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In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light . Max Planck showed that the expression for the relativistic energy of a particle with rest mass and momentum is given by : The energy of an ultrarelativistic particle is almost completely due to its momentum (), and thus can be approximated by . This can result from holding the mass fixed and increasing to very large values (the usual case); or by holding the energy fixed and shrinking the mass to negligible values. The latter is used to derive orbits of massless particles such as the photon from those of massive particles (cf. Kepler problem in general relativity). In general, the ultrarelativistic limit of an expression is the resulting simplified expression when is assumed. Or, similarly, in the limit where the Lorentz factor is very large (). == Ultrarelativistic approximations == Below are some ultrarelativistic approximations in units with . The rapidity is denoted : * * * * Motion with constant proper acceleration: , where is the distance traveled, is proper acceleration (with ), is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details). * Fixed target collision with ultrarelativistic motion of the center of mass: } where and are energies of the particle and the target respectively (so ), and is energy in the center of mass frame. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「ultrarelativistic limit」の詳細全文を読む スポンサード リンク
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