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Getting the Lorentz transformations without requiring an invariant speed (2015)
- fuzzieozzie 3y agoIn 1987 my physics professor presented this proof to our class -- I always wondered why this elegant derivation of the Lorentz transform was not more widely used in undergrad physics education.
- abdullahkhalids 3y agoAs a first introduction, its more instructive to develop physical theories from physical postulates (like speed of light is constant), rather than constraining possible theories using more abstract mathematical principles. Undergrads will not appreciate the latter, as much as they will the first. Especially, because in the third semester, where relativity is first introduced, most physics undergrads don't know any group theory.
- lanstin 3y agoI wonder if we taught Emmy Noether’s theorem in tenth grade if people would love physics more.
- LudwigNagasena 3y agoThe contradiction between Maxwell’s electrodynamics and Newtonian mechanics was the raison d'etre of the relativity foundations laid out by Lorentz, Poincaré and Einstein. And since those subjects are usually studied before the theory of relativity, I think it makes sense to piggyback on them and use the historical reasoning to build the intuition behind relativity.
- alok-g 3y agoA short personal story: While trying to understand special relativity from books, and failing to, I tried doing maths myself based on whatever I had understood till then. I ended up doing what this paper has mentioned. I was surprised. For the next twelve years, I was asking various physicists I knew about what was I doing wrong, however none could give me the time needed. I then saw basically the same proof appear on Wikipedia, so finally had the answer. Einstein's original paper on special relativity, while mentioning the two famous postulates, also later assumes linearity of the transformations (allowing non-linear takes it from special relativity to general relativity). However, the paper did not explicitly call it out as a postulate. Also, Einstein derived a particular equation in the paper from two paths and mentions that there's consistency. This was actually a missed opportunity -- He could have forced consistency as an input assumption, worked backwards, and would then have seen that invariant speed is not needed as an input assumption anymore. With this OP submission, I have now learnt that this has been known for more than a century now, and agree that this should be more popular in books.
- Q-Q 3y agoI find it not believable that - You derived the theory correctly (end result should match textbook result) and thought what you were doing were wrong. - No physicist you asked could explain where you were wrong - No physicist you encountered could see the obvious connection of this and the usual approach It's not really a mysterious or novel fact that you can have these shift of perspectives (at least since Kant who heavily influenced Einstein) e.g. Newton took his three laws as the base, derived relativity as a theorem. Einstein took (modified version) relativity (together with the invariant speed assumption which comes from electromagnetism) as the base and rebuilt the rest of theory of motion that reduces to Newton's theory in the limit. Nothing is amiss here.
- phkahler 3y agoYou are probably on the right path IMHO. What wad that quote where Einstein said the mathematicians got hold of relativity, and turned it into something he didn't understand any more?
- Q-Q 3y agoDid you even read his post? what you are calling the "right" path is the "mathematician" path, assuming relativity + group structure. What he complained about, the Physics textbook approach was the path taken by Einstein who started from the "invariant speed" assumption to derive relativity: https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/origins_pathway/On-the_electrodynamics/index.html https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/... >"introduce another postulate... namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body." There's also nothing really "wrong" with Einstein's approach either, it's motivated by physical constraint from Maxwell's electromagnetism. Mathematician's approach is motivated by imposing logical constraint of an abstract mathematical structure (group of transformations from one coordinate system to another) The two turn out to be connected (physical constraint selects a math model from alternatives). Nothing really strange.
- bobbylarrybobby 3y ago“Since the mathematicians have invaded the theory of relativity I do not understand it myself any more.” https://www.goodreads.com/quotes/78897-since-the-mathematicians-have-invaded-the-theory-of-relativity-i https://www.goodreads.com/quotes/78897-since-the-mathematici...
- alexmolas 3y agoIt's curious that this simple proof -which don't require invariant speed, aka Maxwell equations- was discovered after Einstein's proposal which depends on invariant speed assumption. I wonder how the history of physics would have been if someone proposed this before Einstein. The maths needed for this derivation are quite simple, so I guess Newton or some mathematician before Einstein could have proposed special relativity.
