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Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…
Nonlinear wave propagation in large extra spatial dimensions (on and above $d=2$) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant…
The non zero value of Planck constant $h$ underlies the emergence of several inequalities that must be satisfied in the quantum realm, the most prominent one being Heisenberg Uncertainty Principle. Among these inequalities, Bekenstein bound…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
More general canonical ensemble which gives rise the generalized statistics or $q$-deformed statistics can represent the realistic scenario than the ideal one, with proper parameter sets involved. We study the Planck's law of blackbody…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the…
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of…
This letter explores how a reinterpretation of the generalized uncertainty principle as an effective variation of Planck's constant provides a physical explanation for a number of fundamental quantities and couplings. In this context, a…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Black holes are more than just odd-looking curiosities in gravity theory. They uniquely intertwine the basic principles of General Relativity with those of Quantum Theory. Just by demanding that they nevertheless obey acceptable laws of…
A brief overview of the discovery that macroscopic black holes are thermodynamical systems is presented. They satisfy the laws of thermodynamics and are associated with a temperature and an entropy equal to one quarter of their horizon area…
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 can be seen as a special case when the density matrix is restricted to be…
We generalize, improve and unify theorems of Rumin, and Maassen--Uffink about classical entropies associated to quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different…
We derive the force of the electromagnetic radiation on material objects by a direct application of the Lorentz law of classical electro-dynamics. The derivation is straightforward in the case of solid metals and solid dielectrics, where…
In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is…