Related papers: Reflections on the four facets of symmetry: how ph…
Symmetry is a fundamental concept in modern physics and other related sciences. Being such a powerful tool, almost all physical theories can be derived from symmetry, and the effectiveness of such an approach is astonishing. Since many…
Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…
"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…
Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Biological intelligence is remarkable in its ability to produce complex behaviour in many diverse situations through data efficient, generalisable and transferable skill acquisition. It is believed that learning "good" sensory…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
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…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
In this paper, we argue that there are foundational dilemmas in theoretical physics related to the concept of reality and the nature of mathematics in physics. Physical theory is treated as a conceptual organism which develops under the…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…
These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…