Speed of light as a universal speed limit

Question

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.

Answer 1

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

Answer 2

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.

This discussion might answer your question!

Answer 3

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.

Answer 4

Einstein's STR explains the result of Michelson-Moorley experiment (and all other experiments, of course) as a property of space-time, where inertial systems are equivalent to each other (i.e. no privileged Absolute space and Absolute time exist) and connected by Lorentz transformation (LT). Till that time, physics (like Lorentz) interpreted LT as a property of used materials (e.g. Lotentz contraction of used brass, wave behaviour of used light, and thus independence of the speed of light on the speed of its source).

The impossibility of superluminal speed of an observer (or of anything else able to transfer an information) follows from the fact that two events A, B being causally connected so that form A follows B (and thus $t(A) < t(B)$ ) could be for a superluminally quick observer passed in the reverse order $t(A) > t(B)$. Then, the consequence would precede in time its cause.

Evidently, if such transfer of information is impossible (so called "irreal signal", e.g. the common point of both swards on guillotine or scissors), then its speed is unlimited.

Answer 5

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