In particle physics and string theory, what is mass?
We commonly say that something has a weight, which is synonymous with a mass. Things have a weight because the force of gravity is relative to something’s mass.
Subatomically, what is mass? There are massless particles, like photons. Is the concept of mass relegated to the smallest particles we know of, such as quarks, or is there any further explanation of what it is about some subatomic particles that gives them “mass”, others not?
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In his Australia lectures and his six easy pieces book, Feynman unequivocally states that mass is momentum in the direction of future time.
Anything that experiences the passage of time has mass, and everything that has mass experiences time passing.
Seeing it this way makes many things simpler. For example, if you believe, as I do, that the ants-on-an-expanding-balloon model is accurate, and that the balloon is expanding into future time with the big bang in the center, then mass is naturally seen as the surface of the expanding balloon.
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Generally, mass is the total energy of a particle or system in the frame of reference where its total momentum vanishes. A massless particle is one that can have arbitrarily small (positive) energy. For example, the energy of a photon is proportional to its frequency, which can be arbitrarily low. Note also that in General Relativity, the source of gravitation is not mass, but energy and momentum. In particular, light also has gravitational effects (although they are very small).
In the standard model, generally particle mass is caused by the interaction with the Higgs field; massless particles are those that don't interact with the Higgs field. There's one exception, though, and that is Neutrinos. Measurements show that neutrinos have mass, but according to the standard model they should not be able to interact with the Higgs field (the Higgs field couples left-handed and right-handed particles, and neutrinos only exist in a left-handed variant). As far as I know, the origin of Neutrino masses is not yet known.
I don't know enough about string theory to answer about the mass concept there, but is has to be some energy related to the vibration modes of the strings.
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