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.
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.
We explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space of QM) and special relativity (Minkowski spacetime from the Lorentz transformations of SR) can both be based on one principle (relativity principle). This is made possible by the axiomatic reconstruction of QM via information-theoretic principles, which has successfully recast QM as a principle theory a la SR. That is, in the quantum reconstruction program (QRP) and SR, the formalisms (Hilbert space and Lorentz transformations, respectively) are derived from empirically discovered facts (Information Invariance & Continuity and light postulate, respectively), so QM and SR are "principle theories" as defined by Einstein. While SR has a compelling fundamental principle to justify its empirically discovered fact (relativity principle), QRP has not produced a compelling fundamental principle or causal mechanism to account for its empirically discovered fact. To unify these disparate kinematics, we show how the relativity principle ("no preferred reference frame" NPRF) can also be used to justify Information Invariance & Continuity. We do this by showing that when QRP's operational notion of measurement is spatialized, Information Invariance & Continuity entails the empirically discovered fact that everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations or locations (Planck postulate). Since Poincare transformations relate inertial reference frames via spatial rotations and translations as well as boosts, the relativity principle justifies the Planck postulate just like it justifies the light postulate. Essentially, NPRF + c is an adynamical global constraint over the spacetime configuration of worldtubes for bodily objects while NPRF + h is an adynamical global constraint over the distribution of quanta among those bodily objects.
Abstract Maxwell unified the disparate concepts of electric and magnetic fields with one theory (electromagnetism) and Einstein then unified the disparate theories of electromagnetism and mechanics with one kinematics (Minkowski space of special relativity). In this talk, we will briefly explain how the disparate kinematics of quantum mechanics (finite-dimensional Hilbert space) and special relativity can be unified with one principle (relativity principle). This result follows from the axiomatic reconstruction of quantum mechanics via information-theoretic principles, which has successfully recast quantum mechanics as a principle theory a la Einstein, i.e., the formalism of the theory follows from an empirically discovered fact, just like special relativity. According to the quantum reconstruction program, the empirically discovered fact whence the Hilbert space formalism of quantum mechanics is Information Invariance & Continuity. Of course, the empirically discovered fact whence the Lorentz transformations of special relativity is the light postulate, i.e., everyone measures the same value for the speed of light c, regardless of their relative motions. Obviously, the light postulate can be justified by the relativity principle—the laws of physics are the same in all inertial reference frames—because c is a constant of Nature per Maxwell’s electromagnetism. [We label this “NPRF + c” for short, where NPRF stands for “no preferred reference frame.”] As we will show, Information Invariance & Continuity can also be justified by the relativity principle by first spatializing the quantum reconstruction program’s operational notion of measurement. In that case, Information Invariance & Continuity entails the empirically discovered fact that everyone measures the same value for Planck’s constant h, regardless of their relative spatial orientations or locations (Planck postulate). Since Poincar’e transformations relate inertial reference frames via spatial rotations and translations as well as boosts, and h is a constant of Nature per Planck’s radiation law, the relativity principle justifies the Planck postulate (NPRF + h) just like it justifies the light postulate (NPRF + c). Thus, the kinematics of quantum mechanics and special relativity are unified in that both follow most fundamentally from the relativity principle in the adynamical global constraints NPRF + h and NPRF + c. This approach provides a principle solution to the mystery of quantum entanglement that does not violate locality, statistical independence, intersubjective agreement, or the uniqueness of experimental outcomes and it does not alter quantum mechanics as a principle theory. An ontology consistent with this unification is introduced and we deflate both the ‘big’ and ‘small’measurement problems.
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.
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 6 explains the axiomatic reconstruction of QM via information-theoretic principles. Hardy’s reconstruction is featured because it shows that the quantum probability theory of QM obtains by adding the word “continuous” to the fifth axiom of classical probability theory. As explained in Chapter 0, continuity is responsible for superposition, so the quantum bit (qubit) differs from the classical bit because the states of a qubit are superpositions. The Planck postulate is shown to follow from Brukner and Zeilinger’s principle of Information Invariance & Continuity at the foundation of their reconstruction, so QM can be understood as a principle theory based on NPRF + h. We show that ‘average-only’ projection is one way to characterize the ‘weirdness’ of the qubit. Grinbaum’s reconstruction based on relational quantum mechanics is introduced.
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.