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Related papers: The statistical origins of quantum mechanics

200 papers

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…

Quantum Physics · Physics 2009-11-07 Michael J. W. Hall , Marcel Reginatto

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…

Quantum Physics · Physics 2015-06-03 Petr Hajicek

A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…

Quantum Physics · Physics 2014-12-23 U. Klein

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…

Quantum Physics · Physics 2009-11-13 L. Skala , V. Kapsa

We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…

Quantum Physics · Physics 2007-05-23 Eijiro Sakai

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Leon Brenig

The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…

Quantum Physics · Physics 2012-07-10 Inge S. Helland

We present in this continuation paper a new axiomatic derivation of the Schr\"odinger equation from three basic postulates. This new derivation sheds some light on the thermodynamic character of the quantum formalism. We also show the…

Quantum Physics · Physics 2007-05-23 L. S. F. Olavo

We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…

Mathematical Physics · Physics 2012-01-31 Marco Frasca

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…

Quantum Physics · Physics 2015-05-13 Ariel Caticha

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

Quantum Physics · Physics 2007-05-23 Léon Brenig

We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum…

Quantum Physics · Physics 2007-05-23 Andrei Khrennikov

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…

Quantum Physics · Physics 2007-05-23 L. Skala , V. Kapsa

In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…

Quantum Physics · Physics 2024-06-19 G. B. Lesovik

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…

Quantum Physics · Physics 2018-05-09 C. Wetterich

It is well known, that the causal Schr\"odinger evolution of a quantum state is not compatible with the reduction postulate, even when decoherence is taken into account. The violation of the causal evolution, introduced by the standard…

Quantum Physics · Physics 2007-05-23 Rodolfo Gambini

A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…

Quantum Physics · Physics 2012-07-10 Inge S. Helland

Quantum mechanics is based on a series of postulates which lead to a very good description of the microphysical realm but which have, up to now, not been derived from first principles. In the present work, we suggest such a derivation in…

Quantum Physics · Physics 2011-07-13 Laurent Nottale , Marie-Noëlle Célérier

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…

Quantum Physics · Physics 2009-11-11 Stephan I. Tzenov

One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…

Optimization and Control · Mathematics 2009-02-11 Xiaofei Huang