Wednesday, July 13, 2011

Many-Timelines Interpretation of Superpositions

I want to point out that if the Many-Timelines (MT) proto-interpretation of quantum mechanics (see previous posts) works out, it gives a natural explanation for Schroedinger's Cat. The cat is evolving along its own ontologically distinct timeline. So there is no fact-of-the-matter, in the universe, about the "simultaneous" state of the laboratory and the cat. There is no reference fame/point from which to define "simultaneous" in this sense.

When the box is opened the timelines of the cat and laboratory become the same again, and then there is a fact about the simultaneous states of the laboratory and cat.

Throughout the cat's timeline the cat finds herself to be in a definite state, and throughout the laboratory's timeline the laboratory finds itself to be in a definite state. But the lab and cat are evolving through temporally independent time dimensions. Therefore there is, in the universe, only the information from either frame's perspective what the state of the other could be. This, in this proto-interpretation, is what a superposition is.

This also implies the set of possible states of two particles is given by {states1}x{states2} and not {states1}+{states2}. What about other facets of quantum mechanics?

I don't know.

(1) where do complex numbers and Heisenberg uncertainty relations enter? These are an exercise in working out the geometry.

(2) is it deterministic? I don't know. Maybe quasi-deterministic, in that each object sees a deterministic evolution of other things, but there is no perspective from which everything is simultaneously deterministic.

(3) Where does Born's rule that the square gives the probability come from? I don't know, but I wouldn't be surprised if it has to do with the metric in the uber-ontology (in the sense of Fine and previous posts).

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