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Originally posted by Solasis
Conservation of energy is a principle which we believe to be true, because it helps to explain fundamental observations in the world, and it s predictions pan out. It is NOT a universal law; it is formulated as such because it SEEMS to be a universal law. Perhaps it does hold; I suspect so. But it is NOT hard and fast the way you say.
An important example of such symmetry is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations.
In standard physics, Lorentz covariance (from Hendrik Lorentz) is a key property of spacetime that follows from the special theory of relativity, where it applies globally. Local Lorentz covariance refers to Lorentz covariance applying only locally in an infinitesimal region of spacetime at every point, which follows from general relativity. Lorentz covariance has two distinct, but closely related meanings.
A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a scalar (e.g. the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e. they transform under the trivial representation).
An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). The key property of such equations is that if they hold in one inertial frame, then they hold in any inertial frame (this follows from the result that if all the components of a tensor vanish in one frame, they vanish in every frame). This condition is a requirement according to the principle of relativity, i.e. all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.