We present a group-theoretic reconstruction of quantum mechanics in which the standard formalism emerges from the representation theory of symmetry groups rather than being introduced axiomatically. Starting from physically motivated symmetry principles, we show how the conventional postulates of quantum mechanics, including the Hilbert space structure of states, observables as generators of symmetry transformations, the Born probability rule, unitary time evolution, the composition of multipartite systems, and the measurement framework, can be recovered within a unified representation-theoretic framework. We then examine the measurement problem by interpreting wave-function collapse as the scattering of quantum states, thereby accounting for the apparent loss of information. This framework offers a conceptually unified perspective on the foundations of quantum mechanics, connecting its postulates, measurement theory, and the emergence of quantum phenomena to a common symmetry-based origin.
We present a group-theoretic reconstruction of quantum mechanics in which the standard formalism emerges from the representation theory of symmetry groups rather than being introduced axiomatically. Starting from physically motivated symmetry principles, we show how the conventional postulates of quantum mechanics, including the Hilbert space structure of states, observables as generators of symmetry transformations, the Born probability rule, unitary time evolution, the composition of multipartite systems, and the measurement framework, can be recovered within a unified representation-theoretic framework. We then examine the measurement problem by interpreting wave-function collapse as the scattering of quantum states, thereby accounting for the apparent loss of information. This framework offers a conceptually unified perspective on the foundations of quantum mechanics, connecting its postulates, measurement theory, and the emergence of quantum phenomena to a common symmetry-based origin.
We present a group-theoretic reconstruction of quantum mechanics in which the standard formalism emerges from the representation theory of symmetry groups rather than being introduced axiomatically. Starting from physically motivated symmetry principles, we show how the conventional postulates of quantum mechanics including the Hilbert space structure of states, observables as generators of symmetry transformations, the Born probability rule, unitary time evolution, the composition of multipartite systems, and the measurement framework can be recovered within a unified representation-theoretic framework. We then examine the measurement problem by interpreting wave-function collapse as the scattering of quantum states, thereby providing an account of the apparent loss of information. Finally, we investigate the origin of Planck's constant, proposing that it arises as the conserved charge of the Lorentz symmetry group. In this formulation, ℏ is an invariant that relates Lie algebra generators to observable quantities and fixes the scale of quantum action. This framework offers a conceptually unified perspective on the foundations of quantum mechanics, connecting its postulates, measurement theory, and the emergence of the quantum of action to a common symmetry-based origin while identifying conditions under which the conventional quantum formalism is recovered.
This work presents an axiomatic and structural reconstruction of core elements of quantum mechanics. Starting from minimal principles — symmetry under vanishing preference, normalization, consistency of probability assignments, and coherence-preserving dynamics — we derive several central features of the quantum formalism rather than postulating them. Key results include: A geometric derivation of the constants 1/21/\sqrt{2}1/2 and 1/21/21/2 from symmetry and normalization. A theorem-level derivation of the Born rule (including the qubit case) from noncontextuality and additivity. A reconstruction of Schrödinger dynamics from reversible norm-preserving structure. A derivation of the tensor-product structure for composite systems from composition axioms and local tomography, with entanglement emerging as a necessary consequence. Formal treatment of Bell–CHSH nonlocality, Tsirelson’s bound, and no-signalling. A conditional reconstruction of complex Hilbert space structure from intrinsic phase dynamics and compositional consistency. The manuscript is self-contained and framed in standard mathematical-physics language. It does not propose modifications to quantum mechanics, but instead clarifies why many of its defining structures arise inevitably from deeper structural constraints. Prior computational and model-based work by the authors (including diagnostic toy models exploring phase locking, coherence stabilization, and recursive-time dynamics) is acknowledged but intentionally not reproduced here, in order to keep the present work focused on axiomatic structure rather than model-specific architecture. This upload is intended as a foundations and reconstruction contribution, suitable for readers interested in the mathematical and conceptual structure of quantum theory.
The quantum measurement problem arises from a structural asymmetry in standard formulations of quantum mechanics: while unitary evolution is treated as fundamental, irreversible events are introduced only through ad hoc postulates. As a result, measurement, decoherence, and probability appear conceptually disconnected. In this work, we propose a minimal reformulation in which irreversible interaction events are taken as ontological primitives. An event is defined as a completely positive, trace-preserving map that is not equivalent to any unitary transformation. Unitary evolution emerges as an effective description valid between events. Within this framework, quantum measurement is not a special process but a particular class of irreversible events with outcome-resolving structure. The Born rule arises naturally from the statistical structure of event realizations, and environmental decoherence is reinterpreted as a high density of irreversible events. No collapse postulate, observer-dependent rule, or modification of quantum dynamics is required. This formulation provides a unified and physically grounded resolution of the measurement problem and establishes a conceptual foundation for event-based extensions connecting quantum theory with spacetime and gravity.
Quantum measurement theory traditionally introduces probabilities axiomatically, most notably through the Born rule and projection postulates. In this work, I introduce Constraint Mechanics (CM), a framework in which quantum probabilities arise as conditional statistics over dynamically generated constraint fields acting on configuration space, without modifying unitary Schrödinger evolution or introducing dynamical collapse. A detector-scale conditional measurement operator is defined using soft viability weights that do not alter the wavefunction. I prove that the Born rule is recovered exactly as a theorem in the limit of spatially homogeneous constraints, while structured deviations emerge under heterogeneous constraint profiles with exact norm preservation. Numerical validation using a double-slit geometry confirms unitary evolution, exact normalization, and controlled deviation behavior. CM reframes quantum measurement as conditioning on dynamically viable configuration-space regions and provides a unifying interpretational link between interference, measurement, and selection.
A unique postulate is shown to underly the whole quantum mechanics theory: the invariance of the Heisenberg uncertainty inequality under a group of special nonlinear gauge transformations (NLGT). With this postulate, the quantum mechanics of a free particle is derived from classical mechanics, including the statements of the postulates of quantum mechanics, except for the wave-function-collapse postulate. An explanatory mechanism for the latter postulate is derived by performing an analytical continuation of the NLGTs. This extension results in a Schrödinger-bridge process, intertwined under the NLGT with the standard unitary quantum evolution, and revealing non-quantum (or beyond-quantum) phenomena. Mechanisms of that latter kind, like the ones associated to the quantum measurement process, occur in a new space-like dimension and hence are non causal in nature, in opposition to a time evolution. The present exercice focusses on the free particle in order to highlight the features of the performed derivation in the simplest possible way. Work is in progress to extend the performed derivation beyond that simple case.
This article examines the scope and limitations of quantum mechanics in its Schrödinger and Dirac formulations. Quantum theory provides an extraordinarily precise description of how physical states evolve, interfere, and produce measurable probabilities. However, like other foundational theories, it presupposes a specific mathematical structure—complex Hilbert spaces, linear unitary dynamics, an external time parameter, and the Born rule—that it does not itself explain. The work argues that quantum mechanics answers the question of how quantum states behave, but not the deeper question of why physical reality admits a state-based, probabilistic description at all. To address this missing level of explanation, the article places quantum mechanics within the broader framework of the Thermodynamic Imperative of Order (TIO) and the Granular Entropic Program (GEP). Within this framework, quantum states are interpreted as emergent, statistically stable macroscopic representations of typical correlations in high-dimensional configuration spaces. Linearity, unitarity, and the Born rule arise as necessary consequences of measure concentration and stability, rather than as fundamental postulates. The article does not propose modifications to quantum mechanics. Instead, it clarifies the domain of validity of the theory and explains why a framework with its structure and remarkable universality must exist if stable quantum phenomena are to be observed at all.