相关论文: Local Availability of mathematics and number scali…
The work is based on two premises: local availability of mathematics to an observer at any space time location, and the observation that number systems, as structures satisfying axioms for the number type being considered, can be scaled by…
The relationship between the foundations of mathematics and physics is a topic of of much interest. This paper continues this exploration by examination of the effect of space and time dependent number scaling on theoretical descriptions of…
Effects of local availability of mathematics (LAM) and space time dependent number scaling on physics and, especially, geometry are described. LAM assumes separate mathematical systems as structures at each space time point. Extension of…
A stronger foundation for earlier work on the effects of number scaling, and local mathematics is described. Emphasis is placed on the effects of scaling on coordinate systems. Effects of scaling are represented by a scalar field, $\theta,$…
The origin of this paper starts with the observation by Yang Mills that what state represents a proton in isospin space at one location does not determine what state represents a proton in isospin space at another location. This is…
This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the…
A summary of number structure scaling is followed by a description of the effects of number scaling in nonrelativistic quantum mechanics. The description extends earlier work to include the effects on the states of two or more interacting…
This paper is a small step towards the goal of constructing a coherent theory of physic and mathematics together. It is based on two ideas, the localization of mathematical systems in space or space time, and the separation of the concepts…
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance)…
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…
Independent studies by different authors have proposed that classicality may be induced in quantum objects by cosmological constraints presented by an expanding universe of finite extent in space-time. Cosmological effects on a quantum…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
Real-time evolution of quantum field theories using classical computers requires resources that scale exponentially with the number of lattice sites. Because of a fundamentally different computational strategy, quantum computers can in…