Monday, February 6, 2012

Non-locality in Quantum Mechanics is not a Problem for Ontologists

People are still hung up about non-locality. But what if space is just the order-relation among quantum interactions? Then there's no problem. The two famous particles widely separated but having the same x-spin-squared can be correlated because there have been no quantum interactions between the particles, so there is no "space" (or at least distance) between them.

It must be this way because the location of a particle is represented in a Hilbert space H. This has the same ontology as a superposition of an x-spin (or x-spin-squared or whatever) observable that's represented in a Hilbert space H'. Yet an electron doesn't have the property of spin (or at least simultaneous x-spin-squared, y-spin-squared, and z-spin-squared) before it's observed (by the Kochen-Specker theorem).

Therefore, it doesn't possess the property of location, either, until it's observed.

It's a straightforward consequence of the ontology of H' being the same as the ontology of H. (This assumes neither spin nor location is a preferred variable [as happens in some--in my opinion, implausible--interpretations]). The electron doesn't have the property of being within the measuring apparatus' instantiation of space/spacetime(?). So, it would be wrong to suppose there is space(?) or spacetime(?) "between" the two correlated particles. Neither particle has the property of being within the measuring apparatus' spacetime.

I conclude non-locality in quantum mechanics is not a problem for ontologists.

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