How to Build a Time Machine Read online

  PENGUIN BOOKS

  HOW TO BUILD A TIME MACHINE

  Paul Davies is currently Professor of Natural Philosophy at the Australian Centre for Astrobiology, Macquarie University, Sydney, Visiting Professor at Imperial College in London and Adjunct Professor at the University of Queensland. He obtained a Ph.D. from the University of London and has held academic appointments at the universities of London, Cambridge, Newcastle upon Tyne and Adelaide. His research interests are in the field of black holes, cosmology and quantum gravity. Professor Davies is the author of some twenty-five books, including The Mind of God, About Time and, most recently, The Fifth Miracle.

  Paul Davies

  * * *

  HOW TO BUILD A TIME MACHINE

  PENGUIN BOOKS

  PENGUIN BOOKS

  Published by the Penguin Group

  Penguin Books Ltd, 80 Strand, London, WC2R 0RL, England

  Penguin Putnam Inc., 375 Hudson Street, New York, New York 10014, USA

  Penguin Books Australia Ltd, 250 Camberwell Road, Camberwell, Victoria 3124, Australia

  Penguin Books Canada Ltd, 10 Alcorn Avenue, Toronto, Ontario, Canada M4V 3B2

  Penguin Books India (P) Ltd, 11 Community Centre, Panchsheel Park, New Delhi - 110 017, India

  Penguin Books (NZ) Ltd, Cnr Rosedale and Airborne Roads, Albany, Auckland, New Zealand

  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 in Great Britain by Allen Lane The Penguin Press 2001

  Published in Penguin Books 2002

  9

  Copyright © Paul Davies, 2002

  All rights reserved

  Illustrations by Rebecca Foster and Dan Adams

  The moral right of the author has been asserted

  Except in the United States of America, this book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser

  ISBN: 978-0-14-193042-8

  Contents

  List of illustrations

  Acknowledgements

  A brief history of time travel

  Prologue

  1 How to visit the future

  2 How to visit the past

  3 How to build the time machine

  4 How to make sense of it all

  Epilogue

  Bibliography

  Index

  List of illustrations

  Sir Isaac Newton

  Albert Einstein

  The Hafele–Keating experiment

  The time dilation formula

  Time runs faster in space

  Gravity slows time

  Gravitational timewarp

  The crab nebula

  Energy has mass

  What time is it now?

  Kurt Gödel

  John Wheeler

  Geometry on a curved surface

  A spacewarp round the sun

  Einstein ring

  Black hole spacewarp

  Einstein–Rosen bridge

  A spacetime diagram

  Curved spacetime

  The hazards of entering a black hole

  Sir Roger Penrose

  Carl Sagan

  Kip Thorne

  A wormhole

  Using a wormhole as a time machine

  A time machine factory

  Topology change

  Hendrik Casimir

  Negative energy from a moving mirror

  Stephen Hawking

  H.G. Wells

  Making successive hops back in time

  Information for free?

  Quantum uncertainty

  Many universes?

  Double quasar images

  Acknowledgements

  I am grateful to many people for assisting me with this book. Special thanks are due to colleagues Gerard Milburn, Lee Smolin, Peter Szekeres, Andrew White and David Wiltshire, as well as my agent John Brockman and my editor at Penguin Books, Stefan McGrath.

  A brief history of time travel

  1895 H. G. Wells publishes The Time Machine

  1905 Albert Einstein publishes the special theory of relativity; time dilation predicted

  1908 Einstein conjectures that gravity slows time

  1915 Einstein's general theory of relativity published

  1916 Karl Schwarzschild presents the first black hole/wormhole solution of general relativity

  1917 Ludwig Flamm discovers wormhole character of Schwarzschild's solution

  1917 Einstein proposes a cosmic repulsion force – the first conjecture about ‘antigravity’

  1934 Black holes from collapsing stars predicted

  1935 Einstein–Rosen bridge (wormhole) discussed

  1937 W. J. van Stockum discovers the first solution of Einstein's equations with time loops

  1941 Time dilation clearly observed for the first time

  1948 Kurt Gödel's rotating universe found to incorporate time travel

  1948 The Casimir effect discovered: negative-energy quantum states first discussed

  1957 John Wheeler conjectures existence of wormholes

  1957 Hugh Everett III proposes the many-universes, or parallel-realities, interpretation of quantum mechanics

  1963 Dr Who begins on BBC television

  1963 Roy Kerr discovers spinning black holes could contain time loops

  1974 Cygnus X-1, the first serious contender for a black hole, discovered by X ray satellite

  1974 Frank Tipler shows time travel possible near infinite rotating cylinders

  1977 Spinning black holes as gateways to other universes discussed

  1985 Back to the Future released

  1985 Carl Sagan writes Contact

  1989 Kip Thorne initiates study of wormhole time machines

  1990 Stephen Hawking proposes the chronology protection conjecture

  1991 Richard Gott III discovers cosmic string time machine

  1999 Michael Crichton's book Timeline published

  I am afraid I cannot convey the peculiar sensations of time travelling. They are exceedingly unpleasant. H. G. Wells

  Prologue

  * * *

  Time travel is inconceivable. Kingsley Amis

  What if it were possible to build a machine that could transport a human being through time?

