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.
Highlights
In 1981, Mermin published a 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 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.” we show how “conservation per no preferred reference frame (NPRF)” answers that challenge
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
As physicists work towards “building a picture of the way nature works” we are occasionally confronted with conundrums like that of quantum entanglement as conveyed by Mermin’s challenge
Summary
“raffles with baskets of tickets” to find the subspace of the quantum elliptope occupied by local hidden-variable theories. Bob could partition the data according to his equivalence relation (per his reference frame) and claim that it is Alice who must average her results (obtained in her reference frame) to conserve spin angular momentum This all seems rather straightforward, the quantum correlation function for the Mermin device differs from that of instruction sets (classical correlation function) as necessary to satisfy conservation of spin angular momentum on average. Alice and Bob both always measure ±1 2 , no fractions, in accord with NPRF This fact alone distinguishes the quantum joint distribution from the classical joint distribution[6] (Fig. 1), so this fact alone accounts for the elliptope constraint of Janas et al the “average-only” conservation responsible for the correlation function for the Bell spin states leading to Facts 1 and 2 for the Mermin device is conservation resulting from NPRF. NPRF is a “unifying principle” for non-relativistic quantum mechanics and special relativity per the restricted Lorentz symmetry group
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