# I Could it be that the photon has a non-zero mass?

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1. Mar 14, 2017

### sha1000

Hi,

Can someone tell me the reason why it is impossible for the photon to have a rest-mass? Without referring to the theories which are actually build on the fact that the photon is massless.

Is there any possibility that the speed of light is not about light and that there is some fundamental critical speed (let's call it c)? Why can't we consider that maybe the photon has a very small mass and that the speed of the photon is infinitely close to this critical speed?
For example we could consider that the energy difference between "red" and "blue" photons comes from the speed-difference of this photons. But the speed difference is so infinitely small that we have an impression that the speed of light doesn't depend on it's frequency.

I really can't figure out why we can't assume the possibility of a "heavy" photon. Many people say that if the photon has a non-zero mass it will become short range. But I'm really not convinced by this kind of explanations because they are based on the theories which are build on the "massless photon" assumption. For me, photon will travel infinitely until it hits something.

Last edited: Mar 14, 2017
2. Mar 14, 2017

### vanhees71

Despite the fact that you ask a question and forbid to give an answer, I still try to give one. Without theory you can't answer this question, because it's a theoretical question.

Indeed, there's nothing in the Standard Model that forbids a photon mass, and thus to identify the limiting speed of Minkowski space with the speed of light (in vacuum) is an empirical fact, and indeed all observations lead to very small boundaries for the photon mass. In the Particle Data book they give a bound $m_{\gamma}<10^{-18} \text{eV}$.

http://pdglive.lbl.gov/Particle.action?node=S000&init=

3. Mar 14, 2017

### BvU

Which theories would that be ? Are you referring to special relativity ? I always thought this 'mass' was an outcome, not an assumption...

4. Mar 14, 2017

### sha1000

Thank you.

You got me wrong. It's not that I forbid to give an answer but I would like to know if there is some physical reason for it. I've already read a lot of threads which are related to this problem so I'm aware of possible explanations.

"Indeed, there's nothing in the Standard Model that forbids a photon mass". So actually it's possible to consider that photon can be "massive" but there is no need in doing so?

5. Mar 14, 2017

### vanhees71

Well, there's no need in the sense that so far there's no hint of a non-zero photon mass by observations.

6. Mar 14, 2017

### sha1000

Yes and no. I have no doubt about the special relativity. I'm just saying that we can obtain the same conclusions in SR if we postulate that there is some critical speed in the Universe and that the photon is infinitely close to it (without saying that it is massless).

7. Mar 14, 2017

### Orodruin

Staff Emeritus
Gauge invariance?

8. Mar 14, 2017

### vanhees71

There's no problem with Abelian gauge invariance and massive gauge bosons (known as the Stueckelberg trick). This trick is not working in the non-abelian case. See, e.g.,

https://arxiv.org/abs/hep-th/0304245

or

Collins, Renormalisation, Cambridge University Press

9. Mar 14, 2017

### weirdoguy

And what does it mean physically?

10. Mar 14, 2017

### Orodruin

Staff Emeritus
But would that not require the introduction of a Stueckelberg scalar (even if you gauge it to zero)? Would you still call this the Standard Model?

11. Mar 14, 2017

### vanhees71

Ok, with a Stueckelberg field it's not the Standard Model anymore.

In the most simple form, the Stueckelberg ghost is non-interacting as are the Faddeev-Popoov ghosts (in Abelian theory). So the upshot is for all calculations of S-matrix elements you can just put a photon mass and a photon propogator $D_{\mu \nu}=-g_{\mu \nu}/(p^2-m^2+\mathrm{i} 0^+)$.

12. Mar 14, 2017

### sha1000

I have an average math background so it really difficult for me to grasp well all your statements ( and I'm trying to understand the paper you shared).

If I'm not wrong the gauge invariance is related to the conservation of the physical laws, for example when you change the coordinate system. But I must admit that I don't have a very clear understanding of it. Could you please give an example of gauge invariance in Special Relativity and why the "massive" photon breaks this invariance in terms of the Standart Model.

Last edited: Mar 14, 2017
13. Mar 14, 2017

### sha1000

Sorry. I didn't understand well your question.

14. Mar 14, 2017

### sha1000

Some citations of this paper:

"The electromagnetic potential is described by a neutral vector field A obeying
Maxwell's equations. Its quantization gives rise to a massless particle, the photon.......

