# Mass photon

1. Mar 17, 2009

### ImAnEngineer

I had a discussion with my physics teacher. He claimed that photons have mass (although no rest mass), since they have energy and E=mc². I argued that having energy isn't the same as having mass, but that energy could be converted into mass which is a different thing (e.g. a photon can disintegrate into a positron-electron pair which have mass, but that doesn't mean the photon itself had mass). My second argument against the claim that photons have mass, is that (if v=c): m = m0 / sqrt(1-c²/c²) = 0 / 0 which is undefined.

Who is right?

2. Mar 17, 2009

### CompuChip

Personally, I would favour the second view, although I don't think anyone is really wrong. You just have differing views, where you have two concepts called "(total) energy" and "mass" and he has two concepts called "rest mass" and "relativistic mass" (which is related to your total energy divided by c^2).

There are arguments for both approaches: on one hand they have different units; on the other hand, in many ways objects with higher energy behave like they are in fact more massive (e.g. you can write F = m a where m = m0 γ is the relativistic mass and m0 the rest mass, for the parallel (or was it perpendicular?) component of the force and acceleration).

Just my 2 cents here, perhaps others disagree.

3. Mar 17, 2009

### ZikZak

Does it have something to do with inertia? If mass has something to do with inertia, then photons must have infinite mass, since you cannot accelerate them at all. Does that seem meaningful?

Does it have something to do with gravity? Photons do cause curvature of spacetime, true.... but the curvature they produce is significantly different from that of a mass E/c^2 at rest, and you would get completely wrong ideas about it if you tried to plug E/c^2 into F=Gmm/r^2, for instance.

4. Mar 17, 2009

### ImAnEngineer

Yes
Not really.

Moreover, he mentioned de Broglie wavelength:

$$\lambda=\frac{h}{mc}$$

Then
$$m_p_h_o_t_o_n=\frac{h}{\lambda c}= 3.97 * 10^-^1^9 kg$$ if the wavelength is 500nm????

I also asked: do photons with different frequencies have different mass since E=hf?

If the mass of a photon however is either 0 or infinite, then there shouldn't be any difference in mass. (infinity + a little bit is still infinity). Am I right?

I'm quite confused right now. Please enlighten me :P .

Last edited: Mar 18, 2009
5. Mar 17, 2009

### ZapperZ

Staff Emeritus
You may want to start by reading the FAQ in the General Physics forum.

Zz.

6. Mar 17, 2009

### ImAnEngineer

I read it now. What is in there is exactly what I thought!

So my physics teacher sucks? :P

7. Mar 17, 2009

### ImAnEngineer

By the way, this link in the FAQ is broken:

8. Mar 17, 2009

### Bob S

First, accelerating a photon itself is difficult, but you can accelerate a particle or object that emits photons (like a radioactive source), and you will find that the forward emitted photons have higher energy (doppler shift) even though their velocity has not changed. So if the photon energy has increased, and the velocity has not increased, then its relativistic mass has increased.

Second, If you use an iron-57 source which emits 14.4 keV photons with a very narrow linewidth, and put it on the roof of a building, and measure the energy of these photons at ground level, you will find that the photon energy has increased due to the gravitational potential change. This is called the Mossbauer Effect experiment, which was done in 1959 at Harvard by Pound and Rebka.

9. Mar 17, 2009

### jnorman

this is a long standing debate, with advocates on both sides of this issue. photons have no rest mass. however, E=MC2 does indeed imply that energy and mass are interchangeable, thus implying that the energy of photons does indeed represent a certain quantity of mass, which is born out by the fact that photons can impart momentum. the resolution revolves around (as mentioned above) the definition of mass used in the discussion.

10. Mar 17, 2009

### ImAnEngineer

So would a calculation as I posted in post#4 make sense?

11. Mar 17, 2009

### Count Iblis

12. Mar 17, 2009

### atyy

13. Mar 17, 2009

### confinement

Yes, your teacher sucks at physics if they think that the mass of a photon is given by m = E / c^2.

14. Mar 17, 2009

### Fredrik

Staff Emeritus
My opinion is that the concept of "relativistic mass" is pointless, and I don't use it myself. Note that the formula E=mc² for photons isn't even a derived result. It's the definition of m.

