Space-time in a simple model of a physical system

Máximo García Sucre

Here we analyze the physical concepts of non-locality, multi-universe, and cosmological principle in the framework of a space-time discrete model previously developed. In previous developments of this model we have elucidated as derivative concepts those of time, space-time, reference frame, particle, interaction between systems of particles, field, interaction between fields, detector of particle, and wave function. We start from the primitive concept of preparticle and four postulates alluding simple concepts. The fundamental postulate says that space-time points can be represented by equivalent classes of points of crossing between particles having the same structure. In this way each point of space-time is represented by an equivalent class corresponding to a different structure from the one of any other equivalent class representing a space-time point. We have considered a new way to define system of observation and detector of particles, which leads to non- local properties of the space-time model considered. Finally we have speculated about dark matter and dark energy in the frame work of our model.

Wolfram Schommers

Chuan Sheng Chew, Otto C. W. Kong, Jason Payne

In physics, experiments ultimately inform us about what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the configuration space of a free particle (or the center of mass of a closed system of particles). This configuration space (as well as phase space) can be constructed as a representation space for the relativity symmetry. From the corresponding quantum symmetry, we illustrate the construction of a quantum configuration space, similar to that of quantum phase space, and recover the classical picture as an approximation through a contraction of the (relativity) symmetry and its representations. The quantum Hilbert space reduces into a sum of one-dimensional representations for the observable algebra, with the only admissible states given by coherent states and position eigenstates for the phase and configuration space pictures, respectively. This analysis, founded firmly on known physics, provides a quantum picture of physical space beyond that of a finite-dimensional manifold and provides a crucial first link for any theoretical model of quantum space-time at levels beyond simple quantum mechanics. It also suggests looking at quantum physics from a different perspective.

Tim Maudlin

É. Papp

Belal Ehsan Baaquie

A simple harmonic oscillator, or oscillator in short, is one of the most important systems in physics as well as in quantum mechanics. The path integral and Hamiltonian of a simple harmonic oscillator are leading exemplars for the description of a wide class of physical systems. An oscillator is a theoretical model of great utility, primarily due to its simplicity that allows for the exact derivation of many results. The simple harmonic oscillator can be generalized to the case of infinitely many oscillators, and is also the starting point for analysis of many nonlinear quantum systems. Path integrals for the simple harmonic oscillator are all based on Gaussian integration, which has been discussed in Section 7.2. The harmonic oscillator is described by Gaussian path integrals , and is a bedrock of the general theory of path integration. Moreover, all perturbation expansions of nonlinear path integrals about the oscillator path integral, which includes the semi-classical expansion, are based on results of Gaussian integration. The properties of the harmonic oscillator are analyzed in the coordinate space representation, and its path integral as well as its correlation functions are analyzed. All formulas and derivations are for Euclidean time. In Sections 11.1 and 11.2 the Hamiltonian and state space of the oscillator are studied and the correlator is derived using state space methods. In Section 11.2 the infinite time oscillator is introduced and in Sections 11.3–11.5 the path integral for the oscillator is evaluated.