Arithmetic of Plane Cremona Transformations and the Dimensions of Transfinite Heterotic String Space-Time

It is shown that the two sequences of characteristic dimensions of transfinite heterotic string space-time found by El Naschie can be remarkably well accounted for in terms of the arithmetic of self-conjugate homaloidal nets of plane algebraic curves of orders 3 to 20. A firm algebraic geometrical justification is thus given not only for all the relevant dimensions of the classical theory, but also for other two dimensions proposed by El Naschie, viz. the inverse of quantum gravity coupling constant (~42.36067977) and that of (one half of) fine structure constant (~68.54101967). A non-trivial coupling between the two El Naschie sequences is also revealed.Comment: 4 pages, no figures, accepted in Chaos, Solitons & Fractal

A Further Note on a Formal Relationship Between the Arithmetic of Homaloidal Nets and the Dimensions of Transfinite Space-Time

A sequence of integers generated by the number of conjugated pairs of homaloidal nets of plane algebraic curves of even order is found to provide an >exact< integer-valued match for El Naschie's primordial set of fractal dimensions characterizing transfinite heterotic string space-time.Comment: 3 pages, no figures, submitted to Chaos, Solitons & Fractal

The status and programs of the New Relativity Theory

A review of the most recent results of the New Relativity Theory is presented. These include a straightforward derivation of the Black Hole Entropy-Area relation and its $logarithmic$ corrections; the derivation of the string uncertainty relations and generalizations ; ; the relation between the four dimensional gravitational conformal anomaly and the fine structure constant; the role of Noncommutative Geometry, Negative Probabilities and Cantorian-Fractal spacetime in the Young's two-slit experiment. We then generalize the recent construction of the Quenched-Minisuperspace bosonic $p$-brane propagator in $D$ dimensions ($AACS$ [18]) to the full multidimensional case involving all $p$-branes : the construction of the Multidimensional-Particle propagator in Clifford spaces ($C$-spaces) associated with a nested family of $p$-loop histories living in a target $D$-dim background spacetime . We show how the effective $C$-space geometry is related to $extrinsic$ curvature of ordinary spacetime. The motion of rigid particles/branes is studied to explain the natural $emergence$ of classical spin. The relation among $C$-space geometry and ${\cal W}$, Finsler Geometry and (Braided) Quantum Groups is discussed. Some final remarks about the Riemannian long distance limit of $C$-space geometry are made.Comment: Tex file, 21 page

Non Commutativity, Fluctuations and Unification

We point out that in the non commutativity and breakdown of conventional spacetime at micro scales lies the seed to the unification of gravitation and electromagnetism.Comment: 10 pages, Te

Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge

Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know that the limit area of Sierpinski's carpet and volume of Menger's sponge are equal to zero. It is shown in this paper that recently introduced infinite and infinitesimal numbers allow us to use exact expressions instead of limits and to calculate exact infinitesimal values of areas and volumes at various points at infinity even if the chosen moment of the observation is infinitely faraway on the time axis from the starting point. It is interesting that traditional results that can be obtained without the usage of infinite and infinitesimal numbers can be produced just as finite approximations of the new ones

Chaotic quantization and the mass spectrum of fermions

In order to understand the parameters of the standard model of electroweak and strong interactions, one needs to embed the standard model into some larger theory that accounts for the observed values. This means some additional sector is needed that fixes and stabilizes the values of the fundamental constants of nature. We describe how such a sector can be constructed using the so-called chaotic quantization method applied to a system of coupled map lattices. We restrict ourselves in this short note on verifying how our model correctly yields the numerical values of Yukawa and gravitational coupling constants of a collection of heavy and light fermions using a simple principle, the local minimization of vacuum energy.Comment: 8 pages, 6 figures. To appear in Chaos, Solitons and Fractals (2008

The New Cosmos

We review the broad status of cosmology and discuss a model of fluctuational cosmology in which the universe is created in a phase transition like phenomenon mimicking inflation, and which further consistently explains latest observations like the ever expanding and accelerating feature.Comment: 10 pages, TeX,Inaugural address of the Physics Association of the National Institute of Technology, Warangal, Andhra Pradesh, Indi

Fantappie's group as an extension of special relativity on Cantorian space-time

In this paper we will analyze the Fantappie group and its properties in connection with Cantorian space-time. Our attention will be focused on the possibility of extending special relativity. The cosmological consequences of such extension appear relevant, since thanks to the Fantappie group, the model of the Big Bang and that of stationary state become compatible. In particular, if we abandon the idea of the existence of only one time gauge, since we do not see the whole Universe but only a projection, the two models become compatible. In the end we will see the effects of the projective fractal geometry also on the galactic and extra-galactic dynamics.Comment: 14 pages, accepted in Chaos, Solitons and Fractal

On the origin of the deflection of light

Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post--Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations, where the delay associated with the finite propagation speed is taken into account. Newtonian equations of motion, with post--Newtonian corrections, are often used to approximate the functional differential equations. In ``On the origin of quantum mechanics'', preprint, physics/0505181, May 2005, a simple atomic model based on a functional differential equation which reproduces the quantized Bohr atomic model was presented. The unique assumption was that the electrodynamic interaction has a finite propagation speed. In ``On the origin of the gravitational quantization: The Titius--Bode Law'', preprint, physics/0507072, Jul 2005, a simple gravitational model based on a functional differential equation which gives a gravitational quantification and an explanation of the modified Titius--Bode law is described. In ``On the origin of the anomalous precession of Mercury's perihelion'', preprint, physics/0510086, Oct 2005, an explanation of the anomalous precession of Mercury's perihelion is given in terms of a simple retarded potential, which, at first order, coincides with Gerber's potential of 1898, and which agrees with the author's previous works. In this paper, it is shown how the simple retarded potential presented in physics/0510086 also gives the correct value of the gravitational deflection of fast particles of General Relativity.Comment: 10 pages, 2 figure

Chaotic Dynamics of SU(2) Gauge Fields in the Presence of Static Charges

We have found in numerical simulations that the chaoticity of the classical hamiltonian lattice SU(2) gauge theory is reduced in the presence of static charges at the same total energy. The transition from strongly to weakly chaotic behavior is rather sudden at a critical charge strength.Comment: LaTeX, 10 pages, 2 figs as .PS in ym_figs.uu Submitted to Chaos, Solitons and Fractal