ABSTRACT. It is shown that violation of the Born Rule leads to a breakdown of the correspondence between the quantum electromagnetic field and its classical counterpart. Specifically, the relationship of the quantum coherent state to the classical electromagnetic field turns out to imply that if the Born Rule were violated, this could result in apparent deviations from the energy conservation law applying to the field and its sources (Poynting’s Theorem). The result, which is fully general and independent of interpretations of quantum theory, suggests that the Born Rule is just as fundamental a law of Nature as are the field conservation laws.

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This paper has been sent out for peer review.

I think this paper is not correct. Of course, if one tries to violate the Born rule using only the equations of orthodox quantum theory, then one will get spurious results like an apparent violation of energy conservation. However, it is quite obvious from Rod Sutherland’s retrocausal “weak measurement” completely relativistic Lagrangian formulation of Bohm’s pilot wave/beable theory with the additional post-quantum action-reaction terms between the pilot waves and the beables that the stress-energy current densities are conserved i.e. Tuv^;v = 0 where Tuv = Tuv(pilot wave) + Tuv(be able) + Tuv(pilot wave be able). Kastner’s paper only has, in effect the Tuv(pilot wave) term. There is no consistent way to violate the Born rule without the additional terms. That’s all Kastner has really shown in my opinion. Sutherland has posted his theory elsewhere on this forum.

The submitted paper shows that violation of the Born Rule leads to a breakdown of the correspondence between quantum and classical forms of the electromagnetic field. The paper does not argue that energy conservation is violated at the micro-level, so the arguments put forth here don’t refute anything in the paper. It is straightforward that deviation of the photon detection rates from that given by the Born Rule as applied to coherent states results in deviations from Maxwell’s equations. One can see that simply by looking at how, for violations of the Born Rule, the amplitude envelope of the field would stray from the form required for classical correspondence (see https://en.wikipedia.org/wiki/Coherent_states#/media/File:Coherent_state_wavepacket.jpg) . Evidently the commenter thinks that it would be possible to violate the Born Rule and still preserve the quantum/classical correspondence in a different theory. He is welcome to demonstrate how that would work (even though the referenced figure clearly shows that deviations from Born Rule detection rates spoils the amplitude envelope). In any case, that would not refute the submitted paper, because it is not the subject of the paper.

A referee report has been received.

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Ruth misunderstands my claim. The Sutherland action-reaction post-quantum violation of the Born rule vanishes in the limit where the Glauber coherent state solutions apply to the real world. Therefore, her argument is logically inconsistent.

Referees agreed with arguments in this paper and it has been accepted. Indeed there is no inconsistency; if there is no Born Rule violation in the limit Dr. Sarfatti discusses, then there is also no ‘real world’ applicability of such Born Rule violations as he has previously argued. The paper simply shows that real world Born Rule violations lead to real world deviations from Maxwell’s equations. This is an elementary result that is not controversial.