Born noticed a symmetry among configuration space and momentum space representations of a free particle, in that its wave function description is invariant to a change of variables x → p and p → − x. (It can also be worded such as to include scale factors, e.g. invariance to x → ap and p → − bx where a, b are constants.) Born hypothesized that such symmetry should apply to the four-vectors of special relativity, that is, to the four-vector space coordinates