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Thread: Hardy Paradox - Could Electrons and Positrons be Used Experimentally

  1. #1 Hardy Paradox - Could Electrons and Positrons be Used Experimentally 
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    The experiment by Jeff Lundeen and Aephraim Steinberg which validated Hardy's paradox used photons instead of electrons and positrons. Would it be technically and economically possible to directly use e- and e+ particles as they were the particles that were originally referenced in Hardy's paradox. Note: there is a public lecture presentation on this experiment by Aephraim Steinberg on the Perimeter Institute web site.
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  2. #2  
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    How do you violate a paradox?
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  3. #3  
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    The paradox is that interacting anti-particles do not destroy each other, in the EPR apparatus. This is validated by quantum theory and the experiment conducted by Lundeen and Steinberg on Hardy's paradox.
    Longer explanation: Hardy's Paradox takes the category of EPR experiments to a new level of complexity through the unique concept of concatenating (linking) and thus entangling the two waveforms of fundamental particles on the overlapping paths of separate interferometer structures. The geometric configuration of each half is as found in the half-silvered mirror experiment.
    From the perspective of a particle description, when either particle is on an inner, overlapping path, its presence constitutes a measurement of the system of the other particle. If we consider this in the framework that would normally apply for classical measurement of a quantum system, it would collapse and the particle that was measured would display distribution across both exit ports. Thus, the system displays, a classical-type distribution because it has been disturbed. However, because one particle (not a classical measurement or obstruction on the internal paths) is causing the disturbance of the other particle, called "interaction-free measurement", the effect of measurement has an entirely new framework of causation. This is assessed by recording the paths taken (using special weak-measurement techniques) specifically when both exit ports (D), fire simultaneously.

    The particles chosen for the experiment are important. Each is an anti-particle to the other, which means that if they meet on the two inner paths, in classical terms, they should destroy each other. However, this does not happen at this quantum-level of the interaction between the two particles. Again, the single outcome selected for analysis is that in which the detectors at the two normally dark ports fire simultaneously. What is predicted under quantum theory, for the causal structure and which is confirmed in experiment is counterfactual in classical terms.

    The following is a quote from the paper by Aharonov (found on page 5). Aharonov lists the counterfactual framework for paths taken that apply for the simultaneous firing of the normally dark ports (D+) and (D-), when it is measured at the classical-level on exit from the system. Note: (bracketed numbers added).
    "Let us return now to Hardy’s example. As we will show, the complete description of what occurs is encapsulated in the three basics counterfactual statements which define the paradox:
    (1) • The electron is always in the overlapping arm.
    (2) • The positron is always in the overlapping arm.
    (3) • The electron and the positron are never both of them in the overlapping arms."
    You can see that (3) contradicts (1) and (2). The probability table in the paper by Lundeen and Steinberg even has a negative probability for one set of paths. There is no such thing as negative probability in a classical sense. Zero probability would be the least possible.
    We can conclude, from the above, that the causation of the simultaneous firing of the normally dark ports does not depend on any classical context of the paths taken by particles.
    The presentation by Steinberg at In Praise of Weakness | Perimeter Institute explains all this very well.
    Lundeen and Steinberg used photons that had specific polarizations instead of e- and e+ particles. It was the polarizations that were disturbed. I would like to know if it is feasible to do the experiment with e- and e+ particles as in the originally envisioned. There would have to be some technique of generating the particles simultaneously and then doing weak measurement on which path each took.
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