Related papers: A Physics of Bounded Metric Spaces
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The ability of metric spaces to capture this…
This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…
Motivated by the question of stability, in this letter we argue that an effective "quantum" theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is…
The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…
We show the equivalences of several notions of entropy, like a version of the topological entropy of the geodesic flow and the Minkowski dimension of the boundary, in metric spaces with convex geodesic bicombings satisfying a uniform…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
First, we explain some ambiguities of spacetime and metric field as fundamental concepts. Then, from the Unruh effect point of view and using the Gelfand-Naimark-Segal construction, we construct an operator as a quanta of acceleration that…
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)…
One of the most important problems in Physics is how to reconcile Quantum Mechanics with General Relativity. Some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favor of a more…
The integrals of the Friedmann cosmology equations are identified as constant physical characteristics for both vacuum and non-vacuum cosmic energies. The integrals are found to be numerically coincident. A model shows that the coincidence…
We introduce a generalization for bounded geometry that we call bounded scale measure. We show that bounded scale measure is a coarse invariant unlike bounded geometry. We then show equivalent definitions for spaces with bounded scale…