Related papers: The relativistic reason for quantum probability am…
The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the…
We develop some formalism which is very general Feynman path integral in the case of the action which is allowed to be complex. The major point is that the effect of the imaginary part of the action (mainly) is to determine which solution…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representation of quantum mechanics. Example of entangled probability…
A relativistic equation for a neutral complex field as a probability amplitude is proposed. The continuity equation for the probability density is obtained. It is shown that there are two types of excitations of this field, which describe…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
This is a general description of a probabilistic formalism of mechanics, i.e., an extension of the Newtonian mechanics principles to the systems undergoing random motion. From an analysis of the induction procedure from experimental data to…
In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
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…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
Present quantum theory, which is statistical in nature, does not predict joint probability distribution of position and momentum because they are noncommuting. We propose a deterministic quantum theory which predicts a joint probability…
We revisit an argument proposed by Hardy \cite{Hardy-1} concerning local realistic theories, but in terms of the motion of the probability fluid and its current within standard quantum mechanic. We emphasize surprising properties of the…
This paper explores the issue of the unification of three languages of physics, the geometric language of forces, geometric language of fields or 4-dimensional space-time, and probabilistic language of quantum mechanics. On the one hand,…
The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…