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Why is the speed of light a constant?
Because we have defined our units so that it is constant.Why is the speed of light a constant?
That's a fair statement of the historical path to special relativity (except for the bit about Planck's constant, which is unrelated to both the historical path and the modern understanding). First came measurements of the speed of light, dating back to the 17th century; then Maxwell's laws predicting electromagnetic radiation that propagated at that speed regardless of the speed of the source or the detector; then the inspired guess that light had been that radiation all along; then experimental results confirming the the constant speed of light despite the conflict with Newtonian physics; and finally Einstein's 1905 paper based on the premise that we should take all this history at face value and that the speed of light is constant.Possible "electromagnetism" viewpoint is that it is constant because magnetic and electric constant is constant and going further down it is linked to fine structure constant and Planck constant.
https://en.wikipedia.org/wiki/Vacuum_permeability#Significance_in_electromagnetism
In addition to the points @Nugatory made, classical electromagnetism is an approximation to the quantum theory of electromagnetism, which describes all electromagnetic phenomena in terms of a massless field on spacetime. So it could be seen as simply a roundabout way of assuming the points I made.Possible "electromagnetism" viewpoint is that it is constant because magnetic and electric constant is constant and going further down it is linked to fine structure constant and Planck constant.
https://en.wikipedia.org/wiki/Vacuum_permeability#Significance_in_electromagnetism
Why is the speed of light a constant?
It seems like we get this question almost once a month.
we don't know WHY we live in a universe that works this way (finite invariant speed, fine structure constant has the value that it does) - it could obey other rules, but it doesn't.
Yes. Another internally consistent possibility is Galilean relativity, in which inertial frames are related by the Galilean transformations and there is no invariant speed.Has it been established that there is another possible set of rules?
That's a fair statement of the historical path to special relativity (except for the bit about Planck's constant, which is unrelated to both the historical path and the modern understanding). First came measurements of the speed of light, dating back to the 17th century; then Maxwell's laws predicting electromagnetic radiation that propagated at that speed regardless of the speed of the source or the detector; then the inspired guess that light had been that radiation all along; then experimental results confirming the the constant speed of light despite the conflict with Newtonian physics; and finally Einstein's 1905 paper based on the premise that we should take all this history at face value and that the speed of light is constant.
The modern understanding, however, goes the other direction. We start by defining the meter to be the distance that light travels in 1/299792458 seconds. The electrical and magnetic constants are then defined so that ##c=1/\sqrt{\mu_0\epsilon_0}## and with values that fall within the error bars of previous empirical measurements based on the old definition of the meter and second. With these definitions the speed of light in vacuum has to be constant - if I measure anything but 299792458 meters per second, I'll know that something is wrong with my clock or my meter stick or both.
That's the point of @Dale's post #4 above. @Ibix's post #6 is the justification for taking this approach. And @haushofer's #2 points out that we don't know WHY we live in a universe that works this way (finite invariant speed, fine structure constant has the value that it does) - it could obey other rules, but it doesn't.
The dimensionless constants are likely to be the meaningful ones. The others change value if you change units. And as long as you keep the dimensionless ones constant, changing the others is just a disguised way of changing units.It would be interesting to know which constant is "more fundamental". Meaning: Is speed of light based on fine structure constant or is it the other way? Or is there One Ring, ehm...One Constant to rule them all ? :)
I'd say the fine structure constant seems more fundamental since it is dimensionless. But if you worded your question as, "Which is more fundamental: the constancy of the speed of light for all inertial observers or the fine structure constant?" I think it'd be a more nuanced issue to explore. In that case I'd say both are just core pillars of the universe.It would be interesting to know which constant is "more fundamental". Meaning: Is speed of light based on fine structure constant or is it the other way? Or is there One Ring, ehm...One Constant to rule them all ? :)
It's worth noting that it's perfectly possible to construct a variant on electromagnetic theory in which the speed of light is not the same as the invariant speed. This corresponds to a quantum theory in which photons have mass, and behave like other massive particles - they can be stopped. There are testable consequences, and experiment puts an upper bound on the photon mass of something like 10^{-50}kg (from memory), which would mean that a harsh look would be enough to push them so close to the invariant speed in the looker's frame that we can't measure the difference. So we usually treat the mass as zero. But strictly speaking light speed is only the same as the invariant speed if photons are actually massless, not "eh, close enough".
- The principle of relativity: the laws of physics are the same in all frames of reference.
- Maxwell's equations are laws of physics.
- In any frame of reference Maxwell's equations imply radiation of speed c=1/√(μ_{0}ε_{0}).
- Therefore the speed of this radiation is the same regardless of the motion of the source or the observer.
Perhaps the right question should be why the vacuum looks the same no matter how fast you move through it.The speed of light is not a constant. The speed of light in vacuum is a constant. Since the vacuum is the same everywhere, why would you even expect it to change?