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arXiv:quant-ph/0307121

Discovering Quantum Mechanics Once Again

Ian Duck

Published Jul 17, 2003• 0 citations
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Abstract

We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.

DOI
10.48550/arxiv.quant-ph/0307121

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We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a pretend world' with a pretend' Heisenberg who seeks to construct a dynamical theory of probabilities and is lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.
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The Bohm–Gadella theory, sometimes referred to as the time asymmetric quantum theory of scattering and decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann–Schwinger equation are functionals over spaces of Hardy functions. The preparation–registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann–Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation–registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann–Schwinger equation nor should they appear. It is also shown that the Bohm–Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm–Gadella theory must therefore be abandoned.
The Bohm-Gadella theory, sometimes referred to as the Time Asymmetric Quantum Theory of Scattering and Decay, is based on the Hardy axiom. The Hardy axiom asserts that the solutions of the Lippmann-Schwinger equation are functionals over spaces of Hardy functions. The preparation-registration arrow of time provides the physical justification for the Hardy axiom. In this paper, it is shown that the Hardy axiom is incorrect, because the solutions of the Lippmann-Schwinger equation do not act on spaces of Hardy functions. It is also shown that the derivation of the preparation-registration arrow of time is flawed. Thus, Hardy functions neither appear when we solve the Lippmann-Schwinger equation nor they should appear. It is also shown that the Bohm-Gadella theory does not rest on the same physical principles as quantum mechanics, and that it does not solve any problem that quantum mechanics cannot solve. The Bohm-Gadella theory must therefore be abandoned.