Time and Age: Time Machines, Relativity and Fossils

232 Pages·2015·13.903 MB·English

by  Michael Mark Woolfson

Time Age
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Time Age
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Imperial College Press
ICP
p975hc_9781783265831_tp.indd 2 13/8/14 8:50 am
Published by
Imperial College Press
57 Shelton Street
Covent Garden
London WC2H 9HE
Distributed 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
Library of Congress Cataloging-in-Publication Data
m Woolfson, Michael M. (Michael Mark)
o
c.cy. Time and age : time machines, relativity, and fossils / Michael Mark Woolfson, University of
cientifiuse onl Y o r k, pUaKge.s cm
dsal Includes bibliographical references and index.
orlon ISBN 978-1-78326-583-1 (hardcover : alk. paper) -- ISBN 978-1-78326-584-8 (pbk. : alk. paper)
w.wpers 1. Time measurements. 2. Clocks and watches--History. 3. Space and time. 4. Special relativity
m ww5. For ( PhQyBsi2c1s3) . W5. 8S4t a 2ti0st1i5cal astronomy. 6. Earth (Planet)--Age. 7. Geological time. I. Title.
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Ti Copyright © 2015 by Imperial College Press

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Catherine - Time and Age.indd 1 14/1/2015 3:35:08 PM
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pagev
Introduction
m Theconceptoftimeisonethatisfamiliartoeveryone,yetitisdifficult
o
c.cy. to define. We know that it can be categorized as past, present and
dscientifial use onl fpulatucere,,ththeepapsrtesbeyntevbeenitnsgthdaetfihnaevdebaylreeavdeynttsakinenthpelacpero—cesisnopfritnackiipnlge
orlon something that is known — and the future by events that will take
w.wpers place—whichareunknown,althoughwemaymakepredictionsabout
m ww5. For what is expected to happen. The passage of time is marked by events
o1
d fr27/ and events are what create change; any event that takes place changes
oaden 04/ what will be to what is at the time it happens. We mark the passage
wnl0 o of time by change — the movement of the Sun in the heavens or the
Age Do00.4.15 hwaonudlds onfoatwexaitsct.h — and it has been argued that without change, time
me and by 41.2 In TThheeTiidmeaeoMfaticmhienter,avwerlihttaesnbbeeynHad.Gva.nWceedllsinasnedvepraulbwlioshrkesdoifnfi1ct8io9n5.,
Ti
an English inventor creates a machine that transports the passenger
through time. He travels to a time more than 800,000 years in the
futureinhabitedbychild-likecreatures,theEloi,wholiveanidylliclife
ofidleness,andasavageape-liketroglodyterace,theMorlocks,wholive
undergroundandwhosemaindietistheEloi.Morerecently,in2006,
BBCtelevisionproducedaseries,LifeonMars,chroniclingthestoryof
SamTyler,adetectivewithGreaterManchesterPolicewhoisseriously
injured in a car crash and is undergoing drastic surgery. While under
anaesthetic,hewakesupin1973asadetectiveinManchester.Hefinds
himselfinaworldhestrugglestounderstand.Hissuperior,GeneHunt,
is a tough, ruthless policeman with no regard for political correctness
who,whenSamremindshimabouthumanrightswhenhemaltreatsa
v
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pagevi
vi TimeandAge: TimeMachines,RelativityandFossils
vicious criminal, replies, ‘Human rights are for human beings.’ These
time-travellingnarrativesareindeedpurefantasy—SamTylerevensees
his mother as a woman of about his own age accompanied by himself
as a child — but they make for good entertainment.
These are philosophical and fantastical observations about the
nature of time, but here we shall be concerned with more mundane
and realistic matters. The way that time has been, and is, measured
will be described both from the point of view of day-to-day life and
with the high precision demanded by modern science. When Einstein
introducedhisTheoryofSpecialRelativityin1905,timewaspresented
m in a new way as intimately connected to space, the two being bundled
o
c.cy. together in a concept known as spacetime. There is a chapter devoted
cientifiuse onl totheconsequencesofthistheory,manyoftheminconsistentwithour
dsal instinctive understanding of the way the world behaves and seemingly
w.worlperson fantastic — but these consequences can be scientifically shown to be
wwFor true. The final section of the book is devoted to finding the ages of
m 5. various kinds of object, from the age of the Universe to the age of a
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oaden 04/ Thebookisintendedforthenon-specialistreaderinterestedinsci-
wnl0 o enceinageneralway.Asfaraspossible,mathematicaltreatmentsshould
ge Do0.4.15 beavoidedinsuchabook,butIhaveincludedsomemathematics—not
me and Aby 41.20 mthuatchth—erefoisrathvoesrebathlaetxpcalanndateiaolnwoitfhthite. oHuotwcoemveer,oIfhthaveemaalstoheemnsautirceadl
Ti treatments, backed up by diagrams where possible. Have I succeeded

