# Mass

In physics, mass (from Greek μᾶζα "barley cake, lump (of dough)"), more specifically inertial mass, is a quantitative measure of an object's resistance to acceleration. In addition to this, gravitational mass is a measure of magnitude of the gravitational force which is

1. exerted by an object (active gravitational mass), or
2. experienced by an object (passive gravitational force)

when interacting with a second object. The SI unit of mass is the kilogram (kg).

In everyday usage, mass is referred to as "weight", the units of which may be pounds or kilograms (for instance, a person's weight may be stated as 75 kg). In scientific use, however, the term "weight" refers to a different, yet related, property of matter. Weight is the gravitational force acting on a given body—which differs depending on the gravitational pull of the opposing body (e.g., a person's weight on Earth vs on the Moon) — while mass is an intrinsic property of that body that never changes. In other words, an object's weight depends on its environment, while its mass does not. On the surface of the Earth, an object with a mass of 50 kilograms weighs 491 newtons; on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons. Restated in mathematical terms, on the surface of the Earth, the weight W of an object is related to its mass m by W = mg, where g = 9.80665 m/s2 is the Earth's gravitational field.

The inertial mass of an object determines its acceleration in the presence of an applied force. According to Newton's second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass mA is placed at a distance r (center of mass to center of mass) from a second body of mass mB, each body experiences an attractive force Fg = GmAmB/r2, where G = 6.67×10−11 N kg−2m2 is the "universal gravitational constant". This is sometimes referred to as gravitational mass. Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are equivalent; since 1915, this observation has been entailed a priori in the equivalence principle of general relativity.

Special relativity shows that rest mass (or invariant mass) and rest energy are essentially equivalent, via the well-known relationship E = mc2. This same equation also connects relativistic mass and "relativistic energy" (total system energy). The latter two "relativistic" mass and energy are concepts that are related to their "rest" counterparts, but they do not have the same value as their rest counterparts in systems where there is a net momentum. In order to deduce any of these four quantities from any of the others, in any system which has a net momentum, an equation that takes momentum into account is needed. Mass (so long as the type and definition of mass is agreed upon) is a conserved quantity over time. From the viewpoint of any single unaccelerated observer, mass can neither be created or destroyed, and special relativity does not change this understanding. All unaccelerated observers agree on the amount of invariant mass in closed systems at all times, and although different observers may not agree with each other on how much relativistic mass is present in any such system, all agree that the amount does not change over time.

Macroscopically, mass is associated with matter—although matter, unlike mass, is poorly defined in science. On the sub-atomic scale, not only fermions, the particles often associated with matter, but also some bosons, the particles that act as force carriers, have rest mass. Another problem for easy definition is that much of the rest mass of ordinary matter derives from the invariant mass contributed to matter by particles and kinetic energies which have no rest mass themselves (only 1% of the rest mass of matter is accounted for by the rest mass of its fermionic quarks and electrons). From a fundamental physics perspective, mass is the number describing under which the representation of the little group of the Poincaré group a particle transforms. In the Standard Model of particle physics, this symmetry is described as arising as a consequence of a coupling of particles with rest mass to a postulated additional field, known as the Higgs field.

The total mass of the observable universe is estimated at between 1052 kg and 1053 kg, corresponding to the rest mass of between 1079 and 1080 protons.

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