Mass of Photon: Consequences & Experiments - L.C. Tu et al (2004)

[ZapperZ]

There is a very good review article on the consequences of the mass of the photon, and a list of experiments that tried to detect such consequences. The paper is L.C. Tu et al., Rep. Prog. Phys. v.68. p.77 (2004). Most people forget that the possible mass of a photon effects not only SR and GR, but also the classical maxwellian description of light. Such postulate will produce a number of consequences, such as the variation in the speed of light for different frequencies, etc. The list of experiments that try to test for these consequences have put an increasingly stringent upper limit on any possible mass of a photon.

I should also point out, for people who are not in this field, that this is another example where, if one makes a claim or postulate (such as "a photon has mass"), then there has to be a series of measurable consquences. This is what distinguish physics (and science in general) from pseudoscience and quackeries. Also note that while we accept photons to have no rest mass, it still doesnt't stop us from continually testing this postulate. The often-made accusation that we simply and blindly follow what we have been taught is clearly false here.

Zz.

P.S. If you've read my Journal entries, then you would have had this info already. If you haven't, take note that the article in question here is published by the Institute of Physics (IoP). The online edition of ALL of IoP papers can be accessed for the first 30 days that they appear electronically FOR FREE! (You may need to register first, I think). So even if you have no subscription, you can still get this article. Just go to the IoP journal website at

http://www.iop.org/EJ/S/3/1350/

and look for the relevant journal with this article. This particular article just appeared either today or yesterday. So you have barely a month left to get free access to it.

 

[robphy]

Most people forget that the possible mass of a photon effects not only SR and GR, but also the classical maxwellian description of light.

SR and GR would still be the same.
If the photon had a nonzero mass, then that photon would not travel on a null curve. One would then probably replace the word "light" in "light cone", "light clock", "light-like", "invariance of the speed of light" by something else, e.g. "[maximum] signal".
Historically, "light" was used because it was believed that it traveled at the invariant maximum signal speed.

 

[ZapperZ]

SR and GR would still be the same.
If the photon had a nonzero mass, then that photon would not travel on a null curve. One would then probably replace the word "light" in "light cone", "light clock", "light-like", "invariance of the speed of light" by something else, e.g. "[maximum] signal".
Historically, "light" was used because it was believed that it traveled at the invariant maximum signal speed.

What I meant by "effect" was that there will be a series of consequences from SR, GR, and classical E&M that would show deviations from the assumption of zero rest mass. I didn't mean that they need to be overhaul.

Zz.

 

[selfAdjoint]

If the photon had mass, EM would have a longitudinal component of vibration. But such a compressive type of vibration has never been observed. In fact experiments to establish upper limits for the mass of the photon use this fact because what they really measure is the longitudinal component of radiation. No experiment can ever prove the longitudinal component or the photon mass to be exactly zero, because of finite experimental accuracy. What they do is to limit them into smaller and smaller windows near zero. Currently the mass of the photon can not be bigger than 10^-8 Electron Volts.

 

[pervect]

Just go to the IoP journal website at

http://www.iop.org/EJ/S/3/1350/

and look for the relevant journal with this article. This particular article just appeared either today or yesterday. So you have barely a month left to get free access to it.

Alas, as a non-subscriber and non-registered person, I can say that when I click on the URL above, it tells me "access forbidden" :-(.

 

[robphy]

Try
http://www.iop.org/EJ/toc/-ff30=7
http://www.iop.org/EJ/abstract/-ff30=7/0034-4885/68/1/R02 (has abstract)

 

[pmb_phy]

There is something called the Proca Lagrangian. It is the Lagrangian for the EM field which contains the photon's proper mass. Plug it into Lagrange's equations for fields and you'll get Maxwell's equations which are consistent with a non-zero photon mass.

Pete

 

[pervect]

Try
http://www.iop.org/EJ/toc/-ff30=7
http://www.iop.org/EJ/abstract/-ff30=7/0034-4885/68/1/R02 (has abstract)

OK, that worked -thanks!

