No Preferred Reference Frame at the Foundation of Quantum Mechanics

Abstract

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.

Least Information Principle for Quantum Mechanics

“…The uncertainty relation ∆x∆p ≥ /2 is a consequence of applying the least information principle in the infinitesimal time step, as shown in Section III A. Other authors proposed postulates similar to the no preferred representation assumption, such as no preferred measurement [30], no preferred reference frame [29]. However, these postulates are proposed in very different contexts.…”

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications

“…Relatively few authors explore possible conceptual explanations of the statistical balance. Among those who do, some propose a conservation principle operating across an ensemble, rather than for each of its members [57]; others explain the balance as a feature of independent reality, by involving concepts such as potentia(lity) and propensity [2] (p. 50) [22] (Section 4) [58] (Section 14.3) [59] (pp. 24-27), or irreversibility [36] (pp.…”

“…The fact that the overall result is predictable is hard to explain unless, for example, a statistical description is seen as being as fundamental as a single-run description [ 36 ] (pp. 203, 255) [ 57 ].…”

"Mysteries" of Modern Physics and the Fundamental Constants c, h, and G

“…And it seemed like a worthwhile exercise to try to reduce the mathematical structure of quantum mechanics to some crisp physical statements. [17, p. 285] Along these lines, we recently showed that the qubit Hilbert space structure at the foundation of axiomatic reconstructions of quantum theory following from the information-theoretic principles of "Existence of an Information Unit" [18] and "Continuous Reversibility" [18], or in combined form "Information Invariance & Continuity" [19], entails NPRF applied to the invariant measurement of Planck's constant h [20].…”

“…Figure 2: Two reference frames related by SO(3) each associated with a set of mutually complementary SG spin measurements[23]. Reproduced from Stuckey et al[20].…”