special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...

, the rest frame of a

particle In the physical sciences, a particle (or corpuscule 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 ...

is the

frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...

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

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 Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...

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

momentum In Newtonian mechanics, momentum (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. If is an object's mass ...

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 In physics, the center-of-momentum frame (also zero-momentum frame or COM frame) of a system is the unique (up to velocity but not origin) inertial frame in which the total momentum of the system vanishes. The ''center of momentum'' of a system is ...

. 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, i ...

(times the scale-factor

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...

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 Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

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 is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or whe ...

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 harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

, 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 a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...

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. The common name comes from William Parsons, 3rd Earl of Rosse, who observed the object in 1842 u ...

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 Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. F ...

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 in ...

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