Related papers: Choice of the best geometry to explain physics
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and…
Classical integral geometry takes place in Euclidean space, but one can attempt to imitate it in any other metric space. In particular, one can attempt this in R^n equipped with the metric derived from the p-norm. This has, in effect, been…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
If time has three dimensions, how does a particle move? This paper demonstrates that quantum physics naturally emerges from a framework of three-dimensional time. We present the equations governing the motion of 0-spin, 1-spin, and 1/2-spin…
Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
An enquiry into the physical nature of time and space and into the ontology of quantum mechanics from a metageometric perspective, resulting from the belief that geometric thought and language are powerless to farther understanding of these…
We present the basic concepts of space and time, the Galilean and pseudo-Euclidean geometry. We use an elementary geometric framework of affine spaces and groups of affine transformations to illustrate the natural relationship between…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
In the geometric theory of defects, media with a spin structure, for example, ferromagnet, is considered as a manifold with given Riemann--Cartan geometry. We consider the case with the Euclidean metric corresponding to the absence of…