Related papers: Is symmetry identity?
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary…
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
Just as spontaneous symmetry breaking can be understood in terms of energy, emergent symmetry (more precisely, its `size' and structure) can also be explained by free energy. In particular, in renormalization group flow to rational…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
Analogous to G\"odel's incompleteness theorems is a theorem in physics to the effect that the set of explanations of given evidence is uncountably infinite. An implication of this theorem is that contact between theory and experiment…
If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…
The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this…
A symmetry is a `change without change'. As simple as it sounds, this concept is the fundamental cornerstone that unifies all branches of theoretical physics. Virtually all physical laws -- ranging from classical mechanics and…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Symmetric quantum states are fascinating objects. They correspond to multipartite systems that remain invariant under particle permutations. This symmetry is reflected in their compact mathematical characterisation but also in their unique…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries.…
A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
Symmetry principles underlie and guide scientific theory and research, from Curie's invariance formulation to modern applications across physics, chemistry, and mathematics. Building on a recent matrix Lie group measurement model, this…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…