# Speed of light as a universal speed limit

It follows from special relativity that nothing can travel faster than light. Einstein believed this would have to hold so generally that he assumed the Einstein-Podolsky-Rosen paradox to indicate a contradiction in quantum physics. Nowadays we know we have to be a bit more specific, and maybe it would be safe to say that nothing that can carry information can travel faster than the speed of light.

If information can be transferred faster than light, it would be possible to change the past. If I understand correctly it is the contradictions arising from the hypothetical possibility to influence the past that lead to the assertion that nothing can travel faster than light.

My questions:

1. Is this indeed the reason why it is said to follow from special relativity that nothing can travel faster than the speed of light?
2. Aren't the contradictions associated to influencing the past more of a philosophical nature than of a purely logical (or at least physical) nature?

EDIT

I realize now that instantaneous transfer (action at a distance) is actually physically in contradiction with special relativity: what is instantaneous/simultaneous in one inertial frame is not in the other, so the laws of physics would not be the same. I suspect that for finite velocities faster than that of light there must be a similar argument, I would appreciate if anyone could elaborate on that.

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No it can be proven that no massive particle can be accelerated beyond than the speed of light using the theory of relativity. As speed increases, the inertia opposing a further increase in speed increases, such that as you approach c, you require more and more force to get faster. You will need infinite force to ever get to c. –  Mew May 18 '14 at 6:59
@Mew: I am well aware that no massive particle can be accelerated to the speed of light and that massless particles can only travel at the speed of light, but how could you conclude for example that the propagation of forces (like gravitation) cannot be instantaneous (action at a distance)? –  doetoe May 18 '14 at 7:32
I don't believe the propagation delay is an assumption in general relativity, but rather it falls out of the equations. –  Mew May 18 '14 at 7:40
@Mew: But you can postulate the existence of particles (tachyons) that are already faster than the speed of light and hence don't need to be accelerated. This is consistent with the Lorentz-transformations. However, it does indeed lead to the problem with the future being able to influence the past. It also has another problem of instability, in that it is possible to keep extracting energy out of those tachyonic particles. –  Raskolnikov May 18 '14 at 7:48
@Raskolnikov, correct. –  Mew May 18 '14 at 7:54

To answer your question, I must say the physics is more of a psychological nature when it comes to very fundamental problem such as this. The reason behind the postulate of ultimate speed in special relativity is because of causality. Even if there are propositions of tachyons being able to travel more than speed of light, it's important to understand that the tachyons can't transfer information faster than light. So it's better to frame the second postulate of special theory of relativity as this: it's impossible to transfer information faster than the speed of light.

If you want to send some information encoded in local tachyonic field, and say, you get successful in it, to send it with speed faster than light will require it to become non-local.

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While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. –  DavePhD May 18 '14 at 14:52
@DavePhD Thanks! I am new to this site and I did not know that. However I have edited the answer. Hope it helps. I've even changed the link. –  puru May 18 '14 at 15:35
Thanks puru! If I understand correctly you are saying "yes" to 1 (otherwise the past could be influence, i.e. the effect could precede the cause in certain inertial frames) and maybe "yes" to 2 as well, that the reason causality has to hold is more of a psychological than a physical nature? –  doetoe May 19 '14 at 8:34
Yeah @doetoe! The answer to both of your questions, according to me, is 'yes'! –  puru May 19 '14 at 10:44
The concept of "signal" or "information" is not rigorously defined, so the assertions in your answer, and most textbooks, are based on physical intuition, and not based solely on the laws of Special Relativity. Until you can define your terms, you cannot prove anything. –  joseph f. johnson Jun 1 '14 at 3:28

Bob Geroch of the U. of Chicago has posted a paper on this topic. I extract a little bit and give you a link to the rest.

"We shall argue here that, all this evidence notwithstanding, special relativity need not be construed as prohibiting superluminal signals. Relativity theory with such signals permitted, we shall argue, is as viable and physically acceptable as relativity theory without. We suggest that a universal limitation on signal speeds need not be taken as any fundamental principle of physics. Rather, the whole idea of such a limit has more to do with history and with the types of interactions to which we are commonly exposed. We emphasize that we are not suggesting here that some new theory be introduced to replace special relativity; nor, indeed, that any of the basic structural components of the theory of relativity be changed. What is to be changed is merely our perspective on relativity theory."

posted on arxiv arXiv:1005.1614v1 [gr-qc] link to abstract http://arxiv.org/abs/1005.1614v1

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Thanks for your reply. I'll have a look at the paper. –  doetoe May 29 '14 at 10:03

I recommend that you simply go through Einstein's original paper: "On the Electrodynamics of Moving Bodies". This will allow you to understand, what and how Einstein actually did. Read it carefully, word by word; and pay special attention to sentences like this:

"Let the initial point of one of the systems (k) have a constant velocity in the direction of the X-axis of the other which is stationary system K, the motion being also communicated to the rods and clocks in the system (k)."

"Let the time t be determined for each point of the stationary system (which are provided with clocks) by means of the clocks which are placed in the stationary system, with the help of light-signals as described in § 1."

"Let a ray of light be sent at time $\tau_0$ from the origin of the system k along the X-axis towards x' and let it be reflected from that place at time $\tau_1$ towards the origin of moving co-ordinates and let it arrive there at time $\tau_2$."

As you can see the Special Relativity Theory is about communicating and comparing (measured times, distances, etc.) with the use of light. Therefore, SR simply states the obvious thing: no information can travel faster than light (unless we find a faster medium). That's all there is to it.

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Thanks bright magus, but I have to disagree with you. Relativity is a theory of space and time in which light does not a priori play a special role (although historically it did indeed). –  doetoe May 29 '14 at 10:10
And how did you arrive at this conclusion? –  bright magus May 29 '14 at 10:18
The postulate on the invariance of the speed of light implies that under an admissible change of coordinates the light cone is preserved. From this it follows (a theorem by E.C. Zeeman) that admissible changes of coordinates are essentially just Lorentz transformations. Transformations that leave any other speed constant would preserve a different cone in 4-space, and the conclusions on time dilation, Lorentz contraction, causal order etc. hold in a world where the laws of physics don't change under these transformations, with the speed of light replaced by that other speed. –  doetoe May 29 '14 at 15:39
"The postulate on the invariance of the speed of light...". This is exactly what you call "a special role played a priori" by light. –  bright magus May 29 '14 at 16:11
Not by light, by the speed of light (which is the speed of many other things too). It could be called the speed of a massless particle, the Lorentz-invariant speed, the speed of gravity, etc. –  doetoe May 29 '14 at 16:15

In Quantum electrodynamics light must occupy the possibility of traveling both faster and slower than the speed of light, and these paths cancel out over larger distances. but these virtual photons probably cannot be used to transfer information. also in the relation of a electron and positron; one is just the other traveling the other direction in time so certainly the past can be influenced by the present.

from a relativistic standpoint; causality and chronology are not in general the same thing, chronology is a particular subset of causality. there is a set of points near your current spacetime location that are casually related but not chronological.

the speed of light is pretty much the determining factor for the decoherence time (chronology) for most systems, so it is a good way to set up a basis for all other movement. so it is mostly a convenience not a restriction on what can occur.

other neat thing: In Quantum teleportation while the information cannot travel faster than light, the object being teleported can, as long as all the information has reached the place the object is to be teleported

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