If the Higgs Boson carries mass, why doesn't there exist more bosons that carry other fundamental properties such as volume/distance (space), time, or even spacetime? Also if bosons carry force, but the Higgs carries mass, does that mean boson's don't necessarily carry force, or mass is a type of force?
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It should be clarified that the Higgs boson does not carry mass. The correct statement is that the Higgs field (not boson) is giving mass to some (not all) particles. In fact most of your mass is not given by the Higgs field. Most of the mass of atomic nucleus (protons and neutrons) is due to the binding energy of strong interaction. The Higgs field is giving mass to quarks and leptons (like electrons).
But the Higgs boson is not needed to give particles their mass. Higgs boson is only a "ripple" in the Higgs field. You will most likely never encounter a Higgs boson in your life, but still your electrons have mass. It is because the Higgs field is everywhere (while the Higgs boson is very rare).
There is also a lot of particles that probably do not get their mass from the Higgs field. For example the particles of dark matter may be getting their mass via a completely different mechanism. And remember that there is much more dark matter than ordinary matter in the universe. The Higgs field is also not giving mass to black holes.
Also please note that there actually is something like an "interaction" mediated by the Higgs boson. It is however incredibly short range and it does not give rise to mass. It is just a very weak attraction between fermions. So the Higgs boson does carry a "force", but this force has basically nothing to do with mass.
Mass is definitely not a type of force. Mass is a parameter in the equations and it is causing that particles (which have mass term in their equations) are moving slower than the speed of light. Massless particles are always moving at the speed of light.
Now why was the whole thing with the Higgs field introduced in the first place? Cannot the mass be really just a parameter in the equations? In the early days of quantum theory it was actually like that: mass was just a parameter and there was no Higgs. But when weak interaction was put into the equations, things were not working right with mass. It was more natural for some particles to be massless. Therefore the Higgs mechanism was introduced so that these particles can be massless at the beginning, but acquire mass later when the Higgs field gets to nonzero average value (vacuum expectation value) in the universe. Some of the other quantum fields interact with this "activated" Higgs field and they get mass from that: their particles are moving slower than the speed of light, because their equations of motion have extra term that is altering their behavior.
Now it should become clear that mass is something different than spacetime. Mass can be given to particles by a quantum field, but similar mechanism would not work for spacetime. Mass term appears as part of the equations describing motion of particles, but there is no "spacetime term". The equations contain derivatives with respect to the space and time, but these are just labels.
