# The mass of the photon

1. Nov 23, 2004

### ZapperZ

Staff Emeritus
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.

2. Nov 23, 2004

### robphy

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 travelled at the invariant maximum signal speed.

3. Nov 23, 2004

### ZapperZ

Staff Emeritus
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.

4. Nov 23, 2004

Staff Emeritus
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.

5. Nov 23, 2004

### pervect

Staff Emeritus
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" :-(.

6. Nov 23, 2004

### robphy

7. Nov 23, 2004

### 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

8. Nov 23, 2004

### pervect

Staff Emeritus
OK, that worked -thanks!

9. Nov 24, 2004

### juju

Hi,

If a photon had mass and travelled 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

10. Nov 24, 2004

### 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.

11. Nov 29, 2004

### ZapperZ

Staff Emeritus
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.

12. Dec 4, 2004

### Andrew Mason

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

13. Dec 4, 2004

### ZapperZ

Staff Emeritus
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.

14. Dec 4, 2004

### 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 travelling along a null worldline (I'm sure that some people already prefer a formulation along this lines anyway).

15. Dec 4, 2004

### Andrew Mason

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

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

16. Dec 4, 2004

### 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?

17. Dec 4, 2004

### ZapperZ

Staff Emeritus
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.

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.

18. Dec 4, 2004

### 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.

19. Dec 4, 2004

### Andrew Mason

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

AM

20. Dec 4, 2004

### ZapperZ

Staff Emeritus
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.