Quantum Interference

I'm having trouble understanding a quantum interference experiment, and was wondering if someone more knowledgable on the subject could help me out.The experiment was designed by Marlan Scully of the University of California, and the set up is my avatar, since I couldn't figure out how to upload an image that wasn't already on a webpage.In the first step, an incoming photon is split by a crystal (c) into two weaker photons of different trajectories. These entangled photons are then directed by mirrors (m) to a "beam-splitter" (b). A beam splitter is a device that exploits quantum tunneling, such that a photon will tunnel through the splitter with a probability of 50/50. The photons then either get reflected to the detector on their respective sides, or they pass through the beam-splitter an get detected by the detector on the opposite side. It turns out that in this setup, the two photons always arrive at the same detector, so if the bottom photon gets transmitted, the top on gets reflected, and they both go to D1. The opposite is also true.In the book I am reading, About Time by Paul Davies, he explains this concordance in terms of quantum interference. He writes

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The reason both photons always end up in the same detector, upper or lower, hinges on the fact that, in the setup just described, the experimenter cannot know which photon took which path. It may be that photon 1 took the upper path and photon 2 the lower path, or vice versa, but with the arrangement shown, the experiment cannot reveal that actual routes taken. According to the bizarre rules of quantum physics, this lack of information about the routing implies a schizophrenic world in which both alternatives coexist in a sort of hybrid reality. That is, without knowing which photon took which route, we have to regard the world as made up of both potential realities existing together in a sort of ghostly overlap. This is not merely a way to visualize the wierd goings-on, but leads to real physical effects. For example, we can tell that the two alternatives "photon 1 takes the lower path, photon 2 the upper path" and "photon 1 takes the upper path, photon two takes the lower path" both contribute to the outcome, because these phantom alternatives add together to produce results which are different from either alternative on its own-a process known as "quantum interference." In the present example, it is this interference of the alternative paths that produces the above-mentioned concordance, directing both photons to the same detector.

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The interference arises as a consequence of teh wave nature of light, and has to do with the fact that waves arriving in step reinforce, whereas, those that arrive out of step cancel. Here the interference is between waves associated with one alternative reality combining with waves associated with the other alternative. The overlapping of these alternative-world waves can be convincingly demonstrated by slowly increasing the length of of the paths until the waves associated with the alternative realities now arrive exactlly out of step. In this case, interference causes cancellation of the wave, meaning that the two photons now go to different detectors-i.e., the detectors fire simultaneously. A light additional increase in the path length brings the waves back into phase, and the photons go to the same detectors once more. By gradually extending one path in this way, the experimenters can obtain a series of peaks and troughs-characteristic of an interference pattern-for the simultaneous firings of the two detectors.

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I'm having a lot of trouble understanding this effect. Why does the cancellation of the waves cause them to go to different detectors and why does the reinforcement cause them to go the same detectors? How should I visualize these waves associated with the alternative realities?How does that relate to the probability of quantum tunneling through the beam-splitter, which would seem to imply that the probability of them arriving at the same detector is only 50%?

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That seems like the exact explantion I need. The problem is I can't understand it. More specifically, can you describe this equation:|state) = 1/sqrt(2){|1, up)|1, down) + |1, down)|2, up)}What do the vertical straight lines mean, why are there open paranthesis, and what do commas mean? Is there a link to this equation that is easier to understand?

First off, I'd like to thank you for taking the time to explain this to me. Luckily I just got done learning about the wave functions in physics, so I can follow these steps pretty well. Also, I did a little bit of linear superposition when combining atomic orbitals to get molecular orbitals in chemistry courses.I have a few questions.First off, I think should be ? I think you just made a typo.Second, why do you multiply |1,up> and |2,down> when writing the wave equation? I assume it's because they represent one possible reality, but should I just take it as a given that you multiply them in the function?Third, are |d1> and |d2> identical? If so, why don't you use the same variable for them?Finally, can you explain Once I plug in the wave equations into the original equation, what do I solve for?Thanks again

Is this the total wave equation:1/sqr(2)= 0|state>= 0 { {0(i|1,d1> + |1,d2>)} {0(|2,d1> + i|2,d2>)} + {0(|1,d1> + i|1,d2>)} {0(i|2,d1> + |2,d2>)}}This message has been edited by JustinCy, 12-17-2004 12:47 PM

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Perhaps I should have said reduce the equation to its simplest form, or combine like terms and square the coefficients.

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Yeah, I figured that out right after I wrote the post.Ok, I did the math and got -1/2 for each. So, just one more question. Does it matter that it is negative instead of positive? Or do the probabilities just have to add up to 1, independent of the sign?Edit: Ok, 2 more questions. Why do you have to square the coefficients to get the probability?This message has been edited by JustinCy, 12-17-2004 01:59 PMThis message has been edited by JustinCy, 12-17-2004 02:05 PM

If those questions force you to explain to me the intricacies of statistics and probability, don't worry about it. I never had a statistics class in college and probably wouldn't be able to understand it.

I'm reading Schrodinger's Kittens and The Search For Reality by John Gribbin right now. I should be done by the end of my break. At the end he is going to discuss where the Copenhagan Interpretation breaks down and what might possibly supercede it. So, if I get any insights I'll try and make some comments on the reality of wave function. I think Gribbon's is going to put forth a string theory model from glimpsing at the end.I'm sure, though, that you have already looked at all of these developments carefully and realize that there is no satisfactory explanation at the moment.

Well, the book only talked about string theory vaguely, so I probably couldn't tell you anything new.The thesis was about a reinterpretation of quantum phenomena. Shrodingers kitten is a good example. Let's use the classic version, in which a cat is in a box with a atom that has a 50:50 chance of decaying, and there's a detector in the box which can detect this. If it detects it, it sets off a chain reaction which ends with the release of poisenous gas in the box.This is meant to show the absurdity of quantum physics, since the Copanhagen Interpretation states that the atom is in a state of superposition until it is observed, and hence the cat is also in a state of superposition. It is dead and alive. Absurd.The new interpration is similar to the Wheeler-Feynman absorber theory, which states that electronic resistance is due to "advanced waves" interacting with it. Advanced meaning waves that are travelling in the past direction. "Retarded" is used to describe the waves travelling in the future. These advanced waves are predicted by solving Maxwell's equations, which give two solutions. Well, Shrodinger's equations are the same way (the extended version of the equation, since it seems many books don't teach it this way).So using this as our guide, the initial probability wave is travelling into the future, with the cat. When the wave is observed, a signal is sent back through time. This wave constructively interferes with the original retarded wave, and this collapses the wave function. So the cat was either dead or alive the whole time, no superposition.This also is a convenient way to interpret nonlocality. It's not that there is instantaneous communication going on. The communication takes time, but one of the signals is retarded and the other advanced. These cancel out from our perspective (observing on point in time), and give rise to the instantaneous phenomena.You may of noticed that this has echoes of Einstein's block time, and has implications about free will since the future is affected the past. Gribbons tries and reconciles the two at the end, but I'm not yet decided whether it is satisfactory.