Undergrad Why is the speed of light absolute?

[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.

With these assumptions you get either Einstein-Minkowski (existence 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]

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.

Please pay attention when people ask you to do something:

@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?

Your question doesn't make sense.

 

[strangerep]

With these assumptions you get either Einstein-Minkowski (existence of an invariant speed) or Galilei-Newton (absence of an invariant speed) spacetime. [...]

Heh, you forgot de Sitter.

 

[andresB]

Your question doesn't make sense.

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 $c\to\infty$.

 

[andresB]

That makes more sense.

 

[vanhees71]

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.

 

[stefanbanev]

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)...

 

[PeterPeter]

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]

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]

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.

Yes. The reason why I stressed "in vacuum" is that several optical effects rely on the speed of light being dependent on the medium it travels through. The speed of light in air is not the same as $c_{0}$ (and AFAIK is dependent on the air pressure).

 

[Ad VanderVen]

@Dale You can distinguish two types of why questions within a science: questions that can or cannot be answered with the current state of affairs and questions that can or cannot be answered by that science in principle. I was talking about why questions of the latter type.