in my objective of presenting a book for all the target readers? Only
time will tell!
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pagevii
Contents
Introduction v
m
o
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cientifiuse onl The Measurement of Time
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w.wpers Chapter 1 Astronomical Time 3
wwFor 1.1 Early Concepts of Time . . . . . . . . . . 3
om 15. 1.2 The Day . . . . . . . . . . . . . . . . . . 4
d fr27/ 1.3 The Month . . . . . . . . . . . . . . . . 6
oaden 04/ 1.4 The Year . . . . . . . . . . . . . . . . . . 8
ge Downl0.4.150 o 1.5 T1.h5e.1InfluPelannctesoafnTditmimeeon. L. i.fe. .. .. .. .. .. .. 88
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me and by 41.2 11..55..23 AHnuimmaanlssaannddttiimmee. .. .. .. .. .. .. .. .. 1110
Ti 1.6 Calendars . . . . . . . . . . . . . . . . . 12

1.6.1 The Sumerian calendar . . . . . . 12
1.6.2 The Mayan calendar . . . . . . . 13
1.6.3 The Roman, Julian and Gregorian
calendars . . . . . . . . . . . . . 14
1.7 The Changing of the Seasons . . . . . . . 16
Chapter 2 Early Recording of Time 19
2.1 Sundials . . . . . . . . . . . . . . . . . . 19
2.1.1 The equatorial sundial . . . . . . 19
2.1.2 The equation of time. . . . . . . 23
2.1.3 Other designs of sundials . . . . 24
vii
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pageviii
viii TimeandAge: TimeMachines,RelativityandFossils
2.2 Candle Clocks . . . . . . . . . . . . . . . 25
2.3 Water Clocks. . . . . . . . . . . . . . . . 28
2.3.1 Outflow water clocks . . . . . . . 29
2.3.2 Inflow water clocks . . . . . . . . 31
2.3.3 Mechanized water clocks . . . . 33
Chapter 3 Mechanical Clocks 37
3.1 The Salisbury Cathedral Clock . . . . . . 37
3.2 Pendulum-Controlled Clocks . . . . . . . 39
3.3 Navigation and Time . . . . . . . . . . . 44
m
3.3.1 John Harrison and his sea
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cientific.cuse only. 3.3.2 cHloacrrkisso.n.an.d.h.is.w.a.tc.he.s. .. .. .. .. 4571
dsal 3.4 Modern Mechanical Watches . . . . . . . 53
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om 15. 4.1 Standards of Time . . . . . . . . . . . . . 55
d fr27/ 4.2 Quartz Clocks . . . . . . . . . . . . . . . 56
oaden 04/ 4.2.1 The piezoelectric effect . . . . . 57
ge Downl0.4.150 o 44..22..32 TRheseoensasnencetial.m.ec.h.an.is.m.o.f.aq.u.ar.tz 59
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Ti timepiece . . . . . . . . . . . . . 62

