An impressive use of this kind of thing has been suggested by Avshalom Elitzur and Lev Vaidman. Let us think of our beam-splitter as being part of a Mach–Zehnder type of interferometer, but where we do not know whether a detector C has, or has not, been placed in the transmitted beam of the first beam splitter. Let us suppose that the detector C triggers a bomb, so that the bomb would explode if C were to receive the photon. There are two final detectors A and B, and we know that only A and not B can register receipt of the photon if C is absent. See Fig. 22.6.
We wish to ascertain the presence of C (and the bomb) in some circumstance where we do not actually lose it in an explosion. This is achieved when detector B actually does register the photon; for that can occur only if detector C makes the measurement that it does not receive the photon! For then the photon has actually taken the other route, so that now A and B each has probability ½ of receiving the photon (because there is now no interference between the two beams), whereas in the absence of C, only A can ever receive the photon.
In the examples just given, there is no degeneracy, so the issue that was addressed above that the mere result of the measurement may not determine the state that the system ‘jumps’ into does not arise.
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To be clear, the claim for this experimental set-up is if detector C is absent, then the emitted proton has a 100% probability of being observed at detector A. However, if detector C is present and no photon is observed there, then there is a 100% probability that photon has been reflected at the first beam splitter, and then reflected to the second beam splitter, after which there is a 50% probability of observing the photon at detector A, and a 50% probability of observing the photon at detector B. So the observation of the photon at detector B guarantees the absence of detector C.
From the perspective of Systemic Functional Linguistic Theory, the experimental set-up affords a range of quantum system possibilities, each with interdependent probabilities from which actual instantial events can be reasoned.
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