The general principle of relativity states:
All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.
— C. Møller The Theory of Relativity, p. 220
That is, physical laws are the same in all reference frames—inertial or non-inertial. An accelerated charged particle might emit synchrotron radiation, though a particle at rest doesn't. If we consider now the same accelerated charged particle in its non-inertial rest frame, it emits radiation at rest.
Physics in non-inertial reference frames was historically treated by a coordinate transformation, first, to an inertial reference frame, performing the necessary calculations therein, and using another to return to the non-inertial reference frame. In most such situations, the same laws of physics can be used if certain predictable fictitious forces are added into consideration; an example is a uniformly rotating reference frame, which can be treated as an inertial reference frame if one adds a fictitious centrifugal force and Coriolis force into consideration.
The problems involved are not always so trivial. Special relativity predicts that an observer in an inertial reference frame doesn't see objects they'd describe as moving faster than the speed of light. However, in the non-inertial reference frame of Earth, treating a spot on the Earth as a fixed point, the stars are observed to move in the sky, circling once about the Earth per day. Since the stars are light years away, this observation means that, in the non-inertial reference frame of the Earth, anybody who looks at the stars is seeing objects which appear, to them, to be moving faster than the speed of light.
Since non-inertial reference frames do not abide by the special principle of relativity, such situations are not self-contradictory.
Read more about this topic: Principle Of Relativity
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