Related papers: Extended probability theory and quantum mechanics …
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
We propose an approach to quantum theory based on the energetic causal sets, introduced in Cort\^{e}s and Smolin (2013). Fundamental processes are causal sets whose events carry momentum and energy, which are transmitted along causal links…
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
Quantum theory does not provide a unique definition for the joint probability of two non-commuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were…
We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…
The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of…
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as…
The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated…
In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…