It does make sense to think of a photon's energy as a "mass" expressed in different units. Consider e.g. a box that contains one photon, endlessly bouncing around between its walls. If you put this box on a (ridiculously sensitive) scale, you will see that it weighs more than an identical box that's empty. You can think of this as a consequence of the photon being blueshifted by gravity on the way down, and redshifted on the way up, so when it hits the floor it has more momentum than when it hits the ceiling.

The same box will also be slightly more difficult to accelerate than an empty box, for pretty much the same reason. Just replace the word "gravity" above with "acceleration".

And yes, the amount of momentum and energy gained during the trip from the ceiling to the floor depends on the energy of the photon, so a photon with higher energy changes the "mass" (as measured by the scale) by a larger amount.

That particular formula is for massive particles, so it doesn't apply. The formula that holds for all particles is

$$E^2=\vec p^2c^2+m_0^2c^4$$.

When $\vec p=m\vec v=\gamma m_0 \vec v$, the right-hand side reduces to $m^2c^4$, but $\vec p=\gamma m_0 \vec v$ only holds for massive particles.

15. Mar 17, 2009

### alxm

No, it is not a "long-standing debate". The definitions of 'relativistic mass' and 'rest mass' were made quite clear when special relativity was developed, as well as the fact that the 'm' in E=mc^2 is rest mass and nothing else.

I don't see where the 'debate' would be. Either you've understood SR, including its definitions, or you haven't.

16. Mar 17, 2009

### atyy

17. Mar 18, 2009

### jostpuur

There are those who understand that the definitions of relativistic mass and rest mass are only definitions, and then there are those who insist that relativistic mass is incorrect. This is where the debate originates.

Well that 'm' in that equation surely can be something else than the rest mass, since you did not emphasize that the energy means the rest energy by writing lower index E_0.

18. Mar 18, 2009

### Dmitry67

I understnd that it is slightly belongs to the 'Beyond the Standard model'
But among different definitions of mass we should use the one which still correct when we go deeper and deeper.
So, mass of all prarticles is 0 and the observed mass is a result of interaction of these massless particles with the Higgs condensate. So, no particle can be observed in it's own rest frame. Hence, only reltivistic definition of mass in valid on the long run.

19. Mar 18, 2009

### ImAnEngineer

It is clear to me that a photon has no rest mass. But can anyone come up with a watertight argument that it has no relativistic mass? And that calculating the mass by m=E/c² is wrong? I want to know how I can convince my teacher I am right :) .

Thank you

20. Mar 18, 2009

### robphy

This really depends on your definition of "relativistic mass".

To me, the real [physically-interesting] issue is likely
how would one use or misuse such a quantity.

21. Mar 18, 2009

### jostpuur

You are not right here, since photon has relativistic mass.

Trying to compute rest mass with $m_0=E/c^2$ would be wrong, while $m_0=0$ is right.

Computing relativistic mass with $m_{\textrm{rel}} = E/c^2$ is right.

Here you are right, since "the mass" usually means the rest mass, and we are supposed to use the notation $m=m_0$ (right), and not the non-standard notation $m=m_{\textrm{rel}}$ (wrong).

So $m=E/c^2$ would usually mean $m_0=E/c^2$ which is wrong.

Last edited: Mar 18, 2009
22. Mar 18, 2009

### jnorman

alxm - a rather terse and closed position for you to take here. the debate revolves around the basic concept of relativistic mass as applied to photons, and there are several threads about this in the archives. many people deny relativistic mass outright, while many others see merit in its application to photons. there is no reason to assume any kind of fixed opinion in QM, since even you must agree that nobody understands the underlying reality. we are all in kindergarten as far as i am concerned.

23. Mar 18, 2009

### MathematicalPhysicist

I wonder how did they eventually built the H-bomb with this controvesy.
:uhh:

24. Mar 18, 2009

### lightarrow

Relativistic mass already had another name: total energy. Why do people want to create another name?

25. Mar 18, 2009

### Count Iblis

The controversy was helpful. It meant that people who were not clever enough to see through it would drop out in college.