system
Given the following post, respond as if you're commenting on Reddit:
human
If the Higgs field gives mass to matter, and the mass of matter curves spacetime, and said curvature is the basis of gravity; does this imply that the Higgs field causes gravity?
gpt
Here the distinction between two types of mass becomes important. There’s inertial mass, which is the m in Newton’s F=ma. It takes effort to make something with nonzero inertial mass move. In contrast, something with zero inertial mass, such as photons, must always move at the speed of light. We know that electrons and quarks (which make up neutrons and protons) don’t move at the speed of light, so they must have nonzero inertial mass. The Higgs boson is what gives them this inertial mass.

On the other hand, there’s gravitational mass, which is what makes things gravitate towards each other. Incidentally, this is exactly equal to the inertial mass in Newton’s theory of motion and gravitation. In Einstein’s updated theory (general relativity), this equivalence between inertial and gravitational mass is so central that it has a name, the equivalence principle. However, Einstein extended the definition of this mass to include all forms of energy, so even massless things like light can now gravitationally attract other things. You don’t need inertial mass to have gravity, according to Einstein, so quarks and electrons would gravitate even without the Higgs boson (though it certainly helps).

In the Standard Model of Particle Physics, we included all the known fundamental particles and interactions between them (photons, electrons, quarks, Higgs boson, etc), with the exception of gravity. If we try to include it, then every single particle (with or without inertial mass) will interact with the graviton and lead to gravitation, in a way consistent with Einstein’s generalised mass-energy. However, doing so happens to cause the whole quantum field theory (the mathematics framework of the Standard Model) to utterly break down, so we have not yet understood the precise relation between the Higgs boson (which can only be explained through quantum field theory) and gravity.