What are the transformations between xHy and yH'x ?

In special relativity physical laws must be invariant over frames that are inertially moving relative to each other. In the Relational interpretation, as I see it, physical laws must be invariant over frames that are in a quantum state relative to each other.

Suppose xHy means system x represents system y as a vector in a Hilbert space H. We're after the transformation that preserves the evolution equation and its constant(s), in going from xHy to yH'x, where H and H' have the same dimension.

I'm guessing that, in analogy to special relativity, the transformations are among the parameters of the (quantum) theory. They are time t in some theories, and both space x and time t in most field theories.


I found "Physical Laws Must Be Invariant over Quantum Systems", Phys. Essays 19, 75 (2006). I can't find "On the Relativity of Quantum Superpositions" which came out in Metaphysical Review in the early late middle 90's. The transformations in the former paper may not be right.