Constancy of Speed of Light: Postulate or Assumption?

[Aromalsp]

TL;DR Summary

Is the Constancy of speed of light a postulate or an assumption of theory of relativity?

The theory of relativity is based on two key principles: the principle of relativity and the constancy of the speed of light.

The constancy of the speed of light is one of the fundamental postulates of the theory of relativity.

Which statement is wrong?

 

[Mister T]

The speed of light is is independent of the speed of the source. That was indeed one of Einstein's two postulates that he used to construct his special theory of relativity. But that is not the only way to construct the theory. How one builds up a logical structure based on postulates depends on the postulates chosen.

 

[PeterDonis]

Which statement is wrong?

Neither of them are wrong. Why do you ask?

 

[malawi_glenn]

What is the difference between a postulate and an assumption?

 

[strangerep]

What is the difference between a postulate and an assumption?

Er,... does it have anything to do with the difference between a posterior and an ass?

Slightly more seriously, Google says:

Assumption – a thing that is accepted as true without proof.
Postulate – a thing suggested or assumed as true as the basis for reasoning, discussion, or belief.

 

[malawi_glenn]

Oh, I thought it was assumed that my question was directed to the OP... perhaps I should have postulated it instead

 

[Demystifier]

TL;DR Summary: Is the Constancy of speed of light a postulate or an assumption of theory of relativity?

The theory of relativity is based on two key principles: the principle of relativity and the constancy of the speed of light.

The constancy of the speed of light is one of the fundamental postulates of the theory of relativity.

Which statement is wrong?

Neither is wrong. The two statements above correspond to two slightly different styles of thinking in physics. The latter, based on postulates (axioms), is more mathematical and logical. The former, based on principles and assumptions, is more scientific. When you say that something is a postulate (axiom), after that you are not longer allowed to question it. By contrast, when you say that something is a principle or assumption, then, during the process of thinking, you are allowed to question the validity of it. So it's a matter of the thinking style, not a matter of truth.

 

[Dragon27]

Words like "postulate" and "assumption" can have different shades of meaning and different associations for different people. Instead of trying to put a label on it and playing word games it would better for OP to just say exactly what they mean by calling it an assumption or a postulate (or a principle) so as to avoid any misinterpretations.

 

[PeroK]

I always assumed it was a postulate; rather than postulated that it was an assumption!

 

[pervect]

Possibly relevant here is one's formulation of the philosophy of science. Philosophy is not my field, but my general understanding of the philosophy of science is that one make hypothesis, logically derive the conclusions, and do experiments to test the validity of the hypothesis.

Karl Popper is one name that comes to mind for a more thorough and well-written exposition than I can do in this short post. (I doubt I wouldn't be able to match the quality of Popper's writing even in a longer post, btw). On the other hand, my more informal style is (hopefully) easier to read.

This formulation of the philsophy of science, leads to a third formulation, different from the other two wordings, in which we say that the constancy of the speed of light is a hypothesis. The advantage of taking this approach is that it encourages us then to think about the evidence.

There is in fact quite a bit of evidence that the speed of light is in fact constant, both by direct measurement, and by other indirect measurements. Indirect measurements are part of the scientific method, in which one makes hypothesis and derives conclusions from them, and then tests the conclusion. There's a FAQ on the topic of experimental evidence for the constancy of the speed of light if that is the topic you're interested in, as opposed to the broad philosophical issues. IT should be right near the top of the forum.

 

[vanhees71]

As usual in the natural sciences as with most "general laws" the "constancy of the speed of light" is the result of observations and building mathematical models and theories to describe them. The "constancy of the speed of light" after all is a property inherent in Maxwell's theory of the electromagnetic field, which is a result of decade-long observations by various people, most prominently by Faraday.

Now, one obstacle towards the discovery of relativity was that you can interpret Maxwell's theory in different ways. One way was preferred for some time, i.e., the idea that electromagnetic phenomena after all enabled a physical possibility to determine Newton's preferred frame of reference at rest in an "absolute space". In the very mechanistical worldview of the time this reference frame was concretely postulated to be the rest frame of a substance called "the aether" whose vibrations should just be manifested as the observed electromagnetic phenomena, including light as "electromagnetic waves".

As is well known, at latest with the null result of the attempt by Michelson and Morley to demonstrate the "aether wind", the ideas of relativity came up. After important earlier work by Poincare and Lorentz Einstein famously came up with his "special relativity", according to which there's no absolute space and thus no necessity for an aether, and together with the established fact of the "constancy of the speed of light", i.e., the independence of the phase velocity of electromagnetic wave from the relative motion of the source wrt. the detector/observer, this implied also that one has to give up the notion of an "absolute time". The spacetime model had to be adapted accordingly to be described by an affine pseudo-Euclidean manifold with signature (1,3), the Minkowski space.

