# Why is the speed of light a constant?

• B
• Sjm_dynamo
In summary, the speed of light is a constant because we have defined our units so that it is constant. This is due to the principle of relativity and experimental evidence that our universe follows the latter type of relativity. Additionally, classical electromagnetism and quantum theory both support this idea. While there are other possible sets of rules, they do not accurately describe our observed universe.
Sjm_dynamo
Why is the speed of light a constant?

I think it's safe to say nobody knows.

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
Sjm_dynamo said:
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.

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

Avimanyu Ray and 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

Prometeus said:
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
Prometeus said:
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.

Sjm_dynamo said:
Why is the speed of light a constant?

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

Zz.

Avimanyu Ray
ZapperZ said:
It seems like we get this question almost once a month.

And we also get it every 30 days!

Avimanyu Ray and Sorcerer
Nugatory said:
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?

Mister T said:
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.

Nugatory said:
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 ? :)

Prometeus said:
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.

Prometeus said:
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.

f todd baker said:
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
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?
Perhaps the right question should be why the vacuum looks the same no matter how fast you move through it.

SlowThinker and Nugatory

## 1. Why is the speed of light considered a constant?

The speed of light, denoted by the symbol c, is considered a constant because it does not change in a vacuum regardless of the observer's frame of reference. This means that no matter how fast an observer is moving, the speed of light remains the same. This has been observed and confirmed through numerous experiments and is a fundamental principle in physics known as the principle of relativity.

## 2. What is the significance of the speed of light being a constant?

The constancy of the speed of light is significant because it is a fundamental constant in the universe and has a profound impact on our understanding of space, time, and the laws of physics. It is used in many equations and theories, including Einstein's theory of relativity, and plays a crucial role in our understanding of the universe.

## 3. How was the speed of light first measured?

The first successful measurement of the speed of light was conducted by Danish astronomer Ole Rømer in the late 17th century. He observed the moons of Jupiter and noticed that the time between eclipses of these moons changed depending on the position of Earth in its orbit around the sun. By carefully measuring this time difference, he calculated the speed of light to be approximately 220,000 kilometers per second.

## 4. Can the speed of light ever be exceeded?

According to the current understanding of physics, the speed of light is the ultimate speed limit in the universe. This means that it cannot be exceeded by any object with mass. However, some theories suggest that particles without mass, such as photons, can travel at the speed of light. Additionally, the expansion of the universe can cause objects to appear to be moving faster than the speed of light, but this is due to the space between objects expanding, rather than the objects themselves moving faster.

## 5. Why is the speed of light in a vacuum different from the speed of light in other mediums?

The speed of light in a vacuum is the maximum speed at which electromagnetic waves can travel. In other mediums, such as air, water, or glass, the speed of light is slower due to interactions between the light and the particles in the medium. This is known as the refractive index and is a result of the medium's ability to slow down the speed of light as it passes through. However, in a vacuum, there are no particles to interact with, allowing light to travel at its maximum speed.

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