Related papers: Why does D=4, rather than more (or less)? An Orwel…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
The concept of the space-time as emerging in the world phase transition, vs. a priori existing, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications…
Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
In a very recent paper [1], we have proposed a novel $4$-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of $D\to4$ Einstein-Gauss-Bonnet gravity with the rescaled…
A general sketch of how the problem of space dimensionality depends on Anthropic arguments is presented. A new argument in favor of a stable scenario for space dimensionality for a time scale longer than that required for the existence of…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a…
The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has…
We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…
The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-I) function of the 4-velocity $u^i$, plus a functional of $\eta_{ij}u^i u^j$. The second…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
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…
Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional…
One can try to define the theory of quantum gravity as the sum over geometries. In two dimensions the sum over {\it Euclidean} geometries can be performed constructively by the method of {\it dynamical triangulations}. One can define a {\it…
In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of…
The concept of the space-time as emerging in the world phase transition, vs. a priori exiting, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications for…
Some properties of the world are fixed by physics derived from mathematical symmetries, while others are selected from an ensemble of possibilities. Several successes and failures of ``anthropic'' reasoning in this context are reviewed in…