# What is the mass of a photon?

1. Apr 11, 2007

### brianthewhitie7

What is the mass of a photon?

And is the mass of the photon being measured at the speed of light?

2. Apr 11, 2007

### windscar

A photon should have a rest mass of zero, that would allow it to travel at the speed of light. At the speed of light it has very little or no mass, because light bends in gravitational fields. But, this could be due to haveing a small amount of mass or due to the curvature of space time itself. It could depend on what theory of gravity you are using.

3. Apr 11, 2007

### pervect

Staff Emeritus
try reading the standard sci.physics.faqs on this topic:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photonMass.html [Broken]
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Photons have no invariant mass - some people do say that they have a relativistic mass, but this usage has been depreciated.

Last edited by a moderator: May 2, 2017
4. Apr 12, 2007

### Ballon

Is that relative with the fact that a photon...cannot rest ?

5. Apr 12, 2007

### anantchowdhary

A photon's energy is defined using the frequency of the EM wave.So if a photon is at rest,it will have no energy.....and as a photon is a packet of energy....it ceases to exist at rest...therefore it CANNOT exist at rest

6. Apr 12, 2007

### Ballon

Yes, so if making a reference to the photon rest mass is not valid, since the photon does not exist at rest, does it have a mass in motion ?

Last edited: Apr 12, 2007
7. Apr 12, 2007

### anantchowdhary

It has energy.....and some people prefer and some dont prefer to call it relativistic mass....

The mass in motion can said to be equivalent to:$$\frac {h \nu}{c^2}$$

8. Apr 12, 2007

### rbj

i'm one of the holdouts that do not like calling photons "massless" without at least a little qualification. photons have energy and photons have momentum. i don't think anyone disagrees with that. so, it depends on how one defines mass. if you say that the mass of a particle or object is the same $m$ as in

$$E = m c^2$$

then, since $E = h \nu$, photons have an effective mass ("relativistic mass", whatever term they deprecate) of

$$m = \frac{E}{c^2} = \frac{h \nu}{c^2}$$

they travel at a speed of $c$ relative to any observer, so their momentum is

$$p = m v = m c = \frac{h \nu}{c}$$

(this is the assumed definition of "effective mass" being the momentum of an object, relative to an observer, divided by the velocity of the object, relative to the same observer.)

for an object of velocity, $v$, (relative to some observer), the relationship this "relativistic mass", "effective mass", "inertial mass" $m_0$ (whatever term the "massless" folks want to see go away) and the rest mass (or invariant mass) is:

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

you will notice that if $m_0 > 0$, then if $v$ approaches $c$, this mass goes to infinity. rearranging this:

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}}$$

so if $m$ is finite (in fact it's $m = (h \nu)/c^2$), then when $v=c$, you can see that $m_0 = 0$ no matter what the inertial mass is.

Last edited: Apr 12, 2007
9. Apr 13, 2007

### Meir Achuz

That is one more demonstration that tryiing to use "relativistic mass" leads to confusion.

10. Apr 13, 2007

### pervect

Staff Emeritus
That's why people prefer invariant mass, which however means the same thing as rest mass and means something different than relativistic mass. I think this is mentioned in the two FAQ's I quoted on the topic.

You should probably give them (the links) a read. SR is a much simpler topic than GR, and is necessary to understand GR.

Using geometric units to make the math simpler, E^2 - p^2 = m^2 for any particle is a constant, where m is the invariant mass and thus m^2 is a constant.

(In standard units the formula becomes m = sqrt(E^2 - (pc)^2) / c^2.)

Different observers will measure different values for E (the energy) and p (the magnitude of the momentum). For instance, a co-moving observer will observe p=0, while an observer moving at a different velocity will not observe p=0. However, all observers, moving or comoving, will get the same value for m. Hence m is called the invariant mass.

m can also be regarded as the "rest mass" because it is the value of m when p=0.

Anything other than a photon or other particle moving at c will have a certain frame where it is at rest. A photon, however, will never have a frame in which p=0.

11. Apr 14, 2007

### Antman

The idea of photons having a mass comes from observations of photons bending around stars or planets right? Maybe you could calculate the photons mass with Newtons formula by observing how much a photon bends around an object of known mass as the velocity is known. Just a stupid thought and here is another one. It is easily observed that light bends around corners because of shadows transformation or when letting isotropic lazer light pass through a thin space seperating it inte several dots. This is due to light beeing a wave, right? So when observing a photon bend around a big mass, how do you know it's not due to it being a wave?

I hope Im making some kind of sense.

12. Apr 14, 2007

### ZapperZ

Staff Emeritus
Again, we have an FAQ entry on this topic. This is does not mean that people still can't respond to question like this, but I'd appreciate it if people look at that, and if it isn't reasonably "complete", to let me know so that it can be used whenever question like this pops up again (and they will again and again).

Zz.

13. Apr 14, 2007

### Staff: Mentor

No. In general relativity, photons follow geodesics in curved spacetime. The motion of all objects is affected by curved spacetime.

Remember, in Newtonian gravitation, the gravitational acceleration of an object doesn't depend on its mass. It is indeed possible to use Newtonian gravitation to predict the amount of bending of a ray or beam of light going past the sun. However, actual measurements don't agree with the Newtonian prediction, whereas they do agree with the general-relativistic prediction.

I doubt that edge-diffraction applies here because the sun isn't a solid object. Refraction through the outer layers of the solar atmosphere would be more important, and some people have suggested this. However, actual measurements don't agree with what this model predicts either. In fact, gravitational "bending" of electromagnetic waves has been observed (and compared against general-relativistic predictions) for sources that are located up to 90 degrees away from the sun in the sky, from the earth's point of view. (These actually used radio waves from space probes rather than light.)

14. Apr 14, 2007

### Antman

Thank you for the information. The formula I had in mind was:
F=m1*m2/(r*r)
Wich I thought of as Newtonian but I see now that the mass of the photon is not relevant when you combine the formula with the one for centripetal force.

While on the subject I'd like to ask why photons get a mass at light speed when they obviously couldn't have any mass if they were to travel at a velocity less than lightspeed? (Because they would then not be able to get to light speed).

15. Apr 14, 2007

### ZapperZ

Staff Emeritus
When does it NOT travel at light speed? And please, don't tell me about speed of light in a medium until you read the FAQ.

Zz.

16. Apr 14, 2007

### pmb_phy

I don't see anyone hear arguing that rel-mass is confusing and I see nothing here which implies it either. As far as "confusing things" go it is well known on this and all other boards that there are various things that are inherently confusing in relativity and people are always asking about them either directly or in a "what if" situation. Some peole find length contraction confusing and then there are others who even find time dilation confusing.

Pete

17. Apr 14, 2007

### Antman

Im surprised that someone wearing the title "mentor" did not understand what I meant but I guess my english is even worse than I thought. I know why light is slowed downed when travelling through a medium when photons arn't but that had nothing to do with it. What I meant was that a photon can not have a mass because it is traveling at light speed. Yet it does. Why?

18. Apr 14, 2007

### pervect

Staff Emeritus
A photon does not have a mass. I don't know why you think a photon does have a mass. My guess is that you are confused by the ambiguity of the word mass, but you'll need to be clearer about why you think a photon has a mass if you want a more detailed answer.

Have you read http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken] ?

Last edited by a moderator: May 2, 2017