Relativity
The field tensor derives its name from the fact that the electromagnetic field is found to obey the tensor transformation law, this general property of (non-gravitational) physical laws being recognised after the advent of special relativity. This theory stipulated that all the (non-gravitational) laws of physics should take the same form in all coordinate systems - this led to the introduction of tensors. The tensor formalism also leads to a mathematically simpler presentation of physical laws.
The second equation above leads to the continuity equation:
implying conservation of charge.
Maxwell's laws above can be generalised to curved spacetime by simply replacing partial derivatives with covariant derivatives:
- and
where the semi-colon represents a covariant derivative, as opposed to a partial derivative. These equations are sometimes referred to as the curved space Maxwell equations. Again, the second equation implies charge conservation (in curved spacetime):
Read more about this topic: Electromagnetic Tensor
Famous quotes containing the word relativity:
“By an application of the theory of relativity to the taste of readers, to-day in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!”
—Albert Einstein (1879–1955)