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Photons have no mass. Yet they interact gravitationally, as all energy does, with other energetic and massive particles. This means that if you put multiple photons in a system, you get something that appears to have mass, even though none of the constituent particles do have mass.

That makes me wonder:

Is mass really a fundamental part of reality? Couldn't it be that massive particles (protons/neutrons/electrons) are just composed of massless particles like photons knotted up, confined to a small area and whizzing around in very tight orbits? So everything is, in a sense, massless?

The search for and discovery of the Higgs Boson suggests to me, in my limited understanding, that scientists believe mass is a fundamental property that some particles have. And also that mass is fundamentally different than other types of energy (though conversion is possible). Does all of this preclude a system like I describe?

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    $\begingroup$ I can't make any sense out of the final paragraph. There doesn't seem to be any logical connection between the material about the Higgs and the rest of the question. Note that most of the mass of ordinary matter doesn't come from the Higgs mechanism. $\endgroup$ – Ben Crowell Aug 5 '13 at 0:07
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    $\begingroup$ What Ben Crowell said. Also mass is a fundamental property: it is just the energy a system has when at rest. The "system" can be arbitrarily complicated inside: it could have any amount of kinetic and interaction energy of the internal constituents. But put it in a black box and ask: is the system at rest? If so, the total energy it has is its mass. Photons have no mass simply because they cannot be brought to rest. $\endgroup$ – Michael Brown Aug 5 '13 at 0:17
  • $\begingroup$ Final paragraph is a statement of my ignorance -- I only know that scientists discovered something called a Higgs Boson, and that they said this is the thing that gives particles mass... Based on that limited understanding, this implies to me that scientists believe mass is a fundamental property. But I don't understand exactly why it is... David Z's answer is very helpful. $\endgroup$ – BobIsNotMyName Aug 5 '13 at 0:22
  • $\begingroup$ Added some edits to final paragraph for correctness, and also to help prevent others from getting detracted here. $\endgroup$ – BobIsNotMyName Aug 5 '13 at 1:23
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    $\begingroup$ Related: physics.stackexchange.com/q/64232/2451 and links therein. $\endgroup$ – Qmechanic Aug 5 '13 at 6:06
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It's certainly possible for a particle's mass to come partially from kinetic energy of massless particles; for example, about half of a proton's mass is the kinetic energy of its gluons. But the kind of mass that fundamental particles have, the kind that comes from the Higgs mechanism, doesn't appear to be of that kind. Maybe someday we will discover that it is. (This would be the case if string theory turns out to be correct, for instance.)

By the way, scientists do not believe that mass is fundamentally different from energy. Mass is just one type of energy.

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    $\begingroup$ What the OP is asking about sounds more like preons than strings. Preon theories have difficulties because of the confinement problem: physics.stackexchange.com/a/64646/4552 $\endgroup$ – Ben Crowell Aug 5 '13 at 0:12
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    $\begingroup$ Sure, I just cited string theory as one example (the most recognizable one) of how the fundamental particles' masses could actually be energy. As far as I know, theories of this sort haven't been ruled out, even though there are issues like confinement to deal with. $\endgroup$ – David Z Aug 5 '13 at 0:16
  • $\begingroup$ Thanks for this. Very helpful answer... What I meant when I said "mass is fundamentally different from energy" is that mass is a fundamental property that is different from other types of energy. I realize now that it's badly worded. Thanks for the correction. $\endgroup$ – BobIsNotMyName Aug 5 '13 at 0:29
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    $\begingroup$ @BobIsNotMyName: That's only in non-relativistic newtonian mechanics . In Special Relativity, the total energy (rest + kinetic) is $E=\sqrt{m^2c_0^4+p^2c_0^2}$, where $c_0$ is the speed of light and $p$ is the momentum and $m$ is the mass, (of course you can taylor expand the square root to get the kinetic energy only, as an infinite series), which, for massless particles, reduces to $E=pc_0 $. This stuff can also folllow from the 4-momentum, but let's keep it simpler for now, ; . $\endgroup$ – Abhimanyu Pallavi Sudhir Aug 5 '13 at 1:46
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    $\begingroup$ @BobIsNotMyName Yes, it is. Kinetic energy is defined as the difference between total relativistic energy (the $E$ that Dimension10 gave the formulas for) and mass energy ($mc^2$). $\endgroup$ – David Z Aug 5 '13 at 2:35
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This is a very interesting question. It turns out that in the standard model before symmetry breaking the only particle with a mass term is the Higgs boson itself (and possibly the neutrinos) The fermions and weak gauge bosons acquire mass through the Higgs mechanism and more mass in nature is generated by the confinement of quarks inside the nucleons, but there is a real sense in which everything in the standard model + gravity is made of massless particles except the Higgs and possibly neutrinos.

This is significant because it means that the standard model almost has conformal invariance. This is invariance under a space-time symmetry which can change distance scales locally so long as all angles remain fixed. Only the Higgs mass term breaks the symmetry. It has been suggested that the standard model could have exact conformal invariance in classical form with the Higgs term generated dynamically in the quantum theory, but this is not a highly regarded idea yet.

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