Why doesn't light travel infinitely fast ?

[Simon Bridge]

And I was expecting some reference to "effective rest mass" in a superconductor, or the experimental limits on the photon mass.

I notice that "pounds" is not a unit of pressure here ... in the context of radiation pressure is not even a unit of mass, but iirc of force. Maybe that is the source of the misunderstanding.

1lb of force being the amount of force needed to accelerate 1 pound by 1 foot per second every second? Or is it to accelerate one pound at one gravity? <checks> Ah - it's the gravity one.

Should be written "lbF", shouldn't it, but people often leave the F off.

 

[tms]

One of the things about this recurring question about the speed of light is that the person asking does not usually distinguish between the speed of electromagnetic waves in a vacuum and the limiting speed in relativity - which are the same. Very often the question can be interpreted as "why is it that the speed of EM waves happens to be the relativistic limiting speed?"

Start with $\epsilon_0$ and $\mu_0$, particularly the fact that they have the same values for everybody, regardless of how one is moving with respect to anything else. Because their values are universal, the speed of light is also universal. But to get observers moving relative to each other to measure the same speed for the same bit of light, you have to fiddle with lengths and times in different frames. That fiddling necessarily involves the speed of light, because that is what the fiddling is trying to get right. But the same fiddling has to apply to everything, not just light, because it would be ludicrous for lengths to be contracted when dealing with light but not when dealing everything else; how would the meter stick know to contract when measuring a wavelength, but not when measuring a football field? Since the length and time fiddling apply to everything, and since they imply the impossibility of a massive object reaching the speed of light, the speed of light limits everything.

I realize I am speaking a bit glibly, but I think this chain of reasoning makes sense, modulo the glibness.

 

[Simon Bridge]

It's fun isn't it.
What you end up with is an invariant speed in the equations that describe space-time geometry.

But the fool in his heart may still reason (hopefully in his head) that photons may not travel exactly at the invariant speed and, therefore, may have a very small mass. It may be the invariant speed is actually slightly larger than the observed speed for photons since, as you say, originally the invariant speed was postulated to be the photon speed and all the math worked out on that postulate.

Different observers would, indeed, measure a slightly different speed for light if only their equipment were sensitive enough, and relativity would still work. [*]

This would limit the mass of a photon to be certainly below 10^-14eV/c² (depending on the experiment).

The question in post #1 is certainly phrased in terms of the speed of photons - so maybe it can be answered by pointing out that no particle can be accelerated past the invariant speed of the universe, massive or massless, and so, since the slightest force would accelerate it to that speed, we should not be surprised to see all massless particles move at exactly the invariant speed. The name "the speed of light in a vacuum" is an historical accident.

Hmmm ... it's still glib isn't it?

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[*] though there is the curious problem of how come all light is in a very narrow range of speeds ... which, in a way, would be the question in post #1.