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What exactly is mass from a Higgs boson point of view? I mean my layman definition is mass is the amount of matter, but that doesn’t seem like the thing that th

What exactly is mass from a Higgs boson point of view? I mean my layman definition is mass is the amount of matter, but that doesn’t seem like the thing that the Higgs boson is involved in

nyssos 3y ago
Characterizing what things "are" in a physical theory is not really possible: ultimately physics is only concerned with (and only has access to) what things do. When we say that "The X-ion has mass m", in the context of a quantum field theory, we mean that - The magnitude of its 4-momentum is m (better known as E^2 = p^2 + m^2c^4) - There's an X^2 m^2 term in the Lagrangian of our theory (there are some formal complications here but they're physically irrelevant), which in extremely loose terms means that in the absence of interactions X will behave like a collection of harmonic oscillators with mass m. - The strength of its interaction with gravitational fields, neglecting relativistic effects, is proportional to m. and so on for every other place "m" shows up. The meaning of mass, if you want to assign it one, is the correspondence between all these different quantities. And their meanings, in turn, are other correspondences, all the way down. To get actual physical meaning out, you need to find some place in the theory which you can identify with observational results (the typical case for particle physics is scattering amplitudes and collider experiments). Ideally this is enough of a foothold to interpret everything: the readouts when we objects a and b together match the calculated scattering amplitudes for particles A and B, so we hypothesize that a is an A and b is a B. Now if we smash objects b and c together and get results that match theoretical predictions for B and C, we can be more confident b is a B and hypothesize c might be a C, and so on. But there's no law that says this must be possible, and no guarantee that every term in our theories points to some particular thing in the world.

What exactly is mass from a Higgs boson point of view? I mean my layman definition is mass is the amount of matter, but that doesn’t seem like the thing that the Higgs boson is involved in

nyssos 3y ago

Characterizing what things "are" in a physical theory is not really possible: ultimately physics is only concerned with (and only has access to) what things do. When we say that "The X-ion has mass m", in the context of a quantum field theory, we mean that - The magnitude of its 4-momentum is m (better known as E^2 = p^2 + m^2c^4) - There's an X^2 m^2 term in the Lagrangian of our theory (there are some formal complications here but they're physically irrelevant), which in extremely loose terms means that in the absence of interactions X will behave like a collection of harmonic oscillators with mass m. - The strength of its interaction with gravitational fields, neglecting relativistic effects, is proportional to m. and so on for every other place "m" shows up. The meaning of mass, if you want to assign it one, is the correspondence between all these different quantities. And their meanings, in turn, are other correspondences, all the way down. To get actual physical meaning out, you need to find some place in the theory which you can identify with observational results (the typical case for particle physics is scattering amplitudes and collider experiments). Ideally this is enough of a foothold to interpret everything: the readouts when we objects a and b together match the calculated scattering amplitudes for particles A and B, so we hypothesize that a is an A and b is a B. Now if we smash objects b and c together and get results that match theoretical predictions for B and C, we can be more confident b is a B and hypothesize c might be a C, and so on. But there's no law that says this must be possible, and no guarantee that every term in our theories points to some particular thing in the world.