Related papers: Multiscale spacetimes from first principles
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical…
We consider subsets of the (symbolic) sequence space that are invariant under the action of the semigroup of multiplicative integers. A representative example is the collection of all 0-1 sequences $(x_k)$ such that $x_k x_{2k}=0$ for all…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…
Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may tame the infinities that arise from quantizing gravity, and dispense with the machinery of…
Several approaches to quantum gravity suggest that the standard description of spacetime as probed at low-energy, with four dimensions, is replaced in the Planckian regime by a spacetime with a spectral dimension of two. The implications…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
To unify general relativity and quantum theory is hard in part because they are formulated in two very different mathematical languages, differential geometry and functional analysis. A natural candidate for bridging this language gap, at…
The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant $\alpha$ in space and time. A model construction method is…
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise…
We prove a quantitative distortion theorem for iterated function systems that generate sets of continued fractions. As a consequence, we obtain upper and lower bounds on the Hausdorff dimension of any set of real or complex continued…
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a)…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
We give explicit bounds for the Hausdorff dimension of the unique invariant measure of $C^3$ multicritical circle maps without periodic points. These bounds depend only on the arithmetic properties of the rotation number.
Motivated in part by the bi-gravity approach to massive gravity, we introduce and study the multimetric Finsler geometry. For the case of an arbitrary number of dimensions, we study some general properties of the geometry in terms of its…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
Einstein field equations show how matter curve spacetime, but, does curved spacetime creates matter? And if so, can we have geometrical foundations to every matter in the universe? In this note, we suggest an approach to derive non-general…
Let $\{X(t) : t \in \mathbb{R}^d \}$ be a multivariate operator-self-similar random field with values in $\mathbb{R}^m$. Such fields were introduced in [24] and satisfy the scaling property $\{X(c^E t) : t \in \mathbb{R}^d \} \stackrel{\rm…