Not much later it became clear to Einstein that when trying to find a relativistic description of gravitation one had to give up also this spacetime model and substitute it by a dynamical spacetime description with the notion of inertial reference frames as being realized only locally (as is Poincare symmetry of special relativity). All this, of course, was again based on empirical facts. This time it was Einstein's "equivalence principle", which is the crucial characteristic of the gravitational interactions, which lead to the right description.

 

[DanMP]

Words like "postulate" and "assumption" can have different shades of meaning and different associations for different people. Instead of trying to put a label on it and playing word games it would better ...

Even better it would be to finally explain it (the reason for the constancy of the speed of light), instead of assume or postulate it.

 

[vanhees71]

Natural sciences don't explain anything. They just provide a method to objectively and quantitatively observe natural phenomena and find fundamental rules, from which many phenomena can be described mathematically, building theories and models. It is indeed amazing, how few fundamental laws are needed to order a vast plethora of phenomena into such theories. The existence of a "limiting speed" as a property of the description of space and time, i.e., the mathematical description of temporal and spatial order of phenomena, is one of the fundamental observational facts that cannot be "explained" from other such fundamental facts.

 

[phinds]

Even better it would be to finally explain it (the reason for the constancy of the speed of light), instead of assume or postulate it.

Well, you can "explain" the reason for the constancy of the speed of light by saying that it is a consequence of the fine structure constant. BUT ... that really just pushes the problem off to having to explain why the fine structure constant has the value it has. Try doing THAT in your spare time !

 

[Mister T]

Even better it would be to finally explain it (the reason for the constancy of the speed of light), instead of assume or postulate it.

The only "explanation" is that that is the way Nature behaves.

 

[phinds]

The only "explanation" is that that is the way Nature behaves.

See post #14

 

[vanhees71]

Well, you can "explain" the reason for the constancy of the speed of light by saying that it is a consequence of the fine structure constant. BUT ... that really just pushes the problem off to having to explain why the fine structure constant has the value it has. Try doing THAT in your spare time !

Can you explain what you mean by this? The fine structure constant is just given by $\alpha=e^2/(4 \pi \epsilon_0 \hbar c)$ (written in SI units). How does this be a reason for the speed of light being independent of the relative velocity of th light source and the detector?

 

[russ_watters]

Sure you can have and endless series of how/why questions for anything, like a 6 year old does when he doesn't want to go to bed. But that doesn't make it 'just' an assumption. It's necessary to use it as an assumption/postulate as a matter of rigor in logic, but it's always had good explanations/basis. That's why scientists are confident enough to use it that way.

Not being a physicist I go for the easy, observation-based ones per post #15: it's assumed to be constant because it is always measured to be constant (notwithstanding more recent re-arranging of units to define it as a constant).

I feel like some people think this is a flaw in relativity or a dig against scientists that "we can't prove it so we'll just assume it." That's a misunderstanding of the issue.

 

[phinds]

Can you explain what you mean by this? The fine structure constant is just given by $\alpha=e^2/(4 \pi \epsilon_0 \hbar c)$ (written in SI units). How does this be a reason for the speed of light being independent of the relative velocity of th light source and the detector?

I am parroting what I believe @PeterDonis has said here several times, but I believe his statement was in relation to why the speed of light is what it is, not why SR is correct.

 

[Ibix]

One thing you can do is separate the speed of light from the invariant speed $c$. Then you can answer why light travels at the invariant speed - the answer is that it's massless and "massless" and "travels at $c$" are synonymous in relativity. (Note that you can write theories in which photons have mass and work out the implications, and no such implications have been observed.)

The question of why $c$ is frame invariant remains. It's worth noting that it's fairly straightforward to derive from the principle of relativity and an assumption of homogeneity that there are only two possibilities - Galilean relativity and Einsteinian relativity. So one can argue that the invariance of $c$ isn't really needed as a postulate at all: starting with the principle of relativity one is presented with two choices and one merely selects the one that matches experiment. If you accept that argument then you reduce "why is lightspeed invariant" to "why the principle of relativity" (which you have anyway) and "why not Galilean relativity".

 

[PeterDonis]

I am parroting what I believe @PeterDonis has said here several times, but I believe his statement was in relation to why the speed of light is what it is, not why SR is correct.

That particular item has come up in many PF threads, and I'm sure I'm not the only Mentor or SA to have posted something basically equivalent to what you said.

The fine structure constant is just given by $\alpha=e^2/(4 \pi \epsilon_0 \hbar c)$ (written in SI units). How does this be a reason for the speed of light being independent of the relative velocity of th light source and the detector?

The fine structure constant is the appropriate dimensionless constant that characterizes, heuristically, the strength of the electromagnetic interaction. Since this constant is, in our best current theoretical model, a Lorentz scalar whose value is the same everywhere in spacetime, and since in our best current theoretical model, spacetime is locally Lorentz invariant, we should expect all measurements that depend only on the strength of the electromagnetic interaction to be the same everywhere, at all times, and in all directions, regardless of any other factors. The measurement of the speed of light is such a measurement.

 

[Vanadium 50]

The question "why is the speed of light what it is" is the same question as "why is a nautical mile 1013 fathoms?"

 

[bhobba]

To answer the original question, you need to see a modern derivation of Relativity:

http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf​

The existence of a constant C that appears in the equations follows from the Principle Of Relativity. It is not a postulate or an assumption of the theory of relativity. While it shows such a constant exists, the value is experimentally determined. Many experiments have shown its value is the speed of light.

My personal favourite is it is possible from Coulomb's Law and Relativity to derive Maxwell's equations:
http://richardhaskell.com/files/Special%20Relativity%20and%20Maxwells%20Equations.pdf

Compare the derived equations to the actual equations, and C is immediately seen as the speed of light.

That is just one way of measuring the constant C in Relativity - many others exist. Why it has the value it does is the same as why any other measured fundamental physical value has the value it does. It just does - at least until a more fundamental theory comes along that may explain it. But then again, it likely has constants that must also be measured.

Thanks
Bill

 

[pervect]

Even better it would be to finally explain it (the reason for the constancy of the speed of light), instead of assume or postulate it.

You have to start somewhere. In order to explain something, you need something that you already know so you can explain the thing you don't know in terms of the thing that you do know. For instance, if we were to say that the speed of light is a logical consequence of whoozitz, it does you know good, unless you know what whoozitz is.

See also Feynman's famous lecture on "why". if you're not familiar.

 

[PhDeezNutz]

You have to start somewhere. In order to explain something, you need something that you already know so you can explain the thing you don't know in terms of the thing that you do know. For instance, if we were to say that the speed of light is a logical consequence of whoozitz, it does you know good, unless you know what whoozitz is.

See also Feynman's famous lecture on "why". if you're not familiar.

This was the exact video I was thinking about throughout this entire thread.

“In order to ask the question “why?” you have to be working in a framework where things are allowed to be true otherwise you’re perpetually asking why”

 

[strangerep]

One thing you can do is separate the speed of light from the invariant speed $c$. Then you can answer why light travels at the invariant speed - the answer is that it's massless and "massless" and "travels at $c$" are synonymous in relativity. (Note that you can write theories in which photons have mass and work out the implications, and no such implications have been observed.)

The question of why $c$ is frame invariant remains. It's worth noting that it's fairly straightforward to derive from the principle of relativity and an assumption of homogeneity that there are only two possibilities - Galilean relativity and Einsteinian relativity. So one can argue that the invariance of $c$ isn't really needed as a postulate at all: starting with the principle of relativity one is presented with two choices and one merely selects the one that matches experiment. If you accept that argument then you reduce "why is lightspeed invariant" to "why the principle of relativity" (which you have anyway) and "why not Galilean relativity".

Finally!

I was deliberately staying quiet about the "1-postulate" "relativity-only" derivation, waiting to see how long it would take someone else to mention it.

@Aromalsp: the essence of Ibix's reply about is probably the best answer to your original question: one doesn't need a "postulate" or an "assumption" about constancy of the speed of light in order to derive special relativity. But it takes longer and needs more math, hence teachers still mostly take the shortcut of assuming it. Here are some previous threads on this subject, (if you haven't yet departed PF in frustration):

https://www.physicsforums.com/threa...-1-spacetime-only.1000831/page-2#post-6468652
Post #44.

https://www.physicsforums.com/threads/linearity-of-the-lorentz-transformations.975920/#post-6219004
Post #6.

https://www.physicsforums.com/threads/derivation-of-the-lorentz-transformations.974098/
Post #26.

@DanMP: this is also about as close as one can get to actually "explaining it". HTH.

