A river model of space

Within the theory of general relativity gravitational phenomena are usually attributed to the curvature of four-dimensional spacetime. In this context we are often confronted with the question of how the concept of ordinary physical three-dimensional space fits into this picture. In this work we present a simple and intuitive model of space for both the Schwarzschild spacetime and the de Sitter spacetime in which physical space is defined as a specified set of freely moving reference particles. Using a combination of orthonormal basis fields and the usual formalism in a coordinate basis we calculate the physical velocity field of these reference particles. Thus we obtain a vivid description of space in which space behaves like a river flowing radially toward the singularity in the Schwarzschild spacetime and radially toward infinity in the de Sitter spacetime. We also consider the effect of the river of space upon light rays and material particles and show that the river model of space provides an intuitive explanation for the behavior of light and particles at and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure

Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.Comment: 12 pages, 5 figure

Quantum mechanics: Myths and facts

A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in Found. Phy

Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures

Spatial and/or temporal propagation of light waves in periodic optical structures offers a rather unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.Comment: review article (invited), 14 pages, 7 figures, 105 reference