Related papers: Born's principle and Action-Reaction problem
We have shown that the Born rule $(\rho=|\psi|^{2})$ is inconsistent with Lorentz symmetry of the Salpeter equation (square root Klein-Gordon equation). So we find relativistic modification of the Born rule as…
The description of spontaneous symmetry breaking that underlies the connection between classically ordered objects in the thermodynamic limit and their individual quantum mechanical building blocks is one of the cornerstones of modern…
Radiation reaction (but, more generally, fluctuations and dissipation) occurs when a system interacts with a heat bath, a particular case being the interaction of an electron with the radiation field. We have developed a general theory for…
The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a…
We investigate deviations from Born's rule in quantum systems where the quantum-equilibrium hypothesis, $\rho \neq |\Psi|^2$, fails. Using the quantum-hydrodynamic framework, we show that transit-interference phenomena and intrinsic memory…
This paper presents arguments purporting to show that von Neumann's description of the measurement process in quantum mechanics has a modern day version in the decoherence approach. We claim that this approach and the de Broglie-Bohm theory…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour.
We discuss the dynamics of single particle by laying a hypothesis that the Hamilton's principle of stationary action is not exact. We then postulate that the deviation of the action with sufficiently short time interval from the stationary…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…
Basic problems of a microscopic theory of many body quantum systems and different aspects of a new approach which can help in solving them are discussed in detail. To this effect we make a critical study of the wave mechanics of two hard…
While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…
A fundamental issue in classical electrodynamics is represented by the search of the exact equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field - the so-called radiation-reaction…
Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm's proposal has caused it more…
Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not…
In this work we formulate an efficient method for the description of many-body localized systems in weak contact with thermal environments at temperature $T$. For this purpose we exploit the representation of the system in terms of…
The calculations of the elementary atom (the Coulomb bound state of elementary particles) interaction with the atom of matter, which are performed in the Born approximation, are reviewed. We first discuss the nonrelativistic approach and…