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According to the general theory of relativity, every observer will measure the same speed of light $c$ in vacuum, if they measure in their local inertial reference frame.

I assume that this statement is valid in the following cases:

  1. When measuring within a different gravitational potential.

  2. When the observer moves in the same direction as the light.

  3. When the observer moves in the opposite direction from the direction of the light.

In addition to length contraction, is gravitational time dilation responsible for 1, while (dynamic) time dilation is responsible for 2 and 3?

Additionally:

If I'm not mistaken, length contraction and time dilation had to be added in order for the speed of light to stay the same and match c. Later, these phenomena were confirmed and are considered real. That's why I suppose that we can now say this: Gravitational time dilation is an effect that causes observers in their local inertial frame of reference to measure a constant speed c regardless of the strength of the gravitational field. Also, time dilation and length contraction act on the observer's measurements so that, regardless of their speed and direction, they measure the speed of light c, in their local reference frame.

Einstein's postulate is not the cause of the constancy of the speed of light, but the real (proven) phenomenon of time dilation is the cause of the constancy of the speed of light. Is that point of view correct? That is the essence of my question.

Thank you for taking the time to answer my question.

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    $\begingroup$ Why bother with the light source, it only obfuscates by adding a reference frame that doesn't matter. $\endgroup$
    – JEB
    Mar 15 at 13:17
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    $\begingroup$ @JEB, Saying that the speed of light is constant is sufficient to describe the physical reality, but calling attention to the fact that the relative motion of the observer and the source of the light does not matter somewhat helps to drive the point home. $\endgroup$
    – Solomon Slow
    Mar 15 at 14:33
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    $\begingroup$ A very general point: after going through a lot of that line of thought myself, which is: "The constancy of the speed of light is due to this that and the other" I finally realized that it's much easier to think about it in reverse: "The constancy of the speed of light is responsible for XYZ". Then it's kind of automatic that whatever comes in place of XYZ must be true if it serves to preserve this invariance in inertial frames. I don't know if it helps here I just thought it may clarify things a bit $\endgroup$
    – Amit
    Mar 15 at 16:19
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    $\begingroup$ Constancy of the speed of light is a postulate, rather than a consequence. Based on experimental evidence, of course. $\endgroup$
    – Roger Vadim
    Mar 15 at 16:20
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    $\begingroup$ @RogerVadim, Yes! Maxwell predicted the constant speed, and that prediction threw physics into turmoil until Einstein was able to pull together a mathematically consistent model of space and time that allows light to have that constant speed. $\endgroup$
    – Solomon Slow
    Mar 15 at 16:36

9 Answers 9

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The invariance of the speed of light follows from the principle of relativity. This says there is no experiment that can distinguish between inertial reference frames: physical laws are the same in every inertial frame. For example, Maxwell's equations for electromagnetism are the same in every inertial reference frame, and therefore the speed of light (which is derived from Maxwell's equations) must be the same in every inertial reference frame!

Einstein elevated this principle to a postulate when formulating the theory of relativity. As @Amit pointed out in a comment, it's better to think of relativistic effects like length contraction and time dilation as consequences that follow from requiring a constant speed of light, not the other way around.

EDIT: After consideration, the principle of relativity on its own is not enough to conclude an invariant speed of light. Assuming isotropy of space and the principle of relativity, we are led to two possible sets of spacetime transformations between inertial frames: Galilean transformations and Lorentz transformations. Newton's laws of motion are preserved under Galilean transformations and Maxwell's equations are preserved under Lorentz transformations. At this point we rely on experiment to "pick a side". The second postulate of special relativity picks Maxwell's side, and we are led to an invariant speed of light as discussed above.

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    $\begingroup$ Except that the Lorentz-FitzGerald contraction, as an interpretation of the Michelson–Morley experiment, was one of the experimental inputs to the theory. The theory is a consequence of these inputs. $\endgroup$
    – John Doty
    Mar 15 at 20:40
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The constancy of $c$ is an experimental result, verified to great precision. When we make mathematical models that assume the constancy of $c$, we get predictions that match other experimental results to great precision. Every time you use GPS, you are participating in a grand experiment verifying the constancy of $c$ in curved space. Thus, we have great confidence that the constancy of $c$ is a good assumption to use in building models.

However, since the models are built on the experimental constancy of $c$, they cannot explain it, they can only capture it. Furthermore, in our modern definition of length, $c$ is a defined constant: precise length measurements are traceable to atomic time rather than to some artifact. So, for $c$ not to be constant, you must abandon the SI definition of length.

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    $\begingroup$ To achieve a good precision with GPS, the dependency of c to the air pressure is used too. Light is faster in vacuum than in air. $\endgroup$
    – Uwe
    Mar 17 at 18:34
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This is not a question of cause and effect, but a question of definition. A local inertial frame is defined as one where locally you measure the speed of light to be $c$ (among other properties). So if you ever did a local measurement where the speed of light was not $c$ then it would by definition not be a local inertial frame.

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The constancy of light is that in free space the 3rd along with the 4th Maxwell's equation produce a wave equation which depends only on the electric and magnetic permeability of the medium and because these 2 dont change the speed of light is constant.

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    $\begingroup$ The constancy of the speed of light is not a consequence of Maxwell's equations alone. There are two ways for Maxwell's equations to be consistent: either a constant speed of light, or a privileged reference frame. You need additional information to decide which one is the case. $\endgroup$
    – Mark
    Mar 16 at 0:48
  • $\begingroup$ @Mark a privileged reference doesnt make sense does it? $\endgroup$
    – appliedSciences
    Mar 16 at 19:27
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    $\begingroup$ It makes enough sense that scientists spent about half a century looking for it. $\endgroup$
    – Mark
    Mar 16 at 20:44
  • $\begingroup$ One can compare sound: the relevant parameters of air at sea level do not change, and yet, the speed of sound is not constant in different reference frames $\endgroup$
    – user253751
    Mar 17 at 14:14
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Five year old kids asks the question "Why?" time and time again. In the Toyota production model there is an accepted way to handle root causes known as "Five Whys".

What is the cause of the constancy of the speed of light in vacuum?

This is a really good question. In confronting this question i can only see two strategies: Either accept that it simply is a constant and that the speed of light is the same in all directions. Einstein did this in calling this a postulate. This strategy is probably the less ardous and perhaps more "sane" one. It will allow you to learn a lot of the traditional truths of todays physical science. But why be lazy and correct?

The other strategy, not stopping asking the "Why?" time and time again might be the road to gaining new insights into physics. You would probably have to work hard and be very smart - the people that already has tried to get to the bottom of the "Why?" without succeding were/are both.

In general, physics has difficulty to answer the "Why?" question. The problem is that the world simply seems to be what it is, not really giving any explanations. Our experiments, measurements, model and sophisticated math reaches a murky cellar somewhere where the world to our current knowledge simply is. It might be that there are further levels downwards toward some kind of understanding, but, well, in order to get there you have to work hard and smart in order to answer the "Why?". I wish you a lot of luck.

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  • $\begingroup$ one possible lower level is: well, actually there is a preferred frame, but we can't measure it because movement affects all possible clocks in the same way it affects light clocks. $\endgroup$
    – user253751
    Mar 17 at 8:50
  • $\begingroup$ @user253751 en.wikipedia.org/wiki/Lorentz_ether_theory $\endgroup$
    – John Doty
    Mar 17 at 13:21
  • $\begingroup$ @JohnDoty very similar, but instead of postulating that time dilation is real, I simply postulate that all interactions are similarly affected as the light clock, that is, all interactions require particles to go from one point to another. It seems like a simpler concept. I'm sure there's some reason it doesn't work. (The Wikipedia page you linked says ether-style theories do describe reality "if time dilation and length contraction of bodies moving in the aether have their exact relativistic values") $\endgroup$
    – user253751
    Mar 17 at 14:12
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The physical reason for the constancy of the speed $c$ of light in free space (i.e. perfect vacuum) has nothing to do with Special Relativity but rather with the vacuum itself and Maxwell's Electromagnetism theory which assigns to free space two intrinsic physical constants, its magnetic permeability $μ_{0}$ and electric permittivity $ε_{0}$.