 

[juju]

Hi,

If a photon had mass and traveled at c, then it would have infinite energy according to relativity.

You would have to place the photon outside of relativity or modify relativity to remove the singularity at c.

juju

 

[Chronos]

Energy has a rest mass equivalent, however a photon can have energy without any actual rest mass. The relation between the mass and energy of an object can be written as
E = m c^2 / sqrt(1 - v^2/c^2) ,or
E^2 = m^2 c^4 + p^2 c^2
where E is energy, m is rest mass, v is velocity, and p is momentum.
As you will note, E can have a numerical value even when m is zero.

 

[ZapperZ]

Alas, as a non-subscriber and non-registered person, I can say that when I click on the URL above, it tells me "access forbidden" :-(.

OK, sorry for this late reply. Try this url

http://www.iop.org/

and click on "Journals" link, and then "Electronic Journals". I'm guessing that I gave you the "backdoor" entrance to the journals which requires that you have already registered.

Please let me know if you are still having problems. It is difficult for me to tell which is accessible and which isn't since I have site-wide access to almost everything (one of the perks of working at a Nat'l Lab).

Zz.

 

[Andrew Mason]

What I meant by "effect" was that there will be a series of consequences from SR, GR, and classical E&M that would show deviations from the assumption of zero rest mass. I didn't mean that they need to be overhaul.

The very essence of SR is the principle of relativity which states that all inertial frames are equivalent: the laws of physics are the same in all inertial frames. SR would need an entire overhaul is photons had rest mass. Every photon would define an inertial frame in which the laws of physics would differ from the laws of physics in all other inertial frames: i.e. a frame in which the speed of light is 0: where $\epsilon_0 \mu_0 \rightarrow \infty$

AM

 

[ZapperZ]

The very essence of SR is the principle of relativity which states that all inertial frames are equivalent: the laws of physics are the same in all inertial frames. SR would need an entire overhaul is photons had rest mass. Every photon would define an inertial frame in which the laws of physics would differ from the laws of physics in all other inertial frames: i.e. a frame in which the speed of light is 0: where $\epsilon_0 \mu_0 \rightarrow \infty$

AM

I'm not sure what you mean by "essense" of SR (and how that is separate from the "principle of relativity"), but SR is built on postulates which have been, and continually verified by experiments.

However, it isn't automatic that even if we discover that a photon has a rest mass, that the entire SR needs to be overhaul. There is such a thing as a "weak violation" in nature. We certainly did not have to overhaul our entire physics even after the discovery of CP-violating events, as fundamentally significant as that is. The "how" and "when" the violation occurs are as important as the violation itself in determining to what extent any principle in physics needs to modified.

Zz.

 

[jcsd]

Yep it's pretty obvious how to 'modify' SR in the unlikely event ofa non-zero photon rest mass being discovered i.e. rather than having the second postulate refer dircetly to light, have it refer to some hypothetical particle traveling along a null worldline (I'm sure that some people already prefer a formulation along this lines anyway).

 

[Andrew Mason]

I'm not sure what you mean by "essense" of SR (and how that is separate from the "principle of relativity"), but SR is built on postulates which have been, and continually verified by experiments.

Essence means that which is essential. If SR loses its essential postulate, it has to be overhauled, not tweaked. I am saying that 0 rest mass for the photon is essential to the principle of relativity. And 0 means 0, not .000000000000000000000000000000000000000000000000000000001

However, it isn't automatic that even if we discover that a photon has a rest mass, that the entire SR needs to be overhaul. There is such a thing as a "weak violation" in nature. We certainly did not have to overhaul our entire physics even after the discovery of CP-violating events, as fundamentally significant as that is. The "how" and "when" the violation occurs are as important as the violation itself in determining to what extent any principle in physics needs to modified.

