[deleted]
Lawrence,
Let's see if we can find a classical physics example. Suppose we pre-select all attempted conquests of ancient Rome. Then we post-select the cases where the attacker reached Rome but his conquest route was 100% blocked by the Roman armies. Then we ask for the middle measurement: which route did the invading army took? So what we have? We got Hannibal and his Alps crossing. He got from state |A> = attack Rome at time t_1 to state |B> inside the Italian peninsula but with all known paths blocked at time t_3 and = 0 and at time t_2 he was crossing the Alps (weak measurement with amplified values.) But is this proof of backward causation, or of future affecting the present? Not at all. The only valid conclusion is that if you want to transition between near orthogonal states, you need to do things out of the ordinary, or think/act outside the box.
Aharonov's basic equation is: A_w = / and the amplification happens when = almost zero because of the very small denominator.
Let's have another example: . = nearly zero. Let A=a qualifier-type problem. Now pre-select all PhD physics graduate students and post select all Nobel Prize winners. Then one would expect unusually brilliant solutions of the qualifier-type problems for Feynman and others in their graduate student years. And indeed, this is what it happens on average for most of the Nobel prize winners early in their career. But can we conclude this is evidence of the future (winning Nobel prize) affecting the past (a brilliant solution for qualifier-type problems)? No. This is no guarantee of success; it is only a pre-requisite. And here lies the fault of the argument of Aharonov, Davis, and Popescu. Amplified weak measurements are only a pre-requisite of the evolution toward a final orthogonal state, and not a guarantee. There is no destiny at work here.