Hydrodynamic Stability Hypothesis

In the paper's words

This work identifies a “chronological fallacy” at the heart of quantum foundations: the axiomatization of quantum mechanics by von Neumann (1932) predated the rigorous formulation of classical probability by Kolmogorov (1933), creating an artificial schism between physics and statistics. To resolve the “spectral divergence” between the continuous ontology of hydrodynamic quantum models and the discrete phenomenology of spectroscopy, the hydrodynamic stability hypothesis is proposed. By synthesizing Madelung hydrodynamics, Radon-Nikodým measure theory, and dynamical systems theory, it is demonstrated that “quantization” is not an intrinsic property of the operator algebra, but an emergent dynamical stability phenomenon triggered by the measurement interaction.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. Unlike the Hamiltonian, which has a discrete spectrum of eigenvalues for bound states, the local energy field $E_{loc}$ is a continuous function of position (Reddiger, 2026).

   from 3.7 The Local Energy Field

How it is done

1. In 1932, John von Neumann published Mathematische Grundlagen der Quantenmechanik (von Neumann, 1932), codifying the theory within the framework of Hilbert space operators and establishing the spectral theorem as the primary tool for extracting physical values.

   from 1.1 The

2. However, if classical measure theory is sufficient to describe the chaotic dynamics of turbulence, the burden of proof lies on the assertion that it fails for the wavefunction.

   from 1.2 The

3. This approach moves beyond mere analogy, providing a mathematically sound method for translating quantum operators into functions on the configuration space.

   from 2.3 Geometric Quantum Theory

4. Neo-realism Parallel to the hydrodynamic approach, Döring and Isham (2007) have attempted to construct a realist formalism using topos theory.

   from 2.5 Topos Theory and

What would falsify it

1. The failure mode for the hypothesis is rigorously defined to ensure scientific falsifiability.

   from 5.8 Falsification Criteria

2. If the proposed weak measurement tomography experiment reveals strictly discrete eigenvalues (two sharp peaks) with zero variance between them, even in the limit of vanishing coupling strength, then the hydrodynamic stability hypothesis is falsified.

   from 5.8 Falsification Criteria

3. Yet, this “hybrid” framework predicts that the probability distribution for observables such as energy in a superposition state is continuous, spreading between the eigenvalues.

   from 1.5 The Spectral Divergence

Where the claim stops

1. These are challenges for future work, not invalidations of the core hypothesis.

   from 6.12 Limitations of the Model

2. However, if classical measure theory is sufficient to describe the chaotic dynamics of turbulence, the burden of proof lies on the assertion that it fails for the wavefunction.

   from 1.2 The

3. Dogma and the Operator Fallacy A central tenet of the orthodox formalism is the assumption that physical observables are ontologically equivalent to self-adjoint operators acting on a Hilbert space.

   from 1.4 The Spectral

Where to read

1. Re-grounding192 words · 1 min
2. 1.0 Introduction1,010 words · 4 min
3. 2.0 Literature Review544 words · 2 min
4. 3.0 Methodological Framework963 words · 4 min
5. 4.01,291 words · 6 min
6. 5.0 Analysis & Validation1,123 words · 5 min
7. 6.0 Discussion978 words · 4 min
8. 7. Conclusion603 words · 3 min