# The Mass of Photons

1. May 17, 2013

### AlfieD

Greetings people of Physics,

I was just having a think about E=MC2 (as is common with people these days... probably) and if we assumed that a random photon had an energy of 3 Joules, and we rearranged E=MC2 to work out the mass (M=E/C2), it would mean that our photon has a mass of 1.000692285594456e-8 Kg (if we assume that the speed of light is 299,792,458 m/s). However, I was taught that photons have no mass (I know that they have no 'rest mass' but the sum that I just did stated that while our photon has 3 Joules of energy, it has mass a mass of 1.000692285594456e-8 Kg). Coming on to my question, I was taught that you can only go the speed of light if you have zero mass, but if light itself has mass then how can it go at its own speed and I am seriously confused. If someone could help me with this I would appreciate it.

Kind Regards,
Alfie D

2. May 17, 2013

### phinds

The fact that a photon has an energy equivalent of some amount of mass does not mean that it has a "rest mass" (which, by the way, is a deprecated term in modern physics). You can't GET a photon to "rest" so the concept of a "rest mass" is not meaningful for a photon.

3. May 17, 2013

### Zag

Hello AlfieD,

The tricky thing about the famous equation $E = mc^²$ is that it is valid only for particles with mass. The more general expression is actually $E^2 = {p^2}{c^2} + {m^2}{c^4}$. And then you get that the energy stored in a photon, which has no mass, is $E = pc$, where $p$ is the modulus of the photon's linear momentum.

An interpretation to what you calculated is the following: the energy $E$ of a photon is given by $pc$ - this quantity, during some physical process (usually one involving subatomic particles, or nuclear reactions, etc.), could be converted into a certain quantity of mass given by $m = E/{c^2} = p/c$.

I hope this helps! ;)

Best,
Zag

Last edited: May 17, 2013
4. May 17, 2013

### mathman

To start: E=MC2 does not apply to photons. The M in this case is the rest mass divided by the Lorentz factor (= 0 for anything going at the speed of light), so for photons M = 0/0, when you try to use the equation.

This may help:
http://en.wikipedia.org/wiki/List_of_relativistic_equations

5. May 17, 2013

### BruceW

you have calculated the relativistic mass of the photon, which is a different concept to the rest mass.
yeah, zero rest mass. and the photon does have zero rest mass but nonzero relativistic mass.

6. May 17, 2013

### Ceverett

The thing is though, that the rest mass and relativistic mass are related as Mass(rel) =γMass(rest), where gamma is the relativistic invariant, 1/(1-v^2/c^2). Because of this, even at v=c when γ is infinite, 0 multiplied by ∞ is still 0, so the photon hasn't got relativistic mass.

7. May 17, 2013

### WannabeNewton

This is entirely false. First of all, 0 times $\infty$ is not 0, this is a basic fact of indeterminate forms. Secondly, the formula $m_{\text{rel}} = m_0\gamma$ only applies to time-like particles. The more general equation is $m_{\text{rel}} = E / c^{2}$ which is obviously non-vanishing for photons.

8. May 17, 2013

### ZapperZ

Staff Emeritus

https://www.physicsforums.com/forumdisplay.php?f=210 [Broken]

Zz.

Last edited by a moderator: May 6, 2017
9. May 17, 2013

### Popper

AlfieD - As mentioned above you are confusing proper mass with inertial, aka relativistic, mass. The proper mass of a photon is zero while its inertial mass is m = E/c2 = hf/c2 = p/c.

Note: I use the term proper mass rather than rest mass since a photon can never be at rest. The term proper refers to an intrinsic property of a particle.

The inertial mass of a particle is defined as the ratio of the magnitude of the particle's (mechanical) momentum to its speed.

It's not very meaningful to state whether this does or doesn't apply until one first identifies what each term in the expression means. After that, all else follows. If we take that expression at face value then the M must be inertial mass since the symbol E, without a "0" subscript, always refers to total energy, not rest energy. If m = proper mass then E0 = mc2.

This is never a problem in real life. If you want to know what is meant by m then here are some rules to follow;

E = mc2 => E = total energy, m = inertial mass

E0 = mc2 => E0 = rest/proper energy, m = proper mass

10. May 17, 2013

### Popper

Relativistic mass M is not defined as the M in

M = γm

It's defined as the M in p = Mv, i.e. if we let p = |p| and v = |p| then M is defined as

M = p/v

If the particle has non-zero proper mass m then it can be shown using the law of conservation of momentum that

M = γm

The proof was first derived in the article The Principle of Relativity and Non-Newtonian Mechanics, R.C. Tolman and G.N. Lewis, Philosophical Magazine, 18, (1909), pg. 510-523. Tolman and Lewis defined inertial mass M such that p = Mv is a conserved quantity.

If the particle has zero proper mass then it must be moving at the speed of light and therefore |v| = c and its relativistic mass is readily given by m = p/c. In this case we also have E = pc so that p = E/c. Substitute into expression m = p'c and we obtain m = E/c2 = hf/c2. QED

Last edited: May 17, 2013
11. Jun 5, 2013

### Simon Bridge

... and still no feedback from OP.
@AlfieD: any of this of use to you?

12. Jun 5, 2013

### AlfieD

Thanks guys! Your help was much appreciated. I believe that I now understand.

Kind Regards,
AlfieD

13. Jun 13, 2013

### sirwan

does electron has rest mass?

14. Jun 13, 2013

### jeppetrost

Yes. Only the photon and the gluons are massless in the (neutrino oscillation-corrected) Standard Model.

15. Jun 13, 2013

### sirwan

please. what is meaning by rest mass ? does mean its mass at zero velocity? does electron have zero velocity or it stop ?

16. Jun 13, 2013

### WannabeNewton

The rest mass of a particle is the mass of the particle as measured by an inertial observer who is at rest with respect to that particle. Notice how we can only make sense of the rest mass of massive particles, for which there always exist such rest frames.

17. Jun 13, 2013

### sirwan

we know that the total energy of the electron E=P^2 *C^2 + M^2*C^4 . M Is the rest mass of electron. when the rest mass of electron equal zero?

18. Jun 13, 2013

### ZapperZ

Staff Emeritus
Where did you get the idea that the rest mass of electron can equal to zero? Did you miss the answer that was given to your first question?

You also need to start your own topic. This was a thread on the mass of photons.

Zz.

19. Jun 13, 2013

### lightarrow

But the trickier thing with that equation is that is valid only in a frame of reference in which the object with mass m is stationary.

20. Jun 13, 2013

### lightarrow

And what does "intrinsic" mean, if not "in a frame of reference in which the particle is stationary"?
Better "invariant mass" than "proper mass".