User blogs

Can Hawking's Godless TOE Run without Consciousness Internal and Fundamental to Penrose's Cyclic Universe? (by Graham P. Smetham): Abstract: Hawking-Mlodinow Theory of Everything (“HAM-TOE”) requires the assumption that mathematics has within its own nature the power to ‘breath fire’ into its own equations. But one must ask what actually guarantees that just because ‘the positive energy of matter can be balanced by the negative gravitational energy’ it must follow that the universe ‘will create itself from nothing.’ Hawking was the seventeenth occupant of the Lucasian Chair of Mathematics at Cambridge University. How remarkable then that, when the full implications of the HAM-TOE model are properly drawn out, the resulting theological-metaphysical model bears an uncanny resemblance to the theological perspective of the second occupant of the Lucasian Chair, Sir Isaac Newton, who suggested that space was the ‘sensorium of God.’ The universe uses the perceiving process within the dualistic world of experience in order to explore and experience its own nature. Human beings occupy a central place in this process because they are the universe’s agents (leaving aside the issue of beings elsewhere in the universe) in the process of universal self-exploration, self-perfection and self-transcendence. This indeed is a universal process of self-discovery which modern theologians may wish to call ‘God.’ http://prespacetime.com/index.php/pst/article/view/111

Equivalence of Maxwell’s Source-free Equations to the Time-dependent Schrödinger Equation for a Solitary Particle with Two polarizations and Hamiltonian |CP| (by Steven K. Kauffmann): Abstract: It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the Klein-Gordon and Dirac theories are reviewed: the solitary Dirac free particle has, inter alia, an invariant speed well in excess of c and staggering spontaneous Compton acceleration, but no pathologies whatsoever arise from the square-root relativistic Hamiltonian. Dirac’s key misapprehension of the underlying four-vector character of the time-dependent, configuration-representation Schrödinger equation for a solitary particle is laid bare, as is the invalidity of the standard “proof” that the nonrelativistic limit of the Dirac equation is the Pauli equation. Lorentz boosts from the particle rest frame point uniquely to the square-root Hamiltonian, but these don’t exist for a massless particle. Instead, Maxwell’s equations are dissected in spatial Fourier transform to separate nondynamical longitudinal from dynamical transverse field degrees of freedom. Upon their decoupling in the absence of sources, the transverse field components are seen to obey two identical time-dependent Schrödinger equations (owing to two linear polarizations), which have the massless free-particle diagonalized square-root Hamiltonian. Those fields are readily modified to conform to the attributes of solitary-photon wave functions. The wave functions’ relations to the potentials in radiation gauge are also worked out. The exercise is then repeated without the considerable benefit of the spatial Fourier transform. http://prespacetime.com/index.php/pst/article/view/107

Covariant Isolation from an Abelian Gauge Field of Its Nondynamical Potential, Which, When Fed Back, Can Transform into a “Confining Yukawa” (by Steven K. Kauffmann): Abstract: For Abelian gauge theory a properly relativistic gauge is developed by supplementing the Lorentz condition with causal determination of the time component of the four-vector potential by retarded Coulomb transformation of the charge density. This causal Lorentz gauge agrees with the Coulomb gauge for static charge densities, but allows the four-vector potential to have a longitudinal component that is determined by the time derivative of the four-vector potential’s time component. Just as in Coulomb gauge, the two transverse components of the four-vector potential are its sole dynamical part. The four-vector potential in this gauge covariantly separates into a dynamical transverse four-vector potential and a nondynamical timelike/longitudinal four-vector potential, where each of these two satisfies the Lorentz condition. In fact, analogous partition of the conserved four-current shows each to satisfy a Lorentz-condition Maxwell-equation system with its own conserved fourcurrent. Because of this complete separation, either of these four-vector potentials can be tinkered with without affecting its counterpart. Since it satisfies the Lorentz condition, the nondynamical four-vector potential times a constant with dimension of inverse length squared is itself a conserved four-current, and so can be fed back into its own source current, which transforms its time component into an extended Yukawa, with both exponentially decaying and exponentially growing components. The latter might be the mechanism of quark-gluon confinement: in non-Abelian color gauge theory the Yukawa mixture ratio ought to be tied to color, with palpable consequences for “colorful” hot quark-gluon plasmas. http://prespacetime.com/index.php/pst/article/view/108

Do Experiment and the Correspondence Principle Oblige Revision of Relativistic Quantum Theory? (by Steven K. Kauffmann): Abstract: Recent preliminary data gathered by the Fermilab MINOS Collaboration suggest with 95% confidence that the mass of the muon neutrino differs from that of its antineutrino partner, which contradicts the entrenched relativistic quantum theory notion that a free antiparticle is a negativeenergy free particle compelled to travel backwards in time. Also a discrepancy of about five standard deviations in the value of the proton charge radius recently obtained from muonic hydrogen versus that previously obtained from electronic hydrogen casts doubt on the calculation of the dominant relativistic QED contributions to the effects that are actually measured (e.g., the Lamb shift): these QED contributions dominate proton charge radius contributions less in muonic hydrogen than in electronic hydrogen. The negative-energy “free particles” of entrenched relativistic quantum theory are well-known features of the Klein-Gordon and Dirac equations, which are shown to have many other unphysical features as well. The correspondence principle for relativistic particles is incompatible with these two equations, produces no unphysical features and implies only positive energies for free particles, which eliminates the very basis of the entrenched notion of antiparticles, as well as of the CPT theorem. This principle thus requires antiparticles to arise from charge conjugation (or more generally CP) invariance, whose known breaking is naturally expected to produce mass splitting between particle and antiparticle, in consonance with the preliminary MINOS data. It also requires revamping of relativistic QED, which is in accord with the doubt cast on it by the proton charge radius results, and implies that QED is nonlocal, i.e. has no Hamiltonian density. http://prespacetime.com/index.php/pst/article/view/109

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. http://prespacetime.com/index.php/pst/article/view/103

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. http://prespacetime.com/index.php/pst/article/view/104

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. http://prespacetime.com/index.php/pst/article/view/105

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. http://prespacetime.com/index.php/pst/article/view/106