Related papers: Twelve-dimensions theory in electromagnetic dynami…
We summarize a recent work on the title subject, skipping the detailed calculations but introducing the basic points with enough detail. The theory considered is formulated in a preferred reference frame in a four-dimensional spacetime…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
The $E_8 \otimes E_8$ octonionic theory of unification suggests that our universe is six-dimensional and that the two extra dimensions are time-like. These time-like extra dimensions, in principle, offer an explanation of the quantum…
A global superalgebra with 32 supercharges and all possible central extensions is studied in order to extract some general properties of duality and hidden dimensions in a theory that treats $p$-branes democratically. The maximal number of…
The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
We consider a charged particle moving in the plane subject to electromagnetic potentials with non-vanishing radial limits. We analyse the classical and the quantum dynamics for large time in the case the angular part of the (limiting)…
A cross-dimensional Euclidian space ($\Omega$) is proposed for the state space of dimension varying (control) systems. It is shown that the topological structure of $\Omega$ is consistent with all $\mathbb{R}^n$, which are the state spaces…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
Exact string solutions are presented, where moduli fields are varying with time. They provide examples where a dynamical change of the topology of space is occurring. Some other solutions give cosmological examples where some dimensions are…
Action-at-a-distance electrodynamics - alternative approach to field theory - can be extended to cosmological models using conformal symmetry. An advantage of this is that the origin of arrow of time in electromagnetism can be attributed to…
We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future)…
We review a growing theoretical motivation and evidence that the number of dimensions actually reduces at high energies. This reduction can happen near the Planck scale, or much before, the dimensions that are reduced can be effective,…
We consider a class of two-dimensional solutions of the cold plasma equations compatible with a constant magnetic field and a constant electric field. For this class, under various assumptions about the electric field, we study the…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure, the spatial part of the dimensionless four-velocity and the particle density. Radially symmetric solutions of these equations are studied in two…