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

www.nature.com/scientificreports OPEN Answering Mermin’s challenge with conservation per no preferred reference frame W. M. Stuckey1*, Michael Silberstein2,3, Timothy McDevitt4 & T. D. Le5 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. Physics is a science dedicated to understanding the physical world and, as astrophysicist and writer Adam Becker points out1, p. 7: science is about more than mathematics and predictions—it’s about building a picture of the way nature works. And that picture, that story about the world, informs both the day-to-day practice of science and the future development of scientific theories, not to mention the wider world of human activity outside of science. For example, geocentricism gave way to heliocentricism in part due to the principle of relativity, i.e., the laws of physics are the same in all inertial reference frames, which is sometimes referred to as “no preferred reference frame” (NPRF). Newtonian mechanics and special relativity are both based on the principle of relativity. The difference between the Galilean transformations of Newtonian mechanics and the Lorentz transformations of special relativity resides in the fact that the speed of light is finite, so NPRF entails the light postulate of special relativity, i.e., that everyone measure the same speed of light c, regardless of their motion relative to the source. If there was only one reference frame for a source in which the speed of light equaled the prediction from Maxwell’s equations (c = √µ1o ǫo ), then that would certainly constitute a preferred reference frame. There are those in quantum information theory who have called for a principle(s) of a similar nature for quantum mechanics. Chris Fuchs w rites2, p. 285: Compare [quantum mechanics] to one of our other great physical theories, special relativity. One could make the statement of it in terms of some very crisp and clear physical principles: The speed of light is constant in all inertial frames, and the laws of physics are the same in all inertial frames. And it struck me that if we couldn’t take the structure of quantum theory and change it from this very overt mathematical speak—something that didn’t look to have much physical content at all, in a way that anyone could identify 1 Department of Physics, Elizabethtown College, Elizabethtown, PA 17022, USA. 2Department of Philosophy, Elizabethtown College, Elizabethtown, PA 17022, USA. 3Department of Philosophy, University of Maryland, College Park, MD 20742, USA. 4Department of Mathematical Sciences, Elizabethtown College, Elizabethtown, PA 17022, USA. 5College of Computing, Georgia Institute of Technology, Atlanta, GA 30332, USA. *email: Scientific Reports | (2020) 10:15771 | https://doi.org/10.1038/s41598-020-72817-7 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1.  A Stern–Gerlach (SG) spin measurement showing the two possible outcomes, up (+ 2 ) and down (− 2 ) or +1 and −1, for short. The important point to note here is that the classical analysis predicts all possible deflections, not just the two that are observed. This binary (quantum) outcome reflects Dakic and Brukner’s first axiom in their reconstruction of quantum theory, “An elementary system has the information carrying capacity of at most one bit”5. The difference between the classical prediction and the quantum reality uniquely distinguishes the quantum joint distribution from the classical joint distribution for the Bell spin s tates6. Figure 2.  Alice and Bob making spin measurements on a pair of spin-entangled particles with their Stern– Gerlach (SG) magnets and detectors in the xz-plane. Here Alice and Bob’s SG magnets are not aligned so these measurements represent different reference frames. Since their outcomes satisfy Dakic and Brukner’s Axiom 1 in all reference frames and satisfy explicit conservation of spin angular momentum in the same reference frame, they can only satisfy conservation of spin angular momentum on average in different reference frames. This “average-only” conservation corresponds to the “elliptope constraint” of Janas et al.7. with some kind of physical principle—if we couldn’t turn that into something like this, then the debate would go on forever and ever. And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements. Herein, we make progress on that front by extending NPRF to include the measurement of another fundamental constant of nature, Planck’s constant h. As Steven Weinberg points out, measuring an electron’s spin via Stern–Gerlach (SG) magnets constitutes the measurement of “a universal constant of nature, Planck’s constant”3, p. 3 (Fig. 1). So if NPRF applies equally here, everyone must measure the same value for Planck’s constant h regardless of their SG magnet orientations relative to the source, which like the light postulate is an empirical fact. By “relative to the source” of a pair of spin-entangled particles, we mean relative “to the vertical in the plane perpendicular to the line of flight of the particles”4, p. 943 (Fig. 2). Here the possible spin outcomes ± 2 represent a fundamental (indivisible) unit of information per Dakic and Brukner’s first axiom in their reconstruction of quantum theory, “An elementary system has the information carrying capacity of at most one bit”5. Thus, different SG magnet orientations relative to the source constitute different “reference frames” in quantum mechanics just as different velocities relative to the source constitute different “reference frames” in special relativity. Since NPRF leads to the counterintuitive aspects (“mysteries”) of time dilation and length contraction i (...truncated)