## Does Light have Mass?

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Hernandeza2012
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Joined: Sat Jan 21, 2012 10:51 pm

### Does Light have Mass?

According to modern Physics (and Einstein more importantly) the theory of special relativity which regards light of having a rest mass, but according to the Laws of Momentum P=MV and since light does accumulate momentum would there in theory be mass of light in regards to all the photon particles that it consist of? And if so approximately how small would the mass be?

bfollinprm
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Joined: Sat Nov 07, 2009 11:44 am

### Re: Does Light have Mass?

Light has zero rest mass. It has a positive relativistic mass in all reference frames, given by $hf/c^2$, where f denotes the frequency of the photon in the given reference frame. So, for all intents and purposes, light behaves as if it has mass (couples to the gravitational field, carries momentum, etc).

bfollinprm
Posts: 1199
Joined: Sat Nov 07, 2009 11:44 am

### Re: Does Light have Mass?

As an aside, the idea of a "massless" particle in relativity is a somewhat strange notion. We aren't talking about "true" massless-ness, as in something that has (a) no inertia or (b) doesn't couple to gravity. The term massless really is just a rephrasing of the fact that the particle travles at the speed of light. In the limit as the reference frame goes to the speed of light, the total energy goes to 0--the real meaning of "massless". But since you can't go to a speed of light reference frame (the "rest frame" of a photon), the rest mass is really just not a defined quantity.

The confusion is that in relativity, the mass of a particle isn't a sensical statement. Mass is not lorentz-invariant, so it depends on your frame. The "rest mass" that bears some resemblance to Newtonian mass (though is not, in fact, the mass of the particle at all, since it doesn't tell you anything about its inertia or how it will behave under gravity) is really just an expression of the energy of the particle.

King Vitamin
Posts: 42
Joined: Sat Nov 12, 2011 5:01 pm

### Re: Does Light have Mass?

bfollinprm, I disagree, rest mass is a perfectly well-defined quantity even in general relativity. Granted, you cannot define the rest mass of light by going to an inertial frame, but you can define rest mass to be the invariant length of a particle's four-momentum (mod the sign of your metric), and it will be perfectly well defined and Lorentz-invariant for any particle in both GR and QFT.

To the original poster, as bfollinprm said, there's no rest mass - your expression for momentum is simply incorrect. And in regards to coupling to gravity, it isn't just mass that couples to gravity, energy and pressure cause gravitational interactions. Since mass is a form of energy (E=mc^2), it dominates gravity for nonrelativistic objects, but for objects moving close to/at the speed of light, or objects with enormous pressure, there are additional gravitational terms. This is how light can cause a gravitational pull.

bfollinprm
Posts: 1199
Joined: Sat Nov 07, 2009 11:44 am

### Re: Does Light have Mass?

Our disagreement isn't physical, it's a matter of semantics. I'd like to say that the only number I need to know to determine the strength of the gravitational coupling (or the amount of inertia) of a particle is its mass; since the thing that determines the coupling strength of a particle to gravity (and its inertia) is frame-dependent, the classical idea of defined "mass of a particle" doesn't exist in relativity. Of course rest mass is a perfectly defined quantity; it just isn't a mass in any sense we normally ascribe to the term (unless you happen to be in the rest frame). It isn't the particles inertial mass, it isn't the particles gravitational mass, so my point was simply that it isn't mass in any classical sense, and the statement "mass of a particle" doesn't have a defined answer until you tell me the reference frame. Since you can't be in the rest frame of a photon, the rest mass of the photon, though defined in the theory, has no classical meaning as mass at all.