Why is the speed of light absolute?

[Ad VanderVen]

TL;DR

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?

 

[PeroK]

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?

The correct term is that the speed of light is invariant across all inertial reference frames. There was experimental evidence for this that led Einstein to assume it as a postulate, from which (as you know) Special Relativity, including the Lorentz Transformation (LT), can be derived.

You can also derive the LT from considerations of symmetry and homogeneity of time and space. This derivation results in an invariant speed, which we can call $c$. Anything measured to be moving at speed $c$ in one inertial reference frame will be measured to be moving at speed $c$ in all reference frames.

Moreover, it can be shown that anything massless must travel at this invariant speed $c$. From that perspective, the invariance of the speed of light results from its masslessness.

Then, of course, you can ask why light is massless ...

 

[BvU]

Ours is not to reason why.
It is.
And that it is has been confirmed by experiment.

By the way, what would constitute a satisfactory answer to your question ?

And why is the ratio of circumferernce of a circle to diameter equal to $\pi$ exactly ?

See also

Consult https://en.wikipedia.org/wiki/International_System_of_Units for the definitions
...

 

[Nugatory]

Einstein assumed that the speed of light was absolute (not relative), but is it also known why the speed of light is absolute?

Empirical science doesn’t answer “why?” questions very well. Any “because” answer from physics will on closer examination turn out to be some form of “because that’s how the universe we live in works”. It can accurately describe the behavior of the universe we live in but doesn’t tell us why the universe we live in behaves that way instead of some other way.

So there’s no good answer to the question of why the speed of light is invariant. There is a sensible and internally consistent theory in which the speed of light is invariant and another in which it is not. Either could be right, and experiments have told us which but not why.

A more useful question might be “Why did Einstein think it was a good idea to consider a theory in which the speed of light is invariant?” By the end of the 19th century nature had provided several hints that such a theory might be needed. Perhaps the most important was Maxwell’s discovery in 1864 that the speed of light can be calculated from his laws of electricity and magnetism - and these laws are unsurprisingly the same for all observers. Reconciling Maxwell’s electrodynamics with the rest of classical physics was the great unsolved problem of the second half of the 19th century, and it is telling that the title of Einstein’s first relativity paper was “On the electrodynamics of moving bodies”.

 

[Nugatory]

You can also derive the LT from considerations of symmetry and homogeneity of time and space. This derivation results in an invariant speed,

Are homogeneity and symmetry sufficient, or is an additional assumption required to exclude the possibility of a homogeneous and symmetric universe with no invariant speed?

 

[PeroK]

Are homogeneity and symmetry sufficient, or is an additional assumption required to exclude the possibility of a homogeneous and symmetric universe with no invariant speed?

These considerations yield the LT as an alternative to the classical Galilean transformation (with absolute time). It could then be seen as an experimental matter to decide which applies in our universe. The point, however, is that the invariance of the speed of light is seen not as an ad hoc assumption or experimental oddity, but consistent with some basic principles, which support only two or three possibilities for the nature of space and time in our universe.

 

[vanhees71]

If you start from the special principle of relativity together with homogeneity of space, homogeneity of time, and isotropy of space you inevitably either get the Galilei-Newton spacetime or the Einstein Minkoswki spacetime. So Gailei-Newtonian spacetime is the only realization of a spacetime with all these symmetries which has no "universal speed limit".

Now all empirical evidence shows that Galilei-Newton spacetime is not correct but Einstein-Minkowksi spacetime is (as long as gravity can be neglected).

Now you can ask in a systematic way how the natural laws must look like in Einstein-Minkowski spacetime, and up to today we have no answer to the question, why the electromagnetic field should be described as a massless vector field. No symmetry principle forbids massive Abelian gauge fields. So again we are forced to investigate empirically, whether or not the em. field is massive or massless. The present upper limit for the mass of photons is $10^{-18} \text{eV}$. For how this really very small bound comes about see the papers cited in the PDG listing of the photon.

http://pdg.lbl.gov/2019/listings/rpp2019-list-photon.pdf

 

[timmdeeg]

Now you can ask in a systematic way how the natural laws must look like in Einstein-Minkowski spacetime, and up to today we have no answer to the question, why the electromagnetic field should be described as a massless vector field. No symmetry principle forbids massive Abelian gauge fields. So again we are forced to investigate empirically, whether or not the em. field is massive or massless. The present upper limit for the mass of photons is $10^{-18} \text{eV}$. For how this really very small bound comes about see the papers cited in the PDG listing of the photon.

http://pdg.lbl.gov/2019/listings/rpp2019-list-photon.pdf

Can this whole reasoning ("whether or not the em. field is massive or massless") mutatis mutandis be applied to gravitational waves too?

