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Penguin Group (NZ), 67 Apollo Drive, Rosedale, Auckland 0632, New Zealand

(a division of Pearson New Zealand Ltd)

Penguin Books (South Africa) (Pty) Ltd, 24 Sturdee Avenue, Rosebank 2196, South Africa

Penguin Books Ltd, Registered Offices: 80 Strand, London WC2R 0RL, England

www.penguin.com

First published 2011

Copyright © Brian Cox and Jeff Forshaw, 2011

The moral right of the authors has been asserted

Thanks to Paul Hetherington for recommending the front-cover font: Lÿon, designed by Radim Pesko and Karl Nawrot

Cover art-directed by Peter Saville

Cover photograph by Tina Negus

All rights reserved.

Without limiting the rights under copyright reserved above, no part of this publication may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of both the copyright owner and the above publisher of this book

ISBN: 978-0-14-196803-2

1. Unless of course you are reading an electronic version of the book, in which case you will need to exercise your imagination.

1. But not so ridiculous when you consider that an oft-used unit of power, even to this day, is the ‘horsepower’.

2. Once upon a time, televisions operated using this idea. A stream of electrons generated by a hot wire was gathered, focused into a beam and accelerated by a magnetic field towards a screen that glowed when the electrons hit it.

1. For those who are familiar with mathematics, just exchange the words as follows: ‘clock’ for ‘complex number’, ‘size of the clock’ for ‘modulus of the complex number’ and ‘the direction of the hour-hand’ for ‘the phase’. The rule for adding clocks is nothing more than the rule for adding complex numbers.

1. Or aesthetic appeal, depending on your point of view.

2. If you are having trouble with that last sentence try replacing the word ‘clock’ with ‘wave’.

3. The kinetic energy is equal to mv2/2 and the potential energy is mgh when the ball is a height h above the ground. g is the rate at which all objects accelerate in the vicinity of the Earth. The action is their difference integrated between the times associated with the two points on the path.

4. Wikipedia describes ‘tripe’ as ‘a type of edible offal from the stomachs of various farm animals’, but it is colloquially used to mean ‘nonsense’. Either definition is appropriate here.

5. Shrinking all clocks by the same amount is strictly only true provided that we are ignoring the effects of Einstein’s Special Theory of Relativity. Otherwise, some of the clocks get shrunk more than others. We shan’t need to worry about this.

6. For a particle of mass m that hops a distance x in a time t, the action is ½m(x/t)2t if the particle travels in a straight line at constant speed. But this does not mean the quantum particle travels from place to place in straight lines. The clock-winding rule is obtained by associating a clock with each possible path the particle can take between two points and it is an accident that, after summing over all these paths, the result is equal to this simple result. For example, the clock-winding rule is not this simple if we include corrections to ensure consistency with Einstein’s Theory of Special Relativity.

7. A sand grain typically has a mass around 1 microgram, which is a millionth of a kilogram.

8. There is a chance that the particle travels even farther than the ‘extreme’ case marked out by the large blob in the figure but, as we have shown, the clocks tend to cancel out for such scenarios.

1. You might like to check this explicitly for yourself.

2. ‘Diffraction’ is a word used to describe a particular type of interference, and it is characteristic of waves.

3. Of course if d is very large then one might wonder how we can even measure the momentum. That concern is sidestepped by ensuring that no matter how big d is, L is much bigger than it.

4. Recall that when we draw