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Advanced Science Letters

Fourier Ontology versus Wavelet Local Analysis a Test for the General Validity of Orthodox Mechanics Against the Nonlinear Causal Quantum Physics

J. R. Croca, Augusto Garuccio

Published Jun 1, 2010• 1 citation
Publisher

Abstract

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.

DOI
10.1166/asl.2010.1114

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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.
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.
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.
Introduction: Bell’s concept of local causality assumes more than local action. It also presumes an ontology of point particles. Bell correlations are feasible in nonlinear field ontologies with quantised interactions between suitably correlated participants. Materials and methods: Local causality is unsatisfactory for many reasons, not just Bell’s Theorem. The EPR paradox is due to metaphysical overcommitment to point models. An alternative, distributed concept of long-range interaction is appropriate for field ontologies. Inherently distributed field interaction quanta modify the causal structure of relations between observables. Results: Causal structure of Bell measurements in de Broglie–Bohm EPR experiments: Causal analysis of local realist field models violates Bell Inequalities without violating local action. Experimental Tests: Testable consequences include an observable range dependence of the coherence time of Bell states. Conclusions: Local realist field ontologies are not ruled out by the existence of Bell correlations in nature. The only “conflict” between quantum mechanics and relativity is because lightcone causal analysis effectively presumes a particle ontology.
Explaining observations in terms of cause-and-effect (causal) relations is central to empirical science. However, in his seminal 1964 work [1], John Bell showed that the correlations between entangled quantum systems cannot be explained in terms of, possibly hidden, cause and effect relations. After four decades of experimental effort, Bell's prediction has recently been confirmed in an unambiguous way by a series of loophole-free Bell-test experiments [2-4]. These experiments, however, cannot reveal where exactly quantum mechanics breaks with our classical notion of cause and effect. Specifically, Bell's theorem is based on the central assumptions of realism and local causality. Realism posits that physical systems have real, objective properties, independent of whether we observe them or not, and local causality assumes that causal influences cannot propagate faster than the speed of light.
Focusing on the initial development of quantum mechanics, we will give a brief historical synopsis of the theory foundations, based on the Fourier framework and stating the philosophical conclusions inspired by that same mathematical formalism. We will then proceed, introducing an alternative way of describing the undulatory aspects of quantum entities, using local Gaussian Morlet wavelets. As we shall see, this change implies different philosophical interpretations about quantum reality and, even more, about the contemporary accepted differences between the quantum and the macroscopic realms. From these we will witness the formal and heuristic power of wavelet local analysis applied to the physical description of Nature. The ideas presented in this paper are initial standpoints of what can hopefully be expected to be a more mature and unifying physical theory, still undergoing development.