Mass


Mass is an intrinsic property of a body. In modern physics, it is generally defined as the strength of an object's gravitational attraction to other bodies - as measured by an observer moving along at the same speed.
It was traditionally believed to be related to the quantity of matter in a body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent.
Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration when a net force is applied.
The SI base unit of mass is the kilogram. In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that determines the strength of this force.
In the Standard Model of physics, the mass of elementary particles is believed to be a result of their coupling with the Higgs boson in what is known as the Brout–Englert–Higgs mechanism.

Phenomena

There are several distinct phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena could be independent of each other, current experiments have found no difference in results regardless of how it is measured:
  • Inertial mass measures an object's resistance to being accelerated by a force.
  • Active gravitational mass determines the strength of the gravitational field generated by an object.
  • Passive gravitational mass measures the gravitational force exerted on an object in a known gravitational field.
The mass of an object determines its acceleration in the presence of an applied force. The inertia and the inertial mass describe this property of physical bodies at the qualitative and quantitative level respectively. 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 and is affected by a gravitational field. If a first body of mass m''A is placed at a distance r from a second body of mass mB, each body is subject to an attractive force, where 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 identical; since 1915, this observation has been incorporated a priori in the equivalence principle of general relativity.

Units of mass

The International System of Units unit of mass is the kilogram. The kilogram is 1000 grams, and was first defined in 1795 as the mass of one cubic decimetre of water at the melting point of ice. However, because precise measurement of a cubic decimetre of water at the specified temperature and pressure was difficult, in 1889 the kilogram was redefined as the mass of a metal object, and thus became independent of the metre and the properties of water, this being a copper prototype of the grave in 1793, the platinum Kilogramme des Archives in 1799, and the platinum–iridium International Prototype of the Kilogram in 1889.
However, the mass of the IPK and its national copies have been found to drift over time. The re-definition of the kilogram and several other units came into effect on 20 May 2019, following a final vote by the CGPM in November 2018. The new definition uses only invariant quantities of nature: the speed of light, the caesium hyperfine frequency, the Planck constant and the elementary charge.
Non-SI units accepted for use with SI units include:
Outside the SI system, other units of mass include:

Definitions

In physical science, one may distinguish conceptually between at least seven different aspects of mass, or seven physical notions that involve the concept of mass. Every experiment to date has shown these seven values to be proportional, and in some cases equal, and this proportionality gives rise to the abstract concept of mass. There are a number of ways mass can be measured or operationally defined:
  • Inertial mass is a measure of an object's resistance to acceleration when a force is applied. It is determined by applying a force to an object and measuring the acceleration that results from that force. An object with small inertial mass will accelerate more than an object with large inertial mass when acted upon by the same force. One says the body of greater mass has greater inertia.
  • Active gravitational mass is a measure of the strength of an object's gravitational flux. Gravitational field can be measured by allowing a small "test object" to fall freely and measuring its free-fall acceleration. For example, an object in free-fall near the Moon is subject to a smaller gravitational field, and hence accelerates more slowly, than the same object would if it were in free-fall near the Earth. The gravitational field near the Moon is weaker because the Moon has less active gravitational mass.
  • Passive gravitational mass is a measure of the strength of an object's interaction with a gravitational field. Passive gravitational mass is determined by dividing an object's weight by its free-fall acceleration. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a smaller force than the object with a larger passive gravitational mass.
  • According to relativity, mass is nothing else than the rest energy of a system of particles, meaning the energy of that system in a reference frame where it has zero momentum. Mass can be converted into other forms of energy according to the principle of mass–energy equivalence. This equivalence is exemplified in a large number of physical processes including pair production, beta decay and nuclear fusion. Pair production and nuclear fusion are processes in which measurable amounts of mass are converted to kinetic energy or vice versa.
  • Curvature of spacetime is a relativistic manifestation of the existence of mass. Such curvature is extremely weak and difficult to measure. For this reason, curvature was not discovered until after it was predicted by Einstein's theory of general relativity. Extremely precise atomic clocks on the surface of the Earth, for example, are found to measure less time when compared to similar clocks in space. This difference in elapsed time is a form of curvature called gravitational time dilation. Other forms of curvature have been measured using the Gravity Probe B satellite.
  • Quantum mass manifests itself as a difference between an object's quantum frequency and its wave number. The quantum mass of a particle is proportional to the inverse Compton wavelength and can be determined through various forms of spectroscopy. In relativistic quantum mechanics, mass is one of the irreducible representation labels of the Poincaré group.

    Weight vs. mass

In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" refers to an intrinsic property of an object, whereas "weight" measures an object's resistance to deviating from its current course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass.
The force known as "weight" is proportional to mass and acceleration in all situations where the mass is accelerated away from free fall. For example, when a body is at rest in a gravitational field, it must be accelerated by a force from a scale or the surface of a planetary body such as the Earth or the Moon. This force keeps the object from going into free fall. Weight is the opposing force in such circumstances and is thus determined by the acceleration of free fall. On the surface of the Earth, for example, an object with a mass of 50 kilograms weighs 491 newtons, which means that 491 newtons is being applied to keep the object from going into free fall. By contrast, on the surface of the Moon, the same object still has a mass of 50 kilograms but weighs only 81.5 newtons, because only 81.5 newtons is required to keep this object from going into a free fall on the moon. Restated in mathematical terms, on the surface of the Earth, the weight W of an object is related to its mass m by, where is the acceleration due to Earth's gravitational field,.
For other situations, such as when objects are subjected to mechanical accelerations from forces other than the resistance of a planetary surface, the weight force is proportional to the mass of an object multiplied by the total acceleration away from free fall, which is called the proper acceleration. Through such mechanisms, objects in elevators, vehicles, centrifuges, and the like, may experience weight forces many times those caused by resistance to the effects of gravity on objects, resulting from planetary surfaces. In such cases, the generalized equation for weight W of an object is related to its mass m by the equation, where a is the proper acceleration of the object caused by all influences other than gravity..