The reader will recall that, in Newton’s second law – the one that tells us that force equals mass times acceleration, or more precisely, that force equals the rate of change with time of momentum , defined as the product of mass and velocity–, mass is the resistance to change in the state of motion. It is thus a measure of inertia. When asked what mass is, the first thing we can answer is that mass is not, as it might seem, a measure of the amount of matter. Do not; it is a measure of inertia.
However, this is so in Newtonian mechanics, because when we go to the expression of force in the special theory of relativity it turns out that the momentum appears multiplied by the famous gamma factor, which is the inverse of the square root one minus the speed squared by the speed of light squared. And this complicates things. Because now it turns out that the force is no longer in the acceleration direction, since two terms appear in the derivation. It is not proportional to the acceleration, as we said, except in two particular cases: that of circular motion and that of rectilinear motion.
So what is dough? Well, we could say that it is a dynamic property of the particles that, in the non-relativistic limit, or in the two particular cases that we have mentioned above, accounts for the inertia of a body.
The dough, in a jiffy
In addition, according to Einstein’s famous equation, that energy is equal to the product of mass times the square of the speed of light, it turns out that an energy is associated with the rest mass of a particle. And vice versa: energy also manifests itself as inertia, to the point that, for example, a high percentage of the mass of the nucleon, made up of quarks, is due to the energy of interaction through the field of quantum chromodynamics.
Finally, we cannot omit the illuminating result, provided by the theory of the spontaneous breaking mechanism of the gauge symmetry of the electroweak theory, that the mass of fermions, leptons and quarks, which are the fundamental particles of the standard model , together with the mass of the W and Z bosons, messengers of the weak interaction, comes from their coupling with the recently discovered Higgs boson. So the mass seems to manifest itself, once again, in light of these results, as a mere manifestation of the energy of an interaction.
The very nature of the mass of the Higgs boson and the precise definition of the mass of the quarks would remain open questions, while, since they are always confined, that is, given the impossibility of isolating a quark, the notion of mass itself for a quark it depends on the model under consideration. And with this we believe we have given an exhaustive review of the very important notion of mass. And we may have done it in a jiffy.
