[The Rubber Band Effect]

by

Acknowledgement

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Table of Contents

CHAPTER 1: INTRODUCTION5

Introduction5

Problem Formulation7

CHAPTER 2: LITERATURE REVIEW9

Gravity versus quantum mechanics9

Strings in space-time12

Space-time from strings18

CHAPTER 3: DISCUSSION22

Application to a Neo-Hookean Material22

Free Fall from Rest without Initial Stretch24

General Solution for Arbitrary Initial Data26

Motion in the suspension phase27

Known models (interacting)32

Aspects33

Open and closed strings.35

The Open string35

The closed string36

CHAPTER 4: CONCLUSION37

REFERENCES38

CHAPTER 1: INTRODUCTION

Introduction

String theory is shifting the way we understand the universe. This new scientific idea is based on complex laws of physics that challenge the makeup and behaviors of elementary particles. Its advocates frame it in an easily comprehensive way that is designed to be read and understood by everyone, not only scientists (King , pp. 78).

The findings in this theory challenge established ideas in physics by heightening the inability for previously proven laws of nature to fit together, and by establishing string theory as a new paradigm for thinking about physics (Dobrovolskis, pp. 10). The rhetorical power of this scientific movement is in how the mind-blowing ideas of string theory are accessible to the vernacular reader in popular scientific discourse through popular press literature and documentary film.

This new theory is based on two new ideas that there are multiple dimensions of space. First, the mathematical equations of the theory imply that there are eleven dimensions of space in the universe, as opposed to the three which we experience (updown, left-right, back-forward). Second, the theory's proponents argue that the most elementary parts of nature are not atomic particles, but vibrating strands of energy which have been named strings (Chow, pp. 25).

The free, vertical oscillatory motion of a loaded rubber band has been studied by Dobrovolskis; but the force-extension relation he used does not characterize at all the non-linearly elastic behavior typical of rubberlike materials (Heuman, pp. 52). Consequently, contrary to his claim, his results cannot hold for finite amplitude oscillations necessary to characterize the entire motion. Indeed, based upon the James-Guth statistical mechanical model for a rubberlike substance, King has shown that the simplest approximation that may be derived from this model and admits finite elastic deformation typical of rubberlike materials is provided by the neo-Hookean law

Equation 1.1

relating the string tension T to the amount of stretch i,, the ratio of the current length to the natural, undeformed length of the string. Herein G denotes the shear modulus in the natural state and A is the undeformed cross-sectional area of the string. This law is considerably different from the linear rule proposed by Dobrovolskis, wherein C is a constant (Jeong, pp.624). Moreover, (1.1) has experimental ...