The ABC of Relativity

151 Pages·1959·1.68 MB·English

by  Bertrand Russell

Ask a dozen people to name a genius and the odds are
that 'Einstein' will spring to their lips. Ask them the
meaning of 'relativity' and few of them will be able
to tell you what it is.
The ABC of Relativity is Bertrand Russell's most
brilliant work of scientific popularisation. With
marvellous lucidity he steers the reader who has no
knowledge of maths or physics through the subtleties
of Einstein's thinking; in easily assimilable steps he
explains the theories of special and general relativity
and describes their practical application (among much
else to discoveries about gravitation and the invention
of the hydrogen bomb).
'Einstein', wrote Russell, 'revolutionised our
conception of the physical world, but the innumerable
popular accounts of his theory generally cease to be
intelligible at the point where they begin to say
something important.'
The basic principles of relativity have not changed
since Russell first published his lucid guide for the
general reader. This new edition takes account of the
extension of our knowledge about the theory and its
applications.
BERTRAND
RUSSELL
ABC OF
RELATIVITY
Fourth Revised Edition
Edited by Felix Pirani
LONDON
Preface to the
Fourth Edition
fo selpicnirp cisab ehT .5291 ni deraeppa tsrif koob sihT
relativity have not changed since then, but both the theory
and its applications have been much extended, and some
revision has been necessary for the second and subsequent
editions. For the second and third editions I carried out these
revisions with Bertrand Russell's approval. The revisions for
this fourth edition are entirely my responsibility. I have again
egdelwonk tneserp htiw eerga ot segassap fo rebmun a deretla
or opinion, and I have attempted to eliminate the possessive
em ot demees ti erehw ,seiroeht ro swal ot deilppa sa ,esac
no longer appropriate.
I have also done my best to renounce the convention that
the masculine includes the feminine. Sixty years ago this may
regnol on si ti won ;detarelot tsael ta ro ,elbatpecca neeb evah
so,'and I have little doubt that Russell, who was a pro-feminist
ahead of his time, would have approved of the renunciation.
I have not presumed to meddle with the substance of the
last two chapters, which are largely philosophical, rather than
physical, in character, although there is much in them which
.htiw eergasid I
P.P.
Contents
5 egap noitidE htruoF eht ot ecaferP
1 Touch and Sight: The Earth and the Heavens 9
71 devresbO si tahW dna sneppaH tahW 2
3 The Velocity of Light 26
43 selur-tooF dna skcolC 4
5 Space-Time 45
6 The Special Theory of Relativity 53
7 Intervals in Space-Time 66
8 Einstein's Law of Gravitation 78
9 Proofs of Einstein's Law of Gravitation 91
10 Mass, Momentum, Energy, and Action 100
e srevinU gnid1n13apxE ehT 11
12 Conventions and Natural Laws 124
13 The Abolition of'Force' 133
14 What is Matter? 141
15 Philosophical Consequences 148
Chapter 1
Touch and Sight:
The Earth and the
Heavens
Everybody knows that Einstein did something astonishing,
but very few people know exactly what it was. It is generally
recognised that he revolutionised our conception of the
physical world, but the new conceptions are wrapped up in
mathematical technicalities. It is true that there are
tub ,ytivitaler fo yroeht eht fo stnuocca ralupop elbaremunni
erehw tniop eht ta tsuj elbigilletni eb ot esaec yllareneg yeht
era srohtua ehT .tnatropmi gnihtemos yas ot nigeb yeht
hardly to blame for this. Many of the new ideas can be
enon era yeht tub ,egaugnal lacitamehtam-non ni desserpxe
the less difficult on that account. What is demanded is a
change in our imaginative picture of the world - a picture
which has been handed down from remote, perhaps pre-
human, ancestors, and has been learned by each one of us
syawla si noitanigami ruo ni egnahc A .doohdlihc ylrae ni
difficult, especially when we are no longer young. The
same sort of change was demanded by Copernicus, who
od snevaeh eht dna yranoitats ton si htrae eht taht thguat
on si ereht won su oT .yad a ecno ti tuoba evlover ton
difficulty in this idea, because we learned it before our mental
habits had become fixed. Einstein's ideas, similarly, will
seem easier to generations which grow up with them; but
for us a certain effort of imaginative reconstruction is
unavoidable.
