Relational Quantum Mechanics from Contextual Ontologies: Notes

There was an inaccuracy added to a previous post: "what exists" in the Relational interpretation is not . Rather, for an electron in e.g.

(1)

represents the maximal amount of physical information there is about the electron's x-spin in the measuring apparatus' frame of reference. Equivalently,

(2)

represents the maximal amount of physical information there is about the measuring apparatus' magnetic orientation along x in the electron's frame of reference. The electron necessarily instantiates a frame of reference because there is an object there that exists for which physical laws must hold.

In either frame, if the measurement can happen at any time then

(3)

I doubt the amplitudes (as opposed to probabilities) have to be equal, in which case there's a symmetry involved. Which group it is depends on the evolution (Schoedinger, Dirac, etc.) and the bases.

There is a transformation between the measuring apparatus' frame of reference and the electron's frame of reference that preserves the evolution equation and Plank's constant, exactly analogous to Lorentz transformations among classical but relatively moving frames. (It's non-trivial since the mass etc. of the measuring apparatus is larger than the electron's mass.)

There is no such thing as "the" quantum state of the electron. Its quantum state depends on the (quantum) frame of reference.

That's how it can be that for Wigner's friend, Schroedinger's cat is in the superposition

(4)

whilst the cat finds itself to be in the classical state

(5) alive, or else, dead

at all "times". 

(Time is a reference frame's parameter describing relatively quantum systems... there is a different ontological time for each system... See previous posts.)

In the cat's frame of reference (or coordinate system, or whatever), Wigner's friend is in the state

(6)

Whilst Wigner's friend finds himself to be happy or sad at all (of his) times.

That is how, after the experiment, Wigner's friend can find the cat the be in one of the classical states

(7) alive, or else, dead

and the cat can find Wigner's friend to be in one of the classical states

(8) happy, or else, sad

whilst in Wigner's frame of reference the combined friend-and-cat system is still ("still" in Wigner's time) in the superposition

(9)

[Where I'm headed with this is roughly: quantum state is intransitive and what exists... the total amount of physical information... at some moment, in a system's own notion of time, does not form an equivalence class...]