相关论文: The Definability of Fields

Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…

Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…

This work starts with the observation of a certain "rule" (up to now unexplored) in the fundamental laws of Nature. We show some evidence of this, and formulate it as a fundamental principle which exhibits a number physical consequences. In…

We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.

The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction. While a rigorous natural philosophy cannot take them for granted, there…

The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…

Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…

The paper develops an earlier proposition that the physical universe is a finite system co-ordinatised by a very large finite field $\mathrm{F}_\mathfrak{p}$ which looks like the field of complex numbers to an observer. We construct a place…

Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…

Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…

In 2021, Marco Besier and the first author introduced the concept of rationalizability of square roots to simplify arguments of Feynman integrals. In this work, we generalize the definition of rationalizability to field extensions. We then…

This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…

This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…

The gravitomagnetic field is the force exerted by a moving body on the basis of the intriguing interplay between geometry and dynamics which is the analog to the magnetic field of a moving charged body in electromagnetism. The existence of…

Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…

Thermodynamics provides a transparent definition of the free energy of density functional theory (DFT), and of its derivatives - the potentials, at finite temperatures T. By taking the T to 0 limit, it is shown here that both DFT and…