Einstein for Beginners

FOR BEGINNERS

Text by Joe Schwartz

Illustrations by ~~~1===~ Michael McGuinness r1~MI

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Text Copyright © 1979 by Joe Schwartz Illustrations Copyright © 1979 by Michael McGuinness All rights reserved under International and PanAmerican Copyright Conventions. Published in the United States by Pantheon Books, a division of Random House, Inc., New York, and simultaneously in Canadaby Random House of Canada Limited, Toronto. Originally published in England by Writers and Readers Publishing Cooperative. Library of Congress Cataloging in Publication Data Schwartz, Joe, 1938Einstein for beginners. Bibliography: p. 1. Einstein, Albert, 1879-1955. \. McGuinness, Michael, 1935joint author. I\. Title. QC16.E5S32 530.1'1 79-1889 ISBN 0-394-50588-3 ISBN 0-394-73801-2 pbk. Manufactured in the United States of America

02468B97531

About the Author and Illustrator Joe Schwartz, who is Associate Professor of Physics at the City University of New York, received his Ph.D. in higher energy physics from the University of California in 1964. He is the author of many scientific articles that have appeared in Nature, New Scientist, and other magazines. Michael McGuinness studied fine arts at the Royal Academy in London. He is a former art director at Reader's Digest and designer for the Observer.

'If relativity is proved right the Germans will call me a German, the Swiss will call me a Swiss citizen, and the French will call me a great scientist. If relativity is proved wrong the French will call me a Swiss, the Swiss will call me a German, and the Germans will call me a Jew.'

A\be,rt Einstein was born in ulm, Germany on March 11.1875 'Into a war Id not of his

own making .

.-{ Just like the rest ofus.

]

hat was going on 'In the world? ~~

The 1880'5 marked the beqinning of

the ag5 of

imperialism and mon0p,0ly capitdlisr'n.~~

LENIN 11

6

1870

Franco-Pru..ian War - Prussia annexes Alsace-Lorraine, declares a German Empire, receives 5,000,000,000 francs indemnity and blows it all in financial speculation.

1871

The Parla Commune - Workers and soldiers take over the

1873

The Great World-Wide Financial Crash. The next 17 years

government of Paris for 3 months. The Commune suppressed with the help of the Prussian Army. 30,000 Communards executed by the French authorities.

meant hardship for ordinary people; great profits and consolidation for a few. Small businessmen, like Einstein's father, were badly hit. This was a time of labor struggles, immigration, the rise of militant socialism.

1878

Bismarck passes anti-socialist laws to suppress working-class political agitation.

~! The great questions of

the day w'llI not be settled by resolutions and majority votes but

by blood and iron.~!1

%Ittpis~

CItt
verticallv from 1tle mouth of ire connon should hit the ground ot ihe sometime!

Thafs a strange result! 88

Doesn't the horiz.ontal marion affect the vertical motion at all? When I'm moving smoothly the cannonball's vertical motion isn't affected at all.

Galileo then extended his argument to say that you couldn't use vertical motion orany other kind of motion to detect horizontul motion.

liiillii '

Yes.lve

often wondered in my cobin whether the ship was. moving or standing

still.

still.

89

And ihat's "the principle of relativity. You can "t tell ~~r

it" you're moving smoothly

without looking outside.

lYle r.rinciple of

relativity sounds harmless encqqh. Negati ng the idea of

absolute rest wasn't a burninq issue. / But whel1 app lied l6 the problem of tMe

ae1'He.r it paved /The way tor the pow~rtul

arguments

that Decome-the

1heo~ ofReloTlvi!y

0000

which first.

appeared in

mogozme.