10 ABC of Relativity
lla fo esu ekam ew ,htrae eht fo ecafrus eht gnirolpxe nI
our senses, more particularly of the senses of touch and sight.
deyolpme era ydob namuh eht fo strap ,shtgnel gnirusaem nI
n pire-sciea n' f:tsoiefogiatc a '', cudbeint ai'f,' sedp aerna '
in this way. For longer distances, we think of the time it takes
to walk from one place to another. We gradually learn to
judge distance roughly by the eye, but we rely upon touch
esnes ruo su sevig taht hcuot si ti revoeroM .ycarucca rof
of 'reality'. Some things cannot be touched: rainbows,
elzzup sgniht esehT .no os dna ,sessalg-gnikool ni snoitcelfer
children, whose metaphysical speculations are arrested by
the information that what is in the looking-glass is not 'real'.
Macbeth's dagger was unreal because it was not 'sensible to
tub ,scisyhp dna yrtemoeg ruo ylno osti gtsoahN tg'. nileef
our whole conception of what exists outside us, is based upon
the sense of touch. We carry this even into our metaphors:
a good speech is 'solid', a bad speech is 'gas', because we
e tiuq ton' si srag a taeht leefal'.
sesnes lla morf derrabed era ew ,snevaeh eht gniyduts nI
except sight. We cannot touch the sun, or apply a foot-rule
ylgnitatisehnu evah sremonortsa ,sselehtreveN .sedaielP eht ot
dnuof yeht hcihw scisyhp dna yrtemoeg eht deilppa
serviceable on the surface of the earth, and which they had
nwod thguorb yeht ,os gniod nI .levart dna hcuot nopu desab
trouble on their heads, which was not cleared up until
tahw fo hcum taht tuo denrut tI .derevocsid saw ytivitaler
cifitneicsnu saw hcuot fo esnes eht morf denrael neeb dah
prejudice, which must be rejected if we are to have a true
.dlrow eht fo erutcip
si hcum woh dnatsrednu ot su pleh yam noitartsulli nA
impossible to the astronomer as compared with someone who
is interested in things on the surface of the earth. Let us
uoy sekam hcihw uoy ot deretsinimda si gurd a taht esoppus
evah uoy ekaw uoy nehw taht dna ,suoicsnocnu yliraropmet
lost your memory but not your reasoning powers. Let us
Touch and Sight 11
erew uoy suoicsnocnu erew uoy elihw taht rehtruf esoppus
carried into a balloon, which, when you come to, is sailing
fo htfif eht fo thgin eht - thgin krad a no dniw eht htiw
yluJ fo htruof eht fo ro ,dnalgnE ni era uoy fi rebmevoN
gnieb era hcihw skrowerif ees nac uoY .aciremA ni era uoy fi
sent off from the ground, from trains, and from aeroplanes
dnuorg eht ees tonnac uoy tub ,snoitcerid lla ni gnillevart
or the trains or the aeroplanes because of the darkness. What
sort of picture of the world will you form? You will think
that nothing is permanent: there are only brief flashes of light,
diov eht hguorht levart ,ecnetsixe trohs rieht gnirud ,hcihw
in the most various and bizarre curves. You cannot touch
these flashes of light, you can only see them. Obviously your
etiuq eb lliw scisyhpatem ruoy dna scisyhp ruoy dna yrtemoeg
different from those of ordinary mortals. If an ordinary mortal
were with you in the balloon, you would find his speech
dluow uoy ,uoy htiw erew nietsniE fi tuB .elbigilletninu
,dluow latrom yranidro eht naht ylisae erom mih dnatsrednu
because you would be free from a host of preconceptions
which prevent most people from understanding him.
