# Alexian reference frame

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The *Alexian reference frame* is the transformation of a real physical system whereby the dynamics become pure imaginary via the transformations:

where are the Pauli matrices.

Constraints on physical systems that are invariant under Alexian shifts of reference frame are said to be *Alexian conditions*.

It has been claimed that real systems that are Alexian are dual to the imaginary analogue, but this then leads to the Alexian paradox, whereby a real system and the imaginary system are not covariant under the Alexian transformation with respect to the unitary time-evolution of the observables of the system.

Most scientists consider the Alexian frame of reference to be inconsistent.