4.3 The Atomic Clock . . . . . . . . . . . . . 63
4.3.1 Radiation from atoms
and molecules . . . . . . . . . . 64
4.3.2 The mechanism of an atomic
clock . . . . . . . . . . . . . . . 65
4.3.3 Portable atomic clocks . . . . . . 71
Time and Relativity
Chapter 5 Time and Space 75
5.1 The Concept of Relativity . . . . . . . . . 75
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pageix
Contents ix
5.1.1 Light and the ether . . . . . . . 76
5.1.2 An attempt to detect the
ether . . . . . . . . . . . . . . . 77
5.2 Einstein’s Postulate . . . . . . . . . . . . 82
5.2.1 Physics at the beginning of the
20th century . . . . . . . . . . . 83
5.3 The Theories of Relativity and Their
Consequences . . . . . . . . . . . . . . . 85
5.3.1 Spacetime . . . . . . . . . . . . . 89
5.3.2 Time and gravity . . . . . . . . . 90
m 5.3.3 Before, after or simultaneously? . 91
o
c.cy.
dscientifial use onl The Ages of Astronomical Entities
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w.wpers Chapter 6 The Age of the Universe 97
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m 5. 6.1 Observing the Universe . . . . . . . . . . 97
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oaden 04/ Objects . . . . . . . . . . . . . . . . . . . 98
wnl0 o 6.2.1 The parallax method . . . . . . . 98
ge Do0.4.15 6.2.2 Main-sequence stars . . . . . . . 101
me and Aby 41.20 66..22..34 UThsienDgoCpepplheeriedffveacrtia.bl.es. .. .. .. .. .. 110035
Ti 6.2.5 Spinning galaxies . . . . . . . . . 106

6.2.6 Using supernovae as standard
sources . . . . . . . . . . . . . . 108
6.3 Hubble and the Expanding Universe . . . 109
Chapter 7 The Ages of Globular Clusters and Young Stars 113
7.1 Early Material in the Universe . . . . . . 113
7.2 Clusters of Stars . . . . . . . . . . . . . . 114
7.3 The Birth, Life and Death of a Star . . . . 117
7.3.1 Collapse to the main
sequence . . . . . . . . . . . . . 118
7.3.2 The Final Journey to
Obscurity . . . . . . . . . . . . . 120
January20,2015 15:47 TimeandAge:TimeMachines,RelativityandFossils 9inx6in b1927-fm pagex
x TimeandAge: TimeMachines,RelativityandFossils
7.4 The Duration of the Main Sequence and
the Age of Globular Clusters . . . . . . . 123
7.5 The Age of Evolving Young Stellar
Objects . . . . . . . . . . . . . . . . . . . 124
Chapter 8 The Age of the Solar System 129
8.1 A Brief Description of the Solar
System . . . . . . . . . . . . . . . . . . . 129
8.2 Radioactivity . . . . . . . . . . . . . . . . 130
8.3 Radioactive Dating: A Simple
m
o Procedure . . . . . . . . . . . . . . . . . 132
cientific.cuse only. 8.4 S8o.3m.1e ImRpeoarcttainotnDchecaainyss.fo.r A. g.e. . . . . . 134
dsal Determination . . . . . . . . . . . . . . . 134
orlon
w.wpers 8.5 Rocks, Grains and Minerals . . . . . . . . 134
wwFor 8.6 Examples of Dating Using Radioactive-
m 5. Decay Systems . . . . . . . . . . . . . . . 136
o1
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oaden 04/ system . . . . . . . . . . . . . . 137
ge Downl0.4.150 o 8.6.2 Arubmidatihuemm→aticsatrlotrnetaiutmment of the
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Ti lead . . . . . . . . . . . . . . . . 140

8.6.4 The mathematics of the lead–lead
isochron . . . . . . . . . . . . . 141
8.7 The Age of the Earth . . . . . . . . . . . 142
8.8 The Mass Spectrometer . . . . . . . . . . 146
8.9 The Age of the Solar System . . . . . . . 148
Ages on Earth
Chapter 9 The Age of the Continents 153
9.1 The Mobile Earth . . . . . . . . . . . . . 153
9.2 The Evidence for Continental Drift . . . 154