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Dear Lev, Thank you once again for presenting such an interesting example. To answer to your question: ‘is this example counterfactual according to Bohmian mechanics ?’ I can say that factual means here classical. Your example is indeed counter intuitive on this you agree I think but by intuitive you only mean classical. And indeed due to the quantum potential or the empty wave Bohmian mechanics is not strictly equivalent to clasical physics. This is the same problem you mentionned in you previous examples discuss in ‘Can You Kill with an Empty Wave Bullet?’.
One point to add: your example is not fully quantum since Bob can select the output but can not superpose them in a coherent quantum way. To do that you will need entanglement with degrees of freedom of Bob. This is of course not very difficult to do but then you will certainly realize, like Hardy did in the 90’s with your famous interaction free protocol, that non locality and the time ordering of the differen processes can modify in even more counter classical ways the dynamics of the particles.
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