate on the same plane, and Jupiter being stationary during the propagation of the Earth from L to K (fig 22), during Io's completion of a cycle of rotation, around Jupiter. Furthermore, Roemer ignores the measurement uncertainty, using a 1675 astronomic telescope and pendulum clock (10 seconds for 24 hours and 60 minutes for 6 months). Roemer's experiment is an extremely crude and inaccurate attempt at measuring the velocity of light and has absolutely no scientific merit. Fizeau (1849) and Foucault (1850) velocity of light experiments attempt to measure the velocity of light use rotating devices that continue to emit light, after the signal is produced, since an individual signal cannot form an intensity, after propagating a distance of 8km. In modern physics, a pulse beam is used to measure the velocity of light since a single pulse of light produced by a Kerr shutter (nanoseconds) cannot produce a measurable intensity, after propagating 50km which proves the velocity of light has not been measured.


"Hey, wait a sec! Hubble’s resolution is only 0.1 arcseconds, so the lander is way too small to be seen as anything more than a dot, even by Hubble. It would have to be a lot bigger to be seen at all. In fact, if you do the math (set Hubble’s resolution to 0.1 arcseconds and the distance to 400,000 kilometers) you see that Hubble’s resolution on the Moon is about 200 meters! In other words, even a football stadium on the Moon would look like a dot to Hubble." (By Phil Plait | August 12, 2008, Discover online).


Therefore, if one cannot see the Apollo lander, using the Hubble telescope, then a laser beam, that originates from the space station, cannot be seen on the surface of the moon; consequently, it is not physical possible to determine the velocity of light, using current technology.





Worker Date Method Velocity (km/s)


..........................................................................................................



Ross and Dorsey 1906 Ratio of Units 299,784

Mercier 1923 Wave on Wires 299,782

Michelson 1927 Rotating Mirror 299,798

Mittelstaedt 1928 Kerr cell 299,786

Michelson, Pease, 1933 Rotating Mirror 299,774

and Pearson

Anderson 1937 Kerr cell 299,771

Huttel 1937 Kerr cell 299,771

Anderson 1940 Kerr cell 299,776



These experimental justifications are similar to the experimental verification of Cavendish's experiment which is based on deductive reasoning.


"History shows us examples of scientists who were able to make a great leap forward specifically because they were not limited by the data. One of the most dramatic examples occurs at the beginning of the nineteenth century, when we may find a scientist willing to ignore the limitations of numerical facts for the sake of correct idea or theory, even to the extent of saying that certain numbers probably should be made a little bit bigger, others a little smaller, and so on. It was precisely in this way that Dalton proceeded in developing his atomic theory. Some scientists do not like examples of this sort, because they imply a special virtue "fudging" the evidence or "cooking" the data, and they warn us that we must not ever tell our science students that discoveries have been made in this way." (Suppe, 300


Comparing the wave theory of light to Dalton's atomic theory is similar to using Dalton's gas law for vacuum.




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§ 33. Conclusionμν


μν


The wave theory of light is based on light waves formed by the motion of an optical ether, composed of matter, yet light propagates in vacuum that is void of matter. Bradley's (1725) stellar aberration is used to justify the existence of the optical ether but Bradley's stellar aberration effect of light does not alter the fact that light propagates through a glass vacuum tube that is void of matter. Bradley's and all ether experiments are unnecessary since light propagating in vacuum is definitive and irreversible experimental proof Huygens-Fresnel optical ether, composed of matter, does not physically exist. Lorentz justifies the existence of Fresnel's ether, composed of matter, by reversing the negative result of Michelson's experiment yet light propagating in vacuum is definitive and irreversible experimental proof Fresnel's optical ether, composed of matter, does not physically exist. Also, Einstein (1917) uses the reversal of the negative result of Michelson-Morley experiment, based on Lorentz's transformation, to justify the existence of Fresnel's optical ether, composed of matter, which produces a contradiction since light propagates in vacuum that is void of matter.


Maxwell's electromagnetic theory of light, based on Faraday's induction experiment, was introduced since induction forms in vacuum but Faraday's induction effect is not luminous; therefore, Poynting derives an electromagnetic energy equation of light but Poynting's current wire is not emitting light; consequently, Poynting's energy equation of light cannot be used to represent the energy of light. Hertz's attempts to structurally unite light with induction, using a spark gap experiment, that emits light and the radio induction effect, but Hertz's spark gap emits electrons yet induction is also not an ionization effect. In addition, Planck uses the blackbody radiation effect to structurally unite light with induction but Planck's blackbody emits electrons; the production of light is always accompanied by the emission of electrons yet Faraday's induction experiment is not ionization effect which contradicts Maxwell's theory. In addition, the velocity of light is used to justify Maxwell's theory but Roemer's ten minute time delay is caused by numerous factors, such as, Roemer's assumption that the Earth and Jupiter have circular orbits that rotate on the same plane, and Jupiter being stationary during the propagation of the Earth from L to K (fig 22), during Io's completion of a cycle of rotation, around Jupiter. Roemer's experiment is an extremely crude and inaccurate attempt at measuring the velocity of light and has absolutely no scientific merit. Fizeau (1849) and Foucault (1850) velocity of light experiments attempt to measure the velocity of light use rotating devices that continue to emit light, after the signal is produced, since an individual signal cannot form an intensity, after propagating a distance of 8km. In modern physics, a pulse beam is used to measure the velocity of light since a single pulse of light produced by a Kerr shutter (nanoseconds) cannot produce a measurable intensity, after propagating 50km which proves the velocity of light has not been measured and cannot be used to justify Maxwell's theory.


