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> why make that leap to associate this 'c' with the phenomenon known as light? That's an excellent question! And there are two answers. 1. If you apply the
by lisper 3y ago
> why make that leap to associate this 'c' with the phenomenon known as light?
That's an excellent question! And there are two answers.
1. If you apply the principle of relativity to Maxwell's equations, that's the result you get. Maxwell's equations predict a wave phenomenon that propagates at a constant speed in a vacuum. If the laws of physics, including the laws of electromagnetism, are the same for all inertial observers, then the speed at which those waves propagate have to be the Lorentz-invariant speed.
2. Experiments bear out this prediction! :-)
Note that it did not have to be this way, but if it were not, then EM experiments would give different results for observers in different inertial frames, which would falsify the relativity assumption. The different results for EM experiments would allow you to identify a privileged inertial frame. For a long time, physicists thought this would turn out to be the case, that there was a medium, a "luminiferous aether", through which EM waves propagated, and this medium would define a privileged frame (at least for electromagnetism). It just turns out by experiment that this is wrong, at least in our universe.
- ricksunny 3y agoThat's all fine, but from the moment Maxwell's eq's are invoked, we enter an empirical framing, not a first principles one. (as Maxwell's results follow from observations of the behavior of charged phenomena, current, magnets, & electromagnets). The paper & video seek to postulate the existence of a universal speed limit from first principles. They do so, and without changing the framing from a first principles one to an empirical one, associate their notational 'c' with the observed (i.e. empirical) speed of light. I find this element of their rhetorical strategy at odds with their intentions.
- lisper 3y ago> That's all fine, but from the moment Maxwell's eq's are invoked, we enter an empirical framing, not a first principles one. Yes, of course. First principles only leads you to the conclusion that there is a reference speed. It tells you nothing about its actual value. In fact, first principles cannot rule out the possibility that the reference speed is infinite. They can only lead you to suspect that it might not be.
- ricksunny 3y agoYes, this one also strikes me as an accurate framing of the situation's epistemology, Ty for clarifying :)
- akalin 3y agoI think what's left unsaid in the paper is that if a Lorentz-invariant speed exists, then it is unique. (This is easy enough to show.) Therefore, once you show that the speed of light in a vacuum is Lorentz-invariant, then it has to be the unique Lorentz-invariant speed (i.e., the universal speed limit).
- ricksunny 3y agoYes, this strikes me as an accurate framing of the situation's epistemology.:)
- ajross 3y ago> Maxwell's results follow from observations of the behavior of charged phenomena, current, magnets, & electromagnets I mean, historically yes. But you can define the fields as purely postulates if you like. The theory actually requires very little input to derive.