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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.
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.
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold : due to relativistic effects, it is not silvery like most other metals.
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
Relativistic quantum mechanics (RQM) is quantum mechanics applied with special relativity. Although the earlier formulations, like the Schrödinger picture and Heisenberg picture were originally formulated in a non-relativistic background, a few of them (e.g. the Dirac or path-integral formalism) also work with special relativity.
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 =.
There is Robertson's test theory (1949) which predicts different experimental results from Einstein's special relativity, and there is the Mansouri–Sexl theory (1977) which is equivalent to Robertson's theory. There is also Edward's theory (1963) which cannot be called a test theory because it is physically equivalent to special relativity. [16]
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.