Related papers: Probability in relativistic quantum mechanics and …
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the…
Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian…
In relativistic quantum theory, one sometimes considers integral equations for a wave function $\psi(x_1,x_2)$ depending on two space-time points for two particles. A serious issue with such equations is that, typically, the spatial…
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
In non-relativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
We propose that probability in quantum theory, like energy in general relativity, acquires a fundamentally quasilocal character in curved spacetime. Interpreting Hermiticity as the symmetry associated with inner-product conservation, we…
The quantum mechanics status of the probability vector current density has long seemed to be marginal. On one hand no systematic prescription for its construction is provided, and the special examples of it that are obtained for particular…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
In this paper, a new conserved current for Klein-Gordon equation is derived. It is shown, for $1+1$-dimensions, the first component of this current is non-negative and reduces to $|\phi|^2$ in non-relativistic limit. Therefore, it can be…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
The positivity of the energy in relativistic quantum mechanics implies that wave functions can be continued analytically to the forward tube T in complex spacetime. For Klein-Gordon particles, we interpret T as an extended (8D) classical…
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears…
A simple relativistic quantum hidden-variable theory of particle trajectories, similar to the Bohm theory but without nonlocal forces between the particles, is proposed. To provide compatibility with statistical predictions of quantum…
We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a…
If one assumes there is probability of perception in quantum mechanics, then unitarity dictates that it must have the coefficient squared form, in agreement with experiment.