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This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [1] [2] [3] and that the particles are free.
For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200 000 km/s (124 000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c.
The "time" axis gives the angular frequency (rad⋅s −1) and the "space" axis represents the angular wavenumber (rad⋅m −1). Green and indigo represent left and right polarization. In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p.
Four-velocity. In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime [nb 1] that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all ...
t. e. In special relativity, four-momentum (also called momentum–energy or momenergy[1]) is the generalization of the classical three-dimensional momentum to four-dimensional spacetime. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. The contravariant four-momentum of a particle with ...
Tests of special relativity. Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played (and still play) an important role in its development and justification. The strength of the theory lies in its unique ability to ...
A world line of an object (generally approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresponding to the history of the object. A world line is a special type of curve in spacetime. Below an equivalent definition will be explained: A world line is either a time-like or a null curve in spacetime.
The usual treatment (e.g., Albert Einstein's original work) is based on the invariance of the speed of light. However, this is not necessarily the starting point: indeed (as is described, for example, in the second volume of the Course of Theoretical Physics by Landau and Lifshitz), what is really at stake is the locality of interactions: one supposes that the influence that one particle, say ...