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> Another customarily tacit assumption is that experimenters are free to choose between possible experiments. To be precise, we mean that the choice an experime

> Another customarily tacit assumption is that experimenters are free to choose between possible experiments. To be precise, we mean that the choice an experimenter makes is not a function of the past Garbage in, garbage out. It isn't clarified whether an experimenter in a nondegenerate superposition of states (will choose x, will choose y, will choose z) is considered to have "free will". If you call that free will, then the result that result that the particle can end up in a superposition of states is not novel. If you don't call that free will, then the assumption is false and the theorem vacuous.

n4r9 8y ago
You need this sort of axiom to eliminate superdeterminism. If an experimenter's choice of direction is fully determined by their past light-cone then a shared physical state in the overlapping past light-cones of A and B could conceivably drum up any correlations it wants. It's a conspiratorial line of thought on a par with Descartes' evil demon, but in a rigorous proof you have to rule these sorts of things out. The axiom comes into play at the top-right of p.229: > ...since by MIN the response of b cannot vary with x, y, z, θ^G_0 is a function just of w
- dooglius 8y ago
  Right, I see how it's being used in the proof, my point is that what the theorem proves, regardless of how the notion of "is determined by" is clarified, is not at all interesting or surprising.
  - n4r9 8y ago
    It's essentially a recasting of Bell's Theorem; in that sense it's both interesting and surprising if you thought that local hidden variables might still explain quantum theory. All you need - for both this and Bell's proof - is that directions are chosen with sufficient "randomness" or "freedom" so as to be considered independent of their past light cones. At least, independent enough so that the previously quoted step is possible.

n4r9 8y ago

You need this sort of axiom to eliminate superdeterminism. If an experimenter's choice of direction is fully determined by their past light-cone then a shared physical state in the overlapping past light-cones of A and B could conceivably drum up any correlations it wants. It's a conspiratorial line of thought on a par with Descartes' evil demon, but in a rigorous proof you have to rule these sorts of things out. The axiom comes into play at the top-right of p.229: > ...since by MIN the response of b cannot vary with x, y, z, θ^G_0 is a function just of w

dooglius 8y ago
Right, I see how it's being used in the proof, my point is that what the theorem proves, regardless of how the notion of "is determined by" is clarified, is not at all interesting or surprising.
- n4r9 8y ago
  It's essentially a recasting of Bell's Theorem; in that sense it's both interesting and surprising if you thought that local hidden variables might still explain quantum theory. All you need - for both this and Bell's proof - is that directions are chosen with sufficient "randomness" or "freedom" so as to be considered independent of their past light cones. At least, independent enough so that the previously quoted step is possible.