# Talk:Lorentz transformation

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## Covariant and contravarient metric tensor

The article says As it happens, ημν = ημν" but actually this is specific to the instant form, in other forms of dynamics (light front or point form) this can vary (and the metric has off diagonals). See for example the Brodsky review https://arxiv.org/abs/hep-ph/9705477 page 19. I know almost everything is done in instant form, but the others still exist, how should we deal with this? 129.215.144.93 (talk) 13:02, 2 March 2017 (UTC)

Not at all. YohanN7 (talk) 10:42, 6 March 2017 (UTC)
I did look at the article. Good stuff, but it is a rather trivial point that curvilinear coordinates or other non-standard coordinates (which seems to be what it is all about) yield different entries in the metric. YohanN7 (talk) 11:58, 6 March 2017 (UTC)

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## Different looking symbols for relative velocity in equations and text

The velocity letter v is used for the relative velocity in the x direction in the equations e.g. at \frac{v x} in:

{\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}}

and seemingly the same v in the following text e.g. at {math|v} in

where v is the relative velocity between frames in the ..

But on my computer screen the v in the equation is a script v and in the text it looks like a greek letter v (nu)

?????? RudiPo (talk) 11:24, 6 March 2018 (UTC)

## Lorentz Transformation should be at the top of page

In my opinion the Lorentz transformation itself should appear at the top of the page, since it is the subject matter at hand. Helps if one simply wants a quick reference.

Hope I formatted this correctly - It's been a while since I've been here. — Preceding unsigned comment added by Scot.parker (talkcontribs) 06:11, 29 April 2018 (UTC)

Almost  , but please put new talk page messages at the bottom of talk pages and sign your messages with four tildes (~~~~) — See Help:Using talk pages. Thanks.
Good call. Done. - DVdm (talk) 08:49, 29 April 2018 (UTC)

## Question

So, I'm not too knowledgeable when it comes to science and math but I would like to know; did Lorentz actually create these formulas or where they simply named after him? — Preceding unsigned comment added by 2600:1700:69C1:2A00:CD3F:6125:720C:780B (talk) 21:59, 19 June 2018 (UTC)

Please sign all your talk page messages with four tildes (~~~~) — See Help:Using talk pages. Thanks.
Better ask at the wp:Reference desk/Science. Here we discuss the article, not its content—see wp:Talk page guidelines. Good luck. - DVdm (talk) 10:15, 20 June 2018 (UTC)

## Physical implications of time dilation.

I think that section gives a false idea of the Lorentz transformations , based on the fact that the boosted observer F’ is supposed to measure time intervals by observing a clock at rest in F !

But why should he do that ? He simply takes his own clock (wristwatch time) ! Which of course runs at the same rate than the clock at rest in F !

And by using his own clock he will measure the correct proper time in F’ !

The Lorentz transformations are an intrinsic Physical property of Spacetime! That is completely forgotten in the traditional presentations !

--Chessfan (talk) 07:42, 11 October 2018 (UTC)

Good point. I have reworded the paragraphs to avoid the ambiguous "boosted observer" and to make sure that "ticks" refer to single events, so that time intervals are measured "between two ticks". I also changed the order to remain closer to the standard sources. - DVdm (talk) 08:16, 11 October 2018 (UTC)

## Why not GA ?

The Lorentz Transformation article is very math oriented. But you failed to mention the Geometric Algebra (GA) approach , which is much easier than the tensorial method. For example , I could show you , based on many papers by Hestenes, Doran , ... that all the very basic results of Special Relativity , time dilation , length contraction , time and length units , are contained in a single GA relation

e’0 e0= e’0 . e0 + e’0∧e0

But sorry , I will not do so , because that could be qualified original research !

It’s up to you !


--Chessfan (talk) 16:00, 16 October 2018 (UTC)

For whom are you writing, man???????? Only for yourself, I guess. — Preceding unsigned comment added by Koitus~nlwiki (talkcontribs) 19:42, 8 April 2019 (UTC)

OK I will try.

