Quantum Reconstruction and Phenomenology per the Relativity Principle

Abstract: 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.

• The paper shows that enforcing the relativity principle provides the foundation for quantum discreteness by linking observer-independence of Planck’s constant to quantized outcomes.
• The paper employs an operational derivation of spin-1/2 measurement statistics to reveal how superposition and entanglement emerge as natural kinematic effects.
• The paper presents a unified framework that reframes nonlocality and contextuality as consequences of global invariance, eliminating the need for hidden variables.

Quantum Reconstruction and Phenomenology via the Relativity Principle

Introduction

This paper provides a comprehensive analysis and extension of the quantum reconstruction program (QRP), focusing on linking the operational axioms underpinning quantum mechanics (QM) with the relativity principle—"no preferred reference frame" (NPRF). Addressing longstanding concerns regarding the abstractness and interpretational ambiguity of information-theoretic reconstructions, the work advances the thesis that, analogous to the derivation of special relativity from empirical postulates grounded by the relativity principle, the essential kinematics of QM—particularly superposition and entanglement—are undergirded by the relativity principle in conjunction with the observer-independence of Planck's constant.

The Quantum Reconstruction Program: Axioms and Critique

The QRP aims to derive the mathematical structure of QM from clear, physically motivated axioms, paralleling Einstein's operational derivation of Lorentz transformations from the observer-independence of $c$ and the relativity principle [Hardy 2001, (2607.00045)]. Early reconstructions, such as those by Hardy, Chiribella et al., and Masanes & Müller, deployed information-theoretic principles, notably discreteness (quantization of measurement outcomes) and correspondence (consistency with classical expectations in appropriate limits).

However, objections persist regarding (1) the abstraction of the information-theoretic principles, lacking immediate physical justification, and (2) the claim that reconstructions do not advance unification beyond the established equivalence with QM. The inability to provide a fundamental reason for discreteness (i.e., why measurement outcomes are quantized) has been a principal lacuna.

Completing Quantum Reconstruction: Role of the Relativity Principle

The central claim of the paper is that the relativity principle supplies the missing explanatory grounding for the discreteness requirement. Drawing on the analogy with special relativity, the authors argue:

• For SR, the observer-independence of $c$ is justified by the relativity principle plus Maxwell's equations. The postulate is not arbitrary but a consequence of a general symmetry requirement.
• For QM, the observer-independence of $h$ (i.e., quantization of action) is similarly required by the relativity principle plus Planck's law.

Darrigol's operational derivation of spin-$1/2$ measurement statistics [darrigol2015] is revisited and completed by showing that the quantization (discreteness) of angular momentum outcomes in arbitrary directions (Stern-Gerlach measurements) is a consequence of enforcing NPRF with respect to $h$. The requirement that all observers, regardless of spatial orientation, must agree on the quantization reflects a deep symmetry—mirroring the invariance properties that motivate SR.

This approach renders quantum superposition and entanglement, not as standalone mysteries, but as necessary kinematic consequences of a universality principle—connecting disparate quantum and relativistic effects under a common explanatory umbrella.

Phenomenology and Objectivity: The Integration of Subjective Perspectives

The paper emphasizes a phenomenological perspective, arguing that objective reality, as modeled by physics, should be conceptualized as an integrated structure arising from the equality of all perspectives. This counters interpretations in which quantum correlations (e.g., Bell inequality violations) are framed as undermining intersubjective agreement or requiring fundamental subjectivity (as in some relational or QBist interpretations).

On the contrary, the principle-based reconstruction demonstrates that even the most perplexing quantum phenomena (superposition, entanglement) are manifestations of the universality and impartiality of physical law, not indicators of a fragmented or inherently subjective reality.

Constructive vs. Principle Theories: Epistemic and Metaphysical Status

• Constructive Theories: Attempt to provide causal-mechanical explanations by positing underlying microdynamics. In the quantum context, constructive accounts typically introduce nonlocality or hidden variables, generating tension with relativity and leading to so-called "hideously incoherent physics," including violations of Lorentz invariance or causal structure [Maudlin QNLandSR].
• Principle Theories: Formulated in terms of global constraints (e.g., NPRF), these theories restrict the set of possible phenomena via top-down kinematic requirements rather than bottom-up dynamics. The completion of QRP situates QM as a principle theory where the wavefunction encodes constraints on possible configurations of quantum events, consistent across all subjective reference frames.

This principle-theoretic stance deflates the "big" measurement problem by eliminating any necessity for hidden dynamics or collapse mechanisms, as all measurement outcomes, superpositions, and entanglements unfold as manifestations of spacetime and Hilbert space kinematics dictated by principle-level symmetries.

Implications for No-Go Theorems and Interpretational Debates

PBR Theorem

The Pusey-Barrett-Rudolph (PBR) theorem demonstrates that quantum pure states cannot share underlying "ontic" states in hidden-variable models consistent with QM [PBR2012]. This result is often interpreted as evidence against epistemic (knowledge-based) accounts of the wavefunction and fuel for ontic realism or nonlocality.

The paper contends that reconstructions grounded in the relativity principle—and, by extension, principle-theoretic QM—render such concerns moot. Since the formalism already provides contextually unique, global configurations for pure states via symmetry principles, there is no need to posit constructive ontic states or nonlocal causal mechanisms to "explain" quantum statistics.

Nonlocality, Contextuality, and NPRF

The principle explanation reframes quantum nonlocality as a kinematic effect (arising from NPRF and Hilbert space symmetry), not a manifestation of superluminal causation or agent-dependent facts. Bell inequality violations, accordingly, are further confirmation of the universality of the relativity principle in both the quantum and relativistic domains.

Phenomenological Mediation

By demonstrating the operational roots of QM within the equality of reference frames, the work strengthens the link between formalism and phenomenology. The construction of objective spacetime models thus upholds the comprehensibility and intersubjective agreement advocated by phenomenological analysis, now unified with the abstract structure of quantum theory.

Conclusion

This work completes the information-theoretic quantum reconstruction program by identifying the relativity principle as the fundamental explanatory resource for the discreteness and invariance principles at the core of QM. The result is a unified, principle-based account in which the formal features of both quantum mechanics and special relativity are natural consequences of NPRF—"the equality of all perspectives."

This framework dissolves interpretational paradoxes by removing the need for hidden dynamical mechanisms, nonlocality, or subjectivist strategies, and situates both quantum and relativistic phenomena within a coherent phenomenological and operational model. Future developments may extend these ideas to broader classes of physical theories and deepen the systematic comparison of kinematic and constructive paradigms in foundational physics.

Reference:

"Quantum Reconstruction and Phenomenology per the Relativity Principle" (2607.00045)