Related papers: Destructuring Physics: A functional derivation of …
The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D,…
Our understanding of the four basic concepts of Physics -- space, time, matter and force -- has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to…
A formalism is proposed to generate (the first step of) a discrete spacetime: spacetime with an inbuilt length scale. We follow the celebrated Landau theory of liquid - solid phase transition induced by Spontaneous Symmetry Breaking by a…
Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology…
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…
I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume…
This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question…
We present an elastic constitutive model of gravity where we identify physical space with the mid-hypersurface of an elastic hyperplate called the "cosmic fabric" and spacetime with the fabric's world volume. Using a Lagrangian formulation,…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
We will look for an implementation of new symmetries in the space-time structure and their cosmological implications. This search will allow us to find a unified vision for electrodynamics and gravitation. We will attempt to develop a…
We discuss how developments in physics often imply in the need that spacetime acquires an increasingly richer and complex structure. General Relativity was the first theory to show us the way to connect space and time with the physical…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…
In recent publications in physics and mathematics, concerns have been raised about the use of real numbers to describe quantities in physics, and in particular about the usual assumption that physical quantities are infinitely precise. In…
Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, function of the point $P$ and the vector…
Following recent assumptions to unify quantum mechanics and general relativity, the structure of spacetime is suppose to be a consequence of the relations among some fundamental objects, and its concept can be formulated without the…
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
With the concept of "discrete space-time" the space-time continuum is resolved into discrete points at the scale of the Planck length. We postulate with the "principle of the fermionic projector" that physical equations must be formulated…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
When modelling spacetime and classical physical fields, one typically assumes smoothness (infinite differentiability). But this assumption and its philosophical implications have not been sufficiently scrutinized. For example, we can appeal…
Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of light $c$ not being infinite calls for a redefinition of space-time on large and cosmological scales,…