# Why is the speed of light a constant?

• B
Why is the speed of light a constant?

haushofer
I think it's safe to say nobody knows.

Staff Emeritus
2021 Award
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?

• SlowThinker and Demystifier
Dale
Mentor
2021 Award
Why is the speed of light a constant?
Because we have defined our units so that it is constant.

I think what you really want to know is why doesn’t the fine structure constant change over time.

martinbn
Are you asking why there is a limiting speed, or are you asking why light has that speed?

• Avimanyu Ray and Ibix
Ibix
In a universe where the principle of relativity holds true there is an invariant speed. If that speed is infinite, you get Newtonian physics. If it's finite you get relativity. Experiment tells us our universe is the latter type. Light travels at that invariant speed because it's massless and that's what massless things do in such a universe.

I don't think there's much explanation beyond that. Obviously there are rigorous statements and derivations of what I've said, but they can all be boiled down to the principle of relativity, some experiments, and implications thereof.

• Sorcerer, Klystron and martinbn
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

Nugatory
Mentor
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
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.

• Sorcerer and pinball1970
Ibix
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.

ZapperZ
Staff Emeritus
Why is the speed of light a constant?

It seems like we get this question almost once a month.

Zz.

• Avimanyu Ray
Staff Emeritus
2021 Award
It seems like we get this question almost once a month.

And we also get it every 30 days!

• Avimanyu Ray and Sorcerer
Mister T
Gold Member
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.

Has it been established that there is another possible set of rules?

Nugatory
Mentor
Has it been established that there is another possible set of rules?
Yes. Another internally consistent possibility is Galilean relativity, in which inertial frames are related by the Galilean transformations and there is no invariant speed.
If we drop the requirement for three spatial dimensions, or various symmetries such as space and time translation invariance, then some wildly different sets of rules would become possible. But observations so far suggest that none of these are an accurate description of the universe we live in.

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.

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 ? :)

Ibix
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 ? :)
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.

Obviously nothing really changes if you decide to measure distances in feet instead of metres.

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.

1. The principle of relativity: the laws of physics are the same in all frames of reference.
2. Maxwell's equations are laws of physics.
3. In any frame of reference Maxwell's equations imply radiation of speed c=1/√(μ0ε0).
4. Therefore the speed of this radiation is the same regardless of the motion of the source or the observer.

Ibix
1. The principle of relativity: the laws of physics are the same in all frames of reference.
2. Maxwell's equations are laws of physics.
3. In any frame of reference Maxwell's equations imply radiation of speed c=1/√(μ0ε0).
4. Therefore the speed of this radiation is the same regardless of the motion of the source or the observer.
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 10-50kg (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".

So electromagnetic experiments can certainly determine whether laws of physics are Lorentz invariant or Galilean invariant. But the way you've invoked them (points 2 and 3) here seems to me to contain assumptions you should be wary of.

• Physics Footnotes
Demystifier
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