- westurner 3y ago(nonlinear) retrocausality: https://news.ycombinator.com/item?id=38047149 https://news.ycombinator.com/item?id=38047149 https://news.ycombinator.com/item?id=28402527 https://news.ycombinator.com/item?id=28402527 : /? electrodynamic engineering in the time domain, not in the 3-space EM energy density domain https://www.google.com/search?q=electrodynamic+engineering+in+the+time+domain%2C+not+in+the+3-space+EM+energy+density+domain https://www.google.com/search?q=electrodynamic+engineering+i... "Electromagnetic forces in the time domain" (2022) https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-18-32215&id=493220 https://opg.optica.org/oe/fulltext.cfm?uri=oe-30-18-32215&id... : > [...] On looking through the literature, we notice that several previous studies undertook the analysis of the optical force in the time domain, but at a certain point always shifted their focus to the time average force [67–69] or, alternatively, use numerical approaches to find the force in the time domain [44,70–75]. To the best of our knowledge, only a few publications conducted analytical studies of the optical force evolution. Very recent paper employs the signal theory to derive the imaginary part of the Maxwell stress tensor, which is responsible for the oscillating optical force and torque [76]. The optical force is studied under two-wave excitation acting on a half-space [40] and on cylinders [77], and a systematic analytical study of the time evolution of the optical force has not yet been reported.
- westurner 3y agoIf mass warps space and time nonlinearly per relevant confirmations of General Relativity, and there is observable retrocausality and also indefinite causal order, is forcing time to be the frame of reference, and to be the constant frame of reference necessary or helpful for the OT problem and otherwise?
- Hydraulix989 3y agoWhy doesn't the requirement of a privileged reference frame imply the requirement of an invariant speed?
- lisper 3y agoYou have it backwards. The assumption is that there is no privileged reference frame. And that assumption (along with a few others) does imply an invariant speed. That's the whole point here.
- wangii 3y agoLet's assume there exists one or more privileged ref system(s), and deal the two cases one by one. If there was one privileged reference system, and in our deduction process it's not involved,then the original deduction still holds. therefore the special ref system is an redudunt assumption. If there were many such ref systems, we would have to carefully get them involved in any possible deduction process, which is impossible. QED
- lisper 3y agoA nice video that explains the paper: https://www.youtube.com/watch?v=UHKZMGdj7cI https://www.youtube.com/watch?v=UHKZMGdj7cI
- ricksunny 3y agoBoth the paper and the video (both of which i've skimmed but not gone through the math substantially) make a case for a maximum speed, notated as 'c'. Let me assume they make a very good mathematic case, and there is a maximum speed that satisfies the fundamental assumptions provided. Both the paper and the video then finish off by ontologically tying this maximum speed, notation 'c', to the interesting physical E&M phenomenon we happen to call 'light'. My question - in this framework where we are deconstructing everything (which I applaud), then why make that leap to associate this 'c' with the phenomenon known as light? Inference, sure why not until any future evidence suggests otherwise, but why do so in the intentionally limited scope of the paper & video's derivations?
- lisper 3y ago> why make that leap to associate this 'c' with the phenomenon known as light? That's an excellent question! And there are two answers. 1. If you apply the principle of relativity to Maxwell's equations, that's the result you get. Maxwell's equations predict a wave phenomenon that propagates at a constant speed in a vacuum. If the laws of physics, including the laws of electromagnetism, are the same for all inertial observers, then the speed at which those waves propagate have to be the Lorentz-invariant speed. 2. Experiments bear out this prediction! :-) Note that it did not have to be this way, but if it were not, then EM experiments would give different results for observers in different inertial frames, which would falsify the relativity assumption. The different results for EM experiments would allow you to identify a privileged inertial frame. For a long time, physicists thought this would turn out to be the case, that there was a medium, a "luminiferous aether", through which EM waves propagated, and this medium would define a privileged frame (at least for electromagnetism). It just turns out by experiment that this is wrong, at least in our universe.
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- whatshisface 3y ago"Ignatowsky showed that the only admissible transforma- tions consistent with the principle of inertia, the isotropy of space, the absence of preferred inertial frames, and a group structure (i.e., closure under composition), are the Lorentz transformations, in which c can be any veloc- ity scale, or the Galilei transformations" The interpretation of their result is totally wrong although the result is correct, because excluding Newtons' relativity (the Galilean group) is why electromagnetism or c is necessary.
- ummonk 3y agoExactly. The paper is great for constraining the possibilities, but you still need to show empirically that there is an invariant speed of light and we live in a Minkowskian not a Newtonian world.
