Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig

Quantum mechanics without quanta

In this paper, I argue that light is a continuous classical electromagnetic wave, while the observed so-called quantum nature of the interaction of light with matter is connected to the discrete (atomic) structure of matter and to the specific nature of the light-atom interaction. From this point of view, the Born rule for light is derived, and the double-slit experiment is analysed in detail. I show that the double-slit experiment can be explained without using the concept of a "photon", solely on the basis of classical electrodynamics. I show that within this framework, the Heisenberg uncertainty principle for a "photon" has a simple physical meaning not related to the fundamental limitations in accuracy of the simultaneous measurement of position and momentum or time and energy. I argue also that we can avoid the paradoxes connected with the wave-particle duality of the electron if we consider some classical wave field - an "electron wave" - instead of electrons as the particles and consider the wave equations (Dirac, Klein-Gordon, Pauli and Schrodinger) as the field equations similar to Maxwell equations for the electromagnetic field. It is shown that such an electron field must have an electric charge, an intrinsic angular momentum and an intrinsic magnetic moment continuously distributed in the space. It is shown that from this perspective, the double-slit experiment for "electrons", the Born rule, the Heisenberg uncertainty principle and the Compton effect all have a simple explanation within classical field theory. The proposed perspective allows consideration of quantum mechanics not as a theory of particles but as a classical field theory similar to Maxwell electrodynamics.Comment: 61 pages, 3 figures, Quantum Studies: Mathematics and Foundations, 201

Geometrical aspects and connections of the energy-temperature fluctuation relation

Recently, we have derived a generalization of the known canonical fluctuation relation $k_{B}C=\beta^{2}$ between heat capacity $C$ and energy fluctuations, which can account for the existence of macrostates with negative heat capacities $C<0$. In this work, we presented a panoramic overview of direct implications and connections of this fluctuation theorem with other developments of statistical mechanics, such as the extension of canonical Monte Carlo methods, the geometric formulations of fluctuation theory and the relevance of a geometric extension of the Gibbs canonical ensemble that has been recently proposed in the literature.Comment: Version accepted for publication in J. Phys. A: Math and The

Thermodynamic fluctuation relation for temperature and energy

The present work extends the well-known thermodynamic relation $C=\beta ^{2}< \delta {E^{2}}>$ for the canonical ensemble. We start from the general situation of the thermodynamic equilibrium between a large but finite system of interest and a generalized thermostat, which we define in the course of the paper. The resulting identity $=1+< \delta {E^{2}}> \partial ^{2}S(E) /\partial {E^{2}}$ can account for thermodynamic states with a negative heat capacity $C<0$; at the same time, it represents a thermodynamic fluctuation relation that imposes some restrictions on the determination of the microcanonical caloric curve $\beta (E) =\partial S(E) /\partial E$. Finally, we comment briefly on the implications of the present result for the development of new Monte Carlo methods and an apparent analogy with quantum mechanics.Comment: Version accepted for publication in J. Phys. A: Math and The

Event-Enhanced Quantum Theory And Piecewise Deterministic Dynamics

The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment induced master equations are stressed. Questions: what is classical, what is time, and what are observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes'noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.Comment: 10 pages, twocolumn, REVTE

Are there photons in fact?

There are two opposing points of view on the nature of light: the first one manifests the wave-particle duality as a fundamental property of the nature; the second one claims that photons do not exist and the light is a continuous classical wave, while the so-called “quantum” properties of this field appear only as a result of its interaction with matter. In this paper we show that many quantum phenomena which are traditionally described by quantum electrodynamics can be described if light is considered within the limits of classical electrodynamics without quantization of radiation. These phenomena include the double-slit experiment, the photoelectric effect, the Compton effect, the Hanbury Brown and Twiss effect, the so-called multiphoton ionisation of atoms, etc. We show that this point of view allows also explaining the “wave-particle duality” of light in Wiener experiments with standing waves. We show that the Born rule for light can easily be derived from Fermi’s golden rule as an approximation for low-intense light or for short exposure time. We show that the Heisenberg uncertainty principle for “photons” has a simple classical sense and cannot be considered as a fundamental limitation of accuracy of simultaneous measurements of position and momentum or time and energy. We conclude that the concept of a “photon” is superfluous in explanation of light-matter interactions. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only