Related papers: On the Physical Problem of Spatial Dimensions: An …
Why does the physical 4-dimensional space have a 3 + 1 signature rather than a 4 + 0 or a 2 + 2 for its metric? We give a simple explanation based largely on a group-theoretic argument a la Wigner. Applied to flat spaces of higher…
It is commonly known that the steady-state model of the universe was proposed and championed in a series of influential papers around mid-twenty century by Fred Hoyle, Hermann Bondi, and Thomas Gold. In contrast it is little known that,…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
Within the framework of the hypothesis offered by authors about a complex-valued nature of physical quantities the stability of basic equations of the classical physics concerning complex-valued perturbations of parameters and boundary…
The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…
We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The…
Whether the space where we live is a globally orientable manifold $M_3$, and whether the local laws of physics require that $M_3$ be equipped with a canonical orientation, are among the unsettled questions in cosmology and quantum field…
Painlev\'e showed that there can be inconsistency and indeterminacy in solutions to the equations of motion of a 2D rigid body moving on a sufficiently rough surface. The study of Painlev\'e paradoxes in 3D has received far less attention.…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
Complex particle is a kind of bilocal particle having unexpected symmetry, which was proposed by the authour. In the present paper, we show that critical dimension of the complex particle in Minkowski spacetime is $D = 4$, while $D = 2, 4$…
We consider the Einstein-Maxwell equations in space-dimension $n$. We point out that the Lindblad-Rodnianski stability proof applies to those equations whatever the space-dimension $n\ge 3$. In even space-time dimension $n+1\ge 6$ we use…
All physical process are subject to some laws which determine with math accurately its time-space evolution. These laws are described, in the last analysis for the principle of causality. The physical space can be homogeneous or…
The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions greater than 3 is revisited, considering higher dimensional Euclidean spaces. Previous results which lead to different answers to this question…
We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vectors. The solutions of the Einstein field equations examined specifically for five different set of spacetime. We calculate the…
The 3+1 formulation of scalar-tensor theories of gravity (STT) is obtained in the physical (Jordan) frame departing from the 4+0 covariant field equations. Contrary to the common belief (folklore), the new system of ADM-like equations shows…
The vast majority of scientific community believes that P!=NP, with countless supporting arguments. The number of people who believe otherwise probably amounts to as few as those opposing the 2nd Law of Thermodynamics. But isn't nature…
We prove, in the case of hyperbolic 3-space, a couple of conjectures raised by J. J. Seidel in "On the volume of a hyperbolic simplex", Stud. Sci. Math. Hung. 21, 243-249, 1986. These conjectures concern expressing the volume of an ideal…
It is demonstrated in general that stable gravitational or electrostatic orbits are not possible for spatial dimensions n >=4, and in particular atoms cannot be bound by energy constraints in higher dimensions. Furthermore, angular momentum…
We revise the extended uncertainty relations for the Rindler and Friedmann spacetimes recently discussed by Dabrowski and Wagner in [9]. We reveal these results to be coordinate dependent expressions of the invariant uncertainty relations…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…