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Mass of a Boxful of Extremely Intense Radiation 
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#1
Dec312, 02:58 PM

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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 


#2
Dec312, 03:40 PM

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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. 


#3
Dec312, 03:49 PM

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#4
Dec312, 04:38 PM

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Mass of a Boxful of Extremely Intense Radiation
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=...5&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 stressenergy tensor. The stressenergy tensor is a 4x4 matrix whose 16 entries measure the density of massenergy, the pressure, the flux of massenergy, and the shear stress. In any frame of reference, an electromagnetic field has a nonvanishing massenergy 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 stressenergy tensor has a component that measures massenergy 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 orderofmagnitude estimates, it will not give correct results in general, because the source of gravitational fields in GR is not a scalar massenergy density, it's the whole stressenergy 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, radiationdominated 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 scalefactor 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//...00224.000.html Will, "The Confrontation between General Relativity and Experiment," http://relativity.livingreviews.org/...es/lrr20063/, 2006 Steigman, Ann. Rev. Nucl. Part. Sci. 57 (2007) 463 


#5
Dec312, 05:04 PM

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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). 


#6
Dec312, 05:56 PM

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#7
Dec312, 06:33 PM

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#8
Dec312, 06:39 PM

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


#9
Dec312, 07:06 PM

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#10
Dec312, 08:26 PM

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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_%28physics%29 or a glueball http://en.wikipedia.org/wiki/Glueball , but the geon involves curved spacetime. 


#11
Dec312, 08:36 PM

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