Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!akgua!sdcsvax!sdcrdcf!hplabs!sri-unix!MER.CREON@Ames-VMSB From: MER.CREON%Ames-VMSB@sri-unix.UUCP Newsgroups: net.physics Subject: none Message-ID: <1195@sri-arpa.UUCP> Date: Thu, 24-May-84 09:40:00 EDT Article-I.D.: sri-arpa.1195 Posted: Thu May 24 09:40:00 1984 Date-Received: Fri, 1-Jun-84 04:20:03 EDT Lines: 111 Letter from Dr. Peter Bussy to Dr. Jack Sarfatti - 10 May 1984 [in this typescript, S == PSI, T == THETA, P == PHI] Department of Natural Philosophy University of Glasgow Glasgow, G12 8QQ. Tel. 041-339-8855 10 May 1984 Dr. J Sarfatti PO Box 26584 San Francisco California, USA. Dear Dr Sarfatti, Thank you for your letter of May 3. OK - now I think I see the problem! Let us start with a single beam of photons in a general state |S> = a|U> + b|D>, where |U> and |D> represent the two possible polarisation states. We will not bother about having correlated photons on the other side of the apparatus just yet. This beam now passes into a beam splitter, and the resulting beams will pass through arms 1 and 2 of your apparatus. They can be represented by -1/2 the wave functions |S >, where |S > = 2 |S> as in your (i=1,2) i i equation (3). Now each beam passes through a polariser. Let the polariser in arm i allow photons polarised in a plane at angle T (realtive to the direction of polarization of |U>) i to pass. Let the phase of each beam be P at this point. i This lets us introduce time delays into one arm if we wish. The transmitted beam is now in a state -1/2 |S'> = 2 [ a|U> cos(T /2) + b|D> sin(T /2) ] exp(iP ) (i=1,2) i i i i At this point we have a problem, which you have obviously faced. It would appear at first sight that we can just add the amplitudes to get a recombined beam, as you indicate at the right of your figure 1, and if T and 1 T are both zero and P =P we would obviously expect to 2 1 2 regenerate the original beam precisely (if a=1 and b=0). But it doesn't work! We find a factor of 2/sqrt(2) instead of 1 multiplying |S>. You have got around this by replacing the factor of 1/sqrt(2) with 1/2 in equation (4). This is certainly a departure from normal quantum mechanics and it is no wonder that your transformations end up being non-unitary. The source of the trouble here is fairly subtle and rather interesting, it seems to me. In basic terms, it is impossible to combine the two beams in the simple way that you propose! No piece of apparatus will do it. To illustrate this point, consider figure 1 of Greenberger's review article on the neutron interferometer. (Rev. Mod. Phys., Oct 1983). His apparatus has two counters behind the beam recombiner. If he could make do with one, no doubt he would use only one! You cannot have any piece of apparatus that will make two different arbitrary states A and B of a system both end up in the same state C with probability 1. If you could, then time-reversal invariance that in the inverse process, C will have probability 1 of turning into A and also probability 1 of turning into B. Clearly this is logically impossible. Perhaps you may think that one should not invoke time reversal invariance. Nevertheless, the physical consequences of being able to combine arbitrary beams in the way you suggest would be very remarkable. By combining two beams that are out of phase you could make them both dissappear! By combining them in phase you could double the overall intensity. Needless to say, both of these phenomena would violate conservation of energy and just about everything else! All indications are that the universe does not work this way. I don't know whether this convinces you, but it would seem clear now that the critical component in you apparatus is the beam recombiner and that you must propose a specific piece of physical apparatus that will do the job. Having a second correlated photon in the opposite half of the overall system cannot affect the above line of argument as far as I can see, moreover. Do write again if the above is unclear or if you disagree with it. Yours sincerely, Peter Bussey ------