We consider two references frames ${\displaystyle (e_{0},e_{1})and(f_{0},f_{1})}$  , both pseudo-orthogonal.

${\displaystyle 1/\qquad e_{0}^{2}=f_{0}^{2}=1\qquad e_{1}^{2}=f_{1}^{2}=-1\qquad e_{0}\cdot e_{1}=f_{0}\cdot f_{1}=0}$

${\displaystyle 2/\qquad f_{0}e_{0}=f_{0}\cdot e_{0}+f_{0}\wedge e_{0}}$ ${\displaystyle f_{0}=f_{0}\cdot e_{0}e_{0}+f_{0}\wedge e_{0}e_{0}}$

${\displaystyle 3/\qquad f_{0}\cdot e_{0}=\gamma }$

We define ${\displaystyle \gamma }$  by (3) and we guess that ${\displaystyle \gamma }$  is indeed the Lorentz factor.

We notice that the vector ${\displaystyle f_{0}}$  is decomposed into a vector parallel to ${\displaystyle e_{0}}$  , and a vector orthogonal to it :

${\displaystyle 4/\qquad f_{0}\wedge e_{0}e_{0}=f_{0}-\gamma e_{0}}$ ${\displaystyle (f_{0}\wedge e_{0}e_{0})\cdot e_{0}=0}$

We guess now that ${\displaystyle v}$  is the euclidian velocity wich represents the movement of the f system :

${\displaystyle 5/\qquad v=(f_{0}\wedge e_{0})/(f_{0}\cdot e_{0})}$

In fact v is a bivector , and :

${\displaystyle 5bis/\qquad |v|=v/e_{1}e_{0}}$  a scalar .

${\displaystyle 6/\qquad f_{0}e_{0}=\gamma [1+(f_{0}\wedge e_{0})/(f_{0}\cdot e_{0})]=\gamma (1+v)}$

${\displaystyle 7/\qquad 1=f_{0}e_{0}e_{0}f_{0}=\gamma ^{2}(1-|v|^{2})}$

${\displaystyle 8/\qquad \gamma =(1-|v|^{2})^{-1/2}}$

Thus, as we guessed , ${\displaystyle \gamma }$  is in accordance we the definition of v .

It is now an easy task to deduce the Lorentz transformations and demonstrate the reciprocity.

Chessfan (talk) 17:26, 1 May 2019 (UTC)

Imagine a trajectory from (0,0)to ${\displaystyle \tau f_{0}}$  .What will be the time coordinate in the ${\displaystyle (e_{0},e_{1})}$  frame ? You simply project orthogonally the vector ${\displaystyle \tau f_{0}}$  on the vector ${\displaystyle te_{0}}$  and you find :

${\displaystyle 9/\qquad t=\gamma \tau }$

The reciprocity is obvious with (3) and the fact that we can imagine the ${\displaystyle (e_{0},e_{1})}$  frame moving backwards with velocity ${\displaystyle (-v)}$  .

--Chessfan (talk) 08:24, 2 May 2019 (UTC)

The Clifford (geometric) algebra approach to spacetime physics advocated by Hestenes, Baylis and others[1][2] would be worth a separate article. There does exist a rather unsatisfactory Wikibooks presentation of the subject that would be a guide what NOT to do in writing a Wikipedia article on physics using geometric algebra. Prokaryotic Caspase Homolog (talk) 23:11, 11 May 2019 (UTC)

References

1. ^ Hestenes, David (2003). "Spacetime physics with geometric algebra". American Journal of Physics. 71: 691. doi:10.1119/1.1571836. Retrieved 11 May 2019.
2. ^ Baylis, William E. (2012). Clifford (Geometric) Algebras: with applications to physics, mathematics, and engineering. Springer Science & Business Media.
See Hestenes and Doran for free on : geocalc.clas.asu.edu and geometry.mrao.cam.ac.uk Chessfan (talk) 06:20, 12 May 2019 (UTC)