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One kilogram pattern.

The kilogram is one of the seven SI base units and one of the three defined ad hoc (i.e., without reference to another base unit).

In physics, mass (from the Latin massa) is a physical magnitude and general property of matter that expresses inertia or resistance to change movement of a body. More precisely, it is the property of a body that determines its acceleration when it is under the influence of a given force. It is an intrinsic property of bodies that determines the measure of inertial mass and gravitational mass.. The unit used to measure mass in the International System of Units is the kilogram (kg).

Not to be confused with weight, which is a vector magnitude that represents a force whose unit used in the International System of Units is the newton (N), although from the weight of a body at rest (attracted by the force of gravity), its mass can be known by knowing the value of gravity. Neither should mass be confused with the amount of substance, whose unit in the International System of Units is the mole.

History

Although the concept of mass of an object and weight are pre-scientific notions, it is from the reflections of Galileo, René Descartes and very especially from Isaac Newton when the modern notion of mass arises. Thus, the concept of mass is born from the confluence of two laws: Newton's universal law of gravitation and Newton's second law (or 2nd law). According to the law of universal gravitation, the attraction between two bodies is proportional to the product of two constants, called gravitational mass —one of each of them—, thus gravitational mass being a property of matter by virtue of which two bodies they attract each other; By Newton's 2nd law, the force applied to a body is directly proportional to the acceleration it experiences, calling the constant of proportionality: inertial mass of a body.

For Einstein, gravity is a consequence of the geometry of space-time: a curvature of the geometry of space-time due to the effect of the mass of bodies.

Neither to Newton nor to other physicists before Einstein, it was obvious that inertial mass and gravitational mass coincided. Loránd Eötvös carried out very careful experiments to detect if there was a difference between the two, but both seemed to coincide with high precision and could possibly be the same. In fact, all the experiments show results compatible with the equality of both. For prerelativistic classical physics this identity was accidental. Already Newton, for whom weight and inertia were independent properties of matter, proposed that both qualities are proportional to the amount of matter, which he called "mass." However, for Einstein, the coincidence of inertial mass and gravitational mass was crucial data and one of the starting points for his theory of relativity and, therefore, for better understanding the behavior of nature. According to Einstein, this identity means that: "the same quality of a body manifests itself, according to the circumstances, as inertia or as weight."

This led Einstein to state the equivalence principle: "the laws of nature must be expressed in such a way that it is impossible to distinguish between a uniform gravitational field and an accelerated referential system." Thus, "inertial mass" and "gravitational mass" are indistinguishable and, consequently, there is a single concept of "mass" as a synonym for "quantity of matter", according to Newton's formulation. Traditionally, mass was thought to measure the amount of matter. In the words of D. M. McMaster: "mass is the expression of the amount of matter in a body, revealed by its weight, or by the amount of force necessary to produce a certain amount of motion in a body in a given time". However, this interpretation has been partially falsified by modern knowledge. It is known that the mass of subatomic particles does not depend on the amount of something specific in that type of matter, but on its interaction with the Higgs boson, or on the binding energy of the quarks that make up the majority of them. mass matter, not so much of something that can be called "amount of matter".

In classical physics, mass is a constant of a body. In relativistic physics, the apparent mass is an increasing function of the speed that the body has with respect to the observer (in fact, in relativity the fundamental idea of defining the "true" mass as the value of the force divided by the acceleration experienced, since that this quotient depends on the speed). In addition, relativistic physics demonstrated the relationship between mass and energy, being proven in nuclear reactions; For example, in the explosion of an atomic bomb, it remains that mass is not strictly conserved, as was the case with the mechanical mass of pre-relativistic physics.

Phenomena

There are several different phenomena that can be used to measure mass. Although some theorists have speculated that some of these phenomena are independent of each other, current experiments have found no difference in results regardless of how it is measured:

• Inertial mass measures the resistance of an object to be accelerated by a force (represented by the relationship 1=F=ma).
• The "active gravitational mass" determines the strength of the gravitational field generated by an object.
• The "passive gravitational mass" measures the gravitational force exercised over an object in a known gravitational field.