Contrariwise, if one adds to the wave equation of A a mass term, the gauge
invariance is lost, because the field A transforms inhomogeneously and thus the
mass term in the Lagrangian is not invariant. The three components of A left by
the Lorentz condition are then interpreted as belonging to a massive vector field,
that is a massive particle of spin one. This spin-one object has now a longitudinal
polarization, in addition to the two transverse ones.
Stueckelberg's wonderful trick consists in introducing an extra physical scalar
eld B, in addition to the four components A, for a total of five fields, to describe
covariantly the three polarizations of a massive vector field. With the Stueckelberg
mechanism, which we shall exhibit in more detail below, not only is Lorentz covariance
manifest, but also, and most interestingly, gauge invariance is also manifest.
The Stueckelberg field restores the gauge symmetry which had been broken by the
mass term."

The Maxwell's work was based on the idea that light is the electromagnetic field but it is proven that photon is a particle. Is it still convenient to use the "vector field A formalism" which gives rise to a massless particle. (I suppose it's very naive question)?

15. Mar 14, 2017

### weirdoguy

I'm asking what is the difference between photons speed being "infinitely close to c" and being c. Mathematically (in terms of standard real calculus) being infinitly close to c is equal to being exactly c.

16. Mar 14, 2017

### sha1000

The special relativity is constructed on the fact that the speed of light is the same in every inertial frame and that nothing can go faster that light. From this one can easily demonstrate that the mass of any object increase with the velocity, rising to infinity when the object approaches the speed of light. Since it is postulated that the speed of light is the critical speed limit, one must admit that photon is massless.

But if we consider that the critical speed limit c is independent of light and that nothing can go faster or be equal to this speed limit (even photons), we have no longer to postulate that photon must be massless.

This is how I understand this. There is also a gauge invariance but apparently we can bypass this problem as it was pointed out by "vanhees71".

17. Mar 14, 2017

### weirdoguy

18. Mar 14, 2017

### sha1000

19. Mar 14, 2017

### weirdoguy

Still false. You are using a kind of outdated concept of relativistic mass. It does not mean what you think it means.

This does not answer my question. What is the physical difference between "inifnitely close to c" and "c". Mathematically there is none.

And I know that c has actually nothing to do with light and it is a property of spacetime itself.

20. Mar 14, 2017

### Staff: Mentor

No, it isn't, it's a quantum field. Only some states of quantum fields have useful particle interpretations.

21. Mar 14, 2017

### Staff: Mentor

We can assume that possibility, and then we can test it experimentally. Experimentally it turns out to be false, to a very high degree of confidence; see the particle data book results that vanhees71 linked to in post #2.

22. Mar 14, 2017

### sha1000

Thank you for you link but I'm aware of what is the relativistic mass and that it depends only on the observer and that there is no internal structure changes etc.

Any converging function approaches a certain limit but is never equal to it. I really don't understand what do you want to point out.

23. Mar 14, 2017

### Staff: Mentor

No, it isn't; it's constructed on the fact that there is some finite invariant speed. SR does not require that that finite invariant speed be equal to the speed of light; that is an additional empirical fact.

24. Mar 14, 2017

### Staff: Mentor

But there will be some point at which, due to finite measurement accuracy, the function will be indistinguishable from the limit. Which means that, as far as we are concerned, we can't tell the difference.

25. Mar 14, 2017

### ZapperZ

Staff Emeritus
This is a VERY confusing thread. Typically, it is easier to tackle something when there is a fixed target. Unfortunately, this thread appears to have a moving target in which the actual issue seems to have either moved, shifted, changed, or no longer in existence.

I'm citing the original post, because based on what was written, it appears that you are looking NOT for theoretical formulation, but rather experimental justification. Yet, this thread has morphed into a theoretical issue surrounding the constant c.

Back in 2005 (yes, more than 10 years ago) I posted this in a thread:

It listed many of the experimental measurements made by that time that shows no observation on the variation in c, or if there are anything faster than c. I will point out in particular the paper by Schaefer in which he made a measurement over a large range of photon frequency (i.e. larger than your "red" and "blue". If there is a discrepancy here, it will show up more clearly here.

https://arxiv.org/abs/astro-ph/9810479

As "old" as this paper is, and as many new improvements that have been made in similar measurements of c, no experiment has contradicted this limit to date.

So now, it leaves you holding an empty bag of experimental results in which there are no empirical indication of a variation in c. You may argue that we don't know how this will turn out as our technology and measurement improve over time. Sure. But based on what we know now both from theory and experiments, there is an overwhelming body of evidence to indicate that c is the constant that we know of, and that other scenarios are relegated to postulates and speculation at this point.

This is the present-day reality.

Zz.