Why is the measure and finititude of c critical?

[thack45]

Why is the measure and "finititude" of c critical?

Why is it that c plays such a huge role in SR? Is it the actual relative measured speed of c, or is it that it's finite or both?
I know that this may seem mirky. I "get" time dialation, length contraction, dopppler shift...
What is the significance of c?

 

[bcrowell]

Hi, thack45 -- welcome to Physics Forums!

FAQ: Is the c in relativity the speed of light?

Not really. The modern way of looking at this is that c is the maximum speed of cause and effect. Einstein originally worked out special relativity from a set of postulates that assumed a constant speed of light, but from a modern point of view that isn't the most logical foundation, because light is just one particular classical field -- it just happened to be the only classical field theory that was known at the time. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see, e.g., Morin or Rindler.

One way of seeing that it's not fundamentally right to think of relativity's c as the speed of light is that we don't even know for sure that light travels at c. We used to think that neutrinos traveled at c, but then we found out that they had nonvanishing rest masses, so they must travel at less than c. The same could happen with the photon; see Lakes (1998).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[RexxXII]

The significance is that even though c is finite, light will always be measured to travel at c regardless of your velocity, or inertial reference frame (IRF). A physical property that remains constant in all IRFs is a pretty big deal in a theory concerning the physics of different IRFs.

 

[bcrowell]

The significance is that even though c is finite, light will always be measured to travel at c regardless of your velocity, or inertial reference frame (IRF). A physical property that remains constant in all IRFs is a pretty big deal in a theory concerning the physics of different IRFs.

Note that these are two completely separate points: (a) the speed of light is frame-invariant, and (b) there is a frame-invariant speed c. If we find out tomorrow that the photon has a nonvanishing rest mass, then b still holds, even though a will have turned out not to be true. I would have rephrased this more like this:

The significance is that even though c is finite, the maximum speed of cause and effect will always be c regardless of your velocity, or inertial reference frame (IRF). A physical property that remains constant in all IRFs is a pretty big deal in a theory concerning the physics of different IRFs.

 

[Fredrik]

If the invariant speed is infinite, the group of functions that represent a change of coordinates from one inertial frame to another, is the Galilei group, not the Poincaré group. And since a Galilei transformation maps "space, at time t" to itself, there's no relativity of simultaneity.

Note that the relativity of simultaneity is the reason why there is such a thing as length contraction in SR. It ensures that different observers who measure the length of an object are actually measuring the same coordinate independent property of two different curves in spacetime.

 

[yuiop]

Why is it that c plays such a huge role in SR? Is it the actual relative measured speed of c, or is it that it's finite or both?
I know that this may seem mirky. I "get" time dialation, length contraction, dopppler shift...
What is the significance of c?

It is just a number that scales time units to distance units. If time had been defined in terms of seconds and distance in time of light-seconds, then c would disappear from all the equations and we would asking why the number 1 plays such a huge role in SR.