# Mass (physical)

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May 25, 2022 Mass (from the Greek: μᾶζα, máza, barley cake, lump of dough) is a physical quantity of material bodies which determines their dynamic behavior when they are subjected to the influence of external forces. Throughout the history of physics, in particular of classical physics, mass has been considered an intrinsic property of matter, which can be represented with a scalar value and which is conserved over time and space, remaining constant in every isolated system. Furthermore, the term mass has been used to indicate two potentially distinct quantities: the interaction of matter with the gravitational field and the relationship that binds the force applied to a body with the acceleration induced on it. However, the equivalence of the two masses has been verified in numerous experiments (already implemented by Galileo Galilei first) .In the broader framework of special relativity, relativistic mass is no longer an intrinsic property of matter, but also depends on the reference system in which it is observed. The relativistic mass m {\ displaystyle m} it is related to the mass at rest m 0 {\ displaystyle m_ {0}} , i.e. the mass of the object in the reference system in which it is at rest, by means of the Lorentz factor γ {\ displaystyle \ gamma} : m ( v ) γ m 0 1 1 - ( v / c ) 2 m 0 {\ displaystyle m (v) \ gamma \, m_ {0} {\ frac {1} {\ sqrt {1- (v / c) ^ {2}}}} \, m_ {0}} Since the relativistic mass depends on the velocity, the classical concept of mass is modified, no longer coinciding with the Newtonian definition of the constant of proportionality between the force F applied to a body and the resulting acceleration a. Instead, it becomes a dynamic quantity proportional to the overall energy of the body, through the famous formula E mc². The conservation of mechanical energy now includes, in addition to kinetic energy and potential energy, also a contribution proportional to the rest mass m0, as a further form of energy. The relativistic total energy of the body, given by E mc², includes both the kinetic energy K and that relating to the mass at rest, E0 m0c². Unlike space and time, for which operational definitions can be given in terms of natural phenomena, to define the concept of mass it is necessary to explicitly refer to the physical theory that describes its meaning and properties. Intuitive pre-physical concepts of quantity of matter (not to be confused with quantity of substance, measured in moles) are too vague for an operational definition, and refer to common properties, inertia and weight, which are considered quite distinct. from the first theory that introduces mass in quantitative terms, the Newtonian dynamics. The concept of mass becomes more complex at the level of particle physics where the presence of elementary particles with mass (electrons, quarks, ...) and without mass (photons, gluons) does not yet have an explanation in fundamental terms. In other words, it is not clear why some particles have mass and others do not. The main theories that try to give an interpretation to mass are: the Higgs mechanism, string theory and loop quantum gravity; of these, starting from 4 July 20