We use the relativity principle to complete axiomatic reconstructions of quantum mechanics (QM) via information-theoretic principles that are based on Darrigol's "discreteness" requirement or its equivalent, e.g., Brukner & Zeilinger's Information Invariance & Continuity or Khrennikov's quantum action invariance principle. In this approach to the quantum reconstruction program (QRP), the Hilbert space kinematics of QM is derived most fundamentally from the experimentally motivated postulate of "discreteness," rendering QM a principle theory as defined by Einstein. Special relativity is also a principle theory, since its Lorentz transformation kinematics is derived from the experimentally motivated light postulate. While special relativity has a compelling fundamental principle (relativity principle) to account for its experimentally motivated light postulate, QRP has not produced a compelling fundamental principle to account for its experimentally motivated "discreteness" requirement. We complete QRP by showing how the "discreteness" requirement is necessitated by the relativity principle and Planck's radiation law, just like the light postulate is necessitated by the relativity principle and Maxwell's equations. Accordingly, the fundamental explanans for time dilation, length contraction, quantum superposition, and entanglement is the relativity principle. Phenomenologically speaking, the relativity principle is "the equality of all perspectives." Thus, quantum entanglement isn't evidence for the violation of intersubjective agreement or the need to abandon factive or objective models of reality, as in relational interpretations of QM. It is evidence that reality is not a fragmented collage of different subjective experiences from different perspectives, it's a comprehensive and coherent integration of those different subjective experiences per the equality of all perspectives.
We use the relativity principle to complete axiomatic reconstructions of quantum mechanics (QM) via information-theoretic principles that are based on Darrigol's "discreteness" requirement or its equivalent, e.g., Brukner & Zeilinger's Information Invariance & Continuity or Khrennikov's quantum action invariance principle. In this approach to the quantum reconstruction program (QRP), the Hilbert space kinematics of QM is derived most fundamentally from the experimentally motivated postulate of "discreteness," rendering QM a principle theory as defined by Einstein. Special relativity is also a principle theory, since its Lorentz transformation kinematics is derived from the experimentally motivated light postulate. While special relativity has a compelling fundamental principle (relativity principle) to account for its experimentally motivated light postulate, QRP has not produced a compelling fundamental principle to account for its experimentally motivated "discreteness" requirement. We complete QRP by showing how the "discreteness" requirement is necessitated by the relativity principle and Planck's radiation law, just like the light postulate is necessitated by the relativity principle and Maxwell's equations. Accordingly, the fundamental explanans for time dilation, length contraction, quantum superposition, and entanglement is the relativity principle. Phenomenologically speaking, the relativity principle is "the equality of all perspectives." Thus, quantum entanglement isn't evidence for the violation of intersubjective agreement or the need to abandon factive or objective models of reality, as in relational interpretations of QM. It is evidence that reality is not a fragmented collage of different subjective experiences from different perspectives, it's a comprehensive and coherent integration of those different subjective experiences per the equality of all perspectives.
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.
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.
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell inequalities.
It is well recognized that two of the foundational theories of modern physics, relativity and quantum mechanics, are inconsistent. Efforts to overcome this through intensive pursuit of unifying theoretical frameworks or improvements in experimental precision as pursued by Robertson-Mansouri-Sexl and Standard-Model-Extension test theory protocols, have so far proven unsuccessful. Nonetheless, empirical evidence deriving from investigations inspired by the twentieth-century 'EPR' polemic, can now claim to have identified 'locality' and 'separability' as notions integral to special relativity theory inconsistent with quantum mechanics and experimental evidence supporting it. Following intimations of J.S. Bell, L. Smolin, Maudlin and others, the history and philosophy of science are engaged as research tools to uncover the origins of the assumptions underlying such incompatibility. In particular, known but prevalent fallacies and the deprecation of processes as described by Whitehead, together with recent insights into the functional distinctions between representative models and explanatory theories, are engaged. Analysis of the evolution of optical and electromagnetic theorizing is then suggested to demonstrate that the choice of a mechanically compatible model of electromagnetic radiation, as has conventionally underwritten development of the light-speed postulate of special relativity, is inappropriate. Pursuing options made available within a multiple models idealization of optical and electromagnetic phenomena, replacement of the sponsoring model by a nonlocal and non-separable wavefront process of radiation of the form advanced by Fresnel and Kirchhoff on the basis of Huygens' principle, suggests the possibility of reformulation of relativity theory without incurring such conflicts. However, choice of a wavefront electrodynamic model including the extinction theorem of Ewald and Oseen, equally suggests possible theory reformulation without necessitating a four-dimensional construct of space and time or postulating an absolute constancy of light-speed in vacuum. Such a constancy can in turn be considered as demonstrating an innate limitation on empirical observation resulting from the loss of relative velocity information during electromagnetic transmission due to the memorylessness of the Markov propagation process of refraction together with information flow discontinuity resulting from dielectric boundary extinction events. Such characteristics are shown to be applicable to electromagnetic radiation of all frequencies. Further, from a wavefront reformulated hypothesis of inertial relative motion, it appears possible to demonstrate that the Galilean principle of relativity can be preserved. However, Lorentz invariance would then require reinterpretation wherein the Lorentz transform group would be deemed to quantify the degree of information distortion inherently experienced by any empirical enquiry into electrodynamics involving relative motion.
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.