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If a particle only can be said to exist if it has energy, if it already must have energy to be able to interact with the Higgs field (to acquire mass) but energy is a source of gravity (if it can be localized) so it already (acts as if it) has mass before it even can interact with the Higgs field, then what do we need Higgs for?

Moreover, if when all properties contribute to the energy -and hence to the mass of particles- then shouldn’t the Higgs field also have to provide particles with properties like electric and color charge?

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  • $\begingroup$ If there was no Higgs (nor any condensing gauge group), the fermions would be massless. $\endgroup$ – user178876 Apr 15 '18 at 1:07
  • $\begingroup$ If fermions would be massless then they'd be energyless, i.e., not exist at all. Though you might objects and say that photons are massless, yet contain energy; the problem is that if according to relativity $\endgroup$ – Anton Apr 15 '18 at 10:20
  • $\begingroup$ If fermions would be massless then they'd be energyless, i.e., not exist at all -nor would we exist to worry about such things. While you might objects and say that photons are massless, yet contain energy; if according to the photon’s own clock it has a zero lifetime, then it cannot be said to have energy, exist -never mind that models in which photons are used like quantum electrodynamics work so spectacularly well. $\endgroup$ – Anton Apr 15 '18 at 10:27
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There two distinct things about your question:
1. energy of a field, which is simply the kinetic and the potential energy
2. mass of a field, which is an interaction strength of the field by itself, so it is kind of potential energy if you like.

For example, in quantum field theory, a term as follows $$ m \bar\Psi\Psi $$ is a mass term of a fermion field $\Psi$ (like electron) in the potential energy. It is understood as if a field is created and then annihilated, then you would have a contribution as much as m to the potential energy.

So, when you express the equations of motion for that particle, you would obtain that its total energy has a mass contribution as follows: $$ E^2 = p^2 +m^2 $$ where p is the 3-momentum.

On the other hand, instead of a mass term, you can have an interaction term of a scalar field (i.e. Higgs boson) as $$ g \phi \bar\Psi \Psi $$ where g is the coupling constant of the Higgs with the electron (Yukawa interaction). If the scalar field has a minimum nonzero expactation value in the vacuum, like $\langle \phi \rangle = \nu$, then the term becomes like a mass term with $m=g\nu$, and the Higgs boson is the fluctuation around the value $\nu$.

Therefore, instead of putting a mass parameter to the theory, you put a Higgs field and obtain the masses of all kinds of particles due to the fact that its vacuum expectation value is nonzero.

Of course the most important necessity of the Higgs boson is that it gives you the correct masses for W and Z bosons while it leaves the photon massless as expected. Otherwise you would have to postulate a priori that photon is massless and W/Z bosons have that particular masses.

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In simple words:

We live in the universe we find our selves in, and do experiments with the available materials. These experiments have established , in time of discovery sequence, gravity (Kepler, Newton), electromagnetism( Faraday ...Maxwell), strong interactions (seen as nuclear) and weak interactions ( seen in decays of nuclei as beta decay).

Once differential equations entered the modelling of physics data, and were used as predictive tools the models became complicated . As experiments progressed and predictions of classical models failed to describe the new data, new models were sought. Quantum mechanics was invented to fit the microcosm data ( and not only, think superconductivity).

The continuous target of theoretical models for physics is simplicity, and the beautiful format of Maxwell's equations, which united what eighteenth century physicist thought were two different forces: electric and magnetic. Unification of forces reduces the number of necessary constants and is much stronger in predictions, as for example Maxwell's equations "predicted"/clarified that light was a combination of electric and magnetic fields, not an independent observable.

In a nutshell, this obsession for unification of forces led to models for unifying, from the four forces listed above, the weak with the electromagnetic in one mathematical model using differential equations, because the symmetries observed in particle data gave a strong hint that this could be done.

When the model was proposed it was necessary for the higgs mechanism to be invoked, just for the weak and electromagnetic, to posit that at very large energies the exchanged particles representing the forces, W and Z and photon, were all massless and by a symmetry breaking mechanism acquired the masses we now measure in our laboratory experiments. Below the symmetry breaking scale the elementary particles in the table acquire masses (specific and constant).

The masses of composites of these, protons, neutrons, ... and the tables and chairs, are masses resulting from the four momentum vector additions of the constituents. The strong interaction exchange particle in the current standard model always has a zero mass ( gluon) as it is never free in our energy regime. The proton bag

myproton

It includes innumerable gluon exchanges and quark antiquark creations. These obey the quantum chromodynamic force , and there are calculations which give close to the mass of observed hadrons, in a theory called lattice QCD.

The unification dream is strong in the theoretical researches, and it is proposed that at very high energy all three, weak, electromagnetic and strong are united in one force , as implied by the data from coupling constants of the three interactions :

running

Gravity, with which you start, is at the end of particle considerations. It comes much later because it is such a weak force compared with the other three. The unification of all four forces is the holy grail of researchers in particle theoretical physics, called Theory of Everything. TOE.

First of all gravity must be rigorously quantized, and then a mathematical model found which will embed the standard model, higgs and all, and include gravity, and describe and predict observations that depend on it.

In my opinion string theory theories are on the correct path, since they already have a niche for gravitons and gravitational interactions and can embed the standard model.

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  • $\begingroup$ As far as I am concerned, all properties of particles are manifestations of a single quantity, of its energy, so they all -electric charge, color charge etcetera- contribute to its mass since energy is a source of gravity (if it can be localized). $\endgroup$ – Anton Apr 23 '18 at 7:25
  • $\begingroup$ you are off the mark. that is not within the mainstream physics knowledge $\endgroup$ – anna v Apr 23 '18 at 8:06
  • $\begingroup$ You still haven't explained what is wrong with my question. $\endgroup$ – Anton Apr 24 '18 at 14:32
  • $\begingroup$ you have to understand my answer, you do not understand what the Higgs mechanism is, is what is wrong. It is a mechanism, not an interaction in the sense of feynman diagrams. It is like a change in coordinates, context. $\endgroup$ – anna v Apr 24 '18 at 16:22
  • $\begingroup$ As far as I know, an electron acquires mass by coupling with the Higgs field (see Oktay’s answer above): isn’t a coupling an interaction and doesn’t the electron need to have energy to be able to couple to that field? If it is the electric charge of a proton and electron which binds them in a hydrogen atom and this binding energy has an electromagnetic origin, then doesn’t the electric charge of the electron powering that binding, represent a quantity of energy -which, as it is a source of gravity, acts like mass? $\endgroup$ – Anton Apr 25 '18 at 0:40

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