Alice in Quantumland: An Allegory of Quantum Physics
Page 1
Alice
in
Quantumland
AN ALLEGORY OF QUANTUM PHYSICS
Alice
in
Quantumland
Robert Gilmore
COPERNICUS
AN IMPRINT OF SPRINGER-VERLAG
© 1995 Springer-Verlag New York, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Published in the United States by Copernicus Books, an imprint of Springer-Verlag New York, LLC by arrangement with Birkhauser Boston. A member of Springer Science+Business Media Copernicus Books 37 East 7th Street New York, NY 10003
www.copernicusbooks.com Library of Congress Cataloging-in-Publication Data Gilmore, Robert, 1938Alice in Quantumland : an allegory of quantum physics / Robert Gilmore p. cm. Includes bibliographical references and index. ISBN 0-387-91495-1 (acid-free paper) 1. Quantum theory- Fiction. I. Title PS3557.14595A45 1995 813 x.54- dc20 95-10163
Manufactured in the United States of America. Printed on acid-free paper. 19 18 17 16 15 14 13 12 11 ISBN 0-387-91495-1 SPIN 10992432
Preface
n the first half of the twentieth century, our understanding of the Universe was turned upside down. The old classical theories of physics were replaced by a new way of looking at the world-quantum mechanics. This is in many ways at variance with the ideas of the older Newtonian mechanics; indeed, in many ways it is at variance with our common sense. Nevertheless, the strangest thing about these theories is their extraordinary success in predicting the observed behavior of physical systems. However nonsensical quantum mechanics may at times appear to us, that seems to be the way that Nature wants it-and so we have to play along.
This book is an allegory of quantum physics, in the dictionary sense of "a narrative describing one subject under the guise of another." The way that things behave in quantum mechanics seems very odd to our normal way of thinking and is made more acceptable when we consider analogies to situations with which we are familiar, even though the analogies may be inexact. Such analogies can never be very true to reality as quantum processes are really quite different from our normal experience.
An allegory is an extended analogy, or series of analogies. As such, this book follows more in the footsteps of Pilgrim's Progress or Gulliver's Travels than of Alice in Wonderland. "Alice" appears the more suitable model, however, when we examine the world that we inhabit.
The Quantumland in which Alice travels is rather like a theme park in which Alice is sometimes an observer, while sometimes she behaves as a sort of particle with varying electric charge. This Quantumland shows the essential features of the quantum world: the world that we all inhabit.
Much of the story is pure fiction and the characters are imaginary, although the "real-world" notes described below are true. Throughout the narrative you will find many statements that are obviously nonsensical and quite at variance with common sense. For the most part these are true. Neils Bohr, the father figure of quantum mechanics in its early days, is said to have remarked that anyone who did not feel dizzy when thinking about quantum theory had not understood it.
Seriously, Though . . .
The description of the world that is given by quantum mechanics is undoubtedly interesting and remarkable, but are we seriously expected to believe that it is true? Amazingly, we find that we must. To underline this assertion, throughout this book you will find brief notes which emphasize the importance of quantum mechanics in the real world. The notes look like this:
There are also some longer, end-of-chapter, notes. These amplify some of the trickier points in the text and are denoted thus:
See end-of-chapter note 1
Much of the way that quantum theory describes the world may seem at first sight to be nonsense-and possibly it may seem so at the second, third, and twenty-fifth sight as well. It is, however, the only game in town. The old classical mechanics of Newton and his followers is unable to give any sort of explanation for atoms and other small systems. Quantum mechanics agrees very well with observation. The calculations are often difficult and tedious, but where they have been made, they have agreed perfectly with what has really been seen.
It is impossible to stress too strongly the remarkable practical success of quantum mechanics. Although the outcome of one measurement may be random and unpredictable, the predictions of quantum theory agree consistently with the average results obtained from many measurements. Any large-scale observation will involve very many atoms and thus very many observations on the atomic scale. We again find that quantum mechanics is successful, in that it automatically agrees with the results of classical mechanics for large objects. The converse is not true.
Quantum theory was developed to explain observations made on atoms. Since its conception, it has successfully been applied to atomic nuclei, to the strongly interacting particles which derive from the nucleus, and to the behavior of the quarks of which these are composed. The application of the theory has been extended over a factor of some hundred thousand million. The systems considered have both decreased in size and increased in energy by this factor. This is a long way to extrapolate a theory from its original conception, but so far quantum mechanics appears to be quite able to deal with these extreme systems.
