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Interested in knowing the quantum explanation for what gives particles mass, and why particles like photons are considered massless when they have energy and momentum.

Qmechanic
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Nk07
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2 Answers2

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The idea that a photon is massless is a pedagogic convention, that has not always held sway. When I was taught special relativity in the '70s, there were two kinds of mass that were distinguished. Rest mass and relativistic mass. Relativistic mass was simply and always equal to momentum divided by velocity. Photons have momentum and velocity, and so have relativistic mass.

An advantage of that approach to SR is that mass is conserved. Always. When for example, a radioactive atom emits a gamma ray, the atom becomes lighter, but the lost mass is found in the gamma ray. If one were somehow able to confine the explosion of a nuclear bomb within a sealed container, that permitted no loss of matter or energy, then the container and its contents would weigh exactly the same both before and after the bomb was detonated. (Or the mass would be the same as measured by a non-gravitational spring balance).

The modern approach seems to be that a particle with no rest mass has no mass. Conservation of mass is violated in some cases, and one must replace that law with a law of conservation of mass-energy.

It isn't a big deal which convention is used, but one should be aware that it is a convention, and there are multiple ways of defining terms such that, in the end, the math done under whatever convention, gives the same empirical results.

Math Keeps Me Busy
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Mass is energy that a particle has when it is at rest. Photons are never at rest, and so don't have mass. A related fact is that in the limit that the photon's momentum goes to zero, its energy also goes to zero.

Fundamental particles like electrons, quarks, and the $W$ and $Z$ bosons receive mass by interacting with the Higgs field, via the Higgs mechanism.

However, most of your mass actually comes from nucleons (protons and neutrons). The mass of nucleons predominantly comes from interaction energy among the constituent quarks and gluons due to the strong interactions.

Andrew
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  • "The rest mass of a proton is, thus, the invariant mass of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles is still measured as part of the rest mass of the system." - the last line of the first paragraph in the link you gave for 'mass of nucleons'. This is where my confusion arises. So if the mass of particles is derived from the kinetic energy of massless particles, doesn't that imply that mass increases with kinetic energy and not just it's energy at rest? – Nk07 Apr 24 '22 at 03:27
  • even when you say 'rest' mass, it's because the particles are vibrating/orbiting within a contained space, thus giving the impression of it being at rest from a reference frame with 0 velocity relative to that point. But regardless at least a significant portion of the mass seems to be derived from its kinetic energy, it's just that the motion is not linear in subatomic particles – Nk07 Apr 24 '22 at 03:33
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    @Nk07 In this context, you can think of the proton as a bag of massless particles that are moving around. There's a frame where the "center of energy" of the bag does not move (on average). The rest frame I'm talking about is the rest frame of the bag, not of any constituent quark or gluon. Free massless particles wouldn't stay in the bag -- they'd just zoom off. But, there are strong interactions which keep the massless particles together in the bag. This interaction energy is the origin of the proton mass. – Andrew Apr 24 '22 at 03:50
  • @Nk07 this is relevant https://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/whats-a-proton-anyway/ . I should add that mass in classical physics (galilean relativity) is an invariant, always conserved. It is special relativity that governs the algebra for particle masses http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/conrel.html , http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/relcon.html – anna v Apr 24 '22 at 04:20
  • @annav thanks for the informative links. On a side-note, could you suggest any books or websites which would give me a decent-advanced understanding of the main concepts of special and general relativity and quantum mechanics, including the math? – Nk07 Apr 24 '22 at 09:23
  • @Andrew I see, so does that mean that if an object were not contained and had linear motion, its mass would increase with relative velocity? And would that affect its inertia and gravity? – Nk07 Apr 24 '22 at 09:26
  • @Nk07 The mass I'm referring to is the invariant mass, which is a property of the particle and is the same in any reference frame.So it does not change with relative velocity. – Andrew Apr 24 '22 at 13:41