# Is speed of light in vacuum an axiom in relativity?

• Premanand
In summary, the speed of light is constant in all frame of reference and does not depend on the relative motion of the source of light and the frame of reference from which you are making the measurement.
Premanand
The speed of light is constant in all frame of reference... So the relative motion of the source of light and the frame of reference from which you are making measurement does not matter... Is it an Axiom in relativity ? I understand that they are experimentally proved concepts... But is it an axiom ? Why does not the speed of light influenced by relative motion ? Is there a qualitative explanation ?

The speed of light in vacuum being constant is a fundamental assumption in relativity. This assumption was made based on the experimental observations which indicated that this was the case.

Premanand
Orodruin said:
The speed of light in vacuum being constant is a fundamental assumption in relativity. This assumption was made based on the experimental observations which indicated that this was the case.
Thank you... But is there an explanation for it? Because light can be slowed down/changed direction by matter but however, the velocity of the inertial frame of reference in which light originated does not have any influence on the speed of light ?

Premanand said:
But is there an explanation for it?

If you go looking for underlying "explanations", then physics is not for you. You can describe things and explain things based on the assumptions, but you cannot "explain" the assumptions - unless you have a theory which supersedes the one you are explaining. Physics (and science in general) is about making an accurate description of how the world works, not about explaining it.

There's a much more convincing "derivation" of the SRT space-time structure than the first one given by Einstein in his (by the way brillant also in a didactical sense and still a must-read for every physicist) famous 1905 paper, but it's a bit more complicated.

You start only from the assumption that there are preferred inertial reference frames, that any inertial observer sees his space as a Euclidean continuum and that time is homogeneous. With these (pretty strong) assumptions you analyze the so introduced symmetries, i.e., you construct the symmetry groups of the then possible space-times. As it turns out this leaves you only with two space-time models (up to equivalence): The Galilei-Newton and the Einstein-Minkowski space-time models. The former doesn't contain any fundamental parameter, the latter a "limiting speed".

Now, of course, experiment has to decide, which space-time model describes Nature best, and as we all know, the Einstein-Minkowski space-time wins this competition.

This shows that relativity is a comprehensive model for all physics since it provides us with the very beginning of everything, namely the space-time model, including a causal structure. It's thus much more general than just being the right space-time description for electromagnetic phenomena but applies to all of physics (to include gravity you have to extent the space-time picture to a pseudo-Riemannian manifold itself being part of the dynamics of what's going on "in" it, leading to the General Relativity Theory).

Now, whether or not the "speed of light" (i.e., the phase velocity of electromagnetic waves in a vacuum) is this "limiting speed" is also subject to experimental verification. In a modern way you can formulate it as the question whether the photon is really massless, and there's no hint so far that it might have a little mass. The upper limit is tiny: According to the particle-date booklet of 2014 it's ##m_{\gamma}<10^{-18} \text{eV}##.

Within the SI of units one takes the masslessness of the photon for granted and defines the speed of light based on the definition of the second at a fixed (exact) value, which implies the definition of the metre as the base unit for measuring lengths. For a theorist, given the relativistic space-time structure) it doesn't make much sense to measure lengths in a different unit than time intervals, and thus they usually happily set ##c=1## (except in cases, when one wants to study the non-relavistic limit in the proper sense of an expansion in powers of ##1/c##).

Premanand
Premanand said:
Thank you... But is there an explanation for it? Because light can be slowed down/changed direction by matter but however, the velocity of the inertial frame of reference in which light originated does not have any influence on the speed of light ?

I don't know if this is quite what you're asking, however you seem to be looking for a deeper reason why light always has the same velocity. The reason there is a unique velocity of light, originates from the properties of spacetime. The reason it is constant is that it is a massless particle.

##c## is the value that shows up as the proportionality constant between spatial and temporal displacements. ##c## is more global than only the velocity of a particular particle, or even all massless particles.

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Premanand
Premanand said:
The speed of light is constant in all frame of reference... So the relative motion of the source of light and the frame of reference from which you are making measurement does not matter... Is it an Axiom in relativity ? I understand that they are experimentally proved concepts... But is it an axiom ? Why does not the speed of light influenced by relative motion ? Is there a qualitative explanation ?

As Orodruin and others have said, it is indeed a postulate of relativity. The easiest way to see this is to look at Einstein's 1905 paper introducing special relativity to the world (google for "On the electrodynamics of moving bodies") where he states it as an assumption and then derives special relativity as a consequence of that assumption.

