Alternative Theory of relativity?

[ralph124c]

As I understand it (correct me if I’m wrong) , the whole special theory of relativity comes from the invariance of the velocity of light © . The fact that c is constant, and invariant to any coordinate transform gives rise to the fact that Time is not invariant. Hence all of the interesting effects at high velocities (slowdown of time, etc.)
If however, we assume that time is invariant, and that © can vary, can you come up with a completely equivilent theory?

[Exapno_Mapcase]

Your understanding is wrong. Let me correct it.

Space-time is a single absolute object, not two separate things. What special relatively comes down to, to quote Brian Greene:

the combined speed of any object’s motion though space and its motion through time is always precisely equal to the speed of light.

and

Its name notwithstanding, Einstein’s theory does not proclaim that everything is relative. Special relativity does claim that some things are relative: velocities are relative; distances across space are relative; durations of elapsed time are relative. But the theory actually introduces a grand, new, sweepingly absolute concept: absolute space-time.

Read The Fabric of the Cosmos to get all the background needed to slowly sneak up on this idea, which is not what most people’s understanding of Einstein is.

(It’s true that you can plug three dimensions of time and one of space into the equations and they come out the same, but I don’t think that’s what you’re asking.)

[Complex_Conjugate]

Well it’s not quite true that the speed of light is invaraint in special relaivity under any coordinate transformation, c is invariant in any inertial frame so any transformation which transforms from one inertial frame to another that is true (these trasformations make up the homogenous Lorentz group). This is baiscally the second postulae of special relativity.

Time is a frame-depednent quantity in the STR, so requiring it not to be frame dpenendt obviously requires the re-defining of time. However the proper time between two events, as experinced by an inertial observer co-incidental to those two events, is a Lorentz invariant; this is the invariant interval between two events.

I’m certain thta it would nbot be to diffcult to formulate special relativity in terms of he invariance of the interval.

[MikeS]

@ralph124c

As I understand it (correct me if I’m wrong) , the whole special theory of relativity comes from the invariance of the velocity of light (c) . The fact that c is constant, and invariant to any coordinate transform gives rise to the fact that Time is not invariant. Hence all of the interesting effects at high velocities (slowdown of time, etc.)
If however, we assume that time is invariant, and that (c) can vary, can you come up with a completely equivilent theory?

Well… yes and no. If you’re asking “can we construct a model of mechanics in which all observers measure the same time between two events, and c is different between observers”, then yes: such a theory is called “Galilean relativity”, and it’s an internally consistent theory. Moreover, if you take the speed of light to be infinite (or, in practical terms, much, much bigger than any velocity you’re going to be dealing with), then Einstein’s special relativity reduces to Galilean relativity.

However, if you’re asking “is Galilean relativity equivalent with Special Relativity in all cases”, then no: Galilean relativity doesn’t have “interesting effects” at any velocity. Since we experimentally observe interesting effects at velocities close to c, we conclude that Special Relativity better describes the real world.