Does spacetime have a “preferred” speed/metric? [duplicate]

I read recently that spacetime has a preferred speed, c, and that all observers would agree on the speed of anything moving at c. In particular, there is nothing unique about light when talking about relativity, light just happens to move at c.

1) Is this correct?

2) If so, how do we know this? I have a better than average math background and I would be interested to see how this is derived.

EDIT:

I am not asking about special relativity per se, or relativistic effects. I am quite down with the concept and mathematics of time dilation, length contraction and such. I am specifically asking about whether there is some feature of spacetime that makes c "special," what this feature is, and how we know this feature exists and/or model it mathematically.

• Consider changing the title of this question to more accurately reflect your question about observers agreeing upon the speed of light. – Nick Chapman Jan 22 '15 at 5:01
• I might have done that at roughly the same time as you posted. Are you referring to the current title: Does spacetime have a "preferred" speed/metric?" – Schemer Jan 22 '15 at 5:02
• See: arxiv.org/abs/0710.3398 . There are different possible geometries for homogeneous spacetime, and the Galilean/Newtonian one is only one of them. Which one the universe has must be determined by experiment! – user12029 Jan 22 '15 at 5:10
• And I am not asking about observers agreeing on the speed of light. I am asking about if and why that particular speed is "special" in spacetime irrespective of its obvious relationship to light. – Schemer Jan 22 '15 at 5:10
• You might also be interested to read the answers to Special Relativity Second Postulate – John Rennie Jan 22 '15 at 6:21

From my understanding, the speed of light is an assumption that it is a constant. All the other relativistic effects are derived from this assumption and the space-time geometry theory. See, for example, Relativity: The Special and General Theory.

All observers will agree that something is moving at $c$ when it is moving at $c$. However, all of the observers in their different frames will view the events that are necessary to make the measurement of light's speed ($c$) at completely different times. If you and I are moving in opposite directions at $c/4$ and a photon is shot between us, we will disagree on the time that the photon passed each of us respectively.

The reason we will both be able to observe the photon moving at the speed of light is because we will experience some kind of time dilation and/or length contraction that allows this to happen.

If you are really interested in this you'll want to look up Lorentzian geometry and the gamma stretch factor. Also you can find most of a book by Taylor and Wheeler online which is a pretty solid introduction to relativity and it's written in an easily digestible format.

I am specifically asking about whether there is some feature of spacetime that makes c "special"

C is a characteristic of spacetime, it is a "speed limit" which is due to vacuum permeability and vacuum permittivity. It is unexplained yet how it is possible that spacetime is provided with these two "brakes", without any kind of ether.

• Downvoter - why? – Moonraker Jan 22 '15 at 9:02

The Poincaré-Einstein convention makes the one-way speed of light isotropic in all frames of reference. In the Lorentz theory, the one-way speed of light is principally only equal to the two-way speed in the aether frame, though not in other frames due to the motion of the observer through the aether. However, the difference between the one-way and two-way speeds of light can never be observed due to the action of the aether on the clocks and lengths.

Tere are so few people, who releases that the Lorentz’s approach is “experimentally indistinguishable” from the special relativity.

Is it useful?