 

[vanhees71]

I guess so. Also here the question whether GR is the correct theory is, as any theory of physics, to be tested by experiment and observation. Today we have many highly accurate tests of GR. AFAIK there's no hint at any violation of GR.

 

[Ad VanderVen]

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?

 

[Ibix]

It's pretty trivial. Mass is the modulus of the four momentum, which is a vector tangent to an object's worldline. If the mass is zero then that is a way of saying that the four momentum is null. Therefore the object is following a null worldline - i.e. moving at the speed of light.

 

[Ad VanderVen]

BvU said "Ours is not to reason why."

I do not agree with such an answer. If someone asks: why does the moon have different phases then we all know the answer and it is nonsense to say: Ours is not to reason why.

 

[weirdoguy]

we all know the answer

Yes, and that answer leads to other questions of the "why?" type. And at some point, our answer has to be "because that's the way Universe works".

 

[PeroK]

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?

I had a look online, but I didn't find anything that looked very good. Probably the simplest way is to derive the relativistic expressions for energy $E$ and momentum $p$ of a massive particle:
$$E = \gamma mc^2; \ \ p = \gamma mv$$
Where $v$ is the speed of the particle and
$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$
This implies that a massless particle traveling at less than the speed of light would have no energy or momentum. If massless particles exist, therefore, then they must move at speed $c$. There's no alternative.

The final step, I would say, is to show that massless particles traveling at $c$ are consistent with the rest of SR. If we rearrange the above equations we get:
$$E^2 = p^2c^2 + m^2c^4$$
If this is true for a massless particle, then we have $E = pc$, which agrees with the known De Broglie equations for the energy and momentum of light.

 

[Ad VanderVen]

weirdoguy said:

Yes, and that answer leads to other questions of the "why?" type. And at some point, our answer has to be "because that's the way Universe works". That was the point.

Again I say: that is nonsense, because that would mean that we would no longer ask questions and that is the last thing a scientist must do. It is better than saying: I just don't know the answer.

 

[weirdoguy]

Again I say: that is nonsense

Then you don't understand how science works. Of course we have to ask questions, but appropriate ones. That is one of the things scientists have to learn. And we learn that at the most fundamental level most of the "why?" questions are unanswerable. Physics focuses more on the "how?" questions.

 

[Ad VanderVen]

Perok Your last answer:

Probably the simplest way is to derive the relativistic expressions for energy ...

seems very promising to me. I'm going to take a good look at it. Thanks a lot.

 

[PeroK]

weirdoguy said:

Yes, and that answer leads to other questions of the "why?" type. And at some point, our answer has to be "because that's the way Universe works". That was the point.

Again I say: that is nonsense, because that would mean that we would no longer ask questions and that is the last thing a scientist must do. It is better than saying: I just don't know the answer.

It's not as black and white as that. By definition, and by the rules of logic, you can only prove things based on some prior assumptions. I.e. if you make no assumptions, then you cannot prove anything!

Any scientific theory, therefore, starts with its assumptions. That could be Newton's laws; it could be the invariance of the speed of light; it could be the symmetry and homogeneity of space and time; it could be the basic postulates of quantum mechanics. The theory is then based on these assumptions. The theory itself can never prove those assumptions.

If you find something deeper from which those assumptions can be shown, then you have a new theory. That new theory must, however, have a new set of basic assumptions, laws, axioms, postulates, whatever you want to call them.

There is research at the moment, for example, to provide a theory of quantum gravity, from which things like the nature of space and time may potentially be derived. That may answer the questions like why spacetime is the way it is. But, such a theory of quantum gravity would have its own basic assumptions.

 

[Ad VanderVen]

Perok I totally agree with what you said with "It's not as black and white as that." and further. That is also exactly my opinion of how science works.

 

[Ad VanderVen]

weirdoguy

On Wikipedia in the Article Four causes you can read:

Aristotle held that there were four kinds of answers to "why" questions (in Physics II, 3, and Metaphysics V, 2): Matter, Form, Agent and End of purpose and of course I did not mean an End of purpose answer with my why-question .