- jkafjanvnfaf 3y agoThe mathematics are sound, but the reasoning around is unclear to me. The derivation shows that Lorentz transformations and Galilean transformations are the only ones that allow for the equivalence of all inertial frames, which is a nice result. But it clearly does require the additional assumption of an invariant speed to conclude that Lorentz transformations are anything more than a mathematical curiosity. So what have we really gained? Since we still need the extra assumption that an invariant speed actually exists, we could've just gone the other way and done the light clock calculation to get the Lorentz transformation instead.
- pdonis 3y ago> what have we really gained? I agree that the paper's title is somewhat misleading, since you still do need to assume an invariant speed to rule out the Galilean transformations. However, this derivation does greatly narrow things down before the invariant speed comes in: at the point where the invariant speed is assumed, you already know that there are only two alternatives: an invariant speed (Lorentz transformations) or Galilean transformations. So it's much easier to see why you would assume an invariant speed; the assumption isn't just pulled out of thin air at the start, it is seen to be one of only two alternatives that are compatible with the principle of relativity.
- Q-Q 3y ago>to see why you would assume an invariant speed, the assumption isn't just pulled out of thin air at the start It's not out of thin air, it's from a very empirically successful theory: Maxwell's electrodynamics. The problem back then was that this theory was not relativistic, i.e. the speed of electromagnetic wave in Maxwell's equations was the same under all reference frames. So you either abandon the idea that laws of physics remaining the same under all reference frames, OR abandon Galilean velocity addition. Einstein's approach was modifying the latter so that it fits with the former, by imposing invariant speed. This was written in Einstein's original paper. It's not a mystery assumption. It's also a very common procedure: two empirically successful theories have conflict and you need to resolve them by building something larger than both and reducing to both under limit. I also agree we have gained insight into how kinematic structure is derived from algebra + physical constraint. Though you still need the physical insight to choose which physical constraint.
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- ummonk 3y agoWhat the paper claims it is saying: you can get the Lorentz transformations without requiring an invariant speed. What the paper is actually saying: assuming there isn’t a privileged reference frame, you can show that either the Galilean transformations hold (i.e. simultaneity is invariant, suggesting instantaneous propagation of forces, a special case of Lorentz transformations where c is infinity) or Lorentz transformations hold (i.e. a single invariant speed in all reference frames, suggesting propagation of forces at that speed). Empirically, we know from measuring the speed of light that we live in the latter world. But we can’t prove that a priori as the title suggests.
- alok-g 3y agoThere's indeed a subtlety here. The paper's abstract says: >> "... though the finite value of this speed must, of course, be obtained from experiment" It should state, "the value of this speed..." (removed 'finite'). That the speed is finite does not come from the proof but from measurement.
- snicker7 3y agoWhat’s interesting about this paper is that, with some very generic mathematical assumptions, only Galilean and special relativity are permissible.
- alexmolas 3y agoFun that the paper uses a lot the argument "this is clearly unphysical" while for anyone before Einstein it was clearly unphysical to consider solutions that yield to Lorentz transformations
- cvoss 3y agoYeah, I was disappointed that the paper claims to use only so many premises up front, and then proceeds to smuggle in a few extra ones under the "clearly unphysical" line. I'd like to see a full and rigorous treatment of exactly what are the axioms which produce Lorentz transformations and no alternatives.
- danbmil99 3y agoThe fact that special relativity is completely consistent with an underlying preferred absolute reference frame that simply is not accessible to experiment (unless things break down at the plank scale) seems obvious to me but I've had a lot of grief talking to people who supposedly knew more than me. There's a YouTube channel called dialect that has a few videos on this subject
- tome 3y agoYes > The 19th century Lorentzian ether theory was ruled out by the famous Michelson-Morley experiment, which ruled out the possibility that the Earth moves through the ether. What we propose here is that the Earth (and everything else) is made of ether. No experiment so far ruled out that possibility, so such a neo-Lorentzian ether theory is a viable possibility https://arxiv.org/pdf/1811.11643.pdf https://arxiv.org/pdf/1811.11643.pdf
- clausecker 3y agoThat's in fact the viewpoint Lorentz took when he discovered the Lorentz transform and relativity. He showed that you can make an ether (i.e. a preferred reference frame) consistent with the observations by applying Lorentz transforms to the observations of anybody who is in a different reference frame.