How Schrodinger's Cat Escaped the Box

198 Pages·2015·5.76 MB·English

by  Peter Rowlands

How Schrödinger’s Cat
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How Schrödinger’s Cat
Escaped the Box
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H Peter Rowlands

University of Liverpool, UK
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
9391_9789814635196_tp.indd 2 3/11/14 12:11 pm
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
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cie British Library Cataloguing-in-Publication Data
ds A catalogue record for this book is available from the British Library.
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ow6/1 Copyright © 2015 by World Scientific Publishing Co. Pte. Ltd.
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n Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
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ISBN 978-981-4644-61-7
ISBN 978-981-4635-19-6 (pbk)
In-house Editor: Ng Kah Fee
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
KahFee - How Schrodinger's Cat Escaped.indd 1 30/10/2014 4:33:29 PM
November4,2014 13:10 HowSchr¨odinger’sCatEscapedtheBox 9inx6in b1958-fm pagev
Preface
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w.worle only. at its most fundamental level, the level at which its most profound
wus mysteries occur — mysteries such as: what are space and time? why
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nloade5. For millennia, and don’t seem to be any closer to the answers than our
w1 remote ancestors were, though we have in the process solved many
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Cat Escape5.235.133. tphhoysseicwshhoavheaavneyspheonpteyoefaervseonfbreiggoinronuinsgtrtaoinuinndgerinstamnadththemema.tiIcsdoann’dt
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Ho the attentive and systematic reader can, in the process, acquire the

technicalknowledgetounderstandatleastsomeaspectsofthefunda-
mentalnatureofphysics,includingthequantummechanicssuggested
by the title, at a level far beyond that of popular ‘hand waving’.
And yet, though this can be done, it is still difficult to do, and
requires a great deal of mental discipline. No one, trained scien-
tist or otherwise, finds this way of thinking easy. Complexity has
nothing to do with it. The difficulty is not intrinsic to the subject.
There is an immense barrier to be overcome, but it doesn’t come
v
November4,2014 13:10 HowSchr¨odinger’sCatEscapedtheBox 9inx6in b1958-fm pagevi
vi How Schro¨dinger’s Cat Escaped the Box
from nature’s supposedly complicated ways. It comes from our own
habits of thought. We have to overcome generations of conditioning
which makes us want to see nature in a different way to the one
in which it really acts. Centuries of collective effort, in which we
have forced ourselves to believe in the results of experiments which
often go against the grain, have led us in the right direction, but
perhaps we haven’t yet gone far enough. Only one method has ever
worked though we have always been reluctant to use it. We have to
m
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cie mechanical paradoxofSchro¨dinger’scatissymptomaticofourdesire
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w.e o gible connection with our ordinary world. However, if Schro¨dinger’s
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din the most familiar and reassuring aspects of our everyday world —
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yet science has shown us, as the result of a long process of system-
atic observation and theorising, that the solidity of material things
is only an illusion. Solidity is an emergent property, not a funda-
mental one. Reduce the scope of observations from the usual range
of millimetres to kilometres by 15 orders of magnitude (or 15 suc-
cessive powers of ten) and we find that there is no such thing as
an extended object. There are only dimensionless points interacting
with each other with various forces to give theillusion of rigidity and
November4,2014 13:10 HowSchr¨odinger’sCatEscapedtheBox 9inx6in b1958-fm pagevii
Preface vii
solidity, and even these cannot be located at particular positions in
space.
Considering how much we are conditioned by the complexity of
our environment, it is astonishing that we are able to think at all at
a fundamental level, and imagine things that we can never observe,
which are so very different from the objects of our familiar world.
So,howcanwedothis?Howisitthatwecandofundamentalscience
at all? The answer is a principle that we are only just beginning to
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cie levels. Of course, it is not the actual structures and qualities that it
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w.e o The question that we have posed is: can we access these patterns
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din that we are working only at a superficial level. On the contrary, the
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will be much in this book for the professional physicist, even at the
technical level, and there will certainly be many novel concepts and
methodologies.
Quantummechanicsisseeminglyattheheartofallourdifficulties
in understanding the nature of physical reality, but I hope to show
that it is the key, rather than the problem. However, the only way
to make the breakthrough in understandingis to go to an even more
fundamental level which is at present completely unknown territory,
November4,2014 13:10 HowSchr¨odinger’sCatEscapedtheBox 9inx6in b1958-fm pageviii
viii How Schro¨dinger’s Cat Escaped the Box
and to use mathematical ideas which, though long established, are
relatively unfamiliar, even among physicists. To understand where
quantum mechanics comes from, we have to transform the way we
representit, andthis shouldhave agreat deal of relevance to practis-
ing physicists, especially as the version required seems to be partic-
ularly powerful and transparent to an unprecedented degree. Using
this formulation, I believe, we will be able to see exactly why quan-
tum mechanics is there and exactly what it means. The confining
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cie one’sfavouritecattomakeitsgreatescape,Iamparticularlygrateful
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w.e o mechanics in some of its earlier stages, and to Chas McCaw and
m wwnal us Mike Houlden who made helpful comments on drafts of the book.
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November4,2014 13:10 HowSchr¨odinger’sCatEscapedtheBox 9inx6in b1958-fm pageix
Contents
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worlnly. 1. Introduction 1
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4.1 Keep it simple . . . . . . . . . . . . . . . . . . . . . . 65
4.2 Abstraction . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Missing an open goal . . . . . . . . . . . . . . . . . . 70
4.4 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5. Symmetry and Duality 86
5.1 What is measurement? . . . . . . . . . . . . . . . . . 86
5.2 Conserved and nonconserved . . . . . . . . . . . . . 88
ix