Insofar as it has been investigated, quantum mechanics appears to be of universal applicability. On a large scale, the predictions of quantum theory lose their random aspect and agree with those of classical mechanics, which works very well for large objects. On a small scale, however, the predictions of quantum theory are consistently borne out by experiment. Even those predictions, which seem to imply a nonsensical picture of the world, are supported by experimental evidence. Intriguingly, as is discussed in Chapter 4, quantum mechanics would appear to be in the strange position of agreeing with all observations made, while disputing that any observations can actually be made at all. It seems that the world is stranger than we imagine and perhaps stranger than we can imagine.
For the present, however, let us accompany Alice as she begins her journey into Quantumland.
Robert Gilmore
Contents
Into Quantumland
The Heisenberg Bank
The Mechanic's Institute
The Copenhagen School
The Fermi-Bose Academy
Virtual Reality
Atoms in the Void
Castle Rutherford
The Particle MASSquerade
The Experimental Physics Phun Phair
lice was bored. All her friends were on holiday or visiting relations and it was raining, so that she was marooned indoors watching television. So far that afternoon she had watched part five of a series on introductory Esperanto, a program on gardening, and a paid political broadcast. Alice was really bored.
She looked down at the book lying on the floor beside her chair. It was a copy of Alice in Wonderland, which she had been reading earlier and had dropped there when she finished it. "I do not know why there cannot be more cartoons and interesting programs on the television," she wondered idly to herself. "I wish I could be like that other Alice. She was feeling bored and then she found her way to a land full of interesting creatures and strange happenings. If I could shrink down somehow and float through the television screen perhaps I might find all sorts of fascinating things."
She stared in frustration at the screen, which at that moment carried a picture of the Prime Minister telling her how, all things considered, everything was reall
y far better than it had been three years ago, even if it didn't always seem that way. As she watched she was mildly surprised to see the picture of the Prime Minister's face slowly break apart into a mist of bright dancing speckles which all seemed to be rushing inward, as if they were beckoning her. "Why," said Alice, "I do believe that they want me to follow them in!" She leapt to her feet and started toward the television, but tripped on the book which she had discarded so untidily on the floor and fell headlong.
As she fell forward she was amazed to see the screen grow enormously, and she found herself in among the swirling speckles, rushing with them down into the picture. "I cannot see anything with these dots swirling all around me," thought Alice. "It is just like being lost in a snowstorm; why I cannot even see my feet. I wish I could see just a little. I could be anywhere."
At that moment Alice felt her feet strike something solid and she found herself standing on a hard, flat surface. All around her the swirling dots were fading away and she found that she was surrounded by a number of vague shapes.
She looked more closely at the one nearest to her and observed a small figure, coming roughly up to her waist. It was exceedingly difficult to make out, as all the time it kept hopping rapidly to-and-fro, moving so fast that it was very difficult to see at all clearly. The figure seemed to be carrying some sort of stick, or possibly a rolled umbrella, which was pointing straight up in the air. "Hello," Alice introduced herself politely. "I am Alice. May I ask who you are?"
"I am an electron," said the figure. "I am a spin-up electron. You can readily tell me apart from my friend there who is a spin-down electron, so, of course, she is quite different." Under his breath he added something which sounded rather like "Vive la difference!" As far as Alice could see, the other electron looked very much the same, except that her umbrella, or whatever it was, was pointing down toward the ground. It was very difficult to tell for sure, as this figure also was jigging to-and-fro as rapidly as the first.
"Oh please," said Alice to her first acquaintance. "Would you be good enough to stand still for a moment, as I really cannot see you at all clearly?"
"I am good enough," said the electron, "but I am afraid there is not room enough. However I will try." So saying he slowed his rate of jiggling. But as he moved more slowly, he began to expand sideways and become more and more diffuse. Now, although he was no longer moving at all quickly, he looked so fuzzy and quite out of focus that Alice could no more see what he looked like than she had been able to before. "That is the best I can do," he panted. "I am afraid that the more slowly I move, the more spread out I become. That is the way things are here in Quantumland: The smaller the space you occupy, the faster you have to move. It is one of the rules, and there is nothing I can do about it."
"There isn't really room to slow down here," continued Alice's companion as he began once more to leap rapidly around. "The platform is becoming so crowded that I have to be more compact." Sure enough, the space in which Alice stood had now become very crowded indeed, being closely packed with the small figures, each dancing feverishly to-and-fro.
"What strange beings," thought Alice. "I do not think I shall ever be able to see quite what they look like if they will not stand still for a minute, and there does not seem to be much chance of that." Since it did not look as if she could get them to slow down she tried another topic. "Would you tell me please what sort of platform we are on?" she asked.
"Why a railway platform, of course," replied one of the electrons cheerfully (it was very hard for Alice to say which had spoken; they really did all look very much the same). "We are going to take the wave train to the screen you see. You will change there to the photon express I expect, if you want to go any farther."
"Do you mean the television screen?" asked Alice.
