Probability of stochastic processes and spacetime geometry

Abstract

We made a first attempt to associate a probabilistic description of stochastic processes like birth-death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro-to the micro-domains. We idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive, analogous birth or death rate.

A Birth–Death Toy Model for a Measure of Consciousness

“…In 1D birth-death systems for studies of population growth (e.g., bacterial, customers queuing, etc (see Craw [2018], Canessa [2007])) the expected birth α(t) ≥ 0 and death Ω(t) ≥ 0 rates can be any specified functions of the time (or age) t.…”

OPERA neutrinos and superluminal helical motion

“…As in [11], the local effect could be caused by a scalar field (here associated with the centrifugal force of Eq. ( 4)), which could be sourced by distorted regions of spacetime in the surrounding environment [15], at least for baseline distances of the order of the earth radius.…”

Possible Connection between Probability, Spacetime Geometry and Quantum Mechanics

“…In a recent paper (hereafter denoted as I) [1], we argued how the universe we live in (consisting of an inhomogeneous density of matter in the form of starts, molecules, atoms, etc, that curve space due to their gravitational fields) may be seen fullfilled with nested surfaces. In I we considered Schwarzschild's isotropic metric -which is the base for tests of general relativity and of the existence of black holes-in the vicinity of multiple massive objects.…”

“…) and dr < dR < dR (1) < • • • < dR (n) . This simply means that the system of nested curved surfaces form a spiral (c.f., Fig.…”