The Roots of Things: Topics in Quantum Mechanics

593 Pages·1999·21.724 MB·English

by  Alan A. Grometstein (auth.)

The Roots of Things
Topics in Quantum Mechanics
The Roots of Things
Topics in Quantum Mechanics
Alan A . Grometstein
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Cover illustration: Depiction of a Gaussian wave packet (filled form) representing an electron which
first moves toward, then recoils from, a strong negative potential barrier (open rectangle). Ten
snapshots of the packet are shown from right to left at equispaced epochs from 0 to 9. As the real
and complex components of the packet interact with the nearby barrier, peaks develop which subsied
as the packet reverses direction and moves away from the barrier. By Epoch 9, the Gaussian outline
of the packet is restored. The inevitable dispersion of the packet takes place throughout the "splash"
of the packet against the barrier; this explains why the later forms of the packet are broader and
squatter than the early forms. As with most illustrations in this book, the wave packet sequence was
created on the powerful and versatile computer program MATLAB Version 5.
ISBN 978-1-4613-7213-4 ISBN 978-1-4615-4877-5 (eBook)
DOI 10.1007/978-1-4615-4877-5
© 1999 Springer Science+Business Media New York
Originally published by Kluwer Academic / Plenum Publishers in 1999
Softcover reprint of the hardcover 1st edition 1999
109 8 7 6 5 43 2 1
A C.I.P. record for this book is available from the Library of Congress
All rights reserved
No part of this book may be reproduced, stored ni a retrieval system, or transmitted in any form
or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise,
without written permission from the Publisher
To Margaret:
Pole Star, lodestone, couch ofc omfort, Central Fire.
Foreword: The Root of Things
A
reader of this book is going to have fun. Rarely has good physics been
presented in such a cheerful manner. Alan Grometstein explains modern
physics with enthusiasm, wit, and insight. Perhaps he writes so well about
physics because he is a mathematician. Physicists tend to treat modern physics as
rather commonplace and even boring. We have known about it all our lives; it works;
so why get too enthusiastic? Grometstein has a fresh viewpoint. He really demon
strates how absurd the concepts which govern our world are. They may be correct,
and they may agree with numerous experiments, but they are not sensible. Even
Einstein refused to believe in modern quantum mechanics and continually pre
sented counterarguments.
Grometstein presents the usual milestones in the history of modern physics.
His central focus is the historical debate regarding the nature of light: is it a particle
or is it a wave? Young's two-slit experiment settled the debate on the side of waves.
Not until Einstein explained the photoelectric effect did the particle viewpoint
become reestablished. He carefully discusses Taylor's experiment, in which the
light is so feeble that each light particle must only interfere with itself! Finally, the
wave-particle duality of modern quantum mechanics resulted in a theory in which
waves and particles are on equal footing.
Although this material is traditional, Grometstein explains it quite well, better
than anybody else. I have never read a book on this material in which the
explanations are done as well. Grometstein states, in his preface, that the intended
audience is a well-educated reader. One hopes that reader has a firm grasp of
algebra. My expectation is that this book will be read by generations of students in
physical science who seek a well written discussion of these important issues.
Unlike older textbooks on modern physics, Grometstein includes material
which is quite recent. A whole chapter is devoted to the famous paradox of Einstein,
vii
viii The Roots of Things
Podolsky, and Rosen (EPR). 1Wo additional chapters cover John Bell's work on the
interpretation of EPR. This material is quite new in physics and makes the present
volume particularly useful. Indeed, modem physics is not a dead, uninteresting
topic. Grometstein shows that it is a topic of lively interest and recent advances.
Have fun!
Gerald Mahan
University of Tennessee and Oak Ridge National Laboratory
Preface
W
hy another book on physics, on quantum mechanics in particular? Many
books have been written on this subject, at all levels of exposition from
popularized treatments to theoretical texts for the specialist. Some of these
books are excellent; most are rewarding to read; few are a waste of time. Why, then,
another?
Especially a book such as this, which is not even a comprehensive treatment
of any particular aspect of quantum mechanics. Indeed, it is merely a set of
discourses or essays on selected topics. It is concerned with clarifying definitions
and highlighting questions; there is even a hint that the questions might be more
illuminating than the answers. The book is, frankly, deficient in answers: it is meant
to be provocative rather than satisfying.
