Table Of ContentSeeking Ultimates
An Intuitive Guide to Physics
Peter T Landsberg
University of Southampton
Institute of Physics Publishing
Bristol and Philadelphia
Copyright © 2000 IOP Publishing Ltd.
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN 0 7503 0657 2
Library of Congress Cataloging-in-Publication Data are available
Reprinted with corrections 2001
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Contents
Introduction ix
Acknowledgments x
1 What this book is about 1
1.1 Introduction 1
1.2 My story 1
1.3 Intuition 2
1.4 Incompleteness 3
1.5 Human aspects 6
1.6 Reasons for reading this book 7
1.7 Arrangement of the chapters 8
2 There is no free lunch. Temperature and energy: science
for the environment (Hero: Count Rumford) 9
2.1 Introduction 9
2.2 How cold can we get? 10
2.3 Historical notes on thermodynamics 13
2.4 What is the highest temperature? 15
2.5 What is energy conservation? 16
2.6 A marriage of energy and mass 18
2.7 Perpetual motion? 21
2.8 Energy for mankind 24
2.9 Summary 28
3 Painting by numbers. Elements and particles: science as
prediction (Hero: Dmitri Mendeleev) 29
3.1 Introduction 29
3.2 Chemistry in 1867 30
3.3 The Periodic Table and three predictions 33
3.4 Confirmations 34
3.5 The atom in the 1890s 38
3.6 The atom split 40
3.7 Incompleteness 41
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3.8 Plum-pudding or planetary system? 43
3.9 A taxonomy of particles 50
3.10 Basic forces 55
3.11 Predictions of particles 59
3.12 Electrons yield modern electronics 64
3.13 Summary 66
4 Why you cannot unscramble an egg. Time and entropy:
science and the unity of knowledge
(Hero: Ludwig Boltzmann) 68
4.1 What is entropy? 68
4.2 How can we move in time? 75
4.3 The first problem: can all molecular velocities be
reversed? 81
4.4 A second problem: coarse-graining 82
4.5 Time’s arrow as an illusion 86
4.6 Different arrows of time 87
4.7 Entropy as metaphor 89
4.8 Summary 93
5 How a butterfly caused a tornado. Chaos and life:
science as synthesis (Hero: Charles Darwin) 94
5.1 Introduction 94
5.2 Limits of predictability in Newtonian mechanics 95
5.3 Chemical and population chaos 98
5.4 Abrupt changes (‘phase transitions’) 106
5.5 Self-organization 109
5.6 Entropy is not always disorder 111
5.7 The origin of life 115
5.8 Summary 118
6 Now you see it, now you don’t. Quantum theory: science
and the invention of concepts (Hero: Max Planck) 122
6.1 Introduction 122
6.2 Quantum mechanics: the elimination of unobserv-
ables 123
6.3 Wave mechanics: the optics–mechanics analogy 127
6.4 A brief history of the new mechanics 133
6.5 Wavefunctions and probabilities 136
6.6 Attempts to understand quantum mechanics 140
6.7 Comments on quantum mechanics 148
6.8 Quantum effects 148
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6.9 Can gravity affect temperature or light? 156
6.10 Matter drained of heat 162
6.11 A look at superconductivity 164
6.12 Summary 166
7 The galactic highway. Cosmology: science as history
(Hero: Albert Einstein) 168
7.1 Ages 168
7.2 Hubble’s law 171
7.3 Cosmological models 176
7.4 The ‘relic’ radiation 184
7.5 Olbers’ Paradox 187
7.6 The oscillating universe 189
7.7 The origin of the elements 193
7.8 Black holes 194
7.9 Some problems 197
7.10 Time machines 200
7.11 Summary 203
8 Weirdness or purity. Mathematics: science as numbers
(Hero: Arthur Eddington) 205
8.1 Introduction 205
8.2 Gödel’s theorem: consistency and incompleteness 206
8.3 Complexity and randomness 210
8.4 Infinites 213
8.5 The physical constants 216
8.6 Cosmical coincidences 221
8.7 The anthropic principle 224
8.8 The Copernican principle 226
8.9 Summary 227
9 The last question. Does God exist?
(Hero: Blaise Pascal) 228
9.1 Introduction 228
9.2 Gödelian statements 230
9.3 The evidence of thermodynamics 231
9.4 The evidence from cosmology 233
9.5 The evidence from quantum mechanics 238
9.6 Conclusions 241
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10 Love of my life. Science as human activity
(Hero: readers are invited to choose their own) 244
10.1 Happiness 244
10.2 Limits of science 246
10.3 Distortions: science and the public 247
10.4 Science wars? 250
10.5 Concluding remarks 252
Glossary 253
References 280
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Introduction
An intellectual discipline is one thing—a book about it is another.
Take poetry, for example; you can write it down on a piece of paper
or read it in a book. But you livepoetry by knowing it in your heart
and mind, by reciting it, by lending emphasis here and a pause there.
Similarly with a language—you can learn French from a French
grammar or from a book of French songs. But you live it by speaking
it, even by acting it. The shoulders might move for ‘je m’en fou’ and
you may nod your head ‘Voila!’ So the discipline itself is different
from its version as written down in a book. The book can enable you
to ‘live’ it, by putting something of yourself into it.
