相关论文: String Theory: a mere prelude to non-Archimedean S…

While geometry with transcendental curves, like the Quadratrix of Hippias and the Spiral of Archimedes, played a significant role in our modern developments of geometry and algebra. The investigation has fallen off in the modern era despite…

We give a brief overview of the nature of spacetime emerging from string theory. This is radically different from the familiar spacetime of Einstein's relativity. At a perturbative level, the spacetime metric appears as ``coupling…

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest themselves in Feynman diagrams, spin networks,…

Nottale's special scale-relativity principle was proposed earlier by the author as a plausible geometrical origin to string theory and extended objects. Scale Relativity is to scales what motion Relativity is to velocities. The universal,…

In this work, we review the results of Refs [1]-[5] dedicated to the description of the early Universe cosmology induced by quantum and thermal effects in superstring theories. The present evolution of the Universe is described very…

Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…

We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…

In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…

In this article, the evolution of the ideas about the fourth spatial dimension is presented, starting from those which come out within classical Euclidean geometry and going through those arose in the framework of non-Euclidean geometries,…

Recent astronomical observations indicate that the universe is accelerating. We argue that generic quintessence models that accommodate the present day acceleration tend to accelerate eternally. As a consequence the resulting spacetimes…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

The string theory introduced in early 1971 by Ramond, Neveu, and myself has two-dimensional world-sheet supersymmetry. This theory, developed at about the same time that Golfand and Likhtman constructed the four-dimensional super-Poincar\'e…

String theory suggests modifications of our spacetime such as extra dimensions and the existence of a mininal length scale. In models with addidional dimensions, the Planck scale can be lowered to values accessible by future colliders.…

The model of the Universe in this paper uses equations of the unperturbed Keplerian motion. They have been updated, complementied and generalized when the solution of these equations is the characteristic function of a random value from the…

It is shown that the string concept results naturally from considerations of gravitation. This paper describes a derivation of linearized general relativity based upon the hypotheses of special covariance and the existence of a…

At the end of the 19th century light was regarded as an electromagnetic wave propagating in a material medium called ether. The speed c appearing in Maxwell's wave equations was the speed of light with respect to the ether. Therefore,…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…

This essay discusses the development of key geometric ideas in the 19th century which led to the formulation of the concept of an abstract manifold (which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl in 1913. This…

By considering a new form of dimensional reduction for noncommutative field theory, we show that the signature of spacetime may be changed. In particular, it is demonstrated that a temporal dimension can emerge from a purely Euclidean…

The past year has seen enormous progress in string theory. It has become clear that all of the different string theories are different limits of a single theory. Moreover, in certain limits, one obtains a new, eleven-dimensional structure…