相关论文: Scale Dependent Dimensionality

We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.

When the cosmological "constant" is derived from modern five-dimensional relativity, exact solutions imply that for small systems it scales in proportion to the square of the mass. However, a duality transformation implies that for large…

Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…

Noncommutativity of the spacetime coordinates has been explored in several contexts, mostly associated to phenomena at the Planck length scale. However, approaching this question through deformation theory and the principle of stability of…

We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.

We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate…

In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…

We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…

The Stringy Uncertainty relations, and corrections thereof, were explicitly derived recently from the New Relativity Principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck…

I argue that the laws of physics should be independent of one's choice of units or measuring apparatus. This is the case if they are framed in terms of dimensionless numbers such as the fine structure constant, alpha. For example, the…

Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…

One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of…

This chapter explores the notion of "dimension" of a set. Various power laws by which an Euclidean space can be characterized are used to define dimensions, which then explore different aspects of the set. Also discussed are the…

Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…

In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came…

The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…

Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…

A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of…