Separation of conditions as a prerequisite for quantum theory

Raedt, Hans De; Katsnelson, M. I.; Willsch, Dennis; Michielsen, Kristel

doi:10.1016/j.aop.2019.01.012

Cited by 8 publications

(15 citation statements)

References 60 publications

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“…Consider a learning system described by a coupled dynamics of trainable variables, , and non-trainable or hidden variables, . In "epistomological" kind of approaches [6,[14][15][16] one can identify the trainable variables with characteristics of a human mind whereas the hidden variables represent an external world, but this identification is not needed for our formal consideration which we will try to keep as general as possible. In context of artificial neural networks the trainable variables determine the weight matrix and bias vector, and the hidden variables represent the state vector of neurons [13].…”

Section: Stationary Entropy Productionmentioning

confidence: 99%

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Emergent Quantumness in Neural Networks

Katsnelson

Vanchurin

2021

Found Phys

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Section: Stationary Entropy Productionmentioning

confidence: 99%

“…Despite the obvious success of quantum mechanics in description of our physical world, its conceptual status is still a subject of hot debates, see Refs. [1][2][3][4][5], to name just a few contemporary books; more references can be found in the recent papers [6,7]. As a result, many so-called "no-go theorems" were constructed (e.g.…”

Section: Introductionmentioning

confidence: 99%

Emergent Quantumness in Neural Networks

Katsnelson

Vanchurin

2021

Found Phys

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“…Consider a learning system described by a coupled dynamics of trainable variables, q, and non-trainable or hidden variables, x. In "epistomological" kind of approaches [6,[14][15][16] one can identify the trainable variables with characteristics of a human mind whereas the hidden variables represent an external world, but this identification is not needed for our formal consideration which we will try to keep as general as possible. In context of artificial neural networks the trainable variables determine the weight matrix and bias vector, and the hidden variables represent the state vector of neurons [13].…”

Section: Stationary Entropy Productionmentioning

confidence: 99%

“…1 In some inexplicit way, this change of topology simplifies the description allowing to pass from the nonlinear Madelung equations to the linear Schrödinger equation adding extremely powerful machinery of vectors and operators in a Hilbert space. Phenomenologically, it can be justified by introducing a new principle of "separation of conditions" [6], logically independent from the logical inference approach. However, due to extreme importance of this point one needs to have a more detailed understanding of its origin.…”

Section: Introductionmentioning

confidence: 99%

Emergent Quantumness in Neural Networks

Katsnelson,

Vanchurin

2020

Preprint

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It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schrödinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neurons with an auxiliary subsystem, to show that the free energy must also be multivalued. By imposing the multivaluedness condition on the free energy we derive the Schrödinger equation with "Planck's constant" determined by the chemical potential of hidden variables. This shows that quantum mechanics provides a correct statistical description of the dynamics of the grand canonical ensemble of neural networks at the learning equilibrium. We also discuss implications of the results for machine learning, fundamental physics and, in a more speculative way, evolutionary biology.

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“…The deflection in spatially well-separated directions along the direction of the uniform magnetic field is commonly regarded as an experimental proof that the magnetic moment of the particles is quantized [ 1 , 2 , 4 , 5 ]. Labeling the distinct beams by a two-valued variable

and representing the beams by the corresponding state vectors forms the basis for the well-known quantum-theoretical description of the idealized SG experiment [ 4 , 5 , 6 , 7 , 19 , 20 ].…”

Section: Introductionmentioning

confidence: 99%

Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons

Raedt

Jin

Michielsen

2022

Entropy

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We present a comprehensive simulation study of the Newtonian and quantum model of a Stern–Gerlach experiment with cold neutrons. By solving Newton’s equation of motion and the time-dependent Pauli equation for a wide range of uniform magnetic field strengths, we scrutinize the role of the latter for drawing the conclusion that the magnetic moment of the neutron is quantized. We then demonstrate that a marginal modification of the Newtonian model suffices to construct, without invoking any concept of quantum theory, an event-based subquantum model that eliminates the shortcomings of the classical model and yields results that are in qualitative agreement with experiment and quantum theory. In this event-by-event model, the intrinsic angular momentum can take any value on the sphere, yet, for a sufficiently strong uniform magnetic field, the particle beam splits in two, exactly as in experiment and in concert with quantum theory.

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Separation of conditions as a prerequisite for quantum theory

Cited by 8 publications

References 60 publications

Emergent Quantumness in Neural Networks

Emergent Quantumness in Neural Networks

Emergent Quantumness in Neural Networks

Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons

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