On the time continuous evolution of the universe if time is discrete and irreversible in nature

Roland Riek

doi:10.1088/1742-6596/1275/1/012064

Abstract

The time evolution of the universe is usually mathematically described under a continuous time and thus time reversible. Here, the consequences of studying the evolution of a homogenous isotropic universe by time continuous reversible physics are studied if time is actually discrete and irreversible in nature. The discrete dynamical time concept of Lee and its continuous time limit to the continuous time case is applied to the Newtonian limit of the general relativity theory. By doing so, the cosmic constant as well as the inflation of the universe arise and are predicted quantitatively well by assuming the smallest time step to be the Planck time and by using the current size of the universe.

Highlights

Because experimentally measured time is composed of an array of events, which can be exemplified in physics only by an energy-consuming clock measurement, and can not be measured continuously because of the uncertainty principle between energy and time ( E t > h/2 with h being the Planck constant) time may be regarded discrete in nature
The discrete dynamical time concept of Lee and its continuous time limit to the continuous time case is applied to the Newtonian limit of the general relativity theory
The evolution of a homogenous isotropic universe is explored under a discrete dynamical time and its consequences are discussed if time continuous reversible physics is applied to an universe that expands in time steps

Summary

Introduction

Because experimentally measured time is composed of an array of events, which can be exemplified in physics only by an energy-consuming clock measurement, and can not be measured continuously because of the uncertainty principle between energy and time ( E t > h/2 with h being the Planck constant) time may be regarded discrete in nature (see for example [1,2,3,4,5,6,7,8,9,10]). With dx the space time interval, which is the distance between two events, cthe speed of light, and R(t) the scaling factor It describes the radial evolution of an isotropic homogenous universe under a continuous time tunder the theory of general relativity [14, 16]. In presence of a scaling of time (unequal to 1) the Newton’s law has an additional term, which can be regarded an acceleration or a friction term in dependence on the sign of n It is this friction term, which enables discrete time physics to be time reversible with the following request The derived discrete Newtonian equation (eq 17) is transformed into its corresponding continuous analog: In this time continuous frame the di↵erential equation of the exponential function is given by b s(t) and the Hubble law of eq. By the present translation from the discrete time to a dynamic continuous time with lim t ! 0 the space can be described as usual because no need for a dynamic continuous space is required as space has not the problem of irreversibility

From the Poisson equation to the Evolution of the Universe

The expansion of the universe with its apparent inflation

The apparent acceleration of the universe at late time points

Conclusion