# Does momentum have mass?

by San K
Tags: mass, momentum
 P: 887 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)
 PF Patron Sci Advisor Emeritus P: 5,311
 Sci Advisor Emeritus P: 7,207 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 :-(.
P: 492

## Does momentum have mass?

 Is there anything lighter than light?
Empty space.

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

 Angular momentum is energy (?)
Absolutley.

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

 If we were to convert (mathematically) that energy into mass, what would the value be? (in relation to the relativistic mass of a photon)
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.
P: 492
 You know, I'm not sure that a photon does have angular momentum
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
 Sci Advisor P: 3,456 A photon may also have the plain old orbital type of angular momentum.
PF Patron
P: 5,505
 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)
I think you may be asking how much of the total energy of a photon is carried by it's spin?

Wikipedia says this:

 Photons have only been observed to have spin angular momenta of + or - h bar.....
http://en.wikipedia.org/wiki/Photon_...entum_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.
PF Patron
P: 5,505
oops...forgot:

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

How about the 'new' Higgs boson??
 Sci Advisor P: 3,456 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.
Mentor
P: 10,699
 Quote by San K Angular momentum is energy (?).
Compare the units the units of angular momentum with the units of energy. Are they the same?
 PF Patron P: 5,505 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 ??
P: 492
 Compare the units the units of angular momentum with the units of energy. Are they the same?
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?
 PF Patron P: 5,505 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.....
 P: 743 Energy isn't a scalar, but just one component of a vector.
HW Helper
P: 2,963
 Quote by San K 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)
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).