Einstein uses the aberration effect of light, based on the Doppler effect (Einstein2, § 7), to explain the red and blue shifts, to justify the existence of an electromagnetic light wave but the aberration of light does not change the fact that Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. The stellar red and blue shifts, of Einstein's aberration effect of light, are produced by the earth's daily and yearly motions since the celestial universe is stationary which is verified since every star, in the universe, at different times and positions, forms both the red and blue shifts. Furthermore, Einstein uses the reduction of the inertial mass of an electron that emits an electromagnetic photon to justify Maxwell's theory (Einstein3, p. 639-641) but Maxwell's electromagnetic field originates from Faraday's induction effect that is not luminous. Furthermore, Einstein describes an electromagnetic ether that forms light waves in vacuum but Einstein electromagnetic ether's electromagnetic field originates from Faraday's induction effect that is not luminous.


Quantum mechanics, quantum electrodynamics, string theory, and particle physics, (boson) uses the gauge transformation of Maxwell's equations but representing Maxwell's equations with a potential does not change the fact that Maxwell's equations are derived using Faraday's induction experiment that is not luminous. Nor can the potential of Maxwell's massless electromagnetic induction field represent the structure of a proton, electron or nuclei, that has a mass. Quantum mechanics is based on Planck's quantization of Maxwell's electromagnetic field but Planck's blackbody emits electrons yet Faraday's induction experiment is not an ionization effect which contradicts Planck's quantization of Maxwell's electromagnetic field. In addition, Davisson–Germer electron scattering experiment is used to justify wave interference but the destructive interference of electron matter waves, to form the non-electron fringes of the electron scattering pattern, violates energy conservation. Schrodinger's electron probability waves are used to justify wave interference but an electron's position probability cannot form a negative value required in representing destructive wave interference. Schrodinger's electron probability wave equation (equ 65), using multiple electrons and a spherical coordinate system, is used to derive the equations of the atomic orbitals but an electron position probability cannot form a negative value required in producing destructive wave interference that is used in the formation of the atomic orbitals. Also, the atomic orbits (fig 10) are not spheres, centered around the origin, that is required in using a spherical coordinate system.


In particle physics, subatomic particles are represented using liquid hydrogen tracks formed within a bubble chamber. The accelerated high energy electron beam is incident to an external metallic target that collision produces subatomic particles which propagate through the steel enclosure (more than an inch thick), of the bubble chamber, to form liquid hydrogen tracks but subatomic particles, that have a mass, cannot propagate through the steel container of the bubble chamber, without producing a hole in the steel enclosure and causing an explosion of the liquid hydrogen. In gravitational physics, Weber experimentally detected gravity waves that have the frequency of sound (1662 Hz) yet the vacuum of celestial space does not transmit sound. Wheeler describes electromagnetic gravity waves that Thorne and Ohanian state propagate at the velocity of light. Experimentally, the European pulsar timing array (EPTA) detected an electromagnetic gravity wave of frequency 10-9 Hz which represents a gravity wave that has a wavelength of λ = 1016 meters that is more than a light year in length. In addition, electromagnetic shielding is experimental proof gravity is not an electromagnetic phenomenon.


Modern astronomy uses parallax to determine the distance to a star but parallax requires a change in the position of the star yet since the advent of celestial photography, the celestial universe is stationary (stellar maps); consequently, the calculation of the distance to a star, using the change in the position of a star (parallax), is physically invalid. The same method of deception, based on the earth's daily and yearly rotational motions, that scientists used to justify the theory that the earth is the center of the Universe is used to determine the distances to the stars. In addition, the photograph of the Eagle Nebula (fig 13), using the Spitzer telescope, is fictitiously created, using computer imaginary, since the photograph represents the optical view of a celestial gas yet the vacuum of celestial space is void of the quantity of gas molecules implies in the photographic representation of the Eagle Nebula.


The wave theory of light is based on an optical ether, composed of matter, yet light propagates in vacuum. Einstein describes an electromagnetic ether that forms light waves in vacuum but Einstein's electromagnetic ether's electromagnetic field origin from Faraday's induction effect that is not luminous. I predicts that the aperture diffraction effect of light is formed by the optic particles that enter an aperture and are redirected, by the aperture, to only the intensity areas of the diffraction pattern (fig 20) without involving an optical ether, light waves or wave interference. The scalar energy of the redirected optic particles forms the intensity of the diffraction pattern. Furthermore, Maxwell describes the polarization effect of light using transverse waves but a transverse wave is a surface wave that cannot form within a volume since the disturbance, within a volume, forms a longitudinal wave. In the grid polarization effect, a fine wire grid is used to form linear polarized light. I predict, that the spaces between the wires, that form the wire grid, aligns the optic particles which interact with the polarization wire grid, forming linear polarized light (fig 21).




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