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Suppose I want to know what the universe looks like from the perspective of a frame of reference moving at $c$ relative to my current frame. As discussed at length in various other questions on this forum, from the perspective of the current established theory of special relativity, the notion of such a frame is more or less nonsense.$^{[1]}$

However...

Is it possible to modify the setting of special relativity, by adding dimensions to space-time, or any other hereto unobserved features, such that the restriction of the theory to our 4-D slice of space-time matches special relativity, and such that there is a meaningful way to describe the frame of a photon?

[1] In partiucular, the transformation we get by shoving $v=c$ into the usual formulae is not in the Lorentz group (it doesn't preserve volume of space-time and is not invertible).

Qmechanic
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DanielSank
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  • If photon is moving at c relative to you, then you are moving at c relative to photon. Quite a normal-looking perspective, isn't it? Also, there can be a lot of objects found to move at nearly c relative to us, I.e. distant galaxies. Would the extra couple of km/s make a real difference? Unlikely. – bright magus Jul 06 '14 at 06:16
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    You can modify any important theory you want but if you modify a theory that is correct and essential, like relativity, you get a wrong and worthless theory. Why do you want to "modify" it? It's exactly like asking whether one may modify Darwin's theory so that animals never try to eat each other or compete with each other. Yes, you can "modify" it but the modification is wrong. The equations of relativity make clear conclusions about the value $v=c$ as well - and especially about it - and you can't cherry-pick or modify selective conclusions without destroying the whole structure. – Luboš Motl Jul 06 '14 at 06:33
  • @LubošMotl: SR is far from flawless. Let's take simple time dilatation and length/distance contraction. They mean that time and distance are in inverse proportions. And yet c=x/t and c=x'/t', which gives us x/t=x'/t' show they should change in direct proportions. Tables by the 4th and 5th pictures here: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html show SR does not influence x directly. On the other hand, it is possible to construct simple thought experiment showing time dilatation cannot be real. (And solving the twin paradox through acceleration is an obvious trick.) – bright magus Jul 06 '14 at 07:24
  • See my answer to this question about the non-existence of the $v=c$ frame. – Kyle Kanos Jul 06 '14 at 14:25
  • @LubošMotl: your statement "if you modify a theory that is correct and essential, like relativity, you get a wrong and worthless theory." is false. Suppose I have quantum mechanics but no notion of a density matrix. The theory is correct, but missing an important feature. When I add in the density matrix I do not spoil the rest of the theory, but I can now explain decoherence. This is a demonstration of modifying a correct theory to further explain natural phenomena. – DanielSank Jul 06 '14 at 15:15
  • @LubošMotl: "and you can't cherry-pick or modify selective conclusions without destroying the whole structure." If you would actually explain that statement in a scientific way I would consider that an answer to my question :) – DanielSank Jul 06 '14 at 15:16
  • Density matrix isn't a modification of quantum mechanics. It's just a way to describe incomplete knowledge about the state vector, a straightforward combination of quantum mechanics of pure vectors and the usual classical ways to consider probabilistic weighted averages (without any information about the relative phase). Quantum mechanics cannot be modified by an epsilon without ruining it completely, and it is really the best example of the important principle I was trying to convey. – Luboš Motl Jul 07 '14 at 15:04

1 Answers1

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No, and the reason is quite simple.

The proper time of a photon is zero (according to the principles of special relativity). That means that there is no time difference between the place of emission and absorption. By this, any hypothetical observation of a photon would be reduced to a time period of zero, and it would not be able to distinguish/ to measure time, and thus it cannot serve as a frame of reference.

By the way, the same principle applies also to distances, the proper distance of photons being zero. A rule yielding always the same measure is no rule.

A photon (from its "hypothetical point of view") is not participating in spacetime (except its places of emission and absorption), spacetime is reduced to one point, and thus it cannot be a frame within spacetime.

Moonraker
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  • "That means that there is no time difference between the place of emission and absorption". That would mean an infinite speed. – bright magus Jul 06 '14 at 07:42
  • @bright magus: No, because distance is zero as well. Zero distance in zero time, that means that there is no kind of velocity at all. – Moonraker Jul 06 '14 at 07:45
  • How have you arrived at this conclusion (that everything is one and the same thing for photon - emitter being absorber, etc.)? Actually, the universe would be one big black hole for a photon in such case ... – bright magus Jul 06 '14 at 07:49
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    No. The photon is not a reference frame. – Moonraker Jul 06 '14 at 08:29
  • Classical circular reasoning. And great dodging of contradictions. – bright magus Jul 06 '14 at 08:37
  • I don't agree with your point of view which is not quite clear. See the comment of Lubos Motl: "The equations of relativity make clear conclusions about the value v=c". I agree with this statement. – Moonraker Jul 06 '14 at 09:08
  • OK, let's put my point of view clearer. You gave an answer, but in our conversation your entire reasoning boiled down to: The photon is not a reference frame. Fullstop. Not an explanation to my standards. (And I did see Lubos Motl comment - I even made my own in reply.) – bright magus Jul 06 '14 at 09:14
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    This answer explains why there isn't a frame co-moving with a photon in the standard theory of SR. As explicitly indicated in my question, I already understand this. I would like to know if there can be an extended theory which recovers SR on our space-time but includes frames co-moving with the photon, perhaps in other dimensions or whatever. – DanielSank Jul 06 '14 at 15:22
  • @DanielSank "frames co-moving with the photon" The problem is that it seems there is no movement at all from the "hypothetical point of view" of the photon (proper time=0, proper distance=0). The result is what we all know: It does not make any sense to talk about the frame of a photon. Thus even in an extended sense I think that there is no room for your research of a theory. – Moonraker Jul 06 '14 at 15:29
  • @Moonraker: I'm not looking for a research project, just curious :) Anyway, certainly there I can imagine a world line in a higher dimensional space which, when projected (or something like that) into a subspace, takes on the pathological properties of a world-line Lorentz boosted at c. If this sort of thing is not possible, an explanation of why would be a great answer to my question :) – DanielSank Jul 06 '14 at 15:40
  • @DanielSank: It is even not sure if there is any worldline, with proper time=0, proper distance=0, I would rather talk of a direct transmission of the momentum from the emitting particle to the absorbing particle, without any intermediate worldline (from the "hypothetical point of view" of the photon). Without movement, I really don't see any means for "co-moving". – Moonraker Jul 06 '14 at 15:49