Mass of a Boxful of Extremely Intense Radiation

[Islam Hassan]

If I recall correctly, if one has a very very light box with highly reflective inner walls inside of which very very intense gamma rays are bouncing back and forth, the box will behave exactly like a massive object because it is energetic.

What gives the box this mass if photons are not subject to the Higgs mechanism?


IH

 

[jtbell]

The energy of the photons contributes to the mass of the system, even though the photons themselves individually have no mass.

Most physicists nowadays use "mass" to mean "invariant mass" which is often called "rest mass" in introductory treatments of relativity. It is not an "additive" property, that is, the mass of a system is not, in general, the sum of the masses of its component particles.

 

[PeterDonis]

What gives the box this mass if photons are not subject to the Higgs mechanism?

The photons aren't but the box is; it has to be if it's constraining the motion of the photons. The box can only do that if it's moving on a timelike worldline, and the Higgs mechanism is what makes particles do that (in this case, the particles making up the box). And it's the constraint of the box on the photons' motion that gives the whole system an invariant mass equal to its energy in the box's rest frame: the average of all the photons' motion is a timelike energy-momentum vector, because of the way the box constrains the motion of the individual photons (by reflecting them off the walls), even though each individual photon (between wall collisions) has a null energy-momentum vector.

 

[bcrowell]

The photons aren't but the box is; it has to be if it's constraining the motion of the photons. The box can only do that if it's moving on a timelike worldline, and the Higgs mechanism is what makes particles do that (in this case, the particles making up the box).

I'm not sure that that's even the case. I don't think the Higgs mechanism actually accounts for a very high percentage of the mass-energy of ordinary matter. Popularizations have oversold the Higgs as the source of "all mass." I believe the source of most mass-energy of ordinary matter is the kinetic energy of the quarks in the nucleus.

You don't need any quantum mechanics or field theory to answer this question. It's pure classical GR. Here is a nice explanation: http://74.86.200.109/showpost.php?p=2956775&postcount=15

I wrote up a FAQ on this:

FAQ: Does light produce gravitational fields?

The short answer is yes. General relativity predicts this, and experiments confirm it, albeit in a somewhat more indirect manner than one could have hoped for.
Theory first. GR says that gravitational fields are described by curvature of spacetime, and that this curvature is caused by the stress-energy tensor. The stress-energy tensor is a 4x4 matrix whose 16 entries measure the density of mass-energy, the pressure, the flux of mass-energy, and the shear stress. In any frame of reference, an electromagnetic field has a nonvanishing mass-energy density and pressure, so it is predicted to act as a source of gravitational fields.
There are some common sources of confusion. (1) Light has a vanishing rest mass, so it might seem that it would not create gravitational fields. But the stress-energy tensor has a component that measures mass-energy density, not mass density. (2) One can come up with all kinds of goofy results by taking E=mc^2 and saying that a light wave with energy E should make the same gravitational field as a lump of mass E/c^2. Although this kind of approach sometimes suffices to produce order-of-magnitude estimates, it will not give correct results in general, because the source of gravitational fields in GR is not a scalar mass-energy density, it's the whole stress-energy tensor. However, there is one case of interest where this does happen to work. If a photon gas of total mass E is contained inside a spherical mirror, then the external spacetime is exactly the Schwarzschild solution for a mass E/c^2. The external field has a contribution from the photons that is double this amount, but half of that is canceled by the pressure at the mirror.
Experimentally, there are a couple of different ways that I know of in which light has been tested as a gravitational source. An order of magnitude estimate based on E=mc^2 tells us that the gravitational field made by an electromagnetic field is going to be extremely weak unless the EM field is extremely intense.
One place to look for extremely intense EM fields is inside atomic nuclei. Nuclei get a small but nonnegligible fraction of their rest mass from the static electric fields of the protons. According to GR, the pressure and energy density of these E fields should act as a source of gravitational fields. If it didn't, then nuclei with different atomic numbers and atomic masses would not all create gravitational fields in proportion to their rest masses, and this would cause violations of Newton's third law by gravitational forces. Experiments involving Cavendish balances[Kreuzer 1968] and lunar laser ranging[Bartlett 1986] find no such violations, establishing that static electric fields do act as sources of gravitational fields, and that the strength of these fields is as predicted by GR, to extremely high precision. The interpretation of these experiments as a test of GR is discussed in [Will 1976] and in section 3.7.3 of [Will 2006]; in terms of the PPN formalism, if E fields did not act as gravitational sources as predicted by GR, we would have nonzero values of the PPN zeta parameters, which measure nonconservation of momentum.
Another place to look for extremely intense EM fields is in the early universe. Simple scaling arguments show that as the universe expands, nonrelativistic matter becomes a more and more important source of gravitational fields compared to highly relativistic sources such as the cosmic microwave background. Early enough in time, light should therefore have been the dominant source of gravity. Calculations of nuclear reactions in the early, radiation-dominated universe predict certain abundances of hydrogen, helium, and deuterium. In particular, the relative abundance of helium and deuterium is a sensitive test of the relationships among a, a', and a'', where a is the scale-factor of the universe. The observed abundances confirm these relationships to a precision of about 5 percent.[Steigman 2007]
Kreuzer, Phys. Rev. 169 (1968) 1007
Bartlett and van Buren, Phys. Rev. Lett. 57 (1986) 21
Will, "Active mass in relativistic gravity - Theoretical interpretation of the Kreuzer experiment," Ap. J. 204 (1976) 234, available online at http://articles.adsabs.harvard.edu//full/1976ApJ...204..224W/0000224.000.html
Will, "The Confrontation between General Relativity and Experiment," http://relativity.livingreviews.org/Articles/lrr-2006-3/ , 2006
Steigman, Ann. Rev. Nucl. Part. Sci. 57 (2007) 463

