Related papers: The Many Dimensions of Dimension
This is the second paper by Nordstr{\"o}m on his five dimensional theory. It aims at generalizing the relations $\mathbf{D} = \epsilon \mathbf{E}$, $\mathbf{B} = \mu \mathbf{H}$ of electromagnetism to the five dimensional gravito-electric…
Gunnar Nordstrom constructed the first relativistic theory of gravitation formulated in terms of interactions with a scalar field. It was an important precursor to Einstein's general theory of relativity a couple of years later. He was also…
This is the first paper by Gunnar Nordstr{\"o}m (1881--1923) on his five dimensional theory. In his summary he states: ''It is shown, that a unifying treatment of the electromagnetic and gravitational fields is possible, if one considers…
This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…
Within the context of a $5D$ space-time, we construct a unified theory of gravity and electromagnetism from which the Einstein field equations and Maxwell equations emerge, with homogenous Maxwell equations appearing naturally. We also…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
A new Dimensional Regularization of $\gamma_5$ is proposed. Cyclicity and Lorentz covariance are enforced. The extension to generic dimension is based on the integral representation of the trace of gamma's, presented in a previous paper.
This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…
We live in a four dimensional world. But the idea of unification of fundamental interactions lead us to higher dimensional theories. Recently a new theory with extra dimensions has emerged, where only gravity propagates in the extra…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…
Recently by us was proposed the model where Einstein's equation on the brane was connected with Maxwell's multi-dimensional equations in pseudo-Euclidean space. Based on this idea unification of 4-dimensional gravity and electromagnetism in…
Models that involve extra dimensions have introduced completely new ways of looking up on old problems in theoretical physics. The aim of the present notes is to provide a brief introduction to the many uses that extra dimensions have found…
Several approaches to quantum gravity (including the model of superplastic vacuum; Diakonov tetrads emerging as the bilinear combinations of the fermionis fields; $BF$-theories of gravity; and effective acoustic metric) suggest that in…
Multidimensionality of our Universe is one of the most intriguing assumption in modern physics. It follows naturally from theories unifying different fundamental interactions with gravity, e.g. M/string theory. The idea has received a great…
The numerical dimension is a numerical measure of the positivity of a pseudo-effective divisor $L$. There are several proposed definitions of the numerical dimension due to Nakayama (2004) and Boucksom et al. (2004). We prove the equality…