Should photons be considered massless?

[Dale]

Why are photons considered massless?

I already answered that above. They are considered massless because their invariant mass (formula also given above) is 0 to high precision.

 

[Dale]

That is very interesting, I can't believe I never heard about this. Thanks for that good example.

You are welcome. I hope that helps.

 

[PAllen]

Would it also be appropriate to replace the mass terms in Newtonian gravity with E/c^2?

I recognize that we have much better theories than this small correction to Newtonian gravity, I am asking to bridge the gap between those theories.

This will lead you to nothing but grief and error. You will get corrections that are off by factors of 2 or 4, for example. If you want to deal with first order corrections to Newtonian gravity, use what the people who calculate the Ephemeris use: the Einstein-Infeld-Hoffman equations:

http://en.wikipedia.org/wiki/Einstein-Infeld-Hoffmann_equation

(I have checked that the equations given here by Wiki match those incorporated in the NASA documents).

 

[jtbell]

Does anyone know how you would actually experimentally measure the rest mass as opposed to the total energy of something?

In particle physics experiments it's common to measure the momentum (e.g. by measuring the radius of the curved path in a magnetic field) and the energy (e.g. in a calorimeter) and then use Dale's and my definition to calculate the mass.

 

[ZapperZ]

First off F = -kx lol, sorry I had to.

If you want to nitpick, I can easily point out that that is a scalar equation, i.e. it signifies the amplitude only. So the negative sign is meaningless in this case.

Second, I think there is a misunderstanding. Are you aware that all energy gravitates? At the beginning of this thread I specifically said this is a discussion in a general relativistic setting.

What I am getting at, is what is the functional difference between energy and mass. What does mass do that energy doesn't and vice versa. Why are photons considered massless? What does mass even mean in a general relativistic sense?

But that's my point. You only care about this from ONE point of view, i.e. the mass-energy equivalence. Instead of looking at it as a conversation factor, you are assigning a physical meaning of one being the same as the other. This is absurd if we apply that same logic to other well-known equality!

Your statement of longitudinal polarization is something I have never heard of before so I appreciate it. That seems like something that actually distinguishes mass and energy.

But really, this should not be a surprise. For example, an electron has mass. If you are saying that this is nothing more than a photon with energy E=mc^2, then you're missing a bunch of things and violating a number of conservations laws, namely charge and spin!

As I've stated, if photons have mass, a number of consequences should occur, including the fact that it must also decay.

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.111.021801

So assign a mass to photons at your own risk, because the rest of the experiments that have tried to detect it have produced nothing of that magnitude (i.e. using that conversion).

Zz.

 

[WannabeNewton]

What does mass even mean in a general relativistic sense?

For test particles it's the exact same thing as in SR. For extended bodies (such as black holes, stars, etc.) the situation is much more complicated: http://en.wikipedia.org/wiki/Komar_mass

 

[Jonnyb302]

If you want to nitpick, I can easily point out that that is a scalar equation, i.e. it signifies the amplitude only. So the negative sign is meaningless in this case.

Sorry, it was just meant as a joke. Honest, no offense intended.

But that's my point. You only care about this from ONE point of view, i.e. the mass-energy equivalence. Instead of looking at it as a conversation factor, you are assigning a physical meaning of one being the same as the other. This is absurd if we apply that same logic to other well-known equality!

I agree with you. In a gravitational setting it seems difficult to distinguish the two. But I realize now that there are other fields where mass and energy really are separate in a meaningful way.For example this:

As I've stated, if photons have mass, a number of consequences should occur, including the fact that it must also decay.

Thanks for the help guys, this has been thought provoking and informative. The more advanced physics I learn, the more I have to question the original stuff I think.

 

[BruceW]

I'd say (in relativity), there is no exact analogue to non-relativistic 'mass'. This is the answer I think maybe you were looking for.

edit: and this is not surprising. New theory, new concepts, right?

 

[vanhees71]

The notion of mass is indeed quite different in Newtonian compared to special-relativistic theory. It's more simple in the relativistic case ;-).

Anyway, the argument starts with the formulation of quantum theory in Minkowski or Galilei space-time, which leads you to investigate the unitary ray representations of the corresponding parts of the groups that are continuously connected to the identity, i.e., the proper orthochronous Poincare and (inhomogeneous) Galilei groups, respectively.

In the case of the Poincare group you'll figure out that mass is a Casimir operator of the corresponding Lie algebra given by the relation, m^2=p_{\mu} p^{\mu}, where p^{\mu} are the generators of the space-time translations. The further analysis turns out that any ray representation is induced by a unitary representation of the covering group of the Poincare group, i.e., instead of the proper orthochronous Lorentz group \mathrm{SO}(1,3)^{\uparrow} you use its covering \mathrm{SL}(2,\mathbb{C}). In this way you come to massive, massless and tachyonic representations. The latter seem not to lead to a sensible physical theory (except for non-interacting tachyons, but these are useless because not observable).

In the case of the Galilei group, it turns out that there are non-trivial central extensions of the group, and mass is the central charge. There is no physically sensible unitary representation of the Galilei group or it's covering group, but only the central extension with the non-zero mass as the central charge.

The subtle difference is that this implies a mass-superselection rule, i.e., there cannot be superpositions of states with different mass, which you don't have in relativistic quantum theory. The latter possibility is realized in nature on the elementary-particle level by the neutrinos, which always are produced in flavor eigenstates which are mixtures of mass eigenstates with different masses, leading to the well-established neutrino oscillations.