 

[PeterDonis]

I'm not sure that that's even the case. I don't think the Higgs mechanism actually accounts for a very high percentage of the mass-energy of ordinary matter. Popularizations have oversold the Higgs as the source of "all mass." I believe the source of most mass-energy of ordinary matter is the kinetic energy of the quarks in the nucleus.

My knowledge of the Higgs mechanism is extremely basic, but my understanding is that all of the fundamental fields in the Standard Model are massless, so in the absence of the Higgs mechanism, every fundamental particle (including both fermions like electrons and quarks, and bosons like the W and Z particles) would move at the speed of light. To me, that means that the Higgs mechanism is the fundamental reason why there are timelike objects.

I agree that, once the existence of timelike objects is established, the Higgs mechanism does not account for all of their invariant mass. As you say, most of the observed mass of nucleons, for example, is actually the kinetic energy of the quarks (plus the binding energy between the quarks that arises from the strong interaction).

 

[PAllen]

I agree that, once the existence of timelike objects is established, the Higgs mechanism does not account for all of their invariant mass. As you say, most of the observed mass of nucleons, for example, is actually the kinetic energy of the quarks (plus the binding energy between the quarks that arises from the strong interaction).

That's interesting. Normally, binding energy represents a decrease in invariant mass. But with quarks, you can't separate them, so what does that say about mass contribution from bound quark state? I would be really interested in hearing more from someone who know both QCD and relativity.

 

[bcrowell]

My knowledge of the Higgs mechanism is extremely basic, but my understanding is that all of the fundamental fields in the Standard Model are massless, so in the absence of the Higgs mechanism, every fundamental particle (including both fermions like electrons and quarks, and bosons like the W and Z particles) would move at the speed of light.

Yes.

To me, that means that the Higgs mechanism is the fundamental reason why there are timelike objects.

No. A collection of lightlike objects can have a center of mass that is timelike.

 

[PeterDonis]

A collection of lightlike objects can have a center of mass that is timelike.

Can there be a collection of lightlike objects with a timelike CoM, *and* confined to a finite spatial region? I should have added that last qualifier to my statement about the Higgs.

[Edit: I should also have added "in flat spacetime", since obviously in curved spacetime one can have spatially confined null geodesics.]

 

[Bill_K]

That's interesting. Normally, binding energy represents a decrease in invariant mass. But with quarks, you can't separate them, so what does that say about mass contribution from bound quark state?

Normally the potential that holds a bound system together is some sort of potential well, negative everywhere, and as you say it represents a decrease in mass. But the potential that holds a proton together is quite different - it resembles a harmonic oscillator potential, positive everywhere and rising to plus infinity at large distances. So in this case the binding energy represents an increase in mass.

 

[bcrowell]

Can there be a collection of lightlike objects with a timelike CoM, *and* confined to a finite spatial region? I should have added that last qualifier to my statement about the Higgs.

A box full of photons would be an example.

If you want them to be confined solely by their mutual interaction, then I guess examples would be a geon http://en.wikipedia.org/wiki/Geon_(physics) or a glueball http://en.wikipedia.org/wiki/Glueball , but the geon involves curved spacetime.

 

[PeterDonis]

If you want them to be confined solely by their mutual interaction

Yes, that's what I meant. A box full of photons isn't composed solely of lightlike objects, unless the box itself is also made of photons.

If you want them to be confined solely by their mutual interaction, then I guess examples would be a geon http://en.wikipedia.org/wiki/Geon_(physics) or a glueball http://en.wikipedia.org/wiki/Glueball , but the geon involves curved spacetime.

Hm, I hadn't thought of glueballs. That's a good example.