aqora

Twistor theory and quantum mechanics

Claudio Oleari

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BJan 1, 19750 citations

Non-relativistic Twistor Theory: Newtonian Limits and Gravitationally Induced Collapse

Eleanor March, James Alexander Mabyn Read

Abstract Recently, Dunajski and Gundry (Commun. Math. Phys., 342 (3), 2016) have developed a version of twistor theory for the non-relativistic domain. Unlike relativistic twistor theory, their approach is able to reproduce the entire space of models of Newton–Cartan theory. We critically assess the significance of non-relativistic twistors, in particular with respect to proposals by Dunajski and Penrose (Ann. Phys., 451 , 2023) that using non-relativistic twistors to describe gravitationally induced collapse could play a part in solving the quantum measurement problem.Abstract Recently, Dunajski and Gundry (Commun. Math. Phys., 342 (3), 2016) have developed a version of twistor theory for the non-relativistic domain. Unlike relativistic twistor theory, their approach is able to reproduce the entire space of models of Newton–Cartan theory. We critically assess the significance of non-relativistic twistors, in particular with respect to proposals by Dunajski and Penrose (Ann. Phys., 451 , 2023) that using non-relativistic twistors to describe gravitationally induced collapse could play a part in solving the quantum measurement problem.

Foundations of PhysicsJul 13, 20260 citations

Some remarks concerning the equivalence principle of general relativity with respect to quantum mechanical one-particle state

Gerhard Börner, Siegfried Schlieder

General Relativity and GravitationJan 1, 19809 citations

The equivalence principle in classical and quantum mechanics

Philip D. Mannheim

Jan 1, 20001 citation

On the emergence of quantum mechanics, diffeomorphism invariance and the weak equivalence principle from deterministic Cartan-Randers systems

Ricardo Gallego Torromé

Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.

Feb 20, 20142 citations

On the equivalence principle in quantum theory

Cláus Lämmerzahl

arXiv:gr-qc/9605065General Relativity and GravitationSep 1, 1996100 citations

Quantum state reduction, and Newtonian twistor theory

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Quantum state reduction, and Newtonian twistor theory

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