Related papers: Classical and Quantum Probability
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place…
We study the probability assignment for the outcomes of time-extended measurements. We construct the class-operator that incorporates the information about a generic time-smeared quantity. These class-operators are employed for the…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
Hybrid classical-quantum systems are of interest in numerous fields, from quantum chemistry to quantum information science. A fully quantum effective description of them is straightforward to formulate when the classical subsystem is…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…
I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued…
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who…
In this paper we study stochastic dynamics which leaves quantum gravity equilibrium distribution invariant. We start theoretical study of this dynamics (earlier it was only used for Monte-Carlo simulation). Main new results concern the…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…