Related papers: String Theory: a mere prelude to non-Archimedean S…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…

We consider string theory in a time dependent orbifold with a null singularity. The singularity separates a contracting universe from an expanding universe, thus constituting a big crunch followed by a big bang. We quantize the theory both…

After briefly reviewing basic concepts of perturbative string theory, we explain in simple terms some of the new findings that created excitement among the string physicists. These developments include non-perturbative dualities and a…

We discuss the obstacles for defining a set of observable quantities analogous to an S-matrix which are needed to formulate string theory in an accelerating universe. We show that the quintessence models with the equations of state $-1 < w…

A generalisation of Riemannian geometry is considered, based exclusively on the minimal assumptions that the line element $ds$ is a regular function of position and direction and that the distance of every point from itself is equal to…

In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…

Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…

We illustrate the various ways in which the algebraic framework of noncommutative geometry naturally captures the short-distance spacetime properties of string theory. We describe the noncommutative spacetime constructed from a vertex…

The advent of the 1905 theory of relativity is rightly considered as a breakthrough moment in the history of physics; in particular. it is widely accepted that it brought a new conception of space and time. The purpose of this work is to…

We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…

We consider new cosmological solutions with a collapsing, an intermediate and an expanding phase. The boundary between the expanding (collapsing) phase and the intermediate phase is seen by comoving observers as a cosmological past (future)…

On a scientific meta-level, it is discussed how an overall understanding of the physical universe can be built on the basis of well-proven theories, observations, and recent experiments. In the light of almost a century of struggle to make…

It is argued that string theory predicts unified field theory rather than general relativity coupled to matter fields. In unified field theory all the objects are geometrical, for strings the Kalb-Ramond matter field is identical to the…

As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean…

This contribution, aimed mostly at experimental particle physicists, reviews some of the main ideas and results of String Theory in a non-technical language. It originates from the talks presented by the authors at the Electro-Weak session…

One of the most distinguished features of our algebraic geometrical, pencil concept of space-time is the fact that spatial dimensions and time stand, as far as their intrinsic structure is concerned, on completely different footings: the…

At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…

Almost half a century before Einstein expounded his general theory of relativity, the English mathematician William Kingdon Clifford argued that space might not be Euclidean and proposed that matter is nothing but a small distortion in that…

In this article, we present several apparent paradoxes of special relativity and their respective solutions. These paradoxes have appeared since the advent of relativity in 1905, and in fact they are never paradoxes. From a didactic point…