Similarly, when lecturing on mathematical physics, you might tell
students to ‘forget’ the mathematics, once they have understood it,
and to try to appreciate what has been achieved in an intuitive man-
ner—to absorb it into their bones, as it were—using physical insight.
This is usually found to be a hard task, but an important one, and gets
close to what I have called ‘intuitive’ in the title of this book.
In this way we arrive at ‘popular science’. This is an important
activity, for when the average person contemplates this universe, and
the science which governs it, he must be excused for feeling rather
confused by the language and by the details. Biology, psychology and
even the brain are also at least partially physics-based; many of the
concepts used are remote from normal experience, and the argu-
ments can be mathematical. This book may be a help.
Only a few experiments are discussed in this book, although they pro-
vide the main mechanism for advancing science. We doscience, for
example, by heating a wire in a flame and seeing it turn blue; or by
timing the oscillations of a suspended spring; or by studying the flight
of a ball. Then we may develop equations to describe the trajectory
Copyright © 2000 IOP Publishing Ltd.
of the ball. But that has no place in this book. Thus our constraints are
rather severe. But we still want to attain an appreciation of the results
and arguments of science in order to obtain an intuitive grasp of the
connections between various phenomena; say, between light and
gravity. This can be done, as shown here, but it requires some work
on the part of the reader: at the very least he or she will have to turn
pages forward and backward in order to understand the concepts,
even though they may be standard ones (examples might be ‘pho-
tons’, ‘antimatter’, black holes’, etc). Our constraints (few experi-
ments, no mathematics) thus match those for books on poetry and
French (no singing, no acting, no reciting!).
People have written about ‘the end of science’ and a ‘theory of every-
thing’, and it has been said that with science as it is there may be ‘no
room for a creator’. The average person’s gut reaction that such
notions cannot be strictly correct is here vindicated as part of the text.
That does not mean that we have no excitement. Some very unexpec-
ted effects are noted in the course of the discussion, and there is also
some fun to be had.
I show where there are gaps which are being filled, but also that there
are gaps which are more lasting features of the world as we see it.
Discussions of entropy and time, the chemical elements and elemen-
tary particles, chaos and life, form part of this story, which starts with
simpler ideas such as temperature. Later we explore quantum theory
and cosmology. In all cases we look for ‘ultimates’. Thus, we speak of
‘isolated systems’—do they actually exist? Or does Newtonian mech-
anics really always predict exact results? Incompletenesses and
uncertainties in both physics and in mathematics have to be faced,
leading eventually to a discussion of God and human happiness in the
light of what has been found.
Acknowledgments
I want to thank my family for their help and support and the Univer-
sity of Southampton for facilities made available to me. In particular,
I wish to thank my ‘IT consultants’ Jeff Dewynne, Alistair Fitt and
Colin Please.
Copyright © 2000 IOP Publishing Ltd.
Various colleagues read parts of the manuscript and I thank them for
their comments. They are: Dr V Badescu (Bucharest), Dennis Blu-
menfeld (Chicago), Sir Hermann Bondi (Cambridge), Dmitry Bosky
(London), Lajos Diosi (Budapest), Freeman Dyson (Princeton),
Brian Griffiths (Southampton), Gareth Jones (Southampton),
Andrew Kinghorn (Southampton), Max and Olivia Landsberg
(London), John Liakos (Northampton), Robert Mann (Waterloo),
George Matsas (Sa˜o Paulo), Gunther Stent (Berkeley), Manuel
Velarde (Madrid), James Vickers (Southampton) and notably Garry
McEwen (Southampton), whose construction of, and help with, table
3.2 was particularly helpful.
For comments on Chapter 6 I want to thank Avshalom Elitzur (Jeru-
salem), Asher Peres (Haifa), Abner Shimony (Boston) and Andrew
Whitaker (Belfast).
For comments on Chapter 7 I want to thank Tony Dean (Southamp-
ton), Jeremy Goodman (Princeton) and Malcolm Longair
(Cambridge).
Copyright © 2000 IOP Publishing Ltd.
Chapter 1
What this book is about
1.1 Introduction
Our wish to understand the cosmos takes us to physics! It is the most
fundamental of the sciences: even in biology or studies of the brain,
the concepts from physics are essential. The snag is that physics has
the reputation of being mathematical and hard to understand. We get
around this problem here by the use of intuition. That is my first pur-
pose. There is no mathematics in this book.
A red thread runs through this work to show that things are not as cut
and dried as people often think: I emphasize, and that is my second
purpose, that the notion of incompleteness is central to the whole of
science.
1.2 My story
It may help if I tell you first a little about myself. In the troubled
atmosphere of 1939, when I had just arrived in England and I had to
think about how to make my way in life, there fell into my hands a
copy of Sir Arthur Eddington’s Gifford lectures [1.1]. A single sen-
tence, but an exciting one (in his Chapter 10), lit in me the desire to
become a scientist:
‘All authorities seem to agree that at, or nearly at, the root
of everything in the physical world lies the mystic formula
pq−qp=ih.’
One formula to understand the universe! How exciting! That should
not be beyond me! But Eddington had cheated a little, for now that I
Copyright © 2000 IOP Publishing Ltd.
