Related papers: Numerical search for a fundamental theory
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
The progress of Particle Physics is closely linked to the progress in the understanding of the fundamental constants, like the finestructure constant, the mass of the electron or nucleon, or the electroweak mixing angle. The relation…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
The Cosmological Constant Problem is re-examined from an effective field theory perspective. While the connection between gravity and particle physics has not been experimentally probed in the quantum regime, it is severely constrained by…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
Anthropic models can give testable predictions, which can be confirmed or falsified at a specified confidence level. This is illustrated using the successful prediction of the cosmological constant as an example. The history and the nature…
We use entropy to link fine-structure constant and cosmological constant. We also link nuclear force and gravity. We step on the fundamentals of consciousness for this new millennium with a scientific approach. Statistical and quantum…
The large amount of cosmological data already available (and in the near future) makes necessary the development of efficient numerical codes. Many software products have been implemented to perform cosmological analyses considering one or…
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…
Functions are a fundamental object in mathematics, with countless applications to different fields, and are usually classified based on certain properties, given their domains and images. An important property of a real-valued function is…
The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
We investigate the zeros of two one-parameter families of harmonic functions and describe how the number of zeros depends on the parameter. Our functions have the property that all zeros lie on certain rays in the complex plane and thus we…
We propose several hierarchical graphs that represent the semantic relations between physical theories, their fundamental constants and units of measurement. We begin with an alternative representation of Zelmanov's cube of fundamental…
Many physical theories beyond the Standard Model predict time variations of basic physics parameters. Direct measurement of the time variations of these parameters is very difficult or impossible to achieve. By contrast, measurements of…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities…