Talk:Velocity-addition formula

message: In the section 'Standard configuration', I was confused by gamma sub v. Took me a while to realize it was not gamma times v.73.220.235.20 (talk) 02:46, 2 August 2016 (UTC)
replies: text: I agree. I have made a little change: . - DVdm (talk) 06:41, 2 August 2016 (UTC)
replies: text: I don't. Every gamma refers to some . The previous notation said which . Besides, the rest of the article uses the old notation. YohanN7 (talk) 09:11, 2 August 2016 (UTC)
replies: text: Oops, sorry. I had made a silly typo. Ok now. — Preceding unsigned comment added by DVdm (talk • contribs) 10:31, 2 August 2016 (UTC)
replies: text: It is at any rate no big deal. I meant that since this article by definition involves gammas referring to different velocities, it should i m o be useful to have the notation indicate to which velocity the gamma in question refers. The rest of the article does this. But like I said - no big deal, latest edit works just as wellYohanN7 (talk) 11:02, 2 August 2016 (UTC)
replies: text:  Yes, I hadn't really looked at the remainder of the article yet. You make a valid point. Perhaps instead of what I did, we could lower the V-index and use \gamma_{_V} as opposed to \gamma_V. Much less confusing. - DVdm (talk) 11:16, 2 August 2016 (UTC)
replies: text: Wow, never thought of that. Looks really nice. YohanN7 (talk) 11:41, 2 August 2016 (UTC)
replies: text: Ok, shall I make the change then? - DVdm (talk) 12:11, 2 August 2016 (UTC)
replies: text: Please do! YohanN7 (talk) 12:19, 2 August 2016 (UTC)
replies: text:  . I only did it with the capital V, no need with the lowercase u and v. I also kept the first explicit definition in the 'Standard configuration' section. Looks better indeed. - DVdm (talk) 12:24, 2 August 2016 (UTC)
thread_title:  Confusing Symbols 

message: It looks like the following unsourced part (added here, here and here) was removed for the third time now (, , ):  Rightly so—see edit summaries of removals. It is not just unsourced. It also suffers from typographical, grammatical and semantic errors. It reads like gibberish indeed. - DVdm (talk) 09:15, 16 September 2016 (UTC)
replies: text: You might actually be correct and vector addition in SR be equipollent when looked at the right way but it is not looked at that way in this article and even you might find difficulty understanding how vectors adding noncommutatively could be equipollent. But there are apparently no sources on this subject. JFB80 (talk) 19:31, 16 September 2016 (UTC)
replies: text: Indeed, and without sources, we don't take it. - DVdm (talk) 19:59, 16 September 2016 (UTC)

text: And now it is claimed by this this individual that something is equipollent "when looked at the right way but it is not looked at that way in this article". The same attitude (article bad) prevails in earlier posts by this individual. What does it mean? Perhaps this individual should refrain from editing SR related articles in the future. Misunderstanding the concept of velocity in SR and in Newtonian mechanics is not a good starting point. YohanN7 (talk) 07:17, 19 September 2016 (UTC)
replies: text: First DVdm and especially YohanN7 please stop using disrespectful and abusive language as we are are requested to do in the guidelines. You seem to regard yourselves as some kind of Wiki-policemen who do not have to observe this rule. Secondly you don't have a profound knowledge of this subject and should only express an opinion not a judgement. Thirdly I suggest you make a start by reading the paper of Sommerfeld 1909 referred to at the end of the article. JFB80 (talk) 17:57, 19 September 2016 (UTC)
replies: text:  The sentence was removed because it is unsourced. It is wrong, it is badly formed, it reads like nonsense, but first of all, it is wp:unsourced, and, per wp:BURDEN, it is your job to find a proper source. So, unless you can come with a proper reliable source that completely backs what you were trying to add, you are disrupting this talk page per the wp:talk page guidelines. There is no need to call other editors "kind of Wiki-policemen". Other editors are the ones with whom you are supposed to collaborate and establish a wp:consensus about some change to the article. Consensus for the above sentence is unlikely to happen, so the best thing to do might be to leave it at that. - DVdm (talk) 18:30, 19 September 2016 (UTC)
replies: text: DVdm perhaps it should be added that the sentence in question was only intended as an explanation, principally to yourself, and there was no proposal to put it in the article. Such remarks should not require a source. I see nothing in the guidelines that comments in talk pages require a source, nor should there be, in my opinion, so as to ensure free discussion. Otherwise it is like a medieval disputation using quotations from Aristotle. But I am willing to let the matter drop now.JFB80 (talk) 15:50, 22 September 2016 (UTC)
replies: text:  Indeed, comments on talk pages don't need sources. But the "the sentence in question" was put in the article by you. So it was removed. But then, continuing to argue on the talk page—against consensus—about putting something from the sentence in the article without being able to back it with a source, would be talk-page-disruptive, and therefore, thanks for dropping the matter. - DVdm (talk) 16:13, 22 September 2016 (UTC)

text: That does not support the sentence above at all. Bringing that as a source would be wp:original research by wp:synthesis. - DVdm (talk) 07:58, 19 January 2017 (UTC)
replies: text: What do you understand by equipollence then? Isn't it the possibility in Euclidean geometry of freely moving the point of origin of vectors? It is this which justifies the parallelogram rule in Euclidean space and which does not apply in hyperbolic space. This is basic geometry but I tried to give a relativity source. I think there is no need for you to be always so legalistic quoting Wikilaw as this is a talk page where we try to get mathematical ideas clear. JFB80 (talk) 16:11, 19 January 2017 (UTC)
replies: text:  I know what equipollence is. Silberstein doesn't mention the term. He also does not mention vector origins, nor the difference between pairs of vectors with the same origin  vs pairs with different origins. So he does not make the analysis that is made in the removed sentence. If that particular analysis would be worth being mentioned—as in wp:DUE—in Wikipedia, then surely a source that does indeed make the analysis must exist. It's just a matter of finding it, and you're in business. - DVdm (talk) 16:31, 19 January 2017 (UTC)
thread_title:  Unsourced part removed 

message: In the section "History", it says:
:the speed is c + (1 − ​1⁄n^2)V instead of c + V, where c is the speed of light in the aether
But we are talking from light traveling in a fluid, so c should be replaced with c/n and "aether"  should be replaced with "fluid".
I will wait a day before posting an edit, to give chance for a justification of the current version.   — Preceding unsigned comment added by George Albert Lee (talk • contribs) 20:15, 10 March 2021 (UTC)
replies: text: Let me explain my edit: consider routine real number addition: f(X,Y) = X+Y. Would you expect f(aX, bY) = ab f(X,Y)? It is almost never true, and even if it were true, it is certainly not what is meant by linearity: for an appropriate definition of linearity, I'd appeal to the link listed which then leads us to https://en.wikipedia.org/wiki/Linear_map, in which our function's domain is the direct product space of the two input vectors. The definition refers to a single scalar c operating on the domain, and transliterates in our case to f(cX, cY) = c f(X,Y). This IS true for simple addition, even when X and Y are vectors, matrices, or complex numbers. One might wonder (as I actually did for my application of velocity addition) if I could count on f(aX, aY) = a f(X,Y). It does not hold for relativistic velocity addition, and I gently suggest (as per Wikipedia) the equality is a routine meaning for linearity AND the fact that is does not hold is a useful and interesting observation. To summarize, the equation as it stood was not a test for linearity, and is of little use since no one would expect f(aX, bY) = a b f(X,Y) anyway. My edit shows the routine meaning of linearity does not hold for relativistic velocity addition, and is both useful and, IMHO, kind of interesting! I trust that was a clear enough explanation to warrant replacing my edit? Anyway, stuck it back in there. Randallbsmith (talk) 17:49, 11 February 2022 (UTC)
replies: text:  Still, I think we really need a solid, proper, inline, textbook source for this.I spent some significant time looking for one, and failed to find one. ANYONE? - DVdm (talk) 18:58, 12 February 2022 (UTC)
replies: text:  To my taste, because the ordinary 3-vector addition function f() can be considered a mapping over a six dimensional space with the property f(aX) = af(X) makes the use of the term "linear" so obvious as to obviate the need for a non-Wikipedia reference. However, if this is truly a stretch, perhaps we could get right to the point without the clutter of explaining why some term ("lineraity") might be used here. Rather, simply observe "For the usual addition of 3-vectors \mathbf{v} and \mathbf{u}, we know that \lambda \mathbf{v} + \lambda \mathbf{u} = \lambda (\mathbf{v} + \mathbf{u})  for real \lambda. However, for relativistic velocity addition, in general \lambda \mathbf{v} \oplus \lambda \mathbf{u} \neq \lambda (\mathbf{v} \oplus \mathbf{u}) ." Bottom line: the fact that equality doesn't hold is an important feature, worthy of being pointed out. Randallbsmith (talk) 17:30, 14 February 2022 (UTC)
replies: text:  The formula has a simple geometrical interpretation which makes it quite clear it is not linear. It only becomes linear when v/c -> 0 when it reduces to ordinary vector addition. But I think the article is based on a misunderstanding. This oplus formula does not represent relativistic addition of velocities because it omits the Thomas precession. This is what resulted in the "Mocanu paradox" and the non-associativity of the oplus formula. Regarding DVdm's remark I don't believe there exists any clear textbook explanation and, from what I have seen, in the literature. Ungar and Mocanu wrote about it but what they say is not very easy to follow. JFB80 (talk) 07:47, 15 February 2022 (UTC)
replies: text: It sounds like you are saying the formula using \oplus is simply incorrect? But I just went through my own derivation from scratch using a Lorentz transformation on spacetime intervals for the simpler case of 2+1 dimensions, and it appears to replicate exactly the equation at the end of the "General Configuration" section. Perhaps it is not clear: I assumed all 3 frames start at mutual rest with 2 spatial axes parallel, then take off in arbitrary directions at constant velocity, with no rotation. (Rotation can be physically verified as absent, using a mass on a string or whatever.) Is the error only present in 3 dimensions, or in the case the frames also rotate? Randallbsmith (talk) 19:28, 16 February 2022 (UTC)
replies: text:  No it is not incorrect and represents part of the answer. See p.6 of Thomas' 1927 paper where he says:"A Lorentz transformation with velocity -v followed by one with velocity v+δv where δv is infinitesimal, resolves into a Lorentz transformation with infinitesimal velocity γ {δv + (γ-1)(v.δv)v/v²} together with an infinitesimal rotation (γ-1)(vxδv)/v²". The` first term can be shown to be what is given by the oplus (or ominus) formula. (sorry I don't use the markup - it is too slow, I am not very used to it).JFB80 (talk) 17:09, 17 February 2022 (UTC)
replies: text: You have my sympathies regarding the markup! Well, I am going to come to peace with things was they are then. I can't understand the distinction between "not incorrect" and being just "part of the answer." I would like to use the full answer, not just part, but since I also derived the result in the article, I will go with that. Also the rotation term in the formula you quoted from Thomas has a single cross product and thus has a handiness sensitivity, so it can't be simply an additional term for the resultant, on physical grounds.(If δv is to the left the resultant velocity would point slightly up, if it is to the right, the resultant points slightly down. The universe doesn't work like that, the resultant must be in the plane of the two vectors).  — Preceding unsigned comment added by Randallbsmith (talk • contribs) 20:55, 17 February 2022 (UTC)
replies: text: The paper I quoted is everywhere accepted. Check up yourself if you like on p.6. The link is http://www.clifford.org/drbill/csueb/4250/topics/thomas_papers/Thomas1927.pdf. You might also like to see Wiki  'Wigner rotation'(but very difficult to understand). The mystery is explained by the fact that the Lorentz transformation is really a transformation in hyperbolic space which gives a rotation by 'parallel transport' which is what Thomas' paper was about to explain electron precession.(see also Borel 1913 CR Paris)JFB80 (talk) 16:47, 18 February 2022 (UTC)