We have overwhelming experimental evidence (there's a sticky at the top of this forum with links to a tiny fraction of the evidence) that that's how the world works, so it looks to be a pretty good assumption.

But if you're looking for a qualitative explanation of why it should be that way... Again, as Orodruin has said, physics is a lot better at explaining how the universe is than why it is that way. However, there is a qualitative answer to the "Why?" question that you may find useful, or at least may help persuade you that it's a sensible assumption:

The speed of light in a vacuum is not just something that we measure and then accept the measured value "just because". The speed of light in a vacuum can be and was calculated from Maxwell's laws of electricity and magnetism in 1861, a half-century before relativity. The calculated speed comes out the same regardless of the movement of the source and the receiver, and regardless of which frame is used to calculate that speed. Thus, the only way that observers in different states of motion would find different speeds of light would be if they had different laws of electricity and magnetism. That would be a very bizarre state of affairs; for example, because of the Earth's orbit around the sun we're all moving in a completely different direction in December and June, but we don't expect the laws of E&M to change with the seasons.

The great unsolved problem of 19th-century physics was reconciling this aspect of Maxwell's laws with the classical (and very intuitive) prediction that the speed of light just had to be different for different observers in different states of motion. Before Einstein, the favorite approach was try to save the classical prediction by adding additional assumptions (a hypothetical "luminiferous ether") to Maxwell's theory, but these theories became increasingly complex and unsatisfactory. Einstein's great contribution was to build an internally consistent and experimentally supported theory by letting go of the classical prediction.

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Premanand
vanhees71 said:
You start only from the assumption that there are preferred inertial reference frames, [...]
Er,... was that a typo? Did you mean "...there are no preferred inertial reference frames..." ?

BTW, I'm glad that someone mentioned this approach -- i.e., that the light principle is not essential as an axiom. I was going to mention it, but I suspect others are sick of hearing me say that.

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Premanand
I like the approach in Eric Gourgoulhon's Special Relativity in General Frames. Its completely geometric, starts from Minkowski spacetime and then derives everything you need to know about SR(including the light principle, accelerated and rotating observers,Lorentz group, relativistic EM, Relativistic Hydrodynamics, etc.) as geometrical features of spacetime and worldlines residing on it. From the book's preface:
One of the consequences of the “general observer” approach adopted here is the least weight attributed to the famous Lorentz transformation between the frames of two inertial observers. This transformation, which is usually introduced in the first chapter of a relativity course, appears here only in Chap. 6. In particular, the physical effects of time dilation or aberration of light are derived (geometrically) in Chaps. 2 and 4, without appealing explicitly to the Lorentz transformation. Similarly, the principle of relativity, on which special relativity has been founded at the beginning of the twentieth century (hence its name!), is mentioned here only in Chap. 9, at the occasion of a historical note.

IMHO, this is the best SR book you can find and a must read even if you know SR. Actually I should say you can read it only if you know a bit SR.

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vanhees71 and Premanand
Premanand said:
The speed of light is constant in all frame of reference... So the relative motion of the source of light and the frame of reference from which you are making measurement does not matter... Is it an Axiom in relativity ? I understand that they are experimentally proved concepts... But is it an axiom ? Why does not the speed of light influenced by relative motion ? Is there a qualitative explanation ?
Premanand said:
Thank you... But is there an explanation for it? Because light can be slowed down/changed direction by matter but however, the velocity of the inertial frame of reference in which light originated does not have any influence on the speed of light ?
If you want to understand that it was not like magic falling from heaven, it's better to verify the original postulates: not one but two postulates, each based on experimental evidence. The postulates of SR are:

1. the laws of physics are the same in all inertial frames of reference
2. the speed of light is a constant, independent of the motion of the source
(and this is a law of physics)
See the intro of http://fourmilab.ch/etexts/einstein/specrel/www/

The first axiom or postulate corresponds to the observation that we cannot identify a preferred inertial reference system. The second axiom or postulate originates in the experimentally strongly supported theory of Maxwell, which uses a basic wave model for the propagation of electromagnetic radiation. It is generally assumed that the motion of a wave source has no effect at all on the speed of a wave.

The combination of these two facts of observation results in your axiom.

