Covariance. Covariance is the generalization of the theory of
special relativity, where it is sought that the laws
for nature have the same form in all reference systems, which is
equivalent to all reference systems being indistinguishable. In
other words, that whatever the movement of the observers, the
equations will have the same form and contain the same terms. This
was Einstein’s main motivation for him to study and postulate
general relativity. The covariance principle suggested that the laws
should be written in terms of tensors, whose covariant and
countervariant transformation laws could provide the “invariance”
as intended, satisfying the covariance principle.
Newtonian mechanics equations assumed that space and time were
absolute magnitudes, universal in character. However, this scheme
was incompatible with special relativity, whose main axiom stated
that each observer, depending on his speed, had a local time and a
different spatial framework.
The covariance principle can be summarized by saying that the laws of physics are the
same in all frames of reference. A statement that takes us back to the relativity
principle of the special theory:
All the laws of physics are exactly the same for each observer in each frame of
reference that is at rest or moving with uniform relative speed. This means that there
is no experiment that can be performed within a frame of reference that reveals
whether it is at rest or moving at a uniform speed.
he other basic principle of general theory is the equivalence
principle, which says that the effects due to acceleration and those
due to gravity are indistinguishable. It may seem like a hollow
statement, because we already knew that gravity causes an
acceleration in Newtonian physics and the relationship was already
known to Newton himself.