  Is that credible?

  A hundred years ago, few people believed it possible for humans to travel through outer space. Time travel, like space travel, was merely science fiction. Today, spaceflight is almost commonplace. Might time travel one day become commonplace too?

  Travelling in time is certainly easy to envisage. You step into the time machine, press a few buttons, and step out again, not just somewhere else, but some when else – another time altogether. Writers of science fiction have exploited this theme again and again since H. G. Wells blazed the trail with his famous 1895 story The Time Machine. British audiences (the

  author included) thrilled to the adventures of the time lord Dr Who and his attractive lady accomplices. Hollywood movies such as Back to the Future and Timeline make it all seem so easy.

  So can it really be done? Is time travel a scientific possibility?

  A moment's thought uncovers some tricky questions. Where exactly are the past and future? Surely the past has disappeared and cannot be retrieved, while the future hasn't yet come into being? How can a person go to a world that doesn't exi
st? Sidestepping that, what about the inevitable paradoxes that come from visiting the past and changing it? What does that do to the present? And if time travel were feasible, where are all the time tourists from the future, coming back to peer curiously at twenty-first century society?

  There is no doubt that time travel poses some serious problems, even for physicists used to thinking about outlandish concepts like antimatter and black holes. But maybe that is because we are looking at time in the wrong way. After all, our view of time has changed dramatically over the years. In ancient cultures it was associated with process and change, and rooted in the cycles and rhythms of nature. Later, Sir Isaac Newton took a more abstract and mechanistic view. ‘Absolute, true and mathematical time, flowing equably without relation to anything external’ was the way he expressed it, and this became the accepted notion among scientists for 200 years.

  Everyone assumed without question that, whatever one's preferred definition, time is the same everywhere and for everybody. In other words, it is absolute and universal. True, we might feel time passing differently according to our moods, but time itself is simply time. The purpose of a clock is to sidestep mental distortions and record, objectively, the time. Implicit in this view is that time can be chopped up into three parts: past, present and future. The present – now – is supposed to be the fleeting moment of true reality, with the past banished to history – mere shadowy memory – and the future, still hazy and unformed. And that all-important now is taken to be the same moment throughout the universe: your now and my now are identical wherever we are and whatever we are doing.

  Such is the commonsense picture of time, the one we use in daily life. Few people think about time any differently. But it's wrong – deeply and seriously wrong.

  That it couldn't be right became apparent about the turn of the twentieth century. The credit for exposing the flaws in the everyday notion of time is largely associated with the name of Albert Einstein and the theory of relativity. At a stroke, Einstein's work demolished Newton's view of both space and time, rendered meaningless the universal division of time into past, present and future and paved the way for time travel.

  The theory of relativity is nearly a century old. Following publication of the so-called special theory in 1905, it was accepted by physicists almost immediately. Over the decades it has been exhaustively tested in many experiments. Today, the scientific community is unanimous that ‘time is relative’ and the commonsense notion of an absolute time with a universal ‘now’ is a fiction. Yet among the general public, the relativity of time still comes as something of a shock. Many people seem not to have heard about it at all. Some of them refuse flatly to believe it when told, in spite of the clear experimental evidence.

  In the coming chapters we shall see how the theory of relativity implies that a limited form of time travel is certainly possible, while unrestricted time travel – to any epoch, past or future – might just be possible, too. If this seems hard to swallow, remind yourself of J. B. S. Haldane's famous dictum: ‘the universe is not only queerer than we think, it is queerer than we can think’.

  1 How to visit the future

  * * *

  Time is not absolutely defined. Albert Einstein

  In an obvious sense we are all time travellers. Do nothing, and you will be conveyed inexorably into the future at the stately pace of one second per second. But this is of limited interest. A true time traveller needs to leap forward dramatically in time and reach the future sooner than everyone else.

  Can it be done?

  Indeed it can. Scientists have no doubt whatever that it is possible to build a time machine to visit the future. And they've known the formula for nearly a century.

  Time and motion

  It was in 1905 that Albert Einstein first demonstrated the possibility of time travel. He did this by demolishing the commonsense picture of time dating back to Newton, and replacing it with his own concept of relative time.

  Einstein was twenty-six when he published his ‘special’ theory of relativity. He was not the pipe-smoking dishevelled sage with tousled grey hair who provided the role model for many a fictional nutty professor, but a dapper young man in a suit working at the Swiss patent office. In his spare time, the young Einstein was studying the way light moves. In doing so, he noticed an inconsistency between the motion of light and that of material objects. Using only high-school mathematics, he demonstrated that if light behaves the way that physicists supposed, Newton's straightforward idea of time must be flawed.

