# Mass of the photon

1. Oct 2, 2012

### bgq

Hi,

Is the mass of the photon exactly zero, or it has some little mass?

2. Oct 2, 2012

3. Oct 2, 2012

### mathman

Current theory says anything with mass cannot travel at the speed of light. If photons had mass it would mean photons cannot travel as fast as photons.

4. Oct 3, 2012

### andrien

an indirect way to ask this question is how much valid is the inverse square relationship

5. Oct 3, 2012

### bgq

What if the photons are really have some mass and their speed is slightly less than c; in such case, c may be not called speed of light, but a universal constant. I have read that relativity will not be affected by this.

6. Oct 3, 2012

### bgq

I really can't see the connection, will you clarify this to me please.

7. Oct 3, 2012

### tom.stoer

Massless quanta mediate forces (interactions) which scale (in 3+1 dimensions) as 1/r2; in the case of photons this applies to the Coulomb force of an electric field.
Massive quanta with m>0 mediate forces (interactions) which scale (in 3+1 dimensions) as e-mr (where I have omitted some terms); this is e.g. the case for pions mediating the strong force between nucleons. Due to the exponential suppression these forces are of very short range.
So a long-range electric force puts some upper limits of the photon mass.

8. Oct 3, 2012

### Ashiataka

Of course photons have mass. Mass-energy equivalence gives this:
$$E^2=m_0^2c^4+p^2c^2$$
but for a photon $$m_0=0$$ so that term disappears. We're left with
$$E^2=p^2c^2$$ or
$$E=pc$$
A photon's energy depends only on its frequency:
$$E=h\nu$$
Putting that in and rearranging gives
$$p=\frac{h\nu}{c}$$
This is how you get photon pressure, Newton's second law gives
$$F=\frac{dp}{dt}$$
Which then becomes
$$F=\frac{h}{c}\frac{d}{dt}\nu$$
So the force a photon applies is only dependent on its change in frequency.

9. Oct 3, 2012

### tom.stoer

we are talking about the rest mass i.e. the invariant mass, not about the relativistic mass

10. Oct 3, 2012

### Ashiataka

Note that it doesn't say

11. Oct 4, 2012

### andrien

here is a link which can clarify more of it ,it seems that the account is same as that given in beginning of jackson's book.there is numerous data on upper limit of mass of photon.
"www.princeton.edu/~romalis/PHYS312/.../TuCoulomb.pdf" [Broken]

Last edited by a moderator: May 6, 2017
12. Oct 4, 2012

### vanhees71

Just to clarify. Nowadays we don't use the idea of "relativistic mass" anymore. We call that quantity energy as it should be called. If we talk about mass in quantum field theory we mean the invariant mass of the corresponding quantum fields. The photon (i.e. the electromagnetic field) in the Standard Model has 0 invariant mass.

This is a well tested hypothesis as can be seen in the citations already given in this thread.

13. Oct 5, 2012

### andrien

that link is not working so try this

Last edited by a moderator: May 6, 2017
14. Oct 6, 2012

### BrettJimison

energy = mass.
If photons have energy, then they have mass.
But then again, Einstein also said that anything with mass cant travel at the speed of light..hmmmm

15. Oct 7, 2012

### vanhees71

No! Energy cannot be mass, because energy is the time component of four momentum and mass is a scalar quantity. So these two quantities cannot be equal.

Correct is that the invariant mass of an object changes when somehow the inner energy of the object changes. A nice pedagogic example, which you can evaluate analytically completely, is a capacitor which has a higher mass when charged than the uncharged one. The mass change is given by the stored energy of the electric field between its plates divided by $c^2$.

Well measured is the effect in nuclear physics, where the mass of nuclei is smaller than the sum of the masses of the protons and neutrons that constitute the nucleus. The reason is the binding energy, and the "mass defect" is again given by the binding energy divided by $c^2$.

The opposite effect is the mass of the hadrons. Take the proton. It consists of three quarks, which have a mass of some $\mathrm{MeV}/c^2$ but the proton's mass is about $940 \mathrm{MeV}/c^2$. In a crude model you can understand this by treating the bound state as three quarks in a potential well (the socalled bag model), within which the quarks are confined. This leads to rapid motion of the quarks bouncing back and forth between the edges of the bag. The corresponding kinetic energy makes up most of the mass of the proton. BTW this shows that it is wrong to claim that the mass of the things surrounding us comes from the Higgs mechanism. The Higgs mechanism provides usually some percent of the mass but the main contribution is dynamically generated from the strong interaction, but that's another story.

16. Oct 7, 2012

### Meselwulf

We are missing a conversion factor, the speed of light squared as a coefficient on the mass, and energy equivalent like this does not actually mean that mass is energy per se, rather two different forms of each other.

This is what needs to be kept in mind.

The rest mass of a photon is zero or it is very very small... ridiculously small... something like $$10^{-51}$$ kg.

17. Oct 7, 2012

### bgq

Well, It seems from the above that the mass of the photon is either zero or too small that we can't detect.
Thank you all for your replies.

18. Oct 7, 2012

### Staff: Mentor

Well... current theory (relativity) says that there is a constant speed which is an upper limit for massive particles, and that all massless particles travel at that constant speed.
As light is probably massless, this speed is usually called "speed of light". But the speed limit is independent of light. If photons had a mass, photons could not travel as fast as the speed limit, which is not a contradiction.

19. Oct 7, 2012

### Meselwulf

However... photons under the right kind of circumstances (ie. the medium) can make a photon behave as though it has a mass (rest).

20. Oct 7, 2012

### andrien

Are you trying to say that in a medium photons have speed less than c (refractive index).then it is not right because the phase velocity of light may seem to be c/n but photons always travel with speed C.It is the electric field of light which causes the shaking of electrons of the medium so they emit their own radiation (radiation of protons can be neglected because of their mass) which when combined with original one gives a phase shift which can be described by giving light a speed C/n.