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arXiv:1106.1254

Quantum Theory without Quantization

K. B. Wharton

Published Jun 7, 2011• 1 citation
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Abstract

The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats measurements as boundary constraints. It is well-known that boundaries can induce apparently-discrete behavior in continuous systems, and strong analogies can be drawn to the case of quantum measurement. If quantum discreteness arises in this manner, this would not only indicate an analog reality, but would also offer a solution to the so-called "measurement problem".

DOI
10.48550/arxiv.1106.1254

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The only evidence we have for a discrete reality comes from quantum measurements; without invoking these measurements, quantum theory describes continuous entities. This seeming contradiction can be resolved via analysis that treats measurements as boundary constraints. It is well-known that boundaries can induce apparently-discrete behavior in continuous systems, and strong analogies can be drawn to the case of quantum measurement. If quantum discreteness arises in this manner, this would not only indicate an analog reality, but would also offer a solution to the so-called "measurement problem".
Quantum mechanics presents a profound conceptual challenge: it describes a world that is mathematically continuous but observationally discrete. The equations governing quantum systems are smooth differential equations, yet the physical reality they predict appears relentlessly quantized: energy comes in steps, particles are countable, and measurements register as distinct, indivisible events. This whitepaper proposes a unified taxonomy that organizes all known sources of quantum discreteness into five mutually exclusive, collectively exhaustive categories. We demonstrate that approximately 60% of observed discreteness appears to emerge from geometric and topological constraints on continuous wave dynamics, 25% stems from the mathematical structure of symmetry, and only 15% remains uncertain in its ontological status. By systematizing these mechanisms, this synthesis suggests that quantum discreteness may rarely be a fundamental property of nature's substrate but predominantly a consequence of selective stability: continuous wave dynamics, when subjected to global self-consistency constraints, can only sustain certain resonant patterns characterized by integers.
This paper reanalyzes the Wigner’s Friend scenario as a case of illicit scope transport rather than as evidence of paradox, observer-dependence, or foundational incompleteness in quantum mechanics. It shows that the apparent contradiction arises when descriptive commitments licensed in one representational scope are improperly exported into another without admissible justification. Within a closed admissibility framework, observer-relative descriptions are not interchangeable by default. Each description is licensed only within a specific scope defined by standing, reference, and expressive constraints. The Wigner’s Friend paradox emerges when a state description valid within the friend’s scope is treated as if it must remain valid under an external observer’s incompatible scope, collapsing representational separation into apparent inconsistency. The analysis is eliminative. It does not introduce new interpretations of quantum mechanics, propose resolution mechanisms, or modify measurement postulates. Instead, it establishes a boundary condition: cross-scope state identification is inadmissible unless standing-preserving transport conditions are satisfied. Where these conditions fail, the resulting contradiction is not physical but representational. By classifying Wigner’s Friend as a scope error rather than a quantum mystery, the paper dissolves a class of arguments for observer-relative reality, branching worlds, or relational ontology. It closes the problem by showing that the paradox is generated by an illicit move between descriptive regimes, not by any failure of quantum theory itself.
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is, that we measure at specific moments in time (as opposed to a continuous measurement that spans a long time interval) and that the system is in general affected by our measurement. We believe that this way of presenting quantum mechanics would make it easier to understand by laying out a more cohesive view of the theory and making it resonate more with our physics intuition.
Standard quantum mechanics represents measurement outcomes using probability amplitudes and the Born rule. The present work develops a complementary geometric ontology within the Geometric Monism (GM) framework. In GM, physical entities are modeled as continuous torsional standing-wave structures embedded in a 5-dimensional manifold governed by the Planck Stiffness κT=c4/G\kappa_T=c^4/GκT​=c4/G, while localized observations occur through 4-dimensional boundary interactions. This paper proposes that quantum probability may be interpreted as arising from the boundary projection and partial sampling of continuous higher-dimensional structures by localized measurement apparatuses. The probabilistic character of interaction outcomes is therefore treated as a property of measurement access and boundary localization, rather than as evidence that the underlying entity lacks continuous structure. By establishing a formal ontological distinction between continuous geometric entities and probabilistic boundary interactions, the framework offers a candidate geometric resolution to the measurement problem's ontological tension. The analysis is made compatible with the companion Bell-correlation paper, where GM entities are argued to fall outside Bell factorizability because entangled systems are modeled as non-separable global standing-wave structures. The paper develops a continuum-mechanics interpretation of Born-type probabilities, relates spin/chirality compatibility to standard quantum statistical factors, and shows how a finite-geometry stationary-action principle with a minimal torsional radius constraint yields characteristic 1/21/21/2 accessibility factors. The claims are presented as an interpretive geometric framework that preserves the predictive success of quantum mechanics and quantum field theory while proposing an alternative ontology for the entities participating in interaction events.
Attempting to describe the "collapse of the wave function" of the orthodox quantum theory as a physical process, a natural assumption is that the measurement apparatus is subject to the same physical laws as the measured object, leading to a theory without rules for measurement. This – together with the loss of classical-quantum correspondence for chaotic systems – enforces the inclusion of the environment. I very shortly describe the present state of the art in this field – a challenge for the quantum many body community.