Understanding Covariance in Special Relativity & Lorentz Transformations

[ehrenfest]

Can someone explain to me what it means to be "covariant" in the context of special relativity and Lorentz transformations? I already checked wikipedia.

 

[Dick]

Try wikipedia for "general covariance". It means a physical law is expressed in a form that is valid for all coordinate systems.

 

[StatusX]

There are two possible meanings. One, as Dick has pointed out, refers to the property of a theory that its laws take the same form in any coordinate system (usually by way of being phrased in terms of tensor quantities).

Another related definition is the distinction between covariant and contravariant quantities. These are properties of tensors, or more precisely, of specific indices of a tensor. Briefly, a tensor can be expressed in a given coordinate system as an array of numbers, but in a different coordinate system the same tensor will be denoted by a different array of numbers. There are two kinds of rules for obtaining these new numbers, one for covariant quantities and another for contravariant quantities. These rules are, in a certain sense, opposite, and by putting together a contravariant and covariant quantity in a certain way, we can get a number that is the same in all coordinate systems (called a scalar) - that is, when we transform the two quantities, they transform in opposing ways so that the resulting combination stays the same.