The mass of an object determines its acceleration in the presence of an applied force. Inertia and inertial mass describe this property of physical bodies at a 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. The mass of a body 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 (center of mass to center of mass) from a second body of mass m_B, each body is subject to an attractive force Fg = Gm_Am_B/r2, where G = 6.67×10⁻¹¹ N⋅kg⁻²⋅m² is the universal gravitational constant. It is sometimes called gravitational mass. Repeated experiments since the 17th century have shown that inertial and gravitational mass are identical; since 1915, this observation has been incorporated a priori into the equivalence principle of general relativity.

Units of mass

The kilogram is one of the seven core units of the International Unit System (IS)

The International System of Units (SI) unit of mass is the kilogram (kg). The kilogram has 1000 grams (g), and was first defined in 1795 as the mass of one cubic decimeter of water at the melting point of ice. However, due to the difficulty of accurately measuring a cubic decimeter of water at the specified temperature and pressure, in 1889 the kilogram was redefined as the mass of a metallic object, thus becoming independent of the meter and of 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 (IPK) in 1889.

However, the mass of the IPK and its national copies have been found to drift over time. The redefinition of the kilogram and several other units entered into force on May 20, 2019, following the final vote by the CGPM in November 2018. The new definition uses only invariant quantities of nature: the speed of light, the "cesium hyperfine frequency", Planck's constant and elementary charge.

Among the non-SI units accepted for use with the SI units are:

• the ton (t) (or "metric tonne"), which equals 1000 kg
• the Electronvoltio (eV), an energy unit, used to express the mass in eV/c2 through equivalence between mass and energy
• the dalton (Da), equivalent to 1/12 of the mass of a carbon-free atom, approximately 1.66×10⁻²⁷ kg.

Outside the SI system, other units of mass include:

• the slug (sl), an “imperial unity” of mass (about 14.6 kg)
• the pound (lb), a mass unit (about 0.45 kg), which is used next to the equally called pound (force) (about 4,5 N), a force unit
• the mass of Planck (approximately 2,18⁻⁸kg), an amount derived from fundamental constants
• the solar mass, defined as the mass of the Sun, used mainly in astronomy to compare large masses as stars or galaxies (≈ 1.9³⁰kg
• the mass of a particle, identified with its inverse Compton wavelength (1 cm⁻¹ 3. 3.52⁻⁴¹ kg
• the mass of a black star or hole, identified with its Schwarzschild radio (1 cm 6.73²⁴ kg).

Definitions

In the physical sciences, one can conceptually distinguish between at least seven different aspects of mass, or seven physical notions involving the concept of mass. Every experiment to date has shown that these seven values are proportional, and in some equal cases, and this proportionality gives rise to the abstract concept of mass. There are several ways to measure or operationally define mass:

• Inertial mass is a measure of the resistance of an object to acceleration when a force is applied. It is determined by applying a force to an object and by measuring the acceleration resulting from that force. An object with a small inertial mass will accelerate more than an object with a large inertial mass when it acts on it the same strength. It is said that the larger body has greater inertia.
• The gravitational mass Activeis a measure of the force of the gravitational flow of an object (the gravitational flow is equal to the integral surface of the gravitational field on an enveloping surface). The gravitational field can be measured allowing a small "test object" to fall freely and measure its free fall acceleration. For example, an object in free fall near the Moon is subject to a smaller gravitational field and therefore accelerates more slowly than the same object if it were in free fall near the Earth. The gravitational field near the Moon is weaker because the Moon has a less active gravitational mass.
• The gravitational mass passive is a measure of the force of the interaction of an object with a gravitational field. The passive gravitational mass is determined by dividing the weight of an object by its acceleration in free fall. Two objects within the same gravitational field will experience the same acceleration; however, the object with a smaller passive gravitational mass will experience a lesser force (less weight) than the object with a larger passive gravitational mass.
• Energy also has mass according to the principle of equivalence between mass and energy. This equivalence is exemplified in a large number of physical processes that include pair creation, nuclear fusion and gravitational curvature of light. The production of pairs and nuclear fusion are processes in which mass measurable quantities become energy or vice versa. In the gravitational curvature of light, it is shown that photons of pure energy exhibit a behavior similar to passive gravitational mass.
• The curvature of space-time is a relativistic manifestation of mass existence. Such curvature is extremely weak and difficult to measure. For this reason, the curvature was not discovered until after it was predicted by Einstein's general relativity theory. Extremely precise atomic clocks on Earth's surface, for example, measure less time (lower run) compared to similar timepieces in space. This difference in the time elapsed is a form of curvature called gravitational dilation of time. Other forms of curvature have been measured using the Gravity Probe B satellite.
• The 'quantum mass' is manifested as a difference between the quantum frequency of an object and its wave number. The quantum mass of a particle is proportional to the inverse Compton wavelength and can be determined by various forms of spectroscopy. In relativistic quantum mechanics, the mass is one of the irreductible representation labels of the Poincaré group.

