# Why is the speed of light absolute?

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vanhees71
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PeroK said:

"Moreover, it can be shown that anything massless must travel at this invariant speed c."

Could you provide a reference that shows this?
That's the definition of a massless particle. For the four-momentum you have ##p_{\mu} p^{\mu}=m^2 c^2##. The speed is ##v=\beta c## with
$$\beta=\frac{|\vec{p}|}{p^0}=\frac{|\vec{p}|}{\sqrt{m^2c^2 +\vec{p}^2}}.$$
For ##m=0## you get ##\beta=1##, i.e., ##v=c##.

Note that in the real world there's no massless point-like object. In a very delicate sense you can consider "light beams" as trajectories of fictitious massless particles, but as I said that's a very delicate issue, and one should not (!!!) call these massless particles "photons" since photons are not describable at all in the sense of classical point particles, but that's another story.

sysprog, Dale and weirdoguy
Dale you said:

"In general, science can only answer 'why' questions by appeal to theory, and in the case of 'why' questions about assumptions of theories only by appeal to a more fundamental theory."

I can't say how I agree with you. You have formulated it beautifully.

Dale
Einstein himself wrote on the reasons he expected it to be absolute.

The short version is that, if it is not absolute, then a moving configuration should behave slightly differently than a stationary configuration - for instance, if I was looking at a mirror orthogonal to the direction of motion, my view would be skewed in the direction of motion. (Think about the path of light.)

Einstein expressed this idea in terms of the laws of physics, noting that if the speed of light weren't absolute, the laws of physics would have to depend on our motion relative to some notion of absolute rest, which was in conflict with Galilean relativity.

His choice of making the speed of light absolute was based on a prior version of relativity, basically, noting that a relative speed of light would violate that relativity.

I recommend reading Einstein himself, his writing is quite easy to follow, and he lays out his reasoning well.

ETA:
Basically, two very well-supported theories were in apparent conflict, and making the speed of light absolute resolved the conflict.

strangerep
More recently, it is known that homogeneity and isotropy of space and time allows for a invariable speed.
In fact, to derive an invariant speed, one needs only the relativity principle (physical equivalence of inertial frames), spatial isotropy, and a technical assumption that velocity boosts along a given direction form a 1-parameter Lie group.

dextercioby and vanhees71
In fact, to derive an invariant speed, one needs only the relativity principle (physical equivalence of inertial frames), spatial isotropy, and a technical assumption that velocity boosts along a given direction form a 1-parameter Lie group.

Do Galilean boost don't form a 1-parameter subgroup of the Galilei Group?

vanhees71
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2021 Award
In fact, to derive an invariant speed, one needs only the relativity principle (physical equivalence of inertial frames), spatial isotropy, and a technical assumption that velocity boosts along a given direction form a 1-parameter Lie group.
With these assumptions you get either Einstein-Minkowski (existance of an invariant speed) or Galilei-Newton (absence of an invariant speed) spacetime. The question, which one describes the observations of Nature better is an empirical one, and of course it's well established that Einstein-Minkowski is the way better (approximate) description of spacetime. Only the Einstein (GR) spacetime (or most probably its extension to a Einstein-Cartan spacetime, but that's for purely esthetical reason yet) is even better.

phinds
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2021 Award
Dale you said:

"In general, science can only answer 'why' questions by appeal to theory, and in the case of 'why' questions about assumptions of theories only by appeal to a more fundamental theory."

I can't say how I agree with you. You have formulated it beautifully.

@Ad VanderVen when quoting people please use the quote feature and not just text quotes. You can do that either by clicking on the Reply button to quote the entire post or by selecting the specific text you wish to quote and clicking on the Reply pop-up

strangerep
Do Galilean boost don't form a 1-parameter subgroup of the Galilei Group?

strangerep
With these assumptions you get either Einstein-Minkowski (existance of an invariant speed) or Galilei-Newton (absence of an invariant speed) spacetime. [...]
Heh, you forgot de Sitter.

Galilean relativity doesn't have an invariant speed and it has spatial isotropy and homogenity. Galilean boosts in one axis are also a 1-parameter Liegroup (don't they?). So I don't see how only using the postulates you mention you get an invariatn speed, since those postulates are also in the galilean relativity.

strangerep
Galilean relativity doesn't have an invariant speed and it has spatial isotropy and homogenity. Galilean boosts in one axis are also a 1-parameter Liegroup (don't they?). So I don't see how only using the postulates you mention you get an invariatn speed, since those postulates are also in the galilean relativity.
The "invariant speed" in Galilean relativity turns out to be ##\infty##.

In the more general derivation, one actually derives a constant with dimensions of inverse speed squared. SR corresponds to the choice of ##1/c^2## for this constant. Galilean relativity corresponds to the choice ##0##, which is equivalent to letting ##c\to\infty##.

That makes more sense.

vanhees71
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2021 Award
Heh, you forgot de Sitter.
It's an interesting question, why de Sitter doesn't also follow from these symmetry assumptions. I guess it's because it's not time-translation invariant.

I'm referring to the derivation of the Galilei and Lorentz transformation given here:

https://doi.org/10.1063/1.1665000

strangerep
It's an interesting question, why de Sitter doesn't also follow from these symmetry assumptions. I guess it's because it's not time-translation invariant.
It's because the homogeneity assumption adopted by Berzi+Gorini (and many others) insists that finite intervals are preserved under spatio-temporal translations. That forces the denominator in the more general fractional-linear transformations to become trivial, resulting in linearity.

vanhees71
Summary:: To derive the Lorentz transformation, Einstein assumed that the speed of light was absolute (not relative), but is it also known why the speed of light is absolute?

To describe the movement of the planets, Newton assumed that there was such a thing as gravity. But he didn't know what gravity was. To derive the Lorentz transformation, Einstein assumed that the speed of light was absolute (not relative), but is it also known why the speed of light is absolute?

Well, why experiment may give us a particular result or "Why any observation is possible at all?" ;o) You may consider an observation act as some predicate in some axiomatic thus, any observable reality must be consistent otherwise you can not have definite results of experiments. So, the question "why speed of light is absolute?" is similar to "why it happens to get into existence in this particular reality?" Because otherwise you would have a different set of "why" questions for different realities arrangements. Axiomatic of any reality can not be completely defined it remains open so its expansion/extension is filtered/selected/restricted by requirement to ensure the possibility for its observer to observe definite observations (to provide a local consistency)...

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Does this FermiLab video help?
"Why can't you go faster than light?" by Fermilab’s Dr. Don Lincoln

Svein
The OP and the answers are slightly inaccurate. The correct answer is:

The speed of light in vacuum is constant and given by $c_{0}=\frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}$.

The speed of light in other cases is given by $c=\frac{1}{\sqrt{\mu \epsilon}}$. The speed of light in glass (for example) is about $\frac{2c_{0}}{3}$. This is the reason why prisms and lenses work...

PeroK
Homework Helper
Gold Member
2021 Award
The OP and the answers are slightly inaccurate. The correct answer is:

The speed of light in vacuum is constant and given by $c_{0}=\frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}$.

The speed of light in other cases is given by $c=\frac{1}{\sqrt{\mu \epsilon}}$. The speed of light in glass (for example) is about $\frac{2c_{0}}{3}$. This is the reason why prisms and lenses work...

The key point about the speed of light in vacuum is that it is invariant. The speed of light in other media is not invariant, but constant relative to the medium.

The speed of light now is taken to be exactly ##299,792,458 m/s##, which defines the metre.

Svein