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arXiv:1809.08231 · Scientific Reports

Answering Mermin’s challenge with conservation per no preferred reference frame

W. M. Stuckey, Michael Silberstein, Timothy J. McDevitt, Tuong Le

Published Sep 25, 2020• 28 citations
arXivHTMLPDF

Abstract

In 1981, Mermin published a now famous paper titled, "Bringing home the atomic world: Quantum mysteries for anybody" that Feynman called, "One of the most beautiful papers in physics that I know." Therein, he presented the "Mermin device" that illustrates the conundrum of quantum entanglement per the Bell spin states for the "general reader." He then challenged the "physicist reader" to explain the way the device works "in terms meaningful to a general reader struggling with the dilemma raised by the device." Herein, we show how "conservation per no preferred reference frame (NPRF)" answers that challenge. In short, the explicit conservation that obtains for Alice and Bob's Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their "mysteries" is the restricted Lorentz group.

DOI
10.1038/s41598-020-72817-7

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In 1981, Mermin published a now famous paper titled, "Bringing home the atomic world: Quantum mysteries for anybody" that Feynman called, "One of the most beautiful papers in physics that I know." Therein, he presented the "Mermin device" that illustrates the conundrum of quantum entanglement per the Bell spin states for the "general reader." He then challenged the "physicist reader" to explain the way the device works "in terms meaningful to a general reader struggling with the dilemma raised by the device." Herein, we show how "conservation per no preferred reference frame (NPRF)" answers that challenge. In short, the explicit conservation that obtains for Alice and Bob's Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their "mysteries" is the restricted Lorentz group.
Abstract Chapter 7 uses the ‘average-only’ projection for a qubit found in Chapter 6 to derive ‘average-only’ conservation for qubits entangled in Bell states. This is then used to derive the joint probabilities for particles entangled in Bell states, which map immediately to the mysterious facts of the Mermin device. Therefore, Mermin’s challenge is answered via ‘average-only’ conservation per NPRF. The symmetry of ‘average-only’ conservation in Bell states (highlighted in Chapter 0) is compared to the symmetry of length contraction and time dilation in the relativity of simultaneity for SR. So, contrary to popular opinion, QM and SR are more than compatible, they are both derived from NPRF such that their mysteries display the same kind of reference frame symmetry. The third experiment for the Poincaré symmetric ontology (photon polarization) is explained.
Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance and Continuity, at the foundation of those axiomatic reconstructions, maps to “no preferred reference frame” (NPRF, aka “the relativity principle”) as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance and Continuity. Consequently, the “mystery” of the Bell states is understood to result from conservation per Information Invariance and Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.
Many in quantum foundations seek a principle explanation of Bell state entanglement. While reconstructions of quantum mechanics (QM) have been produced, the community does not find them compelling. Herein we offer a principle explanation for Bell state entanglement, i.e., conservation per no preferred reference frame (NPRF), such that NPRF unifies Bell state entanglement with length contraction and time dilation from special relativity (SR). What makes this a principle explanation is that it's grounded directly in phenomenology, it is an adynamical and acausal explanation that involves adynamical global constraints as opposed to dynamical laws or causal mechanisms, and it's unifying with respect to QM and SR.
We review how the kinematic structures of special relativity and quantum mechanics both stem from the relativity principle, i.e., "no preferred reference frame" (NPRF). Essentially, NPRF applied to the measurement of the speed of light c gives the light postulate and leads to the geometry of Minkowski space, while NPRF applied to the measurement of Planck's constant h gives "average-only" projection and leads to the denumerable-dimensional Hilbert space of quantum mechanics. These kinematic structures contain the counterintuitive aspects ("mysteries") of time dilation, length contraction, and quantum entanglement. In this essay, we extend the application of NPRF to the gravitational constant G and show that it leads to the "mystery" of the contextuality of mass in general relativity. Thus, we see an underlying coherence and integrity in modern physics via its "mysteries" and the fundamental constants c, h, and G. It is well known that Minkowski and Einstein were greatly influenced by David Hilbert in their development of special relativity and general relativity, respectively, but relating those theories to quantum mechanics via its non-Boolean Hilbert space kinematics is perhaps surprising. Quanta 2022; 11: 5–14.
Many in quantum foundations seek a principle explanation of Bell state entanglement. While reconstructions of quantum mechanics (QM) have been produced, the community does not find them compelling. Herein we offer a principle explanation for Bell state entanglement, i.e., conservation per no preferred reference frame (NPRF), such that NPRF unifies Bell state entanglement with length contraction and time dilation from special relativity (SR). What makes this a principle explanation is that it's grounded directly in phenomenology, it is an adynamical and acausal explanation that involves adynamical global constraints as opposed to dynamical laws or causal mechanisms, and it's unifying with respect to QM and SR.
To answer Wheeler's question "Why the quantum?" via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., "Why the Tsirelson bound?" We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub's question addresses Fuchs' desideratum that we "take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity]." Thus, the answer to Bub's question per Fuchs' desideratum is, "the Tsirelson bound obtains due to conservation per NPRF".