Related papers: On Measurements, Numbers and p-Adic Mathematical P…
$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a…
In this paper, we offer a brief introduction to the $p$-adic numbers and operations in the metric space defined under the $p$-adic norm. Specifically, we provide a clear description of the derivation of the $p$-adic number via the…
This review is devoted to dynamical systems in fields of $p$-adic numbers: origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory, quantum mechanics and field theory, spin glasses), continuous dynamical systems and…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.
A brief review of some selected topics in p-adic mathematical physics is presented.
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…
Measurement theory is the cornerstone of science, but no equivalent theory underpins the huge volumes of non-numerical data now being generated. In this study, we show that replacing numbers with alternative mathematical models, such as…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
Some aspects of analysis involving fields with absolute value functions are discussed, which includes the real or complex numbers with their standard absolute values, as well as ultrametric situations like the p-adic numbers.
The p-adic numbers have found applications in a wide range of diverse fields of research. In some applications the algebraic properties of p-adics enter as an indispensable ingredient of the theory. Another class of applications has to do…
Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in…
A field with an absolute value function is a basic type of metric space, which includes the real and complex numbers with their standard metrics, and ultrametrics on fields like the p-adic numbers. Here we try to give some perspectives of…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
In this mainly pedagogical article, we discuss under what circumstances measurements play a special role in quantum processes. In particular we discuss the following facts which appear to be a common area of confusion: i) from a fundamental…
In this survey I discuss A. Buium's theory of ``differential equations in the p-adic direction'' ([Bu05]) and its interrelations with ``geometry over fields with one element'', on the background of various approaches to p-adic models in…
We study the quantum jumps of physical quantities in a strongly correlated many electron systems based on a new p-adic functional integral approach. It is shown that a description in terms of the p-adic numbers leads to the fractal behavior…