C.Gh. Buzea

Some physical implications of the gravitoelectromagnetic field in fractal space-time theory

It is shown that in terms of the fractal space–time theory the gravitoelectric potential is responsible for the quantisation of the planetary and binary galaxy motions. On a cosmic scale a homogeneous gravitomagnetic field allows not only an ordering of the Universe, but a ‘global’ redshift quantisation of galaxies as well.

Gravity and cantorian space-time

Abstract Within the weak field approximation, based on the hypothesis of the superconducting properties of cosmic dust and on fact that the gravitomagnetic field ‘grafts’ a kind of quasi crystal on ‘space’, and holds the so created structure by ‘pinning’ effect, it is argued that space-time may be indeed Cantorian as suggested by El Naschie. In this context the relation between gravitation and ‘composite fermionizing’ mechanism offers a new interpretation of the supplemental precession of the ecliptic tilt as a property of this space.

ε(∞) Cantorian space-time, polarization gravitational field and van der Waals-type forces

Abstract Some abilities of the SRT theory in studying the polarization gravitational field are analyzed. Thus, one builds a set of Maxwell-type equations for the polarization gravitational field and one studies the behaviour of a gravitomagnetic charge in such fields on a fractalic space-time. One finds that the interaction between the gravitomagnetic charge and the polarization gravitational field reduces to the Van der Waals gravitational type dipole–dipole interaction. From the study of GMHD wave, on a fractal cosmological background it results that the speeds in the planetary and galactic structures are discrete and the Cantorian structure is induced by means of a Tifft and Cocke Cantorian effect (at least for the galaxy pairs NGC 4294–NGC 4299, NGC 4085–NGC 4088). By an iterated map, one gets an object which may be identified with a cosmic fractal string, whose 2D projection corresponds to a cosmic string.

Cantorian E(∞) space-time, gravitation and superconductivity

Abstract In a linear gravitation model and on a space-time with a fractal structure, the repulsive component is associated to the gravitational Meissner effect, and the attractive one to the absence of this effect. In this context, by means of a complex time and of a two-dimensional Cantorian fractal time vortex lattice, one shows that there are two mechanisms which induce superconducting properties to matter: one by in-phase oscillations of the vortex lattice (specific to the attraction) and the other by “generation” of anyons (specific to the repulsion). Thus, the assumption of El Naschie that gravitation is generated by the interaction of dipoles (van der Waals-type forces) is confirmed.

El Naschie’s Cantorian space time, Toda lattices and Cooper–Agop pairs

Abstract We show that space time–matter connection works like a quasiautonomous structure by means of cnoidal oscillation modes. Identifying the cnoidal oscillation modes with one-dimensional Toda lattice, by its nonlinear mode works, on the acoustic branch of the phononic spectrum, generalized Cooper pairs (“Cooper–Agop pairs”) are induced. In such a context the fractal characteristic is given by redefining a coefficient in a Korteweg–de Vries (KdV) type equation, and the Cantorian structure are assimilated with two coupled oscillator like in the simple mechanical model of El Naschie’s e(∞) theory.

The Cantorian structure of the background magnetic field and high temperature superconductors

Abstract One builds the solution of GL equation in terms of the elliptic cn function of complex argument. The real part of the complex action, S =ℏ ln cn (u) , corresponds to the potential of a vortex lattice, and from here, through the elliptic function degeneration, to the vortex streets. Considering the vortex streets fixed on vacuum by a background magnetic field through pinning, from equating the current density to zero one determines the field structure: the mean value will be roughly equal to BC2, and its flux will be fractional. The fractional flux will be associated to quasi-particles obeying the ‘anyonic’ statistics. At low temperatures and high external magnetic field, the structure of background field will be of Cantorian type.

Some properties of the world crystal in fractal spacetime theory.

We prove that the wave-particle duality, inertia and the Heisenberg uncertainty relation are properties of a fractal spacetime, self-structured by a gravitomagnetic background field, in the world crystal.

Gravitational paramagnetism, diamagnetism and gravitational superconductivity

In the weak field approximation to the gravitational field equations, we study gravitational paramagnetism and diamagnetism, the gravitational Meissner effect and gravitational superconductivity. The spontaneous symmetry breaking corresponds to crossing from closed geodesics to open ones, and to the existence of a critical temperature in the frame of a gauge model at finite temperature. In this later case one can obtain expressions giving the dependence of several superconducting parameters on temperature.

Some implications of the gravitomagnetic field in fractal spacetime theory.

In a fractal spacetime, the absence of a gravitational Meissner effect is thought of as ordering space as a crystal, at both a microscopic and a macroscopic scale. A gravitational Meissner effect keeps a wormhole open and penetrable and, in the same context, a gravitational superconductor levitates in an external gravitomagnetic field, an external gravitomagnetic field induces quantised vortices in a gravitational superconductor and gravitational rotons in a superfluid, and the planetary systems are self-organised as superconducting structures.

The Time of Diffusion and Infinite Conductivity of High‐Tc Superconductors

In the composite fermion approach, extending in complex space the elliptic cn function (which is the perturbative solution of the Ginzburg-Landau equation in the strong coupling limit), we estimate the diffusion time of the superconductor charge carriers and we find that it diverges for particular values of the coherence length. We believe this mechanism may account for the infinite conductivity of high-temperature superconductors.