Mass in prerelativistic physics

Inertial Mass

Inertial mass for classical physics is determined by Newton's second and third law. Given two bodies, A and B, with inertial masses m_A (known) and m_B (to be want to determine), in the hypothesis he says that the masses must be constant and that both bodies are isolated from other physical influences, so that the only force present on A is the one exerted by B, called F_AB, and the only force present on B is the one exerted by A, called F_BA, according to Newton's second law:

FAB=mAaA{displaystyle F_{AB}=m_{A}a_{A},!}

FBA=mBaB{displaystyle F_{BA}=m_{B}a_{B},!}.

where a_A and a_B are the accelerations of A and B, respectively. It is necessary that these accelerations are not zero, that is, that the forces between the two objects are not equal to zero. One way to achieve this is, for example, to make the two bodies collide and take measurements during the collision.

Newton's Third Law states that the two forces are equal and opposite:

FAB=− − FBA{displaystyle F_{AB}=-F_{BA},!}.

Substituting into the above equations, we get the mass of B as

mB=aAaBmA{displaystyle m_{B}={a_{A} over a_{B}}m_{A},}!.

Thus, measuring a_A and a_B allows us to determine m_B relative to m_A, which was what was wanted. The requirement that a_B be nonzero makes this equation well defined.

In the above reasoning it has been assumed that the masses of A and B are constant. This is a fundamental assumption, known as the conservation of mass, and is based on the assumption that matter cannot be created or destroyed, only transformed (divided or recombined). However, it is sometimes useful to consider the change in the mass of the body over time; For example, the mass of a rocket decreases during its launch. This approximation is made by ignoring matter entering and leaving the system. In the case of the rocket, this matter corresponds to the fuel that is expelled; the combined mass of the rocket and the fuel is constant.

Gravitational Mass

Consider two bodies A and B with gravitational masses M_A and M_B, separated by a distance |r_AB|. Newton's law of gravitation states that the magnitude of the gravitational force that each body exerts on the other is

日本語F日本語=GMAMB日本語rAB日本語2{displaystyle 日本語FUD={GM_{A}M_{B} over Șr_{AB}{2}{2}}

where G is the universal gravitational constant. The previous sentence can be reformulated as follows: given the acceleration g of a reference mass in a gravitational field (such as the Earth's gravitational field), the force of gravity on an object with gravitational mass M is of magnitude

日本語F日本語=Mg{displaystyle 日本語F.

This is the basis on which masses are determined on balances. In bathroom scales, for example, the force |F| is proportional to the displacement of the spring under the weighing platform (see Hooke's law of elasticity), and the scale is calibrated to account for g so that the mass M can be read .

Equivalence of inertial mass and gravitational mass

Inertial mass and gravitational mass are shown experimentally to be the same—with a very high degree of precision. These experiments are essentially tests of the phenomenon already observed by Galileo that objects fall with an acceleration independent of their masses (in the absence of external factors such as friction).

Suppose an object with inertial and gravitational masses m and M, respectively. If gravity is the only force acting on the body, the combination of Newton's second law and the law of gravity gives its acceleration as:

a=Mmg{displaystyle a={M over m}g}

Therefore, all objects located in the same gravitational field fall with the same acceleration if and only if the ratio between gravitational and inertial mass is equal to a constant. By definition, this ratio can be taken to be 1.

Mass in relativistic physics

Special Relativity

In the special theory of relativity, the «inertial mass» defined as the quotient between the force applied to a body and the acceleration it experiences, depends on the speed of the body, so it is an intrinsic property of the body. For this reason, another intrinsic quantity called rest mass is defined, which is determined in a reference frame in which the mass is at rest (known as a “rest frame”). In fact, for practical purposes, the classical physics method for determining inertial mass is still valid, as long as the speed of the object is much less than the speed of light, so that Newtonian mechanics is still valid.

In relativistic mechanics, the rest mass of a free particle is related to its energy and momentum according to the following equation:

E2c2=m2c2+p2{displaystyle {E^{2} over c^{2}}=m^{2}c^{2+}p^{2}{2}}.

Which can be rearranged as follows:

E=mc21+(pmc)2{displaystyle E=mc^{2}{sqrt {1+left({p over mc}right)^{2}}}}}}

The classical limit corresponds to the situation in which the moment p is much less than mc, in which case the square root can be developed into a series of Taylor:

E=mc2+p22m+...... {displaystyle E=mc^{2}+{p^{2} over 2m}+dots }

The main term, which is the largest, is the rest energy of the particle. If the mass is nonzero, a particle always has at least this amount of energy, regardless of its momentum or momentum. Rest energy is normally inaccessible, but it can be released by splitting or combining particles, as in nuclear fusion and fission. The second term is the classical kinetic energy, which is proved using the classical definition of kinetic momentum or linear momentum:

p=mv{displaystyle p=mv,!}

and substituting to get:

E=mc2+mv22+...{displaystyle E=mc^{2}+{mv^{2} over 2}+... !

The relativistic relationship between energy, mass, and momentum also holds for particles that have no mass (which is a poorly defined concept in terms of classical mechanics). When m = 0, the relation simplifies to

E=pc{displaystyle E=pc,!}

where p is the relativistic moment.

This equation defines the mechanics of massless particles like the photon, which are the particles of light.

General Relativity

The concept of mass in general relativity is much more subtle than its analogue in special relativity. In fact, in general, the general theory of relativity there is no single concept of mass, rather the concept of special relativity is generalized in several different and non-equivalent ways. In fact, there are several ways to conceive of mass in general relativity, depending on the case. For some non-stationary complex types of space-time, in fact, the concept of mass cannot even be defined in a physically objective and unambiguous way. Likewise, there is not, in general, a tensor-impulse energy of the gravitational field that represents the local energy of the gravitational field or space-time, which leads to certain problems when defining the total energy, as a global magnitude.

Mass in the quantum physics of fields

The classical and relativistic notion of mass has been revised in modern quantum field theory. In the formulation of said theory, quantum fields can manifest as individual particles of a certain type. Some of those subatomic particles are particles with mass. The mass of said particle is a precise physical quantity, but it is not associated with something like the "amount of matter". In fact, from the perspective of quantum field theory there are two physical processes by which a subatomic particle appears to be endowed with mass:

• The Higgs mechanism, by which the quantum field associated with a specific particle type interacts with the Higgs field that floods the entire universe. As a result of this interaction the propagation of the field is done at sub-plastic speeds. That propagation rate also depends on the energy of the particle, so the interaction between the particle and the Higgs field makes it perceived as a mass particle. This is the main factor of the mass of elemental particles such as leptons, quarks and W and Z bosons.

• For some subatomic particles such as the hadrons there is an additional physical process that makes them have a much larger mass than they would have if they were only affected by the Higgs field. This is the additional inertial effect associated with the ligature energy associated with the chromodynamic interaction between the quarks that constitute such particles. Thus more than 98% of the dough of the proton is due to this effect, if there was no mass of the proton and of all the known moreic matter would be about sixty times less.

Conventional dough

According to document D28 Conventional value of the result of weighing in air of the International Organization of Legal Metrology (OIML), the conventional mass of a body is equal to the mass of a density standard equal to 8000 kg/m³ that balances said body in air under conventionally chosen conditions: air temperature equal to 20 °C and air density equal to 0.0012 g/cm³.

This definition is essential for international trade without disputes about weighing carried out under different conditions of air density and object density. If the scales were to measure mass, it would be necessary to have mass standards of the same density as the objects whose mass is to be determined, which is not practical and is the reason why Conventional Mass was defined, which is the magnitude that scales measure with greater precision.