The mass (from ancient Greek μᾶζα, mâza, “barley cake, lump of dough”) represents the amount of matter that constitutes a material body, attributing dynamic characteristics (inertia) when the bodies are subject to the influence of external forces. In classical mechanics the term mass can refer to three different scalar physical quantities, distinct from each other:

  • inertial mass is proportional to the inertia of a body, which is the resistance to changing its state of motion when a force is applied;
  • passive gravitational mass is proportional to the force of a body’s interaction with the force of gravity;
  • active gravitational mass, on the other hand, is proportional to the intensity of the gravitational field produced by a body.

The mass does not correspond with the amount of substance, the physical quantity for which it has been introduced in the SI a fundamental quantity, the mole (symbol mol). The mass of a body is commonly determined by measuring its inertia which is opposed to a change in its state of motion or the gravitational attraction to other bodies by comparison with a sample (see balance).

In physics, inertial mass is the property of material bodies to resist forces that tend to accelerate them, a resistance that is precisely measured by the value of their mass. Gravitational mass, on the other hand, is the property of any two bodies to attract each other.

The inertial mass is defined according to the principle of action and reaction and is the factor of proportionality m that appears in the fundamental law of dynamics; for each body it coincides with the gravitational mass, which appears as the factor of proportionality m in the expression of the gravitational force acting on the body in the presence of another body with mass M placed at a distance D.

The equivalence of the two masses was precisely verified in 1909 by R. Eötvös, who built an apparatus capable of determining a difference of one part in a hundred million in the gravitational force; in 1964 R.H. Dicke carried out a new version of Eötvös’s experiment, improving its accuracy by several hundred times. In classical physics, the equivalence between inertial mass and gravitational mass was not considered important; in modern physics, however, this equivalence forms the basis for a profound understanding of the phenomenon of gravitation and was laid down by A. Einstein as the foundation for the theory of general relativity.

Throughout the history of physics, especially classical physics, mass has been considered an intrinsic property of matter, which can be represented by a scalar value, and which is conserved in time and space, remaining constant in any isolated system. Moreover, the term mass has been used to denote two potentially distinct quantities: the interaction of matter with the gravitational field, and the relationship that links 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 (first performed by Galileo Galilei).

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.

Unlike space and time, for which operational definitions can be given in terms of natural phenomena, defining the concept of mass requires explicit reference to the physical theory that describes its meaning and properties. The 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 to be quite different from the first theory to introduce mass in quantitative terms, Newtonian dynamics.

The concept of mass becomes even more complex at the level of particle physics, where the existence of elementary particles with mass (electrons, quarks, etc.) and without mass (photons, gluons) still has no fundamental explanation. In other words, it is not clear why some particles have mass and others do not. The main theories trying to provide an explanation are: the Higgs mechanism, string theory and loop quantum gravity; of these, only the Higgs theory has experimental evidence since 2012.

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