Thanks guys for the information. Now I have work on my hands. George
Brent Meeker wrote >Do a search for "transactional quantum mechanics" and look at Vic Stenger's >website. >Brent Meeker scerir wrote: > > > 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)
