One of the central tenets of physics is that experiments should be
reproducible. In other words, if somebody performs a physical experiment today,
and obtains a certain result, then somebody else performing the same
experiment next week ought to obtain the same result, within the experimental
errors. Presumably, in performing these hypothetical experiments, both
experimentalists find it necessary to set up a coordinate frame.
Usually, these two frames do not coincide. After all, the experiments
are, in general, performed in different places and at different times.
Also, the
two experimentalists are likely to orientate their coordinate axes
differently.
Nevertheless, we still
expect both experiments to yield the same result. What exactly do we
mean by this statement? We do not mean that both experimentalists will
obtain the same numbers when they measure something. For instance,
the numbers used to denote the position of a point (i.e., the
coordinates of the point) are, in general, different in different coordinate
frames. What we do expect is that any physically
significant interrelation between physical
quantities (i.e., position, velocity, etc.) which appears to
hold in the coordinate system of the first experimentalist will also
appear to hold in the coordinate system of the second experimentalist.
We usually refer to such interrelationships as *laws of physics*.
So, what we are really saying is that the laws of physics do not
depend on our choice of coordinate system. In particular, if a
law of physics is true in one coordinate system then it is automatically
true in every other coordinate system, subject to the proviso that both
coordinate systems are inertial.

Recall that tensors are geometric objects that possess the property that if a certain interrelationship holds between various tensors in one particular coordinate system then the same interrelationship holds in any other coordinate system that is related to the first system by a certain class of transformations. It follows that the laws of physics are expressible as interrelationships between tensors. In special relativity, the laws of physics are only required to exhibit tensor behavior under transformations between different inertial frames: that is, under translations, rotations, and Lorentz transformations. Parity inversion is a special type of transformation, and will be dealt with separately later on. In general relativity, the laws of physics are required to exhibit tensor behavior under all non-singular coordinate transformations.