More Possible Games in Town: Part 1

Gravitation in a Timeless Quantum Space (by Davide Fiscaletti, Amrit S. Sorli): Abstract: The fundamental arena of the universe is a timeless space that has a granular structure at the Planck scale and clock/time provides only the numerical order of material changes inside this arena. Stellar objects and particles move into space only and not into a temporal dimension that flows on its own. Granularity of space allows speculation that space has a density which is in relation with the amount of matter in a given region. Two fundamental quantities can be introduced in order to describe gravitational interaction: density of universal cosmic mass and density of empty space. The density of universal cosmic mass increases with the increasing of the amount of matter present in a given region. Density of empty space decreases with the increasing of the amount of matter in a given region. Density of empty space provides a quantitative measure of its geometrical structure.

Less dense space is more curved and very dense space is more flat. Physical objects have tendency to move into direction of higher curvature/lower density of space. Gravitational interaction mass-space-mass is immediate: presence of a mass causes change of density of empty space, change of density of empty space causes gravitational motion. A mass acts on another mass indirectly via the change of density of empty space. Gravity is an immediate physical phenomenon carried directly by the quantum space: no motion of particles or waves in space is needed to transmit gravitational interaction from one to another material object, and numerical order of gravity is zero. Finally, a timeless quantum-gravity space theory is suggested which is based on density of universal cosmic mass, density of empty space and the perspectives of this theory as regards the picture of the gravitational space are analyzed.

Elliptic Curves and Hyperdeterminants in Quantum Gravity (by Philip E. Gibbs): Abstract: Hyperdeterminants are generalizations of determinants from matrices to multi-dimensional hypermatrices. They were discovered in the 19th century by Arthur Cayley but were largely ignored over a period of 100 years before once again being recognised as important in algebraic geometry, physics and number theory. It is shown that a cubic elliptic curve whose Mordell-Weil group contains a Z2 x Z2 x Z subgroup can be transformed into the degree four hyperdeterminant on a 2x2x2 hypermatrix comprising its variables and coefficients. Furthermore, a multilinear problem defined on a 2x2x2x2 hypermatrix of coefficients can be reduced to a quartic elliptic curve whose J-invariant is expressed in terms of the hypermatrix and related invariants including the degree 24 hyperdeterminant. These connections between elliptic curves and hyperdeterminants may have applications in other areas including physics.

Nonlinear Theory of Elementary Particles: IV. The Intermediate Bosons & Mass Generation Theory (by Alexander G. Kyriakos): Abstract: The purpose of this section of nonlinear theory of elementary particles (NTEP) is to describe the mechanism of generation of massive elementary particles. The theory, presented below, indicates the possibility of the particle mass production by means of massive intermediate boson, but without the presence of Higgs's boson. It is shown that nonlinearity is critical for the appearance of particles’ masses.

Getting Path Integrals Physically and Technically Right (by Steven K. Kauffmann): Abstract: Feynman’s Lagrangian path integral was an outgrowth of Dirac’s vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton’s first equation of motion, so their use contravenes the uncertainty principle, but they are relevant to semiclassical approximations and relatedly to the ubiquitous case that the Hamiltonian is quadratic in the canonical momenta, which accounts for the Lagrangian path integral’s “success”. Feynman also invented the Hamiltonian phase-space path integral, which is fully compatible with the uncertainty principle. We recast this as an ordinary functional integral by changing direct integration over subpaths constrained to all have the same two endpoints into an equivalent integration over those subpaths’ unconstrained second derivatives. Function expansion with generalized Legendre polynomials of time then enables the functional integral to be unambiguously evaluated through first order in the elapsed time, yielding the Schrödinger equation with a unique quantization of the classical Hamiltonian. Widespread disbelief in that uniqueness stemmed from the mistaken notion that no subpath can have its two endpoints arbitrarily far separated when its nonzero elapsed time is made arbitrarily short. We also obtain the quantum amplitude for any specified configuration or momentum path, which turns out to be an ordinary functional integral over, respectively, all momentum or all configuration paths. The first of these results is directly compared with Feynman’s mistaken Lagrangian-action hypothesis for such a configuration path amplitude, with special heed to the case that the Hamiltonian is quadratic in the canonical momenta.