Related papers: Quaternion Time, Mass, and Particle Velocity
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
We consider relativistic versions of the Ehrenfest relation between the expectation values of the coordinate and momentum of a quantum particle in free space: $d\langle {\bf r} \rangle /dt = \langle {\bf p} \rangle/m$. We find that the…
A conjecture on the origin of elementary particle masses is discussed, based on the micro-universe and quantum state reduction concepts. The reduction of the quantum state of a real particle is understood to take place objectively; in every…
Following an argument by Kirzhnits we rederive an exact expression for the energy loss of a fast charged particle in a relativistic plasma using the quantum field theoretical language. We compare this result to perturbative calculations of…
It is shown that for a specific choice of a particular solution of the relativistic wave equation, it falls into the Helmholtz equation and the Klein -Gordon equation. In this case, the squares of the rest masses of the particle with the…
We consider a two-time (characterized by distinct speeds of causality) and three-space-dimensional Minkowski space and derive relativistic coordinate and velocity transformation formulas and expressions for a new effective speed limit.…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
We discuss the definition of velocity as dE/dp, where E,p are the energy and momentum of a particle, in Doubly Special Relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in…
In a foregoing paper, gravity has been interpreted as the pressure force exerted on matter at the scale of elementary particles by a perfect fluid. Under the condition that Newtonian gravity must be recovered in the incompressible case, a…
The starting point of this work is the axiomatic existence of a smallest measurable interval, viz. the Planck time $t_P$, set by quantum fluctuations in the vacuum metric tensor. By the Relativity Principle, the same limit must then apply…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…
Recent advances in laser technology enable to follow electronic motion at its natural time-scale with ultrafast pulses, leading the way towards atto- and femtosecond spectroscopic experiments of unprecedented resolution. Understanding of…
In this paper, we demonstrate novel relationships between quantum mechanics and the electromagnetic wave equation. In our approach, an invariant interference-dependent electromagnetic quantity, which we call "quantum rest mass", replaces…
Normally we quantize along the space dimensions but treat time classically. But from relativity we expect a high level of symmetry between time and space. What happens if we quantize time using the same rules we use to quantize space? To do…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
Through the analysis of the definition of the duration of proper time of a particle given by the length of its world line, we show that there is no transitivity of the coordinate time function derived from the definition, so there exists an…
We investigate the nonextensivity and the q-distribution of a relativistic gas under an external electromagnetic field. We derive a formula expression of the nonextensive parameter q based on the relativistic generalized Boltzmann equation,…