Principles of Space-Time-Matter: Cosmology, Particles and Waves in Five Dimensions

275 Pages·2018·6.413 MB·English

by  Paul S. Wesson, James M. Overduin

PRINCIPLES OF
SPACE-TIME-MATTER
Cosmology, Particles and Waves in
Five Dimensions
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PRINCIPLES OF
SPACE-TIME-MATTER
Cosmology, Particles and Waves in
Five Dimensions
Paul S Wesson
James M Overduin
Towson University, USA & Johns Hopkins University, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
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Published by
World Scientific Publishing Co. Pte. Ltd.
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Library of Congress Cataloging-in-Publication Data
Names: Wesson, Paul S., author. | Overduin, J. M. (James Martin), 1965– author.
Title: Principles of space-time-matter : cosmology, particles and waves in five dimensions /
Paul S. Wesson, James M. Overduin, Towson University, USA & Johns Hopkins University.
Description: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2019] |
Includes bibliographical references and index.
Identifiers: LCCN 2018051422| ISBN 9789813235779 (alk. paper) | ISBN 9813235772 (alk. paper)
Subjects: LCSH: Relativity (Physics) | Space and time. | Particles (Nuclear physics) |
Wave mechanics.
Classification: LCC QC173.59.S65 W4485 2019 | DDC 530.11--dc23
LC record available at https://lccn.loc.gov/2018051422
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2019 by World Scientific Publishing Co. Pte. Ltd.
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Preface
by First Author
The theory of Space-Time-Matter uses the geometry of the fifth dimension
to explain the matter in the world. It has something in common with
Einstein’s 4D theory of general relativity and its 5D extensions due to
Kaluza and Klein. However, STM has an energy-momentum tensor which
is derived from an extra dimension that is not rolled up or compactified to
an unobservably small size. In fact, we see evidence of the fifth dimension
in things from the mass of an elementary particle to the density of the
cosmological fluid. In this way, STM theory fulfills Einstein’s theorem of
transmuting the “base wood” of matter to the “fine marble” of algebra.
General relativity is an excellent theory, but it does not explain the
origin of the stuff with which it deals, namely matter. Einstein realized
this, though originally his “dream” was unknown to my colleagues and I.
However, it was apparent that the physical quantities like mass and density
could be turned into lengths and geometrized using the fundamental
contexts; and that the 4D equations could be turned into expressions which
combined the fields with their material sources given the appropriate extra
algebra. Hence the fifth dimension. In 1992, we calculated the properties
of matter using the fifth dimension for three physical systems, including
the standard cosmologies, and found agreement with the conventional
results. Soon after, the canonical metric was introduced, which simplified
the calculations and provided an embedding in apparently empty 5D space
for all solutions of the 4D Einstein equations with a finite cosmological
constant or vacuum density. The initial group of workers involved in those
calculations included (in alphabetical order) H. Liu, B. Mashhoon, J.M.
Overduin, and J. Ponce de Leon. This nucleus grew, and eventually
numbered about 20 people. It is slightly ironic that we were in full swing
v
vi Preface by First Author
with our physical calculations before it was pointed out to us that there is
actually a mathematical result which guarantees their validity in principle.
This is Campbell’s embedding theorem, which was sketched by him in a
book of 1926, but lay largely forgotten until it was realized that it implies
the recovery of Einstein’s 4D equations with matter from the 5D Ricci
equations in vacuum. The full 5D field equations describe gravitational,
electromagnetic and scalar fields which can lead to forms of matter with
novel properties.
Nowadays, 5D relativity has a large number of adherents from
both the physical and mathematical sides, those who are attracted by the
elegance of matter from geometry. A significant group of these espouse
Membrane theory as opposed to Space-Time-Matter theory. This was
introduced in 1998 / 1999 by Arkani-Hamed / Dimopoulos / Dvali and
Randall / Sundrum. The approach is typified by a singular surface or
membrane which is identified as spacetime, whereas STM treats all of the
five dimensions on an equal footing (though a divergence can appear under
certain circumstances in the properties of the vacuum which may be
related to the big bang). However, it has been shown that mathematically
STM-theory and M-theory are equivalent, so to this extent they are
complementary.
The present book aims to give a comprehensive account of 5D
relativity, concentrating on how matter is induced in 4D spacetime by the
fifth dimension. It effectively supersedes my two previous volumes on the
subject, namely Space-Time-Matter of 1999 and Five-Dimensional
Physics of 2006. Some of the material in these earlier volumes is also
present in the current one, but there is also much that is new. Most of the
new results are due to my colleagues, whose names are found within. I
am grateful for their assistance, but of course the responsibility for any
errors or omissions rests with me. The coverage is by chapters which I
have attempted to make reasonably self-contained (each has its own
bibliography for ease of reference). It starts with an overview of standard
general relativity, proceeds through established results on astrophysics
and cosmology, and ends with recent material on the nature of the vacuum
and particle physics. The subject matter is perforce mathematical, each
chapter has an introduction and conclusion of a non-technical nature aimed
at maximizing understanding.
vii Preface by First Author
While the idea of matter from geometry goes back to Einstein, it
falls into the kind of philosophy of science promoted by his colleague, Sir
Arthur Eddington. He was Plumian Professor of Astronomy and Natural
Philosophy at Cambridge, and I was influenced by reading his books while
a graduate student at the same place, and acquired a rather liberal view of
what should be considered “real”. For example, one could argue that the
planet Neptune should have been considered “real” before Hershel’s eye
saw it through a telescope, because the perturbations of the other planets
considered within the framework of Newton’s laws of mechanics required
its existence. And in a more modern vein: gravitational radiation should
be considered real even though no human eye has seen it, because the
evolution of the binary pulsar considered within the framework of
Einstein’s general relativity requires its existence. I mention these things
because they are relevant to the question I am frequently asked: “If the
fifth dimension is real, why do we not see it?” The reader is naturally free
to regard the fifth dimension in the Space-Time-Matter theory as he or she
pleases, and at one end of the philosophical spectrum it can be viewed
merely as a mathematical abstraction that gives convenient physical
results. However, I would venture to answer the question posed above in
a bolder way: in a manner, we see the fifth dimension all around us, in the
form of mass and energy.

Paul S. Wesson
Gabriola Island, September 2015
Preface
by Second Author
Notes for this book were found among Paul Wesson’s papers after his
death on September 16, 2015. With the kind encouragement of Paul’s
partner, Patricia Lapcevic, I undertook to see that they were published.
Chapters 1 through 8 are largely as Paul wrote them, with only minor
editorial changes and typographical corrections. (Many thanks to Jonathan
Perry for help in reformatting the equations.) I have added a concluding
Chapter 9 and an Appendix describing Paul Wesson’s life and work as I
knew it. Any errors and omissions in this additional material are entirely
my own. I was fortunate to know Paul as a teacher, colleague and friend,
and I hope that this book, his last work, will be a fitting tribute to a life
dedicated to the search for truth and beauty in physics.

James M. Overduin
Baltimore, September 2018

viii
Contents
Preface by First Author ...................................................................................................... v
Preface by Second Author ............................................................................................... viii
Chapter 1: Standard General Relativity ........................................................................ 1 
1.1 Introduction ............................................................................................................. 1 
1.2 Einstein’s Equations ................................................................................................ 2 
1.3 4D Cosmology ........................................................................................................ 9 
1.4 Astrophysics .......................................................................................................... 17 
1.5 Conclusion............................................................................................................. 21
References ................................................................................................................... 23 
Chapter 2: Space-Time-Matter Theory ....................................................................... 25 
2.1 Introduction ........................................................................................................... 25 
2.2 Higher-Dimensional Theories ............................................................................... 26 
2.3 Field Equations for Neutral Matter ........................................................................ 32 
2.4 Some Simple Solutions ......................................................................................... 40
2.5 Campbell’s Theorem and the Field Equations ....................................................... 44 
2.6 Conclusion............................................................................................................. 48
References ................................................................................................................... 49 
Chapter 3: Cosmology in 5D ......................................................................................... 51 
3.1 Introduction ........................................................................................................... 51 
3.2 Flat 5D Universes .................................................................................................. 52 
3.3 The Singularity as a Shock Wave .......................................................................... 58 
3.4 Bounce versus Bang .............................................................................................. 61
3.5 The Universe as a 5D Black Hole ......................................................................... 66 
3.6 Anisotropic 5D Universes ..................................................................................... 70 
3.7 Divergent Dark Energy ......................................................................................... 72
3.8 Conclusion............................................................................................................. 74
References ................................................................................................................... 75 
ix