Subsequently the speed of light in free space is constant and given by the equation:

$$ c=\frac{1}{\sqrt{\varepsilon_0 \mu_0}} $$

Notice, that if the vacuum is not perfect or light passes through medium like glass for example, the speed of light will be lower than $c$.

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The physical meaning of it is that everywhere in spacetime, and in every direction, there exists a special speed, which you can measure with local experiments. You can imagine that spacetime is crisscrossed with "grooves" (the light cones) which can be detected by, for instance, measuring the motion of light, which follows those grooves.

Using the number $c$ (or $1$) for that speed is just a convention. In special relativity, it simplifies the math considerably. In general relativity it's not so convenient, and people often use coordinates in which the numerical value of the speed varies with position and direction.

In special relativity, if you take the speed to be $c$ and adopt several other specific conventions, and also assume the principle of relativity, then you can derive the existence of length contraction and time dilation, as Einstein showed in 1905. That argument is important because we do use measurement conventions of that sort, but you shouldn't think of length contraction and time dilation as fundamental. The light cones and the principle of relativity are fundamental.

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  • $\begingroup$ No, I did not think of length contraction and time dilation as fundamental. I observe the gravitational dilation of time as one of the proofs of the general theory of relativity, or Einstein's postulates. For example en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment $\endgroup$
    – Spigel
    Mar 16 at 20:45
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Einstein's postulate is not the cause of the constancy of the speed of light, but the real (proven) phenomenon of time dilation is the cause of the constancy of the speed of light. Is that point of view correct? That is the essence of my question.

I think it is a category error to look for a "cause" of the constancy of the speed of light. It is more the inherent nature of spacetime in connection with our oversimplified concepts of "speed" and "length" that result in "constancy of the speed of light" emerging as a property worth stating.

Also, "light" is putting the cart before the horse since spacetime is what gives us c0 as a universal constant for the propagation of interactions and electromagnetic wave propagation is just one aspect of it.

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    $\begingroup$ +1 for pointing out that c isn't inherent to light; because of the nature of light, it travels as fast as possible i.e. at c $\endgroup$
    – lessthanideal
    Mar 18 at 1:24
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The speed of light VARIES with the speed of the emitter, as posited by Newton's theory

https://qph.cf2.quoracdn.net/main-qimg-f10f1c25528a4e5edc9bae200640f31c-pjlq

and unequivocally proved by the Michelson-Morley experiment:

"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887...The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)." https://en.wikipedia.org/wiki/Emission_theory

Banesh Hoffmann, Einstein's co-author, admits that, originally ("without recourse to contracting lengths, local time, or Lorentz transformations"), the Michelson-Morley experiment was compatible with Newton's variable speed of light, c'=c±v, and incompatible with the constant speed of light, c'=c:

"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92 https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768

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    $\begingroup$ Wikipedia says "this theory is considered to be conclusively discredited by most scientists", and gives numerous experimental results which contradict emitter theory. $\endgroup$
    – PM 2Ring
    Mar 16 at 10:06
  • $\begingroup$ The only fact that matters is that, in 1887, the Michelson-Morley experiment confirmed Newton's variable speed of light, c'=c±v. Anything else (alleged failures of the emission theory etc) is irrelevant. $\endgroup$
    – Pentcho Valev
    Mar 16 at 12:09
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    $\begingroup$ The Michelson-Morley experiment had little influence on Einstein's development of SR. As mentioned in physics.stackexchange.com/a/463979/123208 "Among the clues that led Einstein to that supposition were the observations of stellar aberration, and the experiments by Fizeau that compared the speed of light through water that was stationary to the speed of light through water that was moving." $\endgroup$
    – PM 2Ring
    Mar 16 at 12:22
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    $\begingroup$ @Pentcho Valev, I'm no expert, but I'm pretty sure that's not how science works - you can't ignore all results other than the one that conforms to your perspective. I believe that's called confirmation bias. $\endgroup$
    – user127813
    Mar 17 at 8:37

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