text: But surely you accept the statement: product of 2 boosts = boost x rotation matrix. A boost gives a translation in hyperbolic space. So is'nt it the same sort of thing? JFB80 (talk) 13:04, 19 February 2022 (UTC)
replies: text: Absolutely agree. And directly related important to note that for Lorentz Boosts B, B(U) B(V) \neq B( U \oplus V). As to the correctness of the addition formula given here (definition of \oplus) I believe it is correct and is used in many papers discussing Thomas rotation and the Mocanu paradox. The trickiness of the formula is as follows: The formula is correct in giving a resultant vector aiming in the proper direction with the proper length in space. You can literally watch the moving object slide along the resulting velocity vector as time passes.  But to read off the coordinate values of this vector, one needs to account for the relative orientation of the frame axes you are using. This is clearly explained in a short and accessible paper intended for undergraduate level physics by Silagadze "Thomas rotation and Mocanu paradox -- not at all paradoxical."	Lat. Am. J. Phys. Educ. 6 (2012), 67-71 arXiv:0907.4482 [physics.class-ph]. Frames may start out parallel in which case coordinates are easily shared, but after two boosts to a frame moving with U \oplus V the frames are no longer parallel thanks to the Thomas rotation. Randallbsmith (talk) 18:24, 26 February 2022 (UTC)
replies: text: I'm glad you agree. The Silagadze paper was earlier in arXiv at Silagadze 2009 https://arxiv.org/abs/0907.4482v1.JFB80 (talk) 16:16, 27 February 2022 (UTC)

text: It is interesting to note that the oplus formula for addition was originally that stated by Einstein (1905 section 5) and is sometimes correctly called Einstein addition. But the formula omits Thomas rotation and so people, naturally believing in the Einstein result, make a mistake.JFB80 (talk) 19:34, 17 March 2022 (UTC)
thread_title:  Speed of light in fluid, not in aether  

message: As a quick reference, readers need a definition of u' right below the velocity addition formula. The formula is good, but hunting around for u' did not give me an unambiguous definition. Right below the equation, add "where u' is the relative velocity of the systems."97.73.100.22 (talk) 21:53, 31 August 2023 (UTC)
thread_title:  Quick lookup for velocity addition formula 

message: This section starts with the sentence "It was observed by Galileo that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward". As a native English speaker (and incidentally a physicist), this sentence is either broken or written in a way that suggests prior context about a heavy body, why it might falling, etc. It should be edited accordingly, although I will refrain since I am not sure if the original author had other intentions.  — Preceding unsigned comment added by Mrkinzie (talk • contribs) 13:37, 27 January 2024 (UTC)
thread_title:  Broken English or otherwise unmotivated phrasing in Galilean relativity section