Related papers: Wave Mechanics and the Fifth Dimension
Plane gravitational waves can admit a sixth `screw' isometry beyond the usual five. The same is true of plane electromagnetic waves. From the point of view of integrable systems, a sixth isometry would appear to over-constrain particle…
A conformally invariant model of two interacting massless particles in Minkowski space was proposed by Casalbuoni and Gomis [1]. We generalize this model to the case of de Sitter space from the perspective of geodesic distance, in such a…
Einstein theory can be embedded in Kaluza-Klein theory, and in particular all 4D vacuum solutions can be embedded in 5D (pure) canonical space where spacetime is independent of the extra coordinate. The uniqueness of 5D canonical space is…
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
We explore the hydrodynamic analogues of quantum wave-particle duality in the context of a bouncing droplet system which we model in such a way as to promote comparisons to the de Broglie-Bohm interpretation of quantum mechanics. Through…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by…
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…
An exact, ray-based general treatment is shown to hold for any kind of monochromatic wave feature - including diffraction and interference - described by Helmholtz-like equations, under the coupling action of a dispersive function (which we…
A characterization of causal automorphism on Minkowski spacetime is given by use of wave equation. The result shows that causal analysis of spacetime may be replaced by studies of wave equation on manifolds.
Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the…
Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel's theorem. However, such methods are difficult to carry over to non-flat situations (such as wave equations with…
The dynamical triangulations approach to quantum gravity is investigated in detail for the first time in five dimensions. In this case, the most general action that is linear in components of the f-vector has three terms. It was suspected…
We define the de Broglie-Bohm (dBB) weak interpretation as the dBB interpretation restricted to particles in unbound states whose wave function is defined in the three-dimensional physical space, and the dBB strong interpretation as the…
We study the effect of compact extra dimensions on the gravitational wave luminosity and waveform. We consider a toy model, with a compactified fifth dimension, and matter confined on a brane. We work in the context of five dimensional…
The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…