For example, in the framework of special relativity, the Maxwell equations have the same form in all inertial frames of reference.
According to a theoretical result called Noether's theorem, any such symmetry will also imply a conservation law alongside.
The special principle of relativity states that physical laws should be the same in every inertial frame of reference, but that they may vary across non-inertial ones.
In classical physics, fictitious forces are used to describe acceleration in non-inertial reference frames.
Newtonian mechanics added to the special principle several other concepts, including laws of motion, gravitation, and an assertion of an absolute time.
Joseph Larmor and Hendrik Lorentz discovered that Maxwell's equations, used in the theory of electromagnetism, were invariant only by a certain change of time and length units.
This left some confusion among physicists, many of whom thought that a luminiferous aether was incompatible with the relativity principle, in the way it was defined by Henri Poincaré: The principle of relativity, according to which the laws of physical phenomena should be the same, whether for an observer fixed, or for an observer carried along in a uniform movement of translation; so that we have not and could not have any means of discerning whether or not we are carried along in such a motion.In their 1905 papers on electrodynamics, Henri Poincaré and Albert Einstein explained that with the Lorentz transformations the relativity principle holds perfectly.
Using only the isotropy of space and the symmetry implied by the principle of special relativity, one can show that the space-time transformations between inertial frames are either Galilean or Lorentzian.
Special relativity predicts that an observer in an inertial reference frame does not see objects he would describe as 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.