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In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.
The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows: = = (,) In the above, is the proper time of the path through spacetime, called the world-line, followed by the object velocity the above represents, and
This is the formula for the relativistic doppler shift where the difference in velocity between the emitter and observer is not on the x-axis. There are two special cases of this equation. The first is the case where the velocity between the emitter and observer is along the x-axis. In that case θ = 0, and cos θ = 1, which gives:
[1] This is achieved by photons to the extent that effects described by special relativity are able to describe those of such particles themselves. Several approaches exist as a means of describing the motion of single and multiple relativistic particles, with a prominent example being postulations through the Dirac equation of single particle ...
In special relativity, energy is closely connected to momentum. In special relativity, just as space and time are different aspects of a more comprehensive entity called spacetime, energy and momentum are merely different aspects of a unified, four-dimensional quantity that physicists call four-momentum. In consequence, if energy is a source of ...
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun.
The KG equation is undesirable due to its prediction of negative energies and probabilities, as a result of the quadratic nature of – inevitable in a relativistic theory. This equation was initially proposed by Schrödinger, and he discarded it for such reasons, only to realize a few months later that its non-relativistic limit (what is now ...
This, by definition, is 50 km/h, which suggests that the prescription for calculating relative velocity in this fashion is to add the two velocities. The diagram displays clocks and rulers to remind the reader that while the logic behind this calculation seem flawless, it makes false assumptions about how clocks and rulers behave.