"Why of course I do," cried one of the electrons. Alice could have sworn that it was not the same one which had just spoken, but it was very difficult to be certain. "Come on! The train is here and we have to get on."
Sure enough, Alice could see a line of small compartments drawn up at the platform. They were very small. Some were empty, some had one electron in, and some two. All of the empty compartments were filling rapidly-in fact there did not seem to be any left-but Alice noticed that not one of the compartments held more than two electrons. As they passed by any of these compartments, the two occupants would cry out "No room! No room!"
"Surely you could squeeze more than two into a compartment, seeing as the train is so crowded?" Alice asked her companion.
"Oh no! Never more than two electrons together, that is the rule."
"I suppose we shall have to get into different compartments then," declared Alice regretfully, but the electron reassured her.
"There's no problem there for you, no problem at all! You can get into any compartment that you want, of course."
"I am sure that I do not see why that should be," Alice replied. "If a compartment is too full to hold you, then it must surely be too full for me as well."
"Not at all! The compartments are only allowed to hold two electrons, so almost all the places for electrons may be taken up, but you are not an electron! There is not a single other Alice on the train, so there is plenty of room for an Alice in any of the compartments."
This did not seem to follow so far as Alice could see, but she was afraid that the train would start to move off before they got seats, so she began looking for an empty space that could take another electron. "How about this one?" she asked her associate. "Here is a compartment with only one other electron already in it. Can you get in here?"
"Certainly not!" he snapped, sounding quite horrified. "That is another spin-up electron. I cannot share a compartment with another spin-up electron. What a suggestion! It is quite against my principle."
"Don't you mean against your principles?" Alice asked him.
"I mean what I say, against my principle, or rather Pauli's principle. It forbids any two of us electrons from doing exactly the same thing, which includes being in the same space and having the same spin," he responded crossly.
Alice did not really know why she had upset him, but she looked around hastily to find another compartment which might suit him better. She managed to find one that held a single electron who was of the spin-down variety, and Alice's companion leaped into this one readily enough. Alice was surprised to find that although the tiny compartment now seemed full there was somehow enough room for her to fit in quite easily.
No sooner were they settled in than the train moved off. The journey was uneventful and the scenery not very interesting, so Alice was rather glad when the train began to slow down. "This must be the screen, I suppose," thought Alice. "I wonder what will happen here."
As they alighted at the screen there was an enormous bustle everywhere. "Whatever is going on?" Alice wondered aloud. "Why does everyone seem to be so excited?" Her questions were answered by an announcement which appeared to come from the air all around her.
"The screen phosphor is presently being excited by the incoming electrons, and we shall be having photon emission soon. Stand by for the departure of the photon express." Alice looked around to see if she could see the express arriving, when there was a rush of bright shining shapes across the platform. Alice was caught up in the middle of the crowd and carried along with them as they all crowded into one compartment. "Well, they do not seem to be worried by any principle, Pauli or otherwise," thought Alice as they crowded in around her. "These ones are certainly not worried about all being in the same place. I suppose the express is going to start soon. I wonder where ...
"... we shall end up," she concluded as she stepped out onto the platform. "My, that was certainly a fast journey. Why, it seemed to take no time at all." (Alice was quite right about this. The journey did indeed take no time at all, as time is effectively frozen for anything which is traveling at the velocity of light.) Once again she found herself surrounded by a crowd of electrons, all rushing away from the platform.
"Excuse me," Alice asked it tentatively, "are you the same electron that I was talking to before?"
"Yes I am," answered the electron as it darted off down a side passage. Alice was swept along by the crowd of electrons and carried through the main gateway from the platform.
"I declare, this is really too irksome," said Alice. "Now I have lost the only person I know at all in this strange place and have no one to explain what is happening."
"Don't worry Alice," said a voice from about knee level. "I will show you where to go." It was one of the electrons.
"How do you know my name?" asked Alice in surprise.
"That's simple. I am the same electron that spoke to you before."
"You cannot be!" exclaimed Alice. "I saw that electron go off in a different direction. Perhaps he was not the same one I was talking to before?"
"Certainly he was."
"Then you cannot be the same one," said Alice reasonably. "You cannot both be the same one you know."
"Oh yes we can!" replied the electron. "He is the same. I am the same. We are all the same, you know, exactly the same!"
"That is ridiculous," argued Alice. "You are here beside me, while he has run off somewhere over there, so you cannot both be the same person. One of you must be different."
"Not at all," cried the electron, jumping up and down even faster in its excitement. "We are all identical; there is no way whatsoever that you can tell us apart, so you see that he must be the same and I am the same too."
At that point the crowd of electrons which surrounded Alice all began to cry out, "I am the same," "I am the same too," "I am just the same as you are," "I am too, just the same as you." The tumult was dreadful, and Alice closed her eyes and put her hands over her ears until the noise died down again.