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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.
To derive the equations of special relativity, one must start with two other The laws of physics are invariant under transformations between inertial frames. In other words, the laws of physics will be the same whether you are testing them in a frame 'at rest', or a frame moving with a constant velocity relative to the 'rest' frame.
The inertial frame in which the momenta of all particles sums to zero is called the center of momentum frame. In this special frame, the relativistic energy–momentum equation has p = 0, and thus gives the invariant mass of the system as merely the total energy of all parts of the system, divided by c 2
If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
The equation is also valid for photons, which have m = 0: = and therefore = A photon's momentum is a function of its energy, but it is not proportional to the velocity, which is always c. For an object at rest, the momentum p is zero, therefore =.
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 .
A fundamental prediction of special relativity is the relativistic energy–momentum relation; for a particle of rest mass m, and in a particular frame of reference with energy E and 3-momentum p with magnitude in terms of the dot product =, it is: [10]
The consequences of special relativity can be derived from the Lorentz transformation equations. [26] These transformations, and hence special relativity, lead to different physical predictions than those of Newtonian mechanics at all relative velocities, and most pronounced when relative velocities become comparable to the speed of light.