The quick rejoinder to "Why this book?" is I felt compelled to write it. I had
long contemplated my approaching retirement from a career as research mathema
tician. "Shall I take up golf?" [Yes] "Shall I take up duplicate bridge?" [No] "Shall
I ... ?" [Dither]. Then, at the base of a structure in my mind I did not know existed,
a component which must always have been askew slid into place with a psychic
"clunk!" My reaction was a startled, "Of course! I'll write a book on quantum
mechanics!" I felt what Rudyard Kipling's Explorer felt:
Something hidden. Go and find it.
Go and look behind the Ranges.
Something lost behind the Ranges.
Lost and waiting for you. Go.
I had spent my professional life on problems of a mathematical nature in a
research-and-development laboratory. Typically, after the solution to a problem had
been found, there would be talks and written reports to audiences, civilian and
ix
x The Roots of Things
military, already familiar with the problem and eager to absorb the solution. My
task was not to argue the importance of the problem-that was accepted by all
concerned-but to explain the solution so that everyone, most of them specialists
in other fields, could appreciate and apply it. I found that solving a problem gave
me deep satisfaction, but that explaining it gave a different and equally intense
pleasure.
However, there is more to this book than an indulgence in ego: I think the book
is needed. Addressing the public on the subject of quantum mechanics is a different
kettle of fish than outlining the solution of a problem familiar to an eager audience.
What am I trying to accomplish? Two things: first, to inform the reader of the deeply
radical and fascinating aspects of the "new physics" and, second, to convince the
reader that these topics are not beyond his or her grasp.
Ours is an age of science. Technical innovations flood our lives, affecting every
aspect of our being, individual and societal. The pace of innovation has never been
faster, and the pace is accelerating. The economist Kenneth Boulding, writing in
his middle age in 1966, put it strikingly:
The world of today is as different from the world in which I was born as that world was from
Julius Caesar's. I was born in the middle of human history, to date. Almost as much has
happened since I was born as happened before.!
Alvin Toffler, in his influential Future Shock, quotes Boulding and goes on to say:
... if the last 50,000 years of man's existence were divided into lifetimes of approximately
sixty-two years each, there have been about 800 such lifetimes. Of these 800, fully 650 were
spent in caves.
Only during the last seventy lifetimes has it been possible to communicate effectively from
one lifetime to another-as writing made it possible to do. Only during the last six lifetimes
did masses of men ever see a printed word. Only during the last four has it been possible to
measure time with any precision. Only in the last two has anyone anywhere used an electric
motor. And the overwhelming majority of all the material goods we use in daily life today
have been developed within the present, the 800th, Iifetime.2
The innovations to which Boulding alludes and Toffler refers are not abstrac
tions: they are concrete and come home to all of us. My wife's father succumbed
in the 1940s to a pneumonia which resisted the medications of the times but which
would probably have crumbled before those of the 1990s. Much of my professional
life has been spent studying the performance of weapon systems whose operative
principles were not glimpsed when I was born. The computer on which I write this
book vanquished the typewriter two decades ago. The lives of my grandchildren
are shaped by a congeries of factors, many of which were unimagined in my youth.
And-let me emphasize-their life expectancies are longer than mine and their
expected state of health superior. To the extent that the outside world can convey
Preface xi
happiness, they ought to be happier than I. The impact of the technical revolution
is real, massive, and largely beneficial.
The Good Old Days
Yet, change is unsettling. People feel buffeted by waves of novelty, threatened
by forces they don't understand and therefore have no hope of controlling. Unaware
of the benefits inherent in the innovations, they see only the risks, some clearly,
most magnified by fear. A sense of history is a comfort in times of stress, but many
people lack historical perspective and imagine that no age, no culture, has ever been
in such a precarious position. Their ignorance of history feeds their fear of the
future. Characteristically, their despair often takes the form of a yearning for a time
and a land that never were. As Adam and Eve stumbled eastward out of the garden
built in Eden, they muttered, "Oh, for the good old days." The phrase persists with
the legend.