But we are not talking about isolated violations of some kind of principle of symmetry. We are talking about every photon having rest mass, always. The principle of relativity - the equivalence of all inertial frames - would be shattered.

AM

 

[gonzo]

Can someone explain to me the actual meaning of the rest mass of a particle that can never be at rest? Or is it just a value that can be theoretically calculated, and based on that theory, some other events might occur that can be measured, though this value itself can never be directly measured as it doesn't correspond to any "real" event or state in the universe?

 

[ZapperZ]

Essence means that which is essential. If SR loses its essential postulate, it has to be overhauled, not tweaked. I am saying that 0 rest mass for the photon is essential to the principle of relativity. And 0 means 0, not .000000000000000000000000000000000000000000000000000000001

First of all, you do not have to go to this extent to illustrate this. I deal with superconductivity where the resistivity is "0" and not an approximation. So I KNOW this.

Secondly, unlike superconductivity where the resitivity can be proven via First Principle to necessarily be zero to exhibit ALL of the effects we observe, the equivalence of c in all inertial frame is a postulate. It means that it cannot be derived via any First Principle means.

But we are not talking about isolated violations of some kind of principle of symmetry. We are talking about every photon having rest mass, always. The principle of relativity - the equivalence of all inertial frames - would be shattered.

AM

I can easily bring out a specific possible example that is being seriously considered, that "c" might be different at Planck's scale! This is a clear example of a "weak violation" that only occurs with a strict condition, very much like the weak CP-violation. However, even if this were to occur, it has a more significant implication to the nature of "space" and "time" themselves, and thus, the nature of Lorentz transform needs to be modified. It certainly doesn't require wholesale overhaul of SR, considering how convincing it has worked so far!

BTW, if you think that CP-violation is only "some kind of principle of symmetry" and have no fundamental implication throughout ALL of physics, then you have missed a huge part of it.

Zz.

 

[jcsd]

Andrew I thibk you missing the fact that SR can be formulated in an equivalent way indepenedent of the speed of light. I'd argue that a non-zero rets mass photon doesn't need any modifcation to the first postulate or breach Lorentz invaraince.

 

[Andrew Mason]

Can someone explain to me the actual meaning of the rest mass of a particle that can never be at rest? Or is it just a value that can be theoretically calculated, and based on that theory, some other events might occur that can be measured, though this value itself can never be directly measured as it doesn't correspond to any "real" event or state in the universe?

The point is that if it has rest mass, it can be at rest in some inertial frame.

AM

 

[ZapperZ]

The point is that if it has rest mass, it can be at rest in some inertial frame.

AM

Not necessarily... The electron neutrino was thought to have zero rest mass and only travels at c. Now, it has a miniscule, but still non-zero rest mass, and it is still practically at c in any boost frame that we deal with. Even in high energy experiments where the boost frame can be at the same speed at the colliding particles, the electron neutrino is STILL considered, for all practical purposes, to be at c even in that frame. Other than the flavor mixing angle and the need to extend the Standard Model, there hasn't been a "overhaul" of anything.

Zz.

 

[jcsd]

The point is that if it has rest mass, it can be at rest in some inertial frame.

AM

That is true, though apart from making in practical terms little diffculty that wouldn't be the nail in the coffin for SR, clearly electrons, protons, etc, all have rest frames, it is only massless particles that we need to worry about having rest frames in SR. Also clearly there can be relativstic theories of forces whose exchange particles are massive, so a massive photon doesn't imply any trouble for SR merely by being massive. A masisve photon would have very serious ramifcations in QED I imagine.

 

[Andrew Mason]

Secondly, unlike superconductivity where the resitivity can be proven via First Principle to necessarily be zero to exhibit ALL of the effects we observe, the equivalence of c in all inertial frame is a postulate. It means that it cannot be derived via any First Principle means.

Well, it derives from the Principle of Relativity. If that principle is correct, then the speed of a photon has to be the same in all inertial frames. This means it cannot be associated with any rest frame itself, so it cannot have rest mass. But I do agree with you that the principle of relativity is a fundamental postulate. If it is not true, then Special Relativity is wrong.

I can easily bring out a specific possible example that is being seriously considered, that "c" might be different at Planck's scale!

What is important is that it be the same for all inertial observers. Now if the speed of light was x for observer A and y for observer B, there would be a problem. But I don't see a problem if all observers agree on the same value for c.

This is a clear example of a "weak violation" that only occurs with a strict condition, very much like the weak CP-violation. However, even if this were to occur, it has a more significant implication to the nature of "space" and "time" themselves, and thus, the nature of Lorentz transform needs to be modified. It certainly doesn't require wholesale overhaul of SR, considering how convincing it has worked so far!

But this is not what we were talking about. We were talking about all photons having a rest mass and, therefore, attaching a frame of reference to every photon at all times. We are not talking about some narrow exception in some narrow circumstances.

BTW, if you think that CP-violation is only "some kind of principle of symmetry" and have no fundamental implication throughout ALL of physics, then you have missed a huge part of it.

I never said that. You were comparing isolated violations of the principle of relativity to isolated CP violation. I was just saying that we were not talking about an isolated exception to the invariance of c, analagous to isolated violations of CP invariance, (ie as if the invariance of c was some kind of principle of symmetry). Besides exceptions to CP invariance do not shatter any fundamental postulate of physics as far as I am aware. Now if you add time reversal to that we might have a problem.

AM

 

[selfAdjoint]

Besides all the relativistic arguments, failure to find a longitudinal component of EM radiation puts an egregriously tiny upper limit on photon mass.

 

[Andrew Mason]

Not necessarily... The electron neutrino was thought to have zero rest mass and only travels at c. Now, it has a miniscule, but still non-zero rest mass, and it is still practically at c in any boost frame that we deal with. Even in high energy experiments where the boost frame can be at the same speed at the colliding particles, the electron neutrino is STILL considered, for all practical purposes, to be at c even in that frame. Other than the flavor mixing angle and the need to extend the Standard Model, there hasn't been a "overhaul" of anything.

I agree. But the neutrino is not a photon. Its existence is inferred from the dynamics of particle interactions. The laws of physics required it to have energy and momentum and zero charge, but did not require it to have zero mass. It has always been an open question whether it traveled at a little under c and had some rest mass.

While the discovery that a neutrino likely has rest mass is very important, it does not change our understanding of the laws of physics - so long as it travels at something less than c. A photon must travel at the speed of light relative to the neutrino in the neutrino's rest frame.

AM

 

[Andrew Mason]

That is true, though apart from making in practical terms little diffculty that wouldn't be the nail in the coffin for SR, clearly electrons, protons, etc, all have rest frames, it is only massless particles that we need to worry about having rest frames in SR.

But that is a big "only". SR is based on a single postulate: the principle of relativity. Every particle of matter determines a rest frame. If light has a rest frame, then it cannot travel at the speed of light with respect to all inertial frames. It could not even travel at the same speed relative to any two intertial frames. We would have to reinvent the aether. So our understanding of the universe would change dramatically.

Also clearly there can be relativstic theories of forces whose exchange particles are massive, so a massive photon doesn't imply any trouble for SR merely by being massive.

But massive virtual exchange particles can have only very limited ranges on the order of 10^-18 m. This is required by SR. Electromagnetic forces have infinite range. So if the photon, which is the exchange particle for the EM force, had any mass at all, there would have to be a dramatic change in EM theory.

AM

 

[jcsd]

But that is a big "only". SR is based on a single postulate: the principle of relativity. Every particle of matter determines a rest frame. If light has a rest frame, then it cannot travel at the speed of light with respect to all inertial frames. It could not even travel at the same speed relative to any two intertial frames. We would have to reinvent the aether. So our understanding of the universe would change dramatically.

SR is based on two postulates, the second psotulate is that lthe speed of light is constant, but as I said earlier this can be easily changed. Your making too many asusmptions about what we'd have to do

But massive virtual exchange particles can have only very limited ranges on the order of 10^-18 m. This is required by SR. Electromagnetic forces have infinite range. So if the photon, which is the exchange particle for the EM force, had any mass at all, there would have to be a dramatic change in EM theory.

AM

If a photon does have mass we know it is very small, 10^-18 m we are talking about particles which must have hugely greater mass than the photon, clearly what would be needed is a theory with a an exchange particl;e of neglgible mass that can recover em in the limit, I don't see anything inherently unrelatvistic about that.

 

[Andrew Mason]

SR is based on two postulates, the second postulate is that lthe speed of light is constant, but as I said earlier this can be easily changed. Your making too many asusmptions about what we'd have to do

Einstein postulated that the laws of electrodynamics were valid in all inertial frames of reference (which he referred to as the principle of relativity). He also postulated that the speed of light, c, was independent of the speed of its source. However, since Maxwell's equations provide that the speed of light depends only on $\epsilon_0 \text{ and } \mu_0$, the first postulate leads to the second (ie. Maxwell's equations apply without modification in all inertial frames). The two postulates can be combined into a single postulate: the laws of physics are the same (identical) in all inertial frames.

If a photon does have mass we know it is very small, 10^-18 m we are talking about particles which must have hugely greater mass than the photon, clearly what would be needed is a theory with a an exchange particl;e of neglgible mass that can recover em in the limit, I don't see anything inherently unrelatvistic about that.

If it was discovered that photons have rest mass then Maxwell's equations would not apply in all frames of reference. Differences between rest frames would be detectible. The speed of light would depend on the speed of its source. The laws of electrodynamics would not be valid in all inertial frames (ie they would require some frame-dependent modification). What would be left of SR?

AM

 

[Rob Woodside]

Relativity and photon mass

Quote from someone else:
We are talking about every photon having rest mass, always. The principle of relativity - the equivalence of all inertial frames - would be shattered.

Reply:
Special Relativity rests on two postulates as well as many currently credible background assumptions. Einstein distilled these two postulates out of the other assumptions to ensure that the spacetime of mechanics was the same as that of electromagnetism. One of these was Galileo's principle of relativity, which you rightly point out is the "equivalence of all inertial frames". The second postulate ascribes the same maximal speed for a material body in each inertial frame. Einstein identified that speed as the speed of light. This requires light to be massless and is so far well confirmed experimentally. Not so long ago neutrinos were taken as massless and now non zero masses are being measured. If that were to happen to light, light would no longer have the maximal speed; but, as another poster pointed out, the postulate of a maximal speed would remain intact. Notice further that Newtonian Mechanics obeys Galileo's principle of relativity and in Newtonian Mechanics the postulate of a maximal velocity is replaced with an assumption of absolute time and space that is the same in all inertial frames. Consequently the principle of relativity is logically independent from the speed of light and remains intact no matter what speed light has.

 

[dextercioby]

Einstein postulated that the laws of electrodynamics were valid in all inertial frames of reference (which he referred to as the principle of relativity). He also postulated that the speed of light, c, was independent of the speed of its source. However, since Maxwell's equations provide that the speed of light depends only on $\epsilon_0 \text{ and } \mu_0$, the first postulate leads to the second (ie. Maxwell's equations apply without modification in all inertial frames). The two postulates can be combined into a single postulate: the laws of physics are the same (identical) in all inertial frames.



If it was discovered that photons have rest mass then Maxwell's equations would not apply in all frames of reference. Differences between rest frames would be detectible. The speed of light would depend on the speed of its source. The laws of electrodynamics would not be valid in all inertial frames (ie they would require some frame-dependent modification). What would be left of SR?

AM

My guess is that if the photon would have a mass,SR & QM would be the only theories which need no modification.Classical electrodynamics would use a new set of fundamental equations which should be called Proca equations and confrunting them with experience would pose no problem since the experimental evidence of a third degree of freedom for the photon would have led us to the theory of massive photons.

At the quantum field level,the impact wiuld be devastating,since no gauge invariance would exist (massive em field has,just like Dirac field second class constraints and "adieu" to gauge invariance which comes from the existence of first class constraints),then not only QED would modify,but the entire physics.Would we be able to speak about QCD and SM ??If the em field is not gauge invariant,how could one build gluon/YM fields.Gauge invariance would be present only in GR and so far SM and GR have not been put together in the presence of gauge invariance for EM,but whether it vanishes??

The fact that photons have mass simply requires that in the postulates of SR the exression "speed of light" be replaced by the speed of "vqhvhvqlv",where "ndfkjvnbdfqkjv" would not be light or have any possible connection with the new concept of light...

If I said something stupid,please forgive me... :tongue2: Even "science advisors" can be wrong,not to mention "nonspecialists" like me...

 

[jcsd]

Einstein postulated that the laws of electrodynamics were valid in all inertial frames of reference (which he referred to as the principle of relativity). He also postulated that the speed of light, c, was independent of the speed of its source. However, since Maxwell's equations provide that the speed of light depends only on $\epsilon_0 \text{ and } \mu_0$, the first postulate leads to the second (ie. Maxwell's equations apply without modification in all inertial frames). The two postulates can be combined into a single postulate: the laws of physics are the same (identical) in all inertial frames.

Yes, but your not asking yourself whether the postulates can be altered in minor amost superficial ways, to make them independent of light or any theory of light, the answer is yes as long that theory of light is Lorentz covaraint.

If it was discovered that photons have rest mass then Maxwell's equations would not apply in all frames of reference. Differences between rest frames would be detectible. The speed of light would depend on the speed of its source. The laws of electrodynamics would not be valid in all inertial frames (ie they would require some frame-dependent modification). What would be left of SR?

AM

Basically you're assuming Lornetz invaraince won't hold, big usprise that special relativity doesn't work, but the asusmption that Lorntz covariance won't hold is unnecessary.

 

[Nereid]

If the photon were found to have a non-zero mass, experimental physicists would go wild! (not an original point, Zapper made it much earlier).

At least it would point to some potentially very, very interesting 'new physics', and within a decade or three no doubt some other quite curious or intriguing things would be discovered by the experimentalists. The most frustrating scenario would be if all this 'new physics' remained at the very edge of detectability, with large error bars, and results that were really not much more than hints.

The exciting thing is that there's absolutely no way to predict how it would turn out - a dramatic new world that makes the early years of last century look like pure tedium? some almost trivial, subtle modifcation to existing theories that ties up all loose ends? pure validation for one of today's 'fringe' ideas? a slow, hard slog that eventually leaves either M-Theory or LQG the last theory standing?

 

[Andrew Mason]

Special Relativity rests on two postulates as well as many currently credible background assumptions.

No assumptions - other than the two postulates.

Not so long ago neutrinos were taken as massless and now non zero masses are being measured. If that were to happen to light, light would no longer have the maximal speed; but, as another poster pointed out, the postulate of a maximal speed would remain intact.

If photons have rest mass the speed of light would depend on the speed of its source. So it would destroy Einstein's second postulate.

Einstein did not postulate that c is the maximum speed attainable. He postulated that the speed of light depended only upon properties of space and so was independent of the motion of its source. He showed how this postulate with the principle of relativity leads to the conclusion that the speed of light cannot be exceeded. The speed of light can be exceeded if an inertial frame of reference can be attached to a photon. So the discovery of photon rest mass would negate the postulates of relativity.

Consequently the principle of relativity is logically independent from the speed of light and remains intact no matter what speed light has.

SR is inextricably tied to the speed of a photon in free space being the same for all inertial observers. This would be completely destroyed if photons have rest mass, no matter how small an amount. The essential conclusion of SR is not that there is some maximum speed. It is that the speed of a photon cannot be exceeded. So I think your suggestion is incorrect.

AM

 

[Andrew Mason]

If the photon were found to have a non-zero mass, experimental physicists would go wild! (not an original point, Zapper made it much earlier).

At least it would point to some potentially very, very interesting 'new physics', and within a decade or three no doubt some other quite curious or intriguing things would be discovered by the experimentalists. The most frustrating scenario would be if all this 'new physics' remained at the very edge of detectability, with large error bars, and results that were really not much more than hints.

The exciting thing is that there's absolutely no way to predict how it would turn out - a dramatic new world that makes the early years of last century look like pure tedium? some almost trivial, subtle modifcation to existing theories that ties up all loose ends? pure validation for one of today's 'fringe' ideas? a slow, hard slog that eventually leaves either M-Theory or LQG the last theory standing?

I agree completely. I think the theoretical physicists would go wild too.

And I should say that agree with the fundamental point that Zapperz was making at the beginning of this thread, which is that any theory, relativity included, is subject to physical evidence, so experimental testing is always valid. I just think he was understating a little the impact the discovery of photon mass would have.

AM

 

[ZapperZ]

I agree completely. I think the theoretical physicists would go wild too.

And I should say that agree with the fundamental point that Zapperz was making at the beginning of this thread, which is that any theory, relativity included, is subject to physical evidence, so experimental testing is always valid. I just think he was understating a little the impact the discovery of photon mass would have.

AM

No, I'm not trying to understate anything. I'm trying to counter your argument that any discovery of the photon mass, no matter how "weak" the violation is, will AUTOMATICALLY result in the "overhaul" of SR. I disagree with this "automatic" thing. I brought up a few examples where fundamental violation of perceived symmetry of our universe did not require any such overhaul.

Now I'm not saying there won't be one. I'm saying you can't tell based on previous similar instances - after all, the history of such events are all we have to go by. Moreover, the current form of SR already works! That is the biggest "evidence" we have right now that this form has a lot of validity to it! It is the claim that automatically, SR must be over haul with any kind of photon mass discovery. That is what I was arguing against.

Zz.

 

[Rob Woodside]

No assumptions - other than the two postulates.
Reply:
Where does the notion that space-time is made of events come from? Point particles? Worldlines?, Extended bodies?, World tubes?, etc. Then there are the mathematical assumptions behind a manifold that is supposed to descrbe space-time. If those postulates were the only assumptions, the theory would be vaccuous. Your first postulate uses the notion of inertial frame ("all inertial frames are equivalent"), but never tells you what an inertial frame is. The second postulate doesn't say what light is. Without some major assumptions the postulates read: 1)All glorps are equivalent; 2) The speed of zilch in a glorp is independant of the emitter or absorber. People are always using implicit assumptions and should be aware of it.

Quote = Andrew Mason
If photons have rest mass the speed of light would depend on the speed of its source. So it would destroy Einstein's second postulate.

Reply:
Quite so. Are we frozen in history with only Einstein's words to guide us or has special relativity developed in any way in the last century? What is the second postulate really about? If you think it is about light and it turns out experimentally that light has a rest frame, then the second, not the first, postulate fails. Einstein was trying to give mechanics and electromagnetism the SAME space-time. The first postulate was a boulder of truth that came from mechanics and the second from electromagnetism under the natural (since Maxwell) assumtion that light was electromagnetic in origin. Instead of "light" Einstein could have used "changes in the electromagnetic field". Today we could use "changes in space-time curvature" on a flat background, but Einstein's point was to put mechanics and E/M on the same footing. That "something's" speed in an inertial frame is a constant independant of its emitter or absorber seems like a tame and testable assumption and that is probably why Einstein chose it. Logically that assumption leads to the "something" having a maximum invariant velocity. Why not take that as the second postulate? Then if light does have a rest frame, the well tested special relativity remains valid.