 

[vanhees71]

The fine structure constant is the appropriate dimensionless constant that characterizes, heuristically, the strength of the electromagnetic interaction. Since this constant is, in our best current theoretical model, a Lorentz scalar whose value is the same everywhere in spacetime, and since in our best current theoretical model, spacetime is locally Lorentz invariant, we should expect all measurements that depend only on the strength of the electromagnetic interaction to be the same everywhere, at all times, and in all directions, regardless of any other factors. The measurement of the speed of light is such a measurement.

It doesn't characterize the strength of the electromagnetic interaction "heuristically" but "quantitatively". Its value cannot be predicted with present theory but has to be measured, and it's very accurately measured. Within the SI in its newest definition of 2019 the item to be measured is $\epsilon_0$, because the natural constants going into it, i.e., $e$, $\hbar=h/(2 \pi)$, and $c$ leading to $\alpha=e^2/(4 \pi \epsilon_0 \hbar c)$, have all fixed values. Indeed as you say all measurements indicate the universality of these fundamental constants, and that's why one has chosen this very definition of the SI units in 2019.

 

[A.T.]

So one can argue that the invariance of $c$ isn't really needed as a postulate at all: starting with the principle of relativity one is presented with two choices and one merely selects the one that matches experiment.

Once you introduce "pick whatever matches experiment" into the formulation of a physical theory, then you don't have unambiguous predictions. The function of the 2nd postulate is to pick between the two choices.

 

[Hornbein]

You have to start somewhere. In order to explain something, you need something that you already know so you can explain the thing you don't know in terms of the thing that you do know. For instance, if we were to say that the speed of light is a logical consequence of whoozitz, it does you know good, unless you know what whoozitz is.

I came across this when trying to describe the taste of a durian. It doesn't taste at all like anything else, so I could not do it.

 

[Sagittarius A-Star]

An early derivation of the Lorentz transformation without the 2nd postulate was published by Vladimir Ignatowski in 1910. He argued with a group property of the transformation and the Heaviside-Ellipsoid.

Source:
https://en.wikisource.org/wiki/Translation:Some_General_Remarks_on_the_Relativity_Principle

Unfortunately at the most important part of the derivation, it says only "Then it can easily be demonstrated that the following relation exists". A detailed derivation can be found in the following text, of which I found only the original German version:
https://de.wikisource.org/wiki/Das_Relativitätsprinzip_(Ignatowski)

 

[Mister T]

Even better it would be to finally explain it (the reason for the constancy of the speed of light), instead of assume or postulate it.

Well, suppose it's not true. If the speed of light were relative instead of absolute would you be seeking an explanation for that?

 

[jbriggs444]

Well, suppose it's not true. If the speed of light were relative instead of absolute would you be seeking an explanation for that?

@Ibix alluded to such a possibility in #20. It is possible that light is massive and its speed is indeed relative. The idea is that it only seems to always go at $c$ because the photon mass is low. So very low that light speed is negligibly different from the maximum speed for our relativistic universe.

Experiment puts a fiendishly tight upper bound on the photon mass. ($6 \times 10^{-16} \text{ eV}$ per a quick trip to Google).

 

[Ibix]

Once you introduce "pick whatever matches experiment" into the formulation of a physical theory, then you don't have unambiguous predictions. The function of the 2nd postulate is to pick between the two choices.

Fair point. There seems to me to be a distinction in degree, however, between postulating the speed of light as a constant at the start of a derivation and postulating that option 1 is correct not option 2 at the end of it.

 

[strangerep]

Once you introduce "pick whatever matches experiment" into the formulation of a physical theory, then you don't have unambiguous predictions. The function of the 2nd postulate is to pick between the two choices.

That's a misleading representation of what actually happens in the "1-postulate" derivations of SR. Rather, one derives that the Relativity Principle implies that the most general 1-parameter velocity-boosting symmetry group contained therein admits a universal constant with dimensions of inverse speed squared. Experiment determines the value of that constant.

 

[Ibix]

That's a misleading representation of what actually happens in the "1-postulate" derivations of SR. Rather, one derives that the Relativity Principle implies that the most general 1-parameter velocity-boosting symmetry group contained therein admits a universal constant with dimensions of inverse speed squared.

The versions I'm familiar with get you as far as "it's either Galileo, or Einstein with an unknown constant", and I think it was the rejecting Galileo bit that @A.T. was objecting to. Unless you know a way to reject Galilean relativity with a one-postulate approach? Or are you rejecting it as just being the $c\rightarrow\infty$ version of Einsteinian relativity?