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    Beyond Causal Explanation

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    Submitted by: William Stuckey

    In this paper, we offer a principle account of Einstein-Podolsky-Rosen (EPR) correlations (quantum entanglement) and quantum contextuality by applying a generalization of the relativity principle ("no preferred reference frame," NPRF) to the measurement of Planck's constant h to underwrite the qubit Hilbert space structure with its SU(2)/SO(3) transformation properties. Quantum information theorists (QIT) reconstruct denumerable-dimensional quantum mechanics (QM) in composite fashion from the qubit Hilbert space structure. Thus, we see that NPRF is to QIT reconstructions of QM, as NPRF is to the Lorentz transformations of special relativity (SR), since the postulates of SR can be stated as NPRF applied to the measurement of the speed of light c. Unlike retrocausal accounts, our principle explanation is a complete rejection of Reichenbach's Principle.

    Given that the qubit forms the foundation of all (denumerable-dimensional) QM built in composite fashion, the most fundamental entangled states (upon which all others are built) are the Bell states. As we show, the mystery of quantum entanglement per the Bell states resides in "average-only" conservation of whatever is represented by the measurement outcomes. And, again, that follows from the fact that the qubit is the fundamental constituent of the world and therefore cannot be subdivided, which we explain via NPRF applied to the rotational invariance of these measurement outcomes in real space. Thus, Alice(Bob) says Bob(Alice) must average his(her) results to verify conservation of whatever is being measured, so we see that the mystery of "average-only" conservation is the result of conservation per NPRF.

    Conservation per NPRF then accounts for no-signalling and the violations of the Bell inequality precisely to the Tsirelson bound, which explains why so-called "superquantum correlations" and higher-dimensional generalized probability theories are not realized in Nature. Conservation per NPRF also shows so-called "mirror quantum mechanics" to be nonphysical already at the level of the two-qubit system. Thus, besides revealing a deep unity between SR and QM, NPRF resolves many quantum mysteries.

    This certainly isn't what QIT had in mind for their reconstruction project. That is, they intended their reconstructions of QM would be to the "standard axioms of [quantum theory]" as "Einstein's postulates of SR are to the Lorentz transformations." As things stand now, there is no obvious connection between the interpretation-project of QM and the QIT-project. In this regard, keep in mind that the postulates of SR are about the physical world in spacetime; thus, in keeping with this analogy, QIT must eventually make such correspondence to reach their lofty goals and escape the clever, but inherent instrumentalism of standard QM. Our principle account of QM precisely addresses the need for QIT to make correspondence with phenomena in spacetime. Consequently, QM reconstructions built upon the qubit Hilbert space structure explicate the essential mathematical framework for rendering QM a principle theory via NPRF.

    The general idea here is that in order to make progress in the foundations of QM and in unifying QM and SR, we cannot merely continue to provide empirically equivalent constructive interpretations that lead neither to new predictions, new unifying insights, nor to underwriting QM itself. It may seem a bit counterintuitive that NPRF underwrites both SR and QM, since quantum entanglement has been alleged by some to imply faster-than-light influences contra SR.

    Obviously, QM (non-relativistic quantum mechanics) is not Lorentz invariant, so it certainly differs from SR in that regard. QM follows from Lorentz invariant quantum field theory only in the low energy approximation. However, claiming that SR and QM are somehow at odds based on quantum entanglement has empirical consequences, because we have experimental evidence verifying the violation of the Bell inequality in accord with quantum entanglement. Thus, if the violation of the Bell inequality is problematic for SR, then SR is being empirically challenged in some sense.

    Clearly, few people believe that QM has literally falsified SR. But we have gone further to show that not only is there no tension between QM and SR in substance or spirit, NPRF provides a completely local principle account of EPR correlations. Indeed, even the no-signalling feature of entangled qubits follows necessarily from NPRF. Thus, far from being incompatible, SR and QM share a deep coherence via NPRF. This principle explanation for EPR correlations requires no violation of the causal structure of SR and it does not require the addition of a preferred frame as some non-local interpretations do, such as Bohmian mechanics and spontaneous collapse interpretations. Furthermore, this principle explanation for EPR correlations requires no causal or constructive explanation whatsoever, and that includes retrocausal mechanisms and processes.

    Despite the fact that this principle explanation supplies a unifying framework for both QM and SR, some might demand a constructive explanation. In other words, the assumption is that the true or fundamental "explanation" of EPR correlations must be a constructive one in the sense of adverting to causal processes or causal mechanisms. Apparently for people with such a Reichenbachian or constructive mindset, any principle explanation must be accounted for by some such story, e.g., the luminiferous ether. Indeed, contrary to all accepted physics, Brown and Pooley have recently called for such a constructive explanation even in SR. Brown and Pooley like to make this a debate about constructive versus "geometric" explanation. They believe that the principle explanation of Lorentz contractions in SR is underwritten only by the geometry of Minkowski spacetime.

    We think this misses the point, as one could believe that SR provides a principle explanation of Lorentz contractions without being a realist or a substantivialist about Minkowski spacetime. Notice, there is nothing inherently geometric about our principle explanation of EPR correlations in particular, or of NPRF in general. We would say that Brown and Pooley got it exactly wrong. It is QM that needs to become explicitly more like SR, not the other way around. If QM had struck people as being like statistical mechanics, there would be no cottage industry of cooking up constructive interpretations and no need for anything like QIT reconstructions. Thus, we hope to shed some light on why QM actually works as it does. 

    The entry is from 10.3390/e23010114