Saturday 9 March 2019

determinism, and quantum computing


It might seem logical to presume that the exact state of the world around us could have been predicted given a big enough computer to analyse all the particle's interactions and what not. Determinism seems to be logical.


Then comes quantum computing. Since a collection of entangled qubits are only coherent when isolated from their environment, is this new information being fed into our known universe system? Whats going on here? Since you could hypothetically have hardware that starts manipulating particles as a result of these isolated quantum wave collapses, does this put the nail in the coffin of the deterministic universe?


Or are we just awaiting a mechanism by which these wave function's chose the value to collapse to (quantum foam geometry or something)? As far as I understand we don't yet know how the wave function choses its collapsed spin state except that statistically it follows a predictable probability spread.



Answer




Quantum mechanics does not contradict determinism. The relevant equation of motion is something like the Heisenberg equation of motion which predicts how observables change over time. Those observables are Hermitian operators not single numbers. They represent a larger structure than the universe we see around us, which under some circumstances can be approximated by a set of approximately non-interacting parallel universes:


http://arxiv.org/abs/quant-ph/0104033.


Collapse does not happen. All that happens is that when information about the outcome of a measurement spreads it is no longer possible for versions of the same system that produced different outcomes to interfere:


http://arxiv.org/abs/0903.5082.


You can't predict what the outcome of the experiment will be because there is no single fact of the matter about what outcome you will see. Rather there will be different non-interacting versions of you for each outcome.


The probabilities in quantum mechanics have nothing to do with a lack of determinism. They are a result of applying decision theory to quantum mechanics:


http://arxiv.org/abs/quant-ph/9906015


http://arxiv.org/abs/0906.2718.


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