Related papers: Problem of Time and Background Independence: the I…
The paper investigates the type of realism that best suits the framework of decoherence taken at face value without postulating a plurality of worlds, or additional hidden variables, or non-unitary dynamical mechanisms. It is argued that…
The treatment of time in relativity does not conform to that in quantum theory. In the context of quantum gravity this is called "the problem of time". A crucial difference is that time $t$ may be seen as an observable in relativity theory,…
The problem of time evolution in quantum cosmology is studied in the context of a dust-filled, spatially flat Friedmann-Robertson-Walker universe. In this model, two versions of the commonly-adopted notion of internal time can be…
A suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: --1)…
We study bipartite maps on the plane with one infinite face and one face of perimeter 2. At first we consider the problem of their enumeration an then study the connection between the combinatorial structure of a map and the degree of its…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…
The application of Algorithmic Recourse in decision-making is a promising field that offers practical solutions to reverse unfavorable decisions. However, the inability of these methods to consider potential dependencies among variables…
Antiparticles may be interpreted as ordinary particles travelling backwards in time and the two descriptions are considered equivalent, at least in special relativity and relativistic quantum mechanics. It is suggested that, vice versa, the…
The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical systems seem to evolve in paths of…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
Time is one of those issues about which many thinkers and scientists have tried to pronounce their finest thoughts, but the discourse about time has remained vague and often inconsistent. In this paper we put forward a conceptual framework…
Have our fundamental theories got time right? Does size really matter? Or is physics all in the eyes of the beholder? In this essay, we question the origin of time and scale by reevaluating the nature of measurement. We then argue for a…
In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…
From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise…
We review the construction of time-dependent backgrounds with space-like singularities. We mainly consider exact CFT backgrounds. The algebraic and geometric aspects of these backgrounds are discussed. Physical issues, results and…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
In order to perceive that a physical system evolves in time, two requirements must be met: (a) it must be possible to define a "clock" and (b) it must be possible to make a copy of the state of the system, that can be reliably retrieved to…
In recent years, researchers have become increasingly interested in outlying aspect mining. Outlying aspect mining is the task of finding a set of feature(s), where a given data object is different from the rest of the data objects.…
Shape dynamics is an alternative background-independent approach to classical dynamics that implements Leibnizian philosophy and Mach's Principles. It is a formulation of the dynamics of the universe in terms of the intrinsic and relational…