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An interesting thought experiment would be to create a large quantum wave-function describing both a pair of electrons with entangled spins and the equipment needed to measure the electrons' spins. In theory, this wavefunction could be evolved in time and monitored to see if any process mimicking measurement of the electrons' spins occurs.

However, as the QED Lagrangian is local I believe such a system could not violate Bell's inequality. Is that correct?

Does that mean that QED (with measurement) is not a self-consistent theory as it admits two methods of modelling the same physics which produce different results?

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"not a self-consistent theory as it admits two methods of modelling the same physics which produce different results" - this is pretty much the formulation of the generally recognized measurement problem of quantum theory (http://plato.stanford.edu/entries/qt-issues/#MeasProb). In standard quantum theory, it is usually stated that unitary evolution takes place between measurement, and the projection postulate is applicable to measurements. However, it seems strange that the evolution of the system depends on whether we call the relevant process "a measurement" or not.

As for the Bell theorem, I show in my paper http://link.springer.com/content/pdf/10.1140%2Fepjc%2Fs10052-013-2371-4.pdf (published in the European Physical Journal C) that some local realistic models have the same unitary evolution as quantum field theories. This suggests that one probably cannot derive violations of the Bell inequalities in quantum theory using just unitary evolution. Standard proofs of the violations use both unitary evolution and the projection postulate (or something similar), although these assumptions are, strictly speaking, mutually contradictory.

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  • $\begingroup$ Thanks for the answer. Your paper is also very interesting. Do you know why this inconsistency is not a more active area of research? $\endgroup$
    – andypea
    Nov 20, 2016 at 23:55
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    $\begingroup$ @andrew.punnett: Thank you for your kind words. I would say this inconsistency is actually a relatively active area of research (although it would certainly be more active if there were more funding). I don't follow this area closely, but I would like to emphasize recent impressive results by Allahverdyan, Balian, Nieuwenhuizen (arxiv.org/abs/1303.7257, arxiv.org/abs/1107.2138 (published in Phys. Rep.)) $\endgroup$
    – akhmeteli
    Nov 21, 2016 at 2:32
  • $\begingroup$ @andrew.punnett: As for me, I am still trying to improve my results. On the one hand, I derived a relativistically covariant fourth order equation for one component of the Dirac spinor, which is equivalent to the Dirac equation (arxiv.org/abs/1502.02351), on the other hand, I am trying to derive the results of my EPJC article for spinor electrodynamics without introduction of the complex 4-potential of electromagnetic field. $\endgroup$
    – akhmeteli
    Nov 21, 2016 at 2:35
  • $\begingroup$ I summarised ABNs approach to solving the measurement problem here physics.stackexchange.com/questions/278225/…, in case its useful (I refer to a slightly earlier paper). $\endgroup$
    – isometry
    Nov 23, 2016 at 14:34

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