Related papers: The Stochastic-Quantum Theorem
The theories of stochastic quantum mechanics and stochastic electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further previous work regarding the connection…
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,…
We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not…
The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed).…
In this paper for the first time, we construct quantum analogs starting from classical stochastic processes, by replacing random which path decisions with superpositions of all paths. This procedure typically leads to non-unitary quantum…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive…
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the Cameron-Martin-Girsanov theorem. More precisely, the notion…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…