Why is the speed of light absolute?

  • #26
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
19,537
10,296
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.
 
  • Like
Likes sysprog, Dale and weirdoguy
  • #27
102
10
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.
 
  • #28
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.
 
  • #29
strangerep
Science Advisor
3,285
1,272
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.
 
  • Like
Likes dextercioby and vanhees71
  • #30
463
196
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?
 
  • #31
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
19,537
10,296
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.
 
  • #32
phinds
Science Advisor
Insights Author
Gold Member
2021 Award
17,376
8,912
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
 
  • #33
strangerep
Science Advisor
3,285
1,272
Do Galilean boost don't form a 1-parameter subgroup of the Galilei Group?
Your question doesn't make sense.
 
  • #34
strangerep
Science Advisor
3,285
1,272
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. :oldwink:
 
  • #35
463
196
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.
 
  • #36
strangerep
Science Advisor
3,285
1,272
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##.
 
  • #37
463
196
That makes more sense.
 
  • #38
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
19,537
10,296
Heh, you forgot de Sitter. :oldwink:
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
 
  • #39
strangerep
Science Advisor
3,285
1,272
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.
 
  • #40
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)...
 
Last edited:
  • #41
23
0
Does this FermiLab video help?
"Why can't you go faster than light?" by Fermilab’s Dr. Don Lincoln
 
  • #42
Svein
Science Advisor
Insights Author
2,201
737
The OP and the answers are slightly inaccurate. The correct answer is:

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

The speed of light in other cases is given by [itex]c=\frac{1}{\sqrt{\mu \epsilon}} [/itex]. The speed of light in glass (for example) is about [itex]\frac{2c_{0}}{3} [/itex]. This is the reason why prisms and lenses work...
 
  • #43
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2021 Award
20,139
11,475
The OP and the answers are slightly inaccurate. The correct answer is:

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

The speed of light in other cases is given by [itex]c=\frac{1}{\sqrt{\mu \epsilon}} [/itex]. The speed of light in glass (for example) is about [itex]\frac{2c_{0}}{3} [/itex]. 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.
 
  • #44
Svein
Science Advisor
Insights Author
2,201
737
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).
 
  • #45
102
10
@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.
 

Related Threads on Why is the speed of light absolute?

Replies
12
Views
2K
  • Last Post
Replies
10
Views
2K
  • Last Post
2
Replies
30
Views
5K
  • Last Post
Replies
23
Views
11K
  • Last Post
2
Replies
42
Views
9K
Replies
18
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
3
Views
4K
Replies
8
Views
1K
  • Last Post
Replies
1
Views
2K
Top