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Mystery Solved: Oh, the Irony

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

Published Jul 26, 2024• 0 citations
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Abstract

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.

DOI
10.1093/9780198919698.003.0008

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•Jul 26, 2024•0 citations
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.
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.
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.
Abstract Chapter 1 points out that the mystery of entanglement has led Physics Nobel Laureates to claim “nobody understands quantum mechanics.” The Chapter goes on to introduce: the EPR and EPR–Bell paradoxes, various attempts to resolve them, our proposed resolution whereby the relativity principle (no preferred reference frame, NPRF) justifies the Planck postulate (NPRF + h) exactly like the relativity principle justifies the light postulate (NPRF + c), the Planck postulate as a result of Information Invariance & Continuity from quantum information theory, the importance of the relativity principle, subjective versus objective spacetime models of reality, spacelike and timelike relations in spacetime, and four experiments leading to our Poincaré symmetric ontology.
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.
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.
Abstract Chapter 0 is a parable where Alice and Bob discover the mystery of entanglement per the superposition of the imaginary properties of handedness and color for entangled “quantum gloves” in an experimental challenge given to them by Albert. Alice and Bob show how Albert’s quantum gloves experiment leads to the ‘average-only’ conservation of the entangled properties that characterizes the mystery of entanglement. They solve this mystery by using the relativity principle to justify the fact that they both measured the same value of Planck’s constant h, regardless of the relative spatial orientations of their measurement devices. They propose this solution because it is totally analogous to how Albert solved the mystery of length contraction, i.e., he used the relativity principle to justify the fact that everyone measures the same value of the speed of light c, regardless of the relative velocities of their measurement devices.