# Does momentum have mass?

1. Jan 7, 2013

### San K

Is there anything lighter than light?

A photon has zero rest mass. However it has energy which is equivalent to some mass (?)

Angular momentum is energy (?).

The angular momentum of, say, a photon would have some energy.

If we were to convert (mathematically) that energy into mass, what would the value be? (in relation to the relativistic mass of a photon)

2. Jan 7, 2013

### bcrowell

Staff Emeritus
3. Jan 8, 2013

### pervect

Staff Emeritus
It's not terribly clear what you're asking when you ask if "momentum has mass". The best answer is probably that momentum and mass are different things, but they are both related, in a general way, to gravitation. Like forks and spoons are related , perhaps.

But would we ask "do forks have spoons"? I don't think so :-(.

4. Jan 8, 2013

### DiracPool

Empty space.

No. It just has energy. The term "mass" is best thought of strictly as "rest mass." Trying to use E=mc^2 to justify that light has mass will only confound your thinking, that's why the +pc is added to that equation.

Absolutley.

You know, I'm not sure that a photon does have angular momentum and, if so, how it compares to that of a rest mass 1/2 spin particle. Anyone?

Again, it is not accurate to relate this to rest mass. The value you seek would be its momentum (p), and that value is found by DeBroglie's relation which is p=h/wavelength of the photon.

5. Jan 8, 2013

### DiracPool

Well, I guess it does. Of course, it related to the dreaded "spin" property of particle physics. In any case, the qualifications of a photon's angular momentum is a little too involved to delve into here, but you can read all about it in the provided link.

http://en.wikipedia.org/wiki/Photon

6. Jan 8, 2013

### Bill_K

A photon may also have the plain old orbital type of angular momentum.

7. Jan 8, 2013

### Naty1

I think you may be asking how much of the total energy of a photon is carried by it's spin?

Wikipedia says this:

http://en.wikipedia.org/wiki/Photon_polarization#Angular_momentum_and_spin

So if you pick some color light of your choice, you can figure out what fraction of it's energy is from 'spin'..... total energy is hc/λ so it looks like h/2∏ divided by hc/λ........so the 'h's' cancel ...

San K : I have never thought about this issue before, so before you accept this answer, let's wait and see if anyone has corrections to make.

Last edited: Jan 8, 2013
8. Jan 8, 2013

### Naty1

oops...forgot:

If you mean, "Are there any other particles with less energy than a photon".....
then yes, the graviton.

How about the 'new' Higgs boson??

9. Jan 8, 2013

### Bill_K

Energy and angular momentum are separate concepts, gentlemen. To ask how much energy is due to a particle's spin is devoid of meaning!

Is the energy of a photon "small"? No. For it is totally dependent on rest frame - by suitable Lorentz transformation you can make it as small as you like, or as large as you like. Exactly the same thing applies to the (hypothetical) graviton. So its energy is sometimes less than, and sometimes greater than, a photon's energy.

10. Jan 8, 2013

### Staff: Mentor

Compare the units the units of angular momentum with the units of energy. Are they the same?

11. Jan 8, 2013

### Naty1

Oh yea,duh, good catch Bill K....

The link between momentum and energy is their effect on gravitational attraction...as in 'stress-energy-momentum....' tensor

So maybe SanK's question could be answered via a gravitational impact approach??? Compute the SET with and without angular momentum ??

12. Jan 8, 2013

### DiracPool

The angular momentum of a quantum system is proportional to h-bar, whose units are joule-seconds. So the measure of the energy of a quantum system is directly proportional to its angular momentum. Is this not correct?

13. Jan 8, 2013

### Naty1

Note also that momentum is a vector and energy a scalar....not comparable....

but both do have an effect on gravitational attraction....as does, for example, pressure...
so there IS an intrinsic relationship via GR.....

14. Jan 8, 2013

### Khashishi

Energy isn't a scalar, but just one component of a vector.

15. Jan 8, 2013

### BruceW

You're getting two different concepts mixed up. I think you were trying to say that angular frequency is energy, i.e. $E=\hbar \omega$ which is true for a photon.

Also, for a photon, its energy is equal to its relativistic mass, which is also equal to its momentum. (in natural units).

So, you can see that in fact, the angular frequency of the photon is equal to the momentum (and also equal to the relativistic mass).

16. Jan 8, 2013

### Bill_K

No, this is not correct. What about things like a hydrogen atom in its ground state, which has angular momentum zero.