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'The Singular Role of Infinity in Quantum Physics: Towards a Rational theory...' by Dr. Tim Palmer
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Title: The Singular Role of Infinity in Quantum Physics: Towards a Rational theory of Quantum Mechanics
Abstract: Despite decades of effort, we have neither solved the measurement problem in quantum mechanics, nor the unification of quantum and gravitational physics. Are these problems related? Could it be that the underlying difficulty lies in the essential use that the concept of infinity plays in the continuum Hilbert (Foch) state spaces of quantum (field) theory. Here I describe a particular discretisation of Hilbert Space (generating what I call Rational Quantum Mechanics - RaQM) and show, using elementary results from number theory, it accounts for the Uncertainty Principle, wave-particle duality and quantum non-commutativity, whilst at the same time allowing (something impossible in quantum mechanics) a finite deterministic ensemble-based underpinning of the wavefunction in which Born’s rule is automatically satisfied. In this model quantum mechanics is a singular limit of RaQM as the discretisation goes to zero. The violation of counterfactual definiteness in discrete RaQM implies it is not Bell-nonlocal, determinism notwithstanding.
Palmer, T.N., Superdeterminism without Conspiracy. Universe 2024, 1, 47.
Abstract: Despite decades of effort, we have neither solved the measurement problem in quantum mechanics, nor the unification of quantum and gravitational physics. Are these problems related? Could it be that the underlying difficulty lies in the essential use that the concept of infinity plays in the continuum Hilbert (Foch) state spaces of quantum (field) theory. Here I describe a particular discretisation of Hilbert Space (generating what I call Rational Quantum Mechanics - RaQM) and show, using elementary results from number theory, it accounts for the Uncertainty Principle, wave-particle duality and quantum non-commutativity, whilst at the same time allowing (something impossible in quantum mechanics) a finite deterministic ensemble-based underpinning of the wavefunction in which Born’s rule is automatically satisfied. In this model quantum mechanics is a singular limit of RaQM as the discretisation goes to zero. The violation of counterfactual definiteness in discrete RaQM implies it is not Bell-nonlocal, determinism notwithstanding.
Palmer, T.N., Superdeterminism without Conspiracy. Universe 2024, 1, 47.
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