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In physics, a theory is said to be covariant if its formulation is invariant under arbitrary coordinate transformations. This means that the laws of Physics should not be dependent on the observer, whatever its state of motion.

Einstein first formulated this requirement in his special theory of Relativity. However, the theory wasn’t fully covariant, since it only allowed coordinate transformations between observers moving at constant speeds relative to each other. He later extended this principle to any kind of motion, thus giving birth to General Relativity.

Any correct theory of quantum gravity is expected to be covariant.

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