But this is madness. Who would trade places with a swineherd in Merrie Olde
England of the 14th century as the first reports of the Black Death came in? Raise
hands, those who envy a jolly, fat burgess-Protestant, Catholic, or Jew: it makes
no difference-in a small town in central Europe at the onset of the Thirty Years'
War. You who are charmed by W. B. Yeats' Byzantium: would you care to have lived
in that Orthodox city on the Golden Horn when the Catholic Fourth Crusade
breached its walls in sectarian fury, or later when the Moslem assault completed
the ruin?
Do you admire the literary scene of mid-18th-century London? Then you may
know of the letter Samuel Johnson sent to a woman friend, commiserating on the
recent death of her child. After expressing the usual sentiments, Johnson concludes
by pointing out how fortunate she was compared with her peers, because three of
her five young children were still alive. In those good old days, a 60% infant survival
rate was "fortunate."
A century and a half ago, when Thomas Babington Macaulay began his History
ofE ngland in the reign ofJ ames /I-a time 150 years in Macaulay's past-he wrote:
Those who compare the age on which their lot has fallen with a golden age which exists only
in their imagination may talk of degeneracy and decay: but no man who is correctly informed
as to the past will be disposed to take a morose or desponding view of the present. 3
Franklin Pierce Adams converted this sentiment into a wry epigram: "Nothing
is more responsible for the good old days than a bad memory." If you challenge
this, then be specific, ye wailers and regretters: which were "the good old days"?
Give precise dates, latitudes, and longitudes. On which pleasant street, in which
idyllic town, lit by a golden sun, lived the man or woman whom you envy without
reservation? For exactly whom, and in precisely what ways, were the old days good?
xii The Roots of Things
For whom, on the other hand, were they "double-plus ungood"? Would you trade
places, bag, and baggage? If not, perhaps you should stop moaning.
I feel it is a mistake to fear the future. Our predicament is not a new one: it is
the common predicament of human beings in all ages. Technical innovations are
per se neither good nor bad, as the first bronze knife was neither good nor bad. True,
you could supply more meat for the tribe with bronze than with flint, but the bronze
slipped more easily between the ribs of your brother, Abel. The qualities of good
and bad inhere in us and it is a blunder to project them outwardly.4 Innovations are
what we make of them. This is not a new thought:
I have set before you life and death, blessing and cursing: therefore choose life. S
Let Light Shine In
A guiding impulse as I wrote this book was to shed light on the scientific
innovations that are reshaping our lives. Not the new technologies ("What is an
atomic reactor?"), but the new viewpoints in physics which underpin those tech
nologies (''What is an atom?"). These innovative viewpoints are usually presented
as arcane. The average reader consigns them to the limbo containing religion,
computers, finance, contraception, and all subjects that are "beyond me." It is not
considered disgraceful for an adult to boast, "Mathematics was my worst subject
in school:' or, "Physics is too deep for me." The medieval baron, fingering his sword
hilt, mutters, "Learn to read? Nonsense, what do I have a clerk for?" Intellectual
taboos bind as tightly as cultural taboos.
Physics is open to the inquiring layperson, not just to the devoted specialist.
As a tool for shaping the world "closer to our heart's desire:' it ought to be more
widely understood. "Ought" is a dangerous word; I use it here in the same sense as
I might say, "If you plan to become a builder, you ought to know something of the
materials of your trade. Wood is fine if you protect it from termites, damp, and fire.
Iron rusts. Titanium is light and tough but expensive. Concrete is strong if you
compress it; never trust it in tension." To be a builder, you needn't be a miner who
can dig the ores, you needn't be a metallurgist who can cook up batches of steel to
a fare-thee-well, but if you are serious in wanting to build, ignorance of the materials
of your trade can only limit you.
We are not all builders, but we all live in a world that is wondrously built. The
fabric of the world is the canvas on which all aspects of our lives are embroidered.6
To ignore that fabric is willfully to choose ignorance over knowledge-death over
life. Mind you, I am not arguing that familiarity with the scientific roots of things
will make you popular at cocktail parties. Quite the reverse: people will stare at
you, suddenly recognize an old friend at the far end of the room. and drift away. C.
P. Snow's words are more than a literary invention: