A measure of the amount of matter in an object, determining its gravitational pull.Mass is a fundamental property of matter that quantifies the amount of substance in an object and determines its resistance to acceleration (inertia) and its gravitational attraction to other masses. In physics, mass is distinct from weight, which is the force exerted on a mass by a gravitational field. Mass is conserved in isolated systems, meaning it cannot be created or destroyed, though it can be converted to energy according to Einstein's equation E=mc². The standard unit of mass is the kilogram, defined by a platinum-iridium cylinder until 2019, when it was redefined in terms of the Planck constant.
The concept of mass was formalized by Isaac Newton in his 'Principia' (1687), where he distinguished mass from weight. The equivalence principle was articulated by Albert Einstein in 1907 and became a foundation of general relativity (1915). The Higgs mechanism was proposed in 1964 by Peter Higgs and others, and the Higgs boson was discovered at CERN in 2012.
Mass manifests in two ways: inertial mass, which appears in Newton's second law (F=ma), and gravitational mass, which appears in Newton's law of gravitation (F=Gm₁m₂/r²). The equivalence of these two types of mass is a cornerstone of general relativity, which describes gravity as the curvature of spacetime caused by mass and energy. In quantum physics, mass arises from interactions with the Higgs field, which gives elementary particles their rest mass, while most of the mass of protons and neutrons comes from the binding energy of quarks.
Mass measurement is essential in everything from weighing groceries to determining the mass of black holes via gravitational lensing, as described in the article 'Невидимка массой в миллион Солнц'.
The mass of the visible universe is dominated by dark matter, which outweighs ordinary matter by a factor of about five, yet its exact nature remains unknown.
| ds^2 | variable | spacetime interval — spacetime interval metre squared |
| dt | variable | coordinate time differential — time differential second |
| dr | variable | radial coordinate differential — radial coordinate differential metre |
| dΩ^2 | variable | solid angle element squared — solid angle element squared |
| r | variable | radial coordinate — radial coordinate metre |
| t | variable | coordinate time — coordinate time second |
| G | constant | Newton's constant of universal gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| M | constant | mass of the central object — mass kilogram |
| d | operator | infinitesimal change — differential |
| Ψ | variable | Spinor wave function — wave function |
| t | variable | Time — time second |
| i | constant | Square root of -1 — imaginary unit = 1 |
| ħ | constant | Fundamental quantum of action — reduced planck constant = 1.054571817e-34 joule second |
| c | constant | Universal speed limit — speed of light = 299792458 metre per second |
| m | constant | Intrinsic mass of the particle — mass = variable kilogram |
| ∂_t | operator | Differentiates the wave function with respect to time — partial derivative |
| ∇ | operator | Spatial derivative vector — nabla operator |
| T | variable | tunneling probability — transmission probability |
| z1 | variable | left turning point of the barrier — position metre |
| z2 | variable | right turning point of the barrier — position metre |
| m | variable | mass of the tunneling particle — mass kilogram |
| V | variable | potential energy as a function of position — potential energy joule |
| E | variable | energy of the particle — energy joule |
| ħ | constant | fundamental quantum of action divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| ∫ | operator | sums the integrand over the interval — integral |
| √ | operator | takes the non-negative root — square root |
| exp | operator | raises e to the given power — exponential |
| \Omega | variable | Berry curvature — berry curvature square metre |
| m | variable | electron mass — mass kilogram |
| c | variable | speed of light in vacuum — speed metre per second |
| G | variable | gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| M | variable | mass of the object — mass kilogram |
| R | variable | radius of the object — radius metre |
| c | variable | speed of light in vacuum — speed of light metre per second |
