Related papers: Geometry of Psychological Time
The concept of time is discussed in the context of the canonical formulation of the gravitational field. Using a hypersurface orthogonal foliation, the arbitrariness of the lapse function is eliminated and the shift vector vanishes,…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
In this articles we consider very mathematical (if not very plausible) geometric marching. Our marchers will exhibit beautiful mathematics, some familiar and some less so. In a final summary section we discuss the point of all the fancy…
We live in a 3+1 space-time that is intended as a description of the universe with three space dimensions and one time dimension. Space-time dimensionality seems so natural that it is rarely criticized. Experiments and the highly successful…
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
The paper discusses some aspects of real physical space and time: structure of electrodynamics; structure of gravitational-inert theory in the real world; formation of the real matter; Mach's principle and the radiational cosmic mass;…
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier.…
Non-minimal gauge models with exact unbroken improper space-time symmetries are constructed and their cosmological and astrophysical implications explored.
In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.
In this paper, a geometrical interpretation of light diffraction is given using an infinity of fluctuating geodesics that represent paths of least time in an homogeneous space. Without using the wave theory, we provide a geometrical…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…
Even though the concepts of time and space are basic concepts of physics, they have not been vouchsafed a constructive definition. As to space, this is no wonder because a correct notion of space cannot be formed in the frame of the…
This contribution argues that the notion of time used in the scientific modeling of reality deprives time of its real nature. Difficulties from logic paradoxes to mathematical incompleteness and numerical uncertainty ensue. How can the…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a…
We give an explicit formula for the time projection in an arbitrary von Neumann algebra from which all its basic properties can be easily derived. The analysis of the situation when this time projection is a conditional expectation is also…