The theory of relativity depends, to a considerable extent,
upon getting rid of notions which are useful in ordinary life
but not to our drugged balloonist. Circumstances on the
latnedicca ssel ro erom suoirav rof ,htrae eht fo ecafrus
reasons, suggest conceptions which turn out to be inaccurate,
although they have come to seem like necessities of thought.
The most important of these circumstances is that most
ylraen dna tnetsisrep ylriaf era ecafrus s'htrae eht no stcejbo
stationary from a terrestrial point of view. If this were not
the case, the idea of going on a journey would not seem so
definite as it does. If you want to travel from King's Cross
to Edinburgh, you know that you will find King's Cross
eht ekat lliw enil yawliar eht taht ,neeb syawla sah ti erehw
course that it did when you last made the journey, and that
ot pu deklaw evah tonW lliw hagruvbniedE rnil noeitaytS
12 ABC of Relativity
dellevart evah uoy taht kniht dna yas erofereht uoY .eltsaC eht
,uoy ot dellevart sah hgrubnidE taht ton ,hgrubnidE ot
ehT .etarucca sa tsuj eb dluow tnemetats rettal eht hguoht
success of this common-sense point of view depends upon
a number of things which are really of the nature of luck.
gnivom yllauteprep erew nodnoL ni sesuoh eht lla esoppuS
about, like a swarm of bees; suppose railways moved and
changed their shapes like avalanches; and finally suppose that
material objects were perpetually being formed and dissolved
like clouds. There is nothing impossible in these suppositions.
But obviously what we call a journey to Edinburgh would
,tbuod on ,nigeb dluow uoY .dlrow a hcus ni gninaem on evah
by asking the taxi-driver: 'Where is King's Cross this
morning?' At the station you would have to ask a similar
dluow krelc eciffo-gnikoob eht tub ,hgrubnidE tuoba noitseuq
s
reply: 'What part of Edinburgh do you mean? Prince's Street
eht otni pu devom sah eltsaC eht ,wogsalG ot enog sah
Highlands, and Waverley Station is under water in the middle
dluow sno fiotFa htst reiFhot eyhet nforruojt ehht no d.nA'
,htron gnillevart eb dluow emos tub ,teiuq gniyats eb ton
some south, some east or west, perhaps much faster than the
uoy erehw yas ton dluoc uoy snoitidnoc eseht rednU .niart
si eno taht noiton elohw eht deednI .tnemom yna ta erew
etanutrof ehte t io'ntpif eeludad ce smeio' s ni syawla
.ecafrus s'htrae eht no stcejbo egral eht fo tsom fo ytilibommi
:noitamixorppa lacitcarp hguor a a yoelfdn'piol ae schieT '
there is nothing logically necessary about it, and it cannot
.esicerp edam eb
dluohs ew ,nortcele na naht regral hcum ton erew ew fI
ot eud ylno si hcihw ,ytilibats fo noisserpmi siht evah ton
the grossness of our senses. King's Cross, which to us looks
wef a yb tpecxe deviecnoc eb ot tsav oot eb dluow ,dilos
eccentric mathematicians. The bits of it that we could see
gnimoc reven ,rettam fo stniop ynit elttil fo tsisnoc dluow
into contact with each other, but perpetually whizzing round
31 thgiS dna hcuoT
dlrow ehT .ecnad-tellab dipar ylbaviecnocni na ni rehto hcae
of our experience would be quite as mad as the one in which
tnereffid ni sklaw rof og hgrubnidE foe sdhitftrfaerpen t
directions. If - to take the opposite extreme - you were
as large as the sun and lived as long, with a corresponding
slowness of perception, you would again find a higgledy-
stenalp dna srats - ecnenamrep tuohtiw esrevinu ydelggip
would come and go like morning mists, and nothing would
ehT .esle gnihtyna ot ylevitaler noitisop dexif a ni niamer
ruo fo trap smrof hcihw ytilibats evitarapmoc fo noiton
tuoba era ew taht tcaf eht ot eud suht si kooltuo yranidro
the size we are, and live on a planet of which the surface
is not very hot. If this were not the case, we should not find
ew deednI .gniyfsitas yllautcelletni psrce-irseylahtivpity
should never have invented such theories. We should have
had to arrive at relativity physics at one bound, or remain
ignorant of scientific laws. It is fortunate for us that we were
not faced with this alternative, since it is almost inconceivable
that one person could have done the work of Euclid, Galileo,
suineg elbidercni na hcus tuohtiw teY .nietsniE dna notweN
physics could hardly have been discovered in a world where
the universal flux was obvious to non-scientific observation.
In astronomy, although the sun, moon and stars continue
ew dlrow eht stcepser rehto ni tey ,raey retfa raey tsixe ot
have to deal with is very different from that of everyday life.
As already observed, we depend exclusively on sight: the
heavenly bodies cannot be touched, heard, smelt or tasted.
Everything in the heavens is moving relatively to everything
else. The earth is going round the sun, the sun is moving,
ni tniop a sdrawot ,niart sserpxe na naht retsaf hcum yrev
gniyrrucs era se r'hfaitxtse ,ds 'elucreH noitalletsnoc eht
eht ni secalp dekram-llew on era erehT .rehtiht dna rehtih
morf levart ue okyiKl n ,eyhkWs .higrunbnidEg dna 'sssorC
place to place on the earth, you say the train moves and not
the stations, because the stations preserve their topographical
14 ABC of Relativity
ni tuB .yrtnuoc gnidnuorrus eht dna rehto hcae ot snoitaler
hcihw dna niart eht llac uoy hcihw yrartibra si ti ymonortsa
the station: the question is to be decided purely by
convenience and as a matter of convention.
dna nietsniE tsartnoc ot gnitseretni si ti ,tcepser siht nI
Copernicus. Before Copernicus, people thought that the earth
stood still and the heavens revolved about it once a day.
t aht 'thgruat se,uycaidn raea epconCo lsetaltor hytrae eh't
y'alnpop asrie nsrta'.ts dna nus fo noitulover yliad eht dna
sgniht ynam dna ,weiv siht desrodne notweN dna oelilaG
were thought to prove it - for example, the flattening of
reivaeh era seidob taht tcaf eht dna ,selop eht ta htrae eht
eht yroeht nredom eht ni tuB .rotauqe eht ta naht ereht
si sremonortsa reilrae dna sucinrepoC neewteb noitseuq
ereht dna ,evitaler si nof ciooton vemenni oelnl acyel ;erem
is no difference between the two statements: 'the earth rotates
ecno htrae eht tuoba evlover snevad a e'tndhh aaeey c 'no
a day'. The two mean exactly the same thing, just as it means
the same thing if I say that a certain length is six feet or two
naht dexif sa nus eht ekat ew fi reisae si ymonortsA .sdray
lamiced ni reisae era stnuocca sa tsuj ,htrae eht ekat ew fi
coinage. But to say more for Copernicus is to assume absolute
si ti dna ,evitaler si noitom llA .noitcif a si hcihw ,noitom
a mere convention to take one body as at rest. All such
conventions are equally legitimate, though not all are equally
convenient.
hcihw ni ,ecnatropmi taerg fo rettam rehtona si erehT
sti fo esuaceb scisyhp lairtserrey tmd moifnoforefrrtss a
exclusive dependence upon sight. Both popular thought and
demees no ohfifcteoirhnewe e' ,ht desu scisyhp denoihsaf-dlo
.snoitasnes railimaf htiw detaicossa saw ti esuaceb elbigilletni
When we are walking, we have sensations connected with
.llits gnittis era ew nehw evah ton od ew hcihw selcsum ruo
In the days before mechanical traction, although people could
sesroh eht ees dluoc yeht ,segairrac rieht ni gnittis yb levart