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We study a classical model of Helium atom in which, in addition to the Coulomb forces, the radiation reaction forces are taken into account. This modification brings in the model a new qualitative feature of a global character. Indeed, as…

In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…

In June 1925 Heisenberg arrived at Helgoland/Heligoland island to escape a fit of hay fever. He returned with a sketch of a strange theory of the micro-world, which we now call quantum mechanics. This essay attempts to present a look at…

Boltzmann's equation provides a microscopic model for the evolution of dilute classical gases. A fundamental problem in mathematical physics is to rigorously derive Boltzmann's equation starting from Newton's laws. In the 1970s, Oscar…

For a simple quantum system weakly interacting with the environment Wigner's 1932 formulation of quantum physics can be used to derive coupling to the environment using simple algebra. We show that the correct expressions, using coupling…

We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…

In contrast to the intuitively plausible assumption of local realism, entangled particles, even when isolated, are not allowed to possess definite properties in their own right, as quantitatively expressed by violations of Bell's…

Quantum electrodynamics (QED) is considered the most accurate theory in the history of science. However, this precision is based on a single experimental value: the anomalous magnetic moment of the electron (g-factor). An examination of the…

Classical electrodynamics including classical electromagnetic zero-point radiation leads to a ground state and resonant excited states for a charged particle in a Coulomb potential. These resonant states correspond to integer values of the…

The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point…

An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never…

The hydrogen atom in weak external fields is a very accurate model for the multiphoton excitation of ultrastable high angular momentum Rydberg states, a process which classical mechanics describes with astonishing precision. In this paper…

When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…

This is a review of Lee Smolin's "The Trouble with Physics". The main gist of the review is that the physics of the past three decades has been rich with new discoveries in a large number of domains. The Standard Model, while providing a…

Two typical entanglements will be shown to stand on opposite sides on the issue of \emph{instrumental realism}, the issue of whether (as for EPR in the original form or EPRB, Bohm's versions using spin) or not (as for GHZ) observables have…

150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical and…

The assumptions added by Bohr and concerning the Hilbert space (formed by all solutions of Schroedinger equation) changed fundamentally the original physical interpretation of these solutions proposed earlier by Schroedinger. This new…

This note presents an elementary proof of Hilbert's 1891 Ansatz of nesting for $M$-sextics, along the line of Riemann's Nachlass 1857 and a simple Harnack-style argument (1876). Our proof seems to have escaped the attention of Hilbert (and…

We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…

The purpose of this paper is to revisit the infinite Lie group theoretical framework of hydrodynamics developped by V. Arnold in 1966. First of all, we extend this approach from the Lie pseudogroup of volume preserving transformations to an…