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> George Levy > This is interesting. Is it possible to transmit information from the > future to the past? If yes, how would this information be restricted? This is a very difficult issue, as you can see (example below). A single particle [the example is discussed in references 4, 2, 1] at time t_0 is (preselected) in the state |psi_0> = 3 ^ (-1/2) ( |a> + |b> + |c> ) and at a later time t_f is (postselected) in the state |psi_f> = 3 ^ (-1/2) ( |a> + |b> - |c> ) where |a>, |b> and |c> correspond to the particle being found in 3 boxes: A, B and C, respectively. (The N boxes case is discussed in reference 3.) At the intermediate time t_i, where t_0 < t_i < t_f, a measurement is performed on the system. The ABL rule [see reference 5] states that if a measurement is performed, at time t_i, on this system, with the above preselection and postselection of states, the probability for an outcome of either a or b (eigenvalues corresponding to find the particle in box A or in box B, respectively) is 100%. That is to say, the intermediate _measurement_ cannot project the initial state |psi_0> onto the state 2 ^ (-1/2) ( |b> + |c> ) -- particle not found in A -- or onto the state 2 ^ (-1/2) ( |a> + |c> ) -- particle not found in B --. That's because both states are othogonal to the final state |psi_f>. Both states are then impossible. As long as we keep the QM formalism and the ABL rule, in each case any particles (which end up postselected) are ones which could not have been in any box except the one which was opened, be it A or B. Possible solutions? There are some. In example.... 1. QM formalism is right. There is no paradox. That's real. 2. QM formalism is right. That's not real. QM does not speak of reality. 3. Counterfactuals. To make a claim about the elements of reality of an individual system we have to consider the *physical* situation involved in an individual run of the experiment. But here, in each run, we have to make a *choice* to measure A or B. If we choose A, all postselected particles had to be found in box A. If we choose B, all postselected particles had to be found in box B. But the property of being, with certainty, in any one of those 2 boxes (depending on wich one is opened) cannot apply to the *same* *individual* particle in *any* given run of the experiment. 4. We cannot use the ABL rule here [see reference 6], because of the counterfactuals. Regards, -s. [1] David Z. Albert, Yakir Aharonov, Susan D'Amato, Physical Review Letters, vol. 54, pages 5 - 7, (1985) [2] David Z. Albert, Yakir Aharonov, Susan D'Amato, Physical Review Letters, vol. 56, p. 2457, (1986) [3] Yakir Aharonov, Lev Vaidman J. Phys, A-24, pages 2315 - 2328, (1991) [4] Lev Vaidman Foundations of Physics, 26, pages 895 - 906, (1996) [5] Yakir Aharonov, P.G. Begmann, J.L. Lebowitz, Physical Review, 134-B, pages 1410 - 1416, (1964) [6] R. E. Kastner Foundations of Physics, 29, pages 851 - 863, (1999)