LizR wrote:
The point of using quantum states is that the universe guarantees they
are indistinguishable, and hence unless consciousness is magic /
supernatural it must be identical in quantum-identical brains. It's
possible the substitution level for consciousness is above the quantum
level, but (allegedly) it can't be any lower.
However, why would infinite precision be required to simulate them? I
thought the point of quantum states was that they're discrete?
The Hilbert spaces for continuous observables such as position and
momentum are infinite dimensional, so the eigenvalues are continuous.
But the main point is that a generic state is a superposition of the
basis vectors of the relevant Hilbert space, with arbitrary complex
coefficients. The absolute squared value of these coefficients are
probabilities (Born Rule). There is no smallest probability, so infinite
precision is required to simulate the generic quantum state. This
doesn't even require infinite dimensional Hilbert space -- the expansion
coefficients are still general complex numbers even in the two-state
spin projection Hilbert space.
Bruce
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