Related papers: Synthetic Dynamics
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate…
Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
We develop a monadic framework formalising an operational notion of dynamics, seen as the setting and evolution of initial value problems, in general physical theories. We identify in the Eilenberg-Moore category the natural environment for…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…