M. Agop

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.

Superconductivity by means of the subquantum medium coherence

In the hydrodynamic formulation of the scale relativity theory one shows that a stable vortices distribution of bipolaron type induces superconducting pairs by means of the quantum potential. Then, usual mechanisms (as, for example, the exchange interaction used in the bipolaron theory) are reduced to the coherence on the subquantum medium, the superconducting pairs resulting as a one-dimensional projection of a fractal. The temperature dependences of the superconducting parameters (coherence length, critical speed, pair breaking time, carriers concentration, penetration depth, critical field, critical current) and the concordance with the experimental data and other theories are analyzed.

The time dependent Ginzburg–Landau equation in fractal space–time

Abstract We use the hydrodynamic formulation of Scale Relativity Theory to analyze the TDGL equation. As a result, London equations come naturally from the system, when equating to zero the real velocity, the imaginary one turns real, the superconducting fluid act as a subquantum medium energy accumulator, the vector potential, the real and the imaginary velocity are all written in terms of the elliptic function. When solving the resulted system by means of WKBJ method, we get tunneling and quantization. In other words, scale transformation laws produce, on the motion equation of particles governed by the TDGL equation, under some peculiar assumptions, effects which are analogous to those of a “macroscopic quantum mechanics”.

Hydrodynamic formulation of scale relativity theory and unified superconductivity by means of a fractal string

Abstract In the frame of hydrodynamic formulation of scale relativity theory for a coherent quantum fluid, one shows that some parameters of high-temperature superconductors (critical field, critical current, pair breaking time, fluxoid, state density, gap energy, etc.) come from the non-differentiability of the quantum space–time. Then, the vortex streets (responsible for superconductivity by means of the in-phase lattice oscillations mechanism) and the anyons (responsible for superconductivity by means of the composite fermions mechanism) may be considered as two-dimensional projections of a higher-dimensional fractal string, which implies the existence of just one mechanism inducing type II superconductivity.

Cantorian ε(∞) space-time, a hydrodynamical model and unified superconductivity

Abstract We prove that the fractal space-time interpretation of Nelson’s stochastic quantum mechanics may be put into a one-to-one correspondence to the hydrodynamic model of quantum mechanics. Some implications of this correspondence are analyzed: Navier–Stokes type equations, uncertainty relation and type II superconductivity by means of a higher-dimensional fractal string. The two-dimensional (2D) projections of the higher fractal string corresponds to the anyons and 1D projections to the Cooper pair. The Cantorian-fractal structures occur, either by assimilating the Cooper pair with a two coupled oscillators (a simple mechanical model for e (∞) theory), or by El Naschie’s filling factor ν ≡ φ 3 =0.23606 (Cantorian-fractal quantum Hall effect).

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.

Local gravitoelectromagnetic effects on a superconductor

Abstract Maxwell’s and London’s generalized equations, generalized Meissner effect and gravitational shielding in an electromagnetic field are obtained. In such a context, we show that a neutral particle beam in an infinitely thin superconducting cylinder placed in the Earth’s gravitoelectric field is focused, and that the penetration depth increases with the pulsation of the electromagnetic field.