Explanations for it range from stationary ether (Lorentz) to block universe models (Shyan's book?) - but most popular is probably "shut up and calculate", as nobody can prove "what really happens" .

Premanand
strangerep said:
Er,... was that a typo? Did you mean "...there are no preferred inertial reference frames..." ?

BTW, I'm glad that someone mentioned this approach -- i.e., that the light principle is not essential as an axiom. I was going to mention it, but I suspect others are sick of hearing me say that.
Perhaps, "preferred" is a somewhat unfortunate word for what I wanted to express, but off course, the notion of inertial frames separates out these frames from any "accelerated" frame of reference.

What I like about this approach is that it shows that SRT makes very strong assumptions on the symmetry properties of the space-time structure and thus you have a very limited choice of space-times, namely only the Galilei-Newton and the Einstein-Minkowski spacetime. At the same time, it takes out this mentioned postulate about the speed of light being the universal "limiting speed". At the present state of our understanding this is rather an empirical question than a fundamental principle of nature, i.e., whether the photon is massless or not is to be decided by experiment (and as I said before, there's nothing yet indicating that the photon might have a tiny mass). From a didactic point of view the advantage of this more general approach is that it shows that the possible existence of a limiting speed is a general property of the space-time description and not limited to electromagnetic phenomena. To the dismay of the HEP community, who'd like to find some physics beyond the Standard Model, we know pretty well today that the SRT space-time structure is the basis for the entire Standard Model of elementary particles, which is much more comprehensive than just electromagnetic interactions.

However, the principle of the special status of inertial frames is inherited also by GRT, where you just loosen the demand of the existence of a global inertial frame and make it to a local concept, which is the concrete mathematical formulation of the (weak) equivalence principle: The space-time is described as a pseudo-Riemannian manifold with a pseudo-metric (fundamental form) of signature (1,3) (or (3,1) if you prefer the east-coast convention), which implies that you have a torsion free affine connection compatible with the pseudo-metric and local inertial frames (i.e., the tangent space at each space-time point is Minkowskian, modulo possible singularities).

Of course, you can then also specify additional symmetry properties for given physical situations, like admitting a spherical symmetry for a radially symmetric body/point particle (Schwarzschild, Reissner-Nordström) or a maximally symmetric space (FLRW solutions for the large-scale coarse-grained description of the universe in the standard model of cosmology).

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Mentz114
harrylin said:
If you want to understand that it was not like magic falling from heaven, it's better to verify the original postulates: not one but two postulates, each based on experimental evidence.
[..]
The second axiom or postulate originates in the experimentally strongly supported theory of Maxwell, which uses a basic wave model for the propagation of electromagnetic radiation. It is generally assumed that the motion of a wave source has no effect at all on the speed of a wave. [..].
PS in that context the following recent paper may be instructive: http://arxiv.org/abs/1405.3979

## 1. Is the speed of light in vacuum an axiom in relativity?

Yes, the speed of light in vacuum is considered an axiom in relativity. This means that it is a fundamental principle or starting point that is accepted without proof.

## 2. Why is the speed of light in vacuum considered an axiom in relativity?

The speed of light in vacuum is considered an axiom in relativity because it is a constant and universal value that plays a crucial role in the theory. It is the maximum speed at which all matter and information in the universe can travel, and its constancy is a central principle in Einstein's theory of relativity.

## 3. How is the speed of light in vacuum measured?

The speed of light in vacuum is measured using various experimental techniques, such as the Michelson-Morley experiment, which measures the speed of light by comparing the time it takes for light to travel along two perpendicular paths. Today, the most accurate measurement of the speed of light in vacuum is based on the definition of the meter in the International System of Units (SI).

## 4. Can the speed of light in vacuum be exceeded?

According to the theory of relativity, the speed of light in vacuum is the maximum speed at which anything can travel. It cannot be exceeded by any object with mass. However, there are some phenomena, such as quantum tunneling, where particles may appear to travel faster than the speed of light, but they do not actually violate this fundamental principle.

## 5. What are the implications of the speed of light in vacuum being an axiom in relativity?

The speed of light in vacuum being an axiom in relativity has several implications. It means that the laws of physics are the same for all observers, regardless of their relative motion. It also leads to the concept of time dilation, where time appears to pass at different rates for objects moving at different speeds. Additionally, the speed of light in vacuum being an axiom is crucial for understanding the behavior of light and the structure of the universe.

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