Related papers: New crisis in geometry?
Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a missing cardinal link to unification of all physical interactions. Problems of the…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
The algebras of non-relativistic and of classical mechanics are unstable algebraic structures. Their deformation towards stable structures leads, respectively, to relativity and to quantum mechanics. Likewise, the combined relativistic…
The newest model for space-time is based on sub-Riemannian geometry. In this paper, we use a combination of Lorentzian and sub-Riemannian geometry, the suggest a new model which likes to its ancestors, but with the most efficient in…
The question that guides our discussion is "how did the geometry and particles come into being?" To explore this query we suggest the theory of goyaks, which reveals the primordial deeper structures underlying fundamantal concepts of…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
It is often said that time vanishes in quantum gravity. One general approach to quantum gravity accepts this fundamental timelessness but seeks to derive time's emergence at a non-fundamental level. To better assess such approaches, I…
The second-order moment quantum fluctuations or uncertainties are mass-dependent, and the incompatibility between the quantum uncertainty principle and the equivalence principle is at the second-order moment (variation) level, but not the…
In this article, I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the…
Is it possible to induce an effective generalized uncertainty principle (GUP) emerging from geometry and reinterpret the gravitational GUP as the effective uncertainty relation induced by microscopic horizon geometry? More broadly, is it…
This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or…
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…
Several problems in cosmology and astrophysics are described in which critical phenomena of various types may play a role. These include the organization of the disks of spiral galaxies, various aspects of the problem of structure formation…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
We suggest a new scenario of gravitation in which gravity at the fundamental level is described by a Riemannian (i.e. locally Euclidean) theory without the notion of time. The Lorentzian metric structure and the notion of time emerge as…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many…
The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…