scholarly journals Born’s Rule for Arbitrary Cauchy Surfaces

2020 ◽  
pp. 61-69
Author(s):  
Matthias Lienert ◽  
Sören Petrat ◽  
Roderich Tumulka
Keyword(s):  
Born’S Rule

scholarly journals Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

2019 ◽  
Vol 1 (2) ◽  
pp. 130-150 ◽  
Author(s):  
Igor Ya. Doskoch ◽  
Margarita A. Man’ko
Keyword(s):  
Quantum Mechanics ◽  
Probability Distribution ◽  
Particle System ◽  
Superposition Principle ◽  
Quantum States ◽  
Particle State ◽  
Probability Representation ◽  
Tomographic Probability ◽  
Born’S Rule ◽  
System States

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

scholarly journals A Generic Model for Quantum Measurements

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 904 ◽  
Author(s):  
Alexia Auffèves ◽  
Philippe Grangier
Keyword(s):  
Quantum Mechanics ◽  
Quantum Measurements ◽  
Generic Model ◽  
Quantum Thermodynamics ◽  
Simple Set ◽  
Algebraic Quantum ◽  
Algebraic Quantum Theory ◽  
Born’S Rule ◽  
The Continuum

In previous articles, we presented a derivation of Born’s rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization—physically, the structure of QM results of an interplay between the quantized number of “modalities” accessible to a quantum system, and the continuum of “contexts” required to define these modalities. In the present article, we provide a unified picture of quantum measurements within our approach, and justify further the role of the system–context dichotomy, and of quantum interferences. We also discuss links with stochastic quantum thermodynamics, and with algebraic quantum theory.

Born's rule from classical random fields

2008 ◽  
Vol 372 (44) ◽  
pp. 6588-6592 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Random Fields ◽  
Born’S Rule

scholarly journals Bell Could Become the Copernicus of Probability

2016 ◽  
Vol 23 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Probability Model ◽  
Quantum Probability ◽  
Bell’S Inequality ◽  
Probability Models ◽  
Bell's Inequality ◽  
Mathematical Probability ◽  
Model Interpretation ◽  
Born’S Rule ◽  
Quantum Phenomena

Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.

Effects of detector size and position on a test of Born's rule using a three-slit experiment

2014 ◽  
Vol 90 (1) ◽  
Author(s):  
Etienne Gagnon ◽  
Christopher D. Brown ◽  
Amy L. Lytle
Keyword(s):  
Born’S Rule ◽  
Slit Experiment

scholarly journals Justifying Born’s Rule Pα = |Ψα|2 Using Deterministic Chaos, Decoherence, and the de Broglie-Bohm Quantum Theory

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1371
Author(s):  
Aurélien Drezet
Keyword(s):  
Quantum Theory ◽  
Kinetic Theory ◽  
Deterministic Chaos ◽  
Wave Theory ◽  
Fast Relaxation ◽  
Pilot Wave ◽  
Born’S Rule ◽  
H Theorem ◽  
Pilot Wave Theory ◽  
De Broglie Bohm

In this work, we derive Born’s rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to an environment made of “qubits” (i.e., Bohmian pointers), we show that entanglement together with deterministic chaos leads to a fast relaxation from any statistical distribution ρ(x) of finding a particle at point x to the Born probability law |Ψ(x)|2. Our model is discussed in the context of Boltzmann’s kinetic theory, and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

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