  The trail of reasoning that leads from the motion of light to this startling conclusion about time has been discussed thoroughly and need not concern us here. What matters for our purposes is the central claim of the special theory of relativity, which is that:

  Time is elastic.

  It can be stretched and shrunk.

  How? By simply moving very fast.

  What precisely do I mean by ‘stretching time’? Let me state it more carefully. According to the theory of relativity, the exact duration of time between two specified events will depend on how the observer is moving. The interval between successive chimes on my clock might be one hour when I am sitting still in my living room, but it will be less than one hour if I spend that time moving about.

  To express the same thing in a more practical manner: suppose I board an airplane in London and fly to Cape Town and back while you stay at Heathrow airport. Then the duration of the journey according to me isn't the same as the duration according to you. In fact, it is a bit less for me.

  Two points need to be made at the outset. First, I'm not talking about the apparent duration of the journey. Your experience of being bored at the airport with the hours seeming to drag by, while I am happily occupied watching airline movies, is not the effect being discussed here. Mental time is a fascinating topic in psychology, but my concern is with physical time, the sort measured by mindless clocks. The second point is that the time discrepancy for the example given is miniscule – only a few hundred-millionths of a second – far too small to be noticed by a human being; however, it is measurable by modern clocks.

  That is pretty much what physicists Joe Hafele and Richard Keating did in 1971. They put highly accurate atomic clocks into airplanes, flew them around the world, and compared their readings with identical clocks left on the ground. The results were unmistakable: time ran more slowly in the airplane than in the laboratory, so that when the experiment was over the airborne clocks were 59 nanoseconds slow relative to the

  grounded clocks – exactly the amount predicted in Einstein's theory.

  Because your time and my time get out of step if we move differently, there can obviously be no universal, absolute time, as Newton assumed. Talk of the time is meaningless. The physicist is bound to ask: Whose time?

  Significant though the Hafele-Keating experiment may be historically, it is hardly the stuff of science fiction: a timewarp of 59 nanoseconds doesn't make for an adventure. To get a really big effect you have to move very fast. The benchmark here is the speed of light, a dizzying 300,00 kilometres per second. The closer to the speed of light you travel, the bigger the timewarp gets.

  Physicists call the slowing of time by motion the time dilation effect. Think of a speed. Divide by the speed of light. Square it. Subtract from 1. Take the square root. The answer is… Einstein's time dilation formula! This is a graph of the ‘slowdown factor’. Notice how the graph shows the dilation factor as a function of speed and starts out fairly flat, but plummets as light speed is approached. At half the speed of light, time is about 13 per cent slowed; at 99 per cent, it is 7 times slower -1 minute is reduced to about 8.5 seconds.

  Technically, the timewarp becomes infinite when the speed of light is reached. This is a sign of trouble. In fact, it tells us that a normal material body can't reach the speed of light.

  There is a ‘light barrier’ which can never be breached. The no-faster-than-light rule is a key result of the theory of relativity:
<
br />   Nothing can break the light barrier.

  This includes not just material bodies, but waves, field disturbances – physical influences of any sort. It spoils a lot of science fiction because, fast though it goes, light still takes a long time to cover interstellar distances. The nearest star, for example, is over 4 light years away, which means it takes light over 4 years to get there from Earth. The Milky Way galaxy is about 100,000 light years across. Administering a galactic empire would be a slow process.

  However, there is some compensation. Because time is stretched by speed, interstellar journeys would seem quicker for the astronauts than for those left on Earth at mission control. In a spaceship travelling at 99 per cent of the speed of light a trip across the galaxy would be completed in only 14,000 years. At 99.99 per cent of the speed of light the gain is even more spectacular: the trip lasts a mere 1,400 years. If you could reach 99.999999 per cent of the speed of light, the trip could be completed in a human lifetime.

  Speeds like this are far beyond current spacecraft technology. (Our best spacecraft reach a paltry 0.01 per cent of the speed of light.) But there are objects that travel very close to the speed of light. These are subatomic particles, such as cosmic rays and atomic fragments emitted in radioactive decays, or purposely accelerated in giant ‘atom smashers’. It's possible to observe very large time dilations by using these particles as simple clocks. The particle accelerator known as the Large Electron Positron (LEP) collider at the Organisation Européenne pour la Recherches Nucléaire (CERN) laboratory near Geneva could propel electrons to 99.999999999 per cent of the speed of light. This is so fast it falls short of the speed of sound by a literal snail's pace. At this speed, timewarp factors approaching a million were achieved. Even this pales into insignificance compared to timewarp factors of billions experienced by some cosmic rays.