There are mathematical transformations physicists use for their convenience, like viewing the system as an amplitude distribution over momenta rather than positions, which throw away this neighborhood structure (e.g. by making potential energy a non-locally-computable property). Well, mathematical convenience is a fine thing. But I strongly suspect that the physically real wavefunction has local dynamics.
Could someone who knows the physics confirm whether this paragraph makes sense? I am confused by it.
Eliezer notes that the amplitude assigned to a specific position-configuration in the near future depends only on the present amplitudes assigned to configurations that are similar position-wise.
But suppose that we represented the state of our system as an amplitude distribution over a momentum-configuration space, instead of a position-configuration space. Would not the amplitude assigned to a specific momentum-configuration in the near future depend only on the present amplitudes assigned to configurations that are similar momentum-wise?
Is it not true in general that, for any observable Q, the Q-amplitude distribution evolves locally on the Q-configuration space. I.e., doesn't the evolution of amplitude at a point in the Q-configuration space depend only on the amplitude assigned to configurations that are similar Q-wise?
If so, then I don't understand what kind of "locality" Eliezer is pointing to as privileging the position-configuration space.
But suppose that we represented the state of our system as an amplitude distribution over a momentum-configuration space, instead of a position-configuration space. Would not the amplitude assigned to a specific momentum-configuration in the near future depend only on the present amplitudes assigned to configurations that are similar momentum-wise?
No.
Today's post, The Quantum Arena was originally published on 15 April 2008. A summary (taken from the LW wiki):
Instead of a system state being associated with a single point in a classical configuration space, the instantaneous real state of a quantum system is a complex amplitude distribution over a quantum configuration space. What creates the illusion of "individual particles", like an electron caught in a trap, is a plaid distribution - one that happens to factor into the product of two parts. It is the whole distribution that evolves when a quantum system evolves. Individual configurations don't have physics; amplitude distributions have physics. Quantum entanglement is the general case; quantum independence is the special case.
Discuss the post here (rather than in the comments to the original post).
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