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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum indeterminism: a direct consequence of Fourier ontology

J. R. Croca

Published Oct 1, 2013• 2 citations
Publisher

Abstract

Fourier ontology and consequent quantum indeterminism and the way to overcome it shall be discussed. Furthermore it shall be proven that recent experimental technology goes far beyond the limits imposed by Heisenberg indetermination relations. These experiments are perfectly integrated in the new causal nonlinear quantum physics. Keywords: Orthodox quantum mechanics, Fourier ontology, Heisenberg indetermination relations, nonlinear quantum physics, general uncertainty relations, beyond Heisenberg limits.

DOI
10.1117/12.2025291

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Fourier ontology and consequent quantum indeterminism and the way to overcome it shall be discussed. Furthermore it shall be proven that recent experimental technology goes far beyond the limits imposed by Heisenberg indetermination relations. These experiments are perfectly integrated in the new causal nonlinear quantum physics. Keywords: Orthodox quantum mechanics, Fourier ontology, Heisenberg indetermination relations, nonlinear quantum physics, general uncertainty relations, beyond Heisenberg limits.
Fourier ontology claims that only the physically inexistent abstract harmonic plane waves do have a pure perfect frequency, therefore, a finite wave being in this ontology a sum of many harmonic plane waves cannot have a single pure frequency. The causal nonlinear approach based onto the more general wavelet analysis assumes that a finite wave may indeed have a single frequency. An experimental process is proposed for testing nonlocal and nontemporal Fourier ontology against local wavelet analysis. The experiment also checks the general validity of Heisenberg indetermination relations. The proposed experiment uses an asymmetric Mach-Zehnder interferometer and increasingly better monochromators.
The Heisenberg uncertainty principle constitutes one of the foundational pillars of quantum mechanics and represents a definitive rupture with the deterministic ideal of classical physics. This work develops a comprehensive analysis of the uncertainty principle from a mathematical, physical, and philosophical perspective, demonstrating that it should not be interpreted as an instrumental or epistemological limitation, but rather as an ontological property inherent to the formalstructure of quantum theory.Within the framework of Hilbert spaces, self-adjoint operators, and non-commutative algebras, it is shown that uncertainty emerges necessarily as a consequence of the structural incompatibility between conjugate observables. The study articulates the uncertainty principle with classical chaos theory and the sciences of complexity, establishing a fundamental distinction between epistemological unpredictability and ontological indeterminacy. While classical chaos preserves well-defined trajectories that are practically inaccessible, quantum mechanics eliminates the very notion of trajectory as a fundamental entity.This rupture manifests itself in the granularity of phase space, the impossibility of defining exact initial conditions, and the consequent reformulation of determinism. Contemporary experimental developments designed to exclude instrumental disturbances are analyzed, reinforcing the ontological interpretation of the uncertainty principle.Finally, the implications for simulation, predictability, and quantumOverall, this work argues that the uncertainty principle does not undermine scientific rationality, but rather redefines itsscope and deepens our understanding of physical reality. Keywords: uncertainty principle; quantum mechanics; mathematical structure; non-commutative operators; chaos theory; complexity; determinism; physical ontology.
Orthodox quantum mechanics has another implicit postulate stating that temporal and spatial frequencies of the Planck–Einstein and de Broglie formulas can only be linked with the infinite, in time and space, harmonic plane waves of Fourier analysis. From this assumption, nonlocality either in space and time follows directly. This is what is called Fourier Ontology. In order to build nonlinear causal and local quantum physics, it is necessary to reject Fourier ontology and accept that in certain cases a finite wave may have a well defined frequency. Now the mathematical tool to describe this new approach is wavelet local analysis. This more general nonlinear local and causal quantum physics, in the limit of the linear approximation, contains formally orthodox quantum mechanics as a particular case.
We add nonlinear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, nonlinear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of measurement. We explore the consequences of such terms and show that nonlinear quantum effects can be observed in macroscopic systems even in the presence of decoherence. We find that current experimental bounds on these nonlinearities are weak and propose several experimental methods to significantly probe these effects. The locally exploitable effects of these nonlinearities have enormous technological implications. For example, they would allow large-scale parallelization of computing (in fact, any other effort) and enable quantum sensing beyond the standard quantum limit. We also expose a fundamental vulnerability of any nonlinear modification of quantum mechanics---these modifications are highly sensitive to cosmic history and their locally exploitable effects can dynamically disappear if the observed universe has a tiny overlap with the overall quantum state of the universe, as is predicted in conventional inflationary cosmology. We identify observables that should persist in this case and discuss opportunities to detect them in cosmic ray experiments, tests of strong field general relativity and current probes of the equation of state of the universe. Nonlinear quantum mechanics also enables novel gravitational phenomena and may open new directions to solve the black hole information problem and to uncover the theory underlying quantum field theory and gravitation.
The concept of 'super-indeterminism' captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, "universal indeterminism"). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter "freedom", "free will", or "free choice", is redundant in relation to the predictive success of orthodox quantum mechanics. Accordingly, super-indeterminism views as redundant also, from a technical standpoint, whether an affirmative or a negative answer is claimed in reference to universal indeterminism as a necessary precondition for experimenter freedom. Super-indeterminism accounts, for example, for the circular reasoning which is implicit in the free will theorem by Conway and Kochen [1,2]. The concept of super-indeterminism is of great assistance in clarifying the often misunderstood meaning of the concept of "free variables" as used by John Bell [3]. The present work argues that Bell sought an operational, effective free will theorem , one based upon the notion of "determinism without predetermination", i.e., one wherein "free variables" represent universally uncomputable variables. In conclusion, the standard interpretation of quantum theory does not answer, and does not need to answer in order to ensure the predictive success of orthodox theory, the question of whether either incompatibilism or compatibilism is valid in relation to free-will metaphysics and to the free-will phenomenology of experimenter agents in quantum mechanics.