B Could There Be a Cosmic Speed Limit Higher Than the Speed of Light?

[geordief]

TL;DR Summary

The universal speed limit and the speed of light

I think when the speed of light was measured (and predicted from Maxwell's equations) that the assumption was made that this speed was a cosmic speed limit

Suppose that the cosmic speed limit was higher than c (not infinite) and that perhaps another form of radiation traveled at that speed but we were unaware of it

If that was a possibility (let us call this speed f) would the existing equations in Relativity such as the Lorentz transformations(or perhaps other basic equations) have some form of counterpart in equations that involved this f quantity?

 

[jbriggs444]

If that was a possibility (let us call this speed f) would the existing equations in Relativity such as the Lorentz transformations(or perhaps other basic equations) have some form of counterpart in equations that involved this f quantity?

If the universal speed limit were something greater than the speed of light, that would mean that photons have mass. But experiment places an extremely low limit on the photon mass.

A quick trip to Google says < $10^{-18}$ electron volts.

 

[Dale]

Summary:: The universal speed limit and the speed of light

I think when the speed of light was measured (and predicted from Maxwell's equations) that the assumption was made that this speed was a cosmic speed limit

Suppose that the cosmic speed limit was higher than c (not infinite) and that perhaps another form of radiation traveled at that speed but we were unaware of it

If that was a possibility (let us call this speed f) would the existing equations in Relativity such as the Lorentz transformations(or perhaps other basic equations) have some form of counterpart in equations that involved this f quantity?

There cannot be two invariant speeds. There is only one invariant speed and it is c.

 

[geordief]

There cannot be two invariant speeds. There is only one invariant speed and it is c.

So it is because c is invariant that there cannot be a higher speed?

Would any hypothetical cosmic speed limit have to also be invariant?

 

[Dale]

So it is because c is invariant that there cannot be a higher speed?

Would any hypothetical cosmic speed limit have to also be invariant?

The invariant speed and the cosmic speed limit are not two separate concepts, they are two descriptions of the same concept.

 

[Ibix]

There are at least two ways to interpret this. One is to do as @jbriggs444 has done and let the invariant speed remain $c$ and give the photon a small non-zero mass. Light wouldn't have a defined speed any more and photons could, in principle, be stopped. The physics of this is well understood (look up Proca potentials) and not terribly exciting. Since the maximum possible mass for the photon is so tiny only really sensitive experiments could detect any consequences.

The other option is to do as @Dale did, and leave physics as it is and bolt on your new higher invariant speed. That gives you two invariant speeds, and you can't have that. Certainly not without completely jettisoning the principle of relativity. And at that point you're off in the weeds - I don't know a way to reconcile that with what we know of physics.

Would any hypothetical cosmic speed limit have to also be invariant?

If it's not invariant, consider two things traveling in opposite directions at this speed limit. Now start moving parallel to one of those things and, since the speed isn't invariant, relative to you the two things are now moving at different speeds, one slower and one faster than the "speed limit". Your only recourse is to define an absolute rest frame and define the maximum speed in that frame, but in doing so you've denied the principle of relativity and hence have no reason to expect any of physics since Galileo to work. So you've got to rewrite everything ever in order to reconcile this. I won't say it's impossible to do that, but it's really not plausible that it could be done.

 

[PeterDonis]

I think when the speed of light was measured (and predicted from Maxwell's equations) that the assumption was made that this speed was a cosmic speed limit

First, the finite speed of light was first measured at least a century (IIRC) before Maxwell's Equations were even discovered.

Second, while Maxwell's Equations did predict a finite speed of light, they did not say anything about whether that speed was a cosmic speed limit. The first physical theory to claim that was Special Relativity.

 

[vanhees71]

There cannot be two invariant speeds. There is only one invariant speed and it is c.

I'd say, today, that we know that relativistic spacetime descriptions are very accurate, the "natural constant" $c$ is defined as the limiting speed of relativistic spacetime models. In "natural units" it's just 1, in the SI it defines the meter as the unit of lengths given the definition of the second as the unit of times. In this sense $c$ is a much more fundamental constant than just the propagation speed of electromagnetic waves.

Whether or not electromagnetic waves propagate with this limiting speed, is a question to be decided by observations, and as quoted above the upper limit of the "photon mass" is $10^{-18} \;\text{eV}$.

From a theoretical point of view, there's nothing in the Standard Model that would prevent that the electromagnetic field has a non-zero mass. For Abelian gauge fields you don't even need a Higgs mechanism to make it massive without breaking the underlying Abelian gauge invariance!