The logic of quantum mechanics derived from classical general relativity

Hadley, Mark J

doi:10.1007/bf02764119

Cited by 13 publications

(26 citation statements)

References 10 publications

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“…Finally, it can also be mentioned a further work [504], where it is shown that a orthomodular lattice of propositions characteristic of quantum logic can be constructed for manifolds in Einstein's theory of general relativity, where both state preparation and measurement apparatus constrain results of experiments (future observations represent hidden variables).…”

Section: Determinism At Planck Scale?mentioning

confidence: 99%

Research on hidden variable theories: A review of recent progresses

2005

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Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various aspects concerning its very foundations still remain to be clarified. Among them, the transition from a microscopic probabilistic world into a macroscopic deterministic one and quantum non-locality. A possible way out from these problems would be if QM represents a statistical approximation of an unknown deterministic theory.This review is addressed to present the most recent progresses on the studies related to Hidden Variable Theories (HVT), both from an experimental and a theoretical point of view, giving a larger emphasis to results with a direct experimental application.More in details, the first part of the review is a historical introduction to this problem. The Einstein-Podolsky-Rosen argument and the first discussions about HVT are introduced, describing the fundamental Bell's proposal for a general experimental test of every Local HVT and the first attempts to realise it.The second part of the review is devoted to elucidate the recent progresses toward a conclusive Bell inequalities experiment obtained with entangled photons and other physical systems.Finally, the last sections are targeted to shortly discuss Non-Local HVT.1

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Section: Determinism At Planck Scale?mentioning

confidence: 99%

Research on hidden variable theories: A review of recent progresses

2005

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“…A measure over initial conditions and measurement conditions would also give a Boolean logic as required by Mackey (Mackey 1963); but a measure over initial conditions alone would give a different logical structure which must be orthomodular (Hadley 1997, Beltrametti & Cassinelli 1981. The orthomodular structure can be represented by the projections on a Hilbert Space (Beltrametti & Cassinelli 1981).…”

Section: Resultsmentioning

confidence: 99%

“…It is known that if a breakdown in causal structure is an inherent feature of elementary particles then the propositions associated with the theory could have the, non-Boolean, logical structure of quantum mechanics (Hadley 1997). In this paper models are constructed upon which it is impossible to define complete initial data independently of future measurements.…”

Section: Introductionmentioning

confidence: 99%

“…This paper does not consider singularities, it retains the framework of classical general relativityincluding a continuous spacetime manifold with a continuous metric. The breakdown in causal structure is actually seen as advantageous because it offers a way of reconciling classical and quantum physics (Hadley 1997). The examples are created by relaxing the assumptions of Geroch's theorem.…”

Section: Introductionmentioning

confidence: 99%

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Hadley¹

1999

International Journal of Theoretical Physics

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The non-classical features of quantum mechanics are reproduced using models constructed with a classical theory -general relativity. The inability to define complete initial data consistently and independently of future measurements, non-locality, and the non-Boolean logical structure are reproduced by these examples. The key feature of the models is the role of topology change. It is the breakdown of causal structure associated with topology change that leads to the apparently non-classical behaviour. For geons, topology change is required to describe the interaction of particles. It is therefore natural to regard topology change as an essential part of the measurement process. This leads to models in which the measurement imposes additional non-redundant boundary conditions. The initial state cannot be described independently of the measurement and there is a causal connection between the measurement and the initial state.

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“…Although this paper is entirely classical, the lack of a time orientation gives new results and is motivated by earlier work linking spacetimes that are not time orientable with foundations of quantum theory [4,5], the existence of electric charges [6], and spin half transformations of elementary particles [7].…”

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confidence: 99%

Electrodynamics and Time Orientability

Hadley

2017

Int J Theor Phys

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On spacetimes that are not time orientable we construct a U(1) bundle to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell's equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path. The boundary of a time reversing region can therefore have a net electric flux and appear exactly as a region containing an electric charge. The treatment is purely classical, but motivated by links between acausal structures and quantum theory.

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The logic of quantum mechanics derived from classical general relativity

Cited by 13 publications

References 10 publications

Research on hidden variable theories: A review of recent progresses

Research on hidden variable theories: A review of recent progresses

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Electrodynamics and Time Orientability

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