Related papers: P-Structures, P-Geometry and Observer's Perceptive…
In ordinary quantum field theory, one can define the algebra of observables in a given region in spacetime, but in the presence of gravity, it is expected that this notion ceases to be well-defined. A substitute that appears to make sense…
Physical theories must stem from observation. The possibility that perceived events are simulated, not real, raises a crucial dilemma about the credibility of known physics, known as the simulation hypothesis. To analyze this hypothesis in…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
The paper deals with the observer design problem for a wide class of triangular nonlinear time-varying systems. The results of the present work generalize previous results in the literature dealing with the observer design problem for…
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from…
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
The concept of {\em complexity} (as a quantity) has been plagued by numerous contradictory and confusing definitions. By explicitly recognising a role for the observer of a system, an observer that attaches meaning to data about the system,…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
I have recently shown that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of space-times whose structure is governed by observer-independent scales of both velocity and…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
Using the parametrised representation of field theory (in which the location in spacetime of a part of a field is itself represented by a map from the base manifold to Minkowski spacetime) I demonstrate that in both local and global cases,…
Physical time intervals are attributes of single physical object whereas physical space intervals are a relational attribute of two physical objects. Some consequences of the breaking of the space-time exchange symmetry inherent in the…
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead…