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Related papers: Born Rule and Logical Inference in Quantum Mechani…

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According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…

Quantum Physics · Physics 2024-08-19 S. S. Afonin

We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…

Quantum Physics · Physics 2026-05-01 Keano De Vos , Gert de Cooman , Alexander Erreygers , Jasper De Bock

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would…

Quantum Physics · Physics 2023-03-10 Andrea Oldofredi , Gabriele Carcassi , Christine A. Aidala

Quantum mechanics predicts many surprising phenomena, including the two-slit interference of electrons. It has often been claimed that these phenomena cannot be understood in classical terms. But the meaning of "classical" is often not…

History and Philosophy of Physics · Physics 2018-02-07 Tim Maudlin

It is argued that the nature of probability is essentially informational rather than physical and that quantum mechanical predictions should be viewed as logical inferences made on the basis of the information content of a given…

Quantum Physics · Physics 2011-07-04 Mohammad Mehrafarin

The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…

Quantum Physics · Physics 2021-10-19 Nikodem Popławski , Michael Del Grosso

The interpretation of the squared norm as probability and the apparent stochastic nature of observation in quantum mechanics are derived from the strong law of large numbers and the algebraic properties of infinite sequences of simultaneous…

Quantum Physics · Physics 2007-05-23 Robert A. Van Wesep

The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the…

Quantum Physics · Physics 2007-05-23 Mark A. Rubin

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual…

Quantum Physics · Physics 2015-05-07 Alexia Auffèves , Philippe Grangier

Quantum Mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and…

Quantum Physics · Physics 2009-11-13 A. F. Kracklauer

The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…

Quantum Physics · Physics 2009-11-10 Andrei Khrennikov

I. The arena of quantum mechanics and quantum field theory is the abstract, unobserved and unobservable, M-dimensional formal Hilbert space [not equal to] spacetime. II. The arena of observations and, more generally, of all events (i.e.…

General Physics · Physics 2023-10-05 Johan Hansson

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…

Quantum Physics · Physics 2018-03-06 David Ellerman

Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…

Artificial Intelligence · Computer Science 2007-05-23 Joseph Y. Halpern , Riccardo Pucella

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

Probability · Mathematics 2025-05-01 Jason Swanson

General relativity required the abandonment of Euclidean geometry. Here we show that quantum theory requires the abandonment of classical logic. We show that the Hilbert space representation of quantum theory is logically inevitable. There…

Quantum Physics · Physics 2021-11-23 Lars M. Johansen

Interpretation is not the only way to explain a theory's success, form and features, and nor is it the only way to solve problems we see with a theory. This can also be done by giving a reductive explanation of the theory, by reference to a…

History and Philosophy of Physics · Physics 2025-12-17 Karen Crowther

Quantum Mechanics, almost 80 years after its arrival, is a well established and experimentally not falsified theory. It has predicted and explained a whole series of natural phenomena of a very delicate nature. But its interpretation has…

Quantum Physics · Physics 2009-05-30 Dimitris Lazarou

A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…

Quantum Physics · Physics 2010-12-09 Natalia Gorobey , Alexander Lukyanenko , Inna Lukyanenko

Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics.…

Quantum Physics · Physics 2021-04-23 Jianhao M. Yang