 

[Dale]

Again I say: that is nonsense, because that would mean that we would no longer ask questions and that is the last thing a scientist must do.

I think that you are misunderstanding @weirdoguy’s correct point.

Science is a tool for answering questions. Like all tools it is useful for the job for which it is designed but it has limitations. One of the limitations of science as a tool for answering questions is the type of question that it can answer. Science is notoriously bad at answering “why” questions for the assumptions of our fundamental theories.

So his comments are not claiming that scientists should not ask questions, but he is recognizing that not all questions can be answered by science. A good scientist must be very careful in asking the right questions if they want to get a scientific answer. Careless questions produce poor science.

Don’t you think it is wise to understand the limitations of a tool?

 

[Ad VanderVen]

Dale, you said:

"Science is notoriously bad at answering “why” questions for the assumptions of our fundamental theories."

One of the assumptions of Newton's Mechanics was the assumption of the existence of something like gravity. People asked him: what is gravity and where does it come from? He did not answer that question with: You should not ask that question because science cannot answer all questions. He simply said: Hypotheses non fingo or freely translated: I don't know. Fortunately, there was a man who thought the question was meaningful and he (Einstein) gave an answer about 200 years later (it's a space-time phenomenon).

Furthermore the following. As far as I know, there is still no science that tells exactly which questions physics can answer and which physics cannot. Maybe logic, but I don't know.

 

[andresB]

Dale, you said:

"Science is notoriously bad at answering “why” questions for the assumptions of our fundamental theories."

One of the assumptions of Newton's Mechanics was the assumption of the existence of something like gravity. People asked him: what is gravity and where does it come from? He did not answer that question with: You should not ask that question because science cannot answer all questions. He simply said: Hypotheses non fingo or freely translated: I don't know. Fortunately, there was a man who thought the question was meaningful and he (Einstein) gave an answer about 200 years later (it's a space-time phenomenon).

Why is gravity a space-time phenomenom?. Can you give an answer that doesn't lead to another why?

Besides this semi-philosophical debate, the questions you asked at the beginning was already answered. There were experimental and theoretical reasons to formulate a theory where c was invariable, even if it were just to see what kind of prediction that theory would make. The prediction end up to be consistent with experiments.

More recently, it is known that homogenity and isotropy of space and time allows for a invariable speed.

 

[russ_watters]

He did not answer that question with: You should not ask that question because science cannot answer all questions.

Science not being able to answer is not the same as discouraging people from asking. You just have to accept that sometimes there is no answer.

As far as I know, there is still no science that tells exactly which questions physics can answer and which physics cannot.

That is not correct. The limitations tend to be pretty well known by each discipline. You have to know where the edges are before you can move past them.

 

[Dale]

@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

One of the assumptions of Newton's Mechanics was the assumption of the existence of something like gravity. People asked him: what is gravity and where does it come from? He did not answer that question with: You should not ask that question because science cannot answer all questions. He simply said: Hypotheses non fingo or freely translated: I don't know. Fortunately, there was a man who thought the question was meaningful and he (Einstein) gave an answer about 200 years later (it's a space-time phenomenon).

This is actually a good example. Science simply could not answer that question while it was an assumption of our fundamental theory of gravity. What was required was a new fundamental theory of gravity which included Newtonian gravity as a limiting case. Then that "why" question could be answered by appeal to the new fundamental theory. However, as before, all of the "why" questions about the assumptions of the new fundamental theory are inherently unanswerable by science.

Currently, relativity is our fundamental theory of spacetime. The invariant speed of light is an assumption of that theory. Therefore there is no scientific answer to the question about why it is invariant. To get an answer to that question would require a new fundamental theory of spacetime, which does not exist at this time.

Furthermore the following. As far as I know, there is still no science that tells exactly which questions physics can answer and which physics cannot. Maybe logic, but I don't know.

Actually, we are very aware of this as scientists. We have several centuries of experience applying the scientific method, so at this point we have a very good handle of which types of questions can and cannot be answered by science.

Based on that experience it is clear that "why" questions about the fundamental theories cannot be answered at all. 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. If there is no more fundamental theory then the question cannot be answered.

 

[vanhees71]

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.

 

[Ad VanderVen]

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.

 

[AdirianSoan]

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.

 

[andresB]

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?