special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity, "On the Ele ...

, the rest frame of a

particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

is the

frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system, whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale have been specified in physical space. It ...

coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

attached to physical markers) in which the particle is at rest. The rest frame of compound objects (such as a fluid, or a solid made of many vibrating

atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...

s) is taken to be the frame of reference in which the average

momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...

of the particles which make up the substance is zero (the particles may individually have momentum, but collectively have no net momentum). The rest frame of a container of gas, for example, would be the rest frame of the container itself, in which the gas molecules are not at rest, but are no more likely to be traveling in one direction than another. The rest frame of a river would be the frame of an unpowered boat, in which the mean velocity of the water is zero. This frame is also called the center-of-mass frame, or center-of-momentum frame. The center-of-momentum frame is notable for being the reference frame in which the total energy (total relativistic energy) of a particle or compound object, is also the

invariant mass The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, ...

(times the scale-factor

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

squared). It is also the reference frame in which the object or system has minimum total energy. In both special relativity and

general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

it is essential to specify the rest frame of any time measurements, as the time that an event occurred is dependent on the rest frame of the observer. For this reason the timings of astronomical events such as

supernova A supernova (: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last stellar evolution, evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion ...

e are usually recorded in terms of when the light from the event reached

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

, as the "real time" that the event occurred depends on the rest frame chosen. For example, in the rest frame of a

neutrino A neutrino ( ; denoted by the Greek letter ) is an elementary particle that interacts via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is so small ('' -ino'') that i ...

particle travelling from the

Crab Nebula The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus (constellation), Taurus. The common name comes from a drawing that somewhat resembled a crab with arm ...

supernova to Earth, the supernova occurred in the 11th Century AD only a short while before the light reached Earth, but in Earth's rest frame the event occurred about 6300 years earlier.

References

*{{cite book , title=Gravitation , publisher=W.H. Freeman and Company , year=1973 , isbn=0-7167-0334-3, author= Charles W. Misner, Kip S. Thorne,

John Archibald Wheeler John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr to e ...

See p. 139-140 for discussion of the stress-energy tensor for a perfect fluid such as an ideal gas.

References

See also