Why are the masses of elementary particles not invariant?

In physics, the mass and weight of an object represent two essentially different concepts. The mass of an object is a measure of the amount of matter it contains, unlike weight, which is a measure of the gravitational force to which it is subjected. According to Newton’s laws, that gravitational force or weight is proportional to mass, so the two concepts are often used interchangeably, albeit inappropriately, in colloquial language.

An object at sea level is slightly less heavy at the top of Everest because it is farther away from the center of the Earth, enough so that the intensity of gravity is slightly weaker. On the surface of the Moon, where the intensity of the gravitational force is six times weaker than the one on Earth, its weight is correspondingly six times less. Its mass, on the other hand, is an invariant quantity, characteristic of the object and independent of its location. To be precise, instead of asking «how much do I weigh?», we should always ask the question «how much mass do I have?».

In the microscopic world something similar happens. Although the force of gravity is not usually relevant among elementary particles, they are subject to other fundamental forces such as the strong, weak and electromagnetic forces, and the intensity of all these forces is not always the same, but depends largely on the energy at which the elementary particles accelerate and collide with each other.

The extraordinary thing in this case is that due to the quantum laws governing the microcosm, the masses of the elementary particles also cease to be an intrinsically immutable quantity. That variability, however, is not arbitrary. Although the theory called the Standard Model cannot predict the value of the masses of elementary particles or the intensity of the fundamental forces, it does predict with great precision how they change as a function of energy. That is, by measuring the masses and intensities of the forces in one experiment at a reference energy, we can predict what their values will be in another experiment where the particles interact at a different energy.

This variability is determined by the quantum fluctuations of the vacuum allowed by the theory. These fluctuations generate from the vacuum virtual particles that appear and disappear affecting the mass and the intensity of the forces depending on the distance, or equivalently energy, at which we observe the particle. The so-called quarks should, according to the Standard Model, become lighter and lighter as we perform experiments at higher energies. In contrast, the Higgs boson and leptons, like electrons and muons, would be more massive.

Proving that the masses of elemental particles change depending of the energy of the experiment is, in the first place, a prove of its quantum behavior. Measuring this change with high precision allows, on the one hand, testing of the Standard Model predictions at the limit and, on the other hand, detecting the possibility of existence of new particles or forces in case that the data diverges from the expected evolution.