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arXiv:quant-ph/0004077 · Lecture notes in physics

Probability in Orthodox Quantum Mechanics: Probability as a Postulate Versus Probability as an Emergent Phenomenon

Stephen L. Adler

Published Jan 1, 2001• 4 citations
arXivHTMLPDF
DOI
10.1007/3-540-44966-3_7

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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.
Entanglement and the tunnel effect phenomena have been repeatedly observed and are generically accepted under orthodox quantum mechanics formalism. However, they remain rather inexplicable in the context of spacetime usual conceptualization. In the present work, we suggest an alternative quantum mechanics formalism, refining the pilot-wave theory initially proposed by de Broglie. We suggest that spacetime is an emergent phenomenon from a prior subquantum medium and that entanglement and the tunnel effect can be explained in terms of a nonlinear relation between space and time that is imposed by subquantum waves.