Talk:Wigner rotation

Summary of new changes
This article (Wigner rotation) was a redirect to Thomas precession, and so was Thomas rotation.

It has been agreed here that this article (Wigner rotation) should contain all the content of combining two Lorentz boosts, and the equivalence to a boost and rotation. The rotation is the Wigner or Thomas rotation, and Thomas rotation now redirects to this article. Thomas precession is different, and should be about the rotation of frames with an angular velocity. Lorentz transformation is about single boosts or rotations (but could mention somewhere about the compositions with links).

Content has been transferred from Lorentz transformation and Thomas precession. The duplication (compositions of boosts) in Lorentz transformation has been largely removed. It remains to remove the duplication from Thomas precession. 'M'&and;Ŝc2ħεИτlk 11:22, 25 December 2015 (UTC)

There's still a problem with article titles (and possibly with the wording in them). A Wigner rotation is not even necessarily a rotation. If $p$ is a given four-momentum, then there's a subgroup of the Lorentz group, the little group that leaves this momentum invariant. See Lorentz group for some visualization. The little group is one of $SO(3)$, $E(2)$ (Euclidean group), $SO(2, 1)$ and $SO(3, 1)$ itself. Thus (in certain contexts), elements of these groups are called Wigner rotations. It is this that was the actual topic in Wigner's (freely available, referenced in article) paper, not any sort of analysis of the computational problem of actually algebraically finding Wigner rotations in the $SO(3)$ case.

This stuff (what I outlined above) is properly (in the future) belonging to representation theory of the Poincaré group, and is related to Wigner's classification. The present article probably should be renamed (and edited to this effect) to Combining Lorentz boosts or the like. YohanN7 (talk) 11:56, 2 August 2017 (UTC)

Associative?
Quick question. I am a complete novice in this material. Other web sites treat boosts as a 4x4 matrix, and the composition of boosts as matrix multiplication. This would mean that boost composition is associative, yet the text says that isn't. Is this a typo or is composition truly non-associative?

JavautilRandom (talk) 22:34, 11 September 2017 (UTC)


 * It says that velocity addition is non-associative. Each boost can be associated with a three-velocity. When combining boosts (which follows the rules of matrix multiplication) and then reverse engineering a three-velocity from the resulting Lorentz transformation (that is generally not a pure boost), you'll find that, while it can be expressed in terms of the individual three-velocities of the factor boosts, the composition laws of three-velocities aren't particularly nice. YohanN7 (talk) 08:10, 12 September 2017 (UTC)

Brought back missing refs
Bright back missing referred-to books, etc, mostly from Thomas precession. Varicak and Sexl-Urbantke still don't link. Einstein 1922 and Macfarlane 1962 still missing... where are they? The order is random. User:YohanN7 ? Cuzkatzimhut (talk) 13:39, 26 April 2018 (UTC)


 * Hello. I searched the internet and the Einstein archives.  I could not find the reference [2] "Einstein 1922"  Did you find this reference?
 * Thanks! CANISTEOPHD (talk) 16:06, 5 December 2023 (UTC)

Angle expression gives absolute value.

 * $$\cos\epsilon = \frac{(1+\gamma+\gamma_\mathbf{u}+\gamma_\mathbf{v})^2}{(1+\gamma)(1+\gamma_\mathbf{u})(1+\gamma_\mathbf{v})} - 1 $$

This expression only gives out positive rotation angles, but the rotation can also be negative. We should point out that it's an absolute values of the rotation angle. --MadsVS (talk) 16:34, 13 February 2020 (UTC)

Diagrams disagree with text.
According to the text of the article and the caption in the diagram, the rotation angle's vector should be parallel with


 * $$\mathbf{e} = \frac{\mathbf{u}\times\mathbf{v}}{|\mathbf{u}\times\mathbf{v}|}$$

In the diagrams that would make the angle of rotation positive (counterclockwise) yet it is shown to be negative. — Preceding unsigned comment added by 184.157.243.160 (talk) 01:55, 1 May 2020 (UTC)

The caption of the first diagram seems wrong.
There is text for each of the 3 diagrams.

For the rightmost diagram, the comment in unclear

Right: In frame Σ′′, Σ moves with velocity −wd relative to Σ′′ and then moves with velocity wd relative to Σ.

Should this actually read as follows?:

Right: In frame Σ′′, Σ moves with velocity −wd; in frame Σ, Σ′′ moves with velocity wd.

Description Wigner rotation incorrect
What is being called here the Wigner rotation (L.L' = L''.R) was first described on p.169 of Silberstein's 1914 book 'Relativity' which is on the internet. He used only simple algebra, not even matrices. It is however quite easily shown by a little matrix algebra and doesn't need sophisticated methods taking up over 50 pages like Wigner's derivation by unitary representations. Of course, even Poincaré (1906) observed the Lorentz group includes spatial rotations.JFB80 (talk) 13:22, 8 April 2021 (UTC)''' JFB80 (talk) 18:41, 8 April 2021 (UTC) JFB80 (talk) 18:51, 8 April 2021 (UTC)

In his 1927 paper, having described the Lorentz transformation in page 5 as equation (2.1), Thomas says in the last paragraph of this page, that the combination of two transformations of this form  is not in general another transformation of this form but such a transformation followed by a rotation. He says this before going into details for the infinitesimal case so he was quite aware of what is being called here the Wigner rotation. JFB80 (talk) 06:17, 16 April 2021 (UTC)

History
Check the book by Silberstein 1914 (1 st edition) 2nd edition in google books go to page 164. You have a discussion of the Lorentz group which highlights the subject of the relative velocity. Read the preface, the lessons were taught at the University College (London) 1912-1913. Please, change the historical part. https://en.wikipedia.org/w/index.php?title=Talk:Wigner_rotation&action=edit&section=new

in addition, the reference [6] to Einstein, 1922 is missing. I thought it referred to But I was unable to find anything close to it in the searchable text. Please, write the correct source. Hgsolari (talk) 15:07, 15 May 2021 (UTC)

@ Hgsolari: You did not give the correct reference. The decomposition is clearly stated by Silberstein 1914 p.170 who justifies it with an argument basically correct. I see that Wigner 1930 p.165 section C gives credit to Silberstein 1924 p.142 for the result. So if Wigner did~ why not Wikipedia? JFB80 (talk) 20:46, 23 October 2021 (UTC)