~~

~

90

rns

osed on the principle of t:ek;1iiv·~ Albert ~rgued he should be able iO eee his (moO e norma!!y even if he were moving ar the speed ot ight

o

Because if your image disappeared when you were moving at the speed of light, you could tell you were moving at the speed of light just by looking in a mirror, right? You wouldn't need to look outside, right? Which would violate the principle of relativity I

91

Damn!

there gOO? my

lrY10t oqoln.l kee ten in_q them ~o 18'6,000 miles- er-second

not

mm;;;;;;;;;;;;m;;;;;;;;;;;;;;;;;;;;;;;;m;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;m;;;,when tin shovi~. //

Speed is distance

That was half the problem solved. Albert's image should be normal. But could Albert see the light move away from his face at the speed of light relative to him . . . while, at the same time, observers on the ground would see the light leave Albert's face at the same speed of light relative to them? How could this be possible?

92

divided by time (as in miles/nour). So Albert realizeQ thai if the speed were to be 1rle some ihen me disTance and time wo~ld have to be difrerent. Which meant that there

must be .something suspect with time.

Perhaps "the moving ~b58rver and 1he stationary observer observed cliflerent times ...

If both

were to observe the same

velocitv fOr /igrTt.

Because Albert

took the principle

of relativity as a starting point,

ne was led tOk

rettun the

concepts

of space

and

time

in order

make it come out

all right 93

This is how Albert

finally' expressed it in his Annalen der

Physikarticle in 19°5: ON THE

ELECTRODYNAMICS OF MOVING BODIES ... the unsuccessful attempts to discover any motion of the earth relatively to the light medium

like the Michelson -Morley experiment suggest that the phenomena of electrodynamics

he mean~ ihe propagation oF'light which isthe same thing /// as well as of mechanics possess n~ properties corresponding to the idea of absolute rest.

He means Galileo's principle of relativity ohould be good for light as well as for ordinory motion. We will raise this conjecture (the purport of which will be hereafter be called the 'Principle of Relativity') to the status of a postulatej"

*postulate: a basic assumption and also introduce another postulate, which is only apparently. irreconcilable with the former

he means he's found a

way out of the contradiction

namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.

He means everY,~>ne should always observe the

same velocity iOr light.

These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

The introduction of a 'luminiferous aether' will prove to be superfluous inasmuch as the view here to be developed will not require an 'absolutely stationary space' provided with special properties ...

He means he's doing awoy with the oemer once and for 011 . Space will no longer require . r.special properties' in order TO transmit light.

Bur, cerroin

conventional ideas

about time about lenqths, about moss ,

obout velocity

had to be chucked out and replaced.

95

· Ibert5 arquments ore veCY simple because "they are very logicar. If .yOU accept file two postulates Albert shows exac11y now to make it come out O. K. Albert was ver.v pleased with the result. He wrote to his friend Conrod'

Habicht··· ... '

.' 6reot! He's reallY done it!

96

ow. Do you see what is .

happening? Albert says:

Nice and 5u y I dnn to thin~.I'll qo r (j drive.

no matler how liqht propagates Wflen:you are

srandi"h9 still ....

. .. it pro 899 ates exactlY the eorne way when

movln.9'

This i5the Such a nice

principle of • relativitv, Alberrs first posfuIare.

doy.

9,

ut Albert also says rr

Liqht is alwa~5. propaQ~ted in empty space wd:h q detinrle velocity C which is Indej:?endent of

the stcfte of mo1ion at The emitting or receiving body"

An observer an /he ground hos ID see light moving ot the same velocity os the moving observer. lhis is Alberts 2na postulate.

96

Bur what does it mean?

P-B1mate.

I'm not sure.

what about, KtxP dis ch?

Remem ber the compass?

Albert wondered how the cornROss needIe interacted with fue Earth's magnetism. How do maqnetic(or electric) effects get transmitted from one pl ace to another?

Maxwell and Hertz fact they showed "that such In showed magnetjc that every interactions could electromagnetic only take place effeq takes ota certain maximum speed. time to get transmiITed. 99

Radio waves, microwaves. sun rays,etc., all take time to getfrom place to place.

100

o Albert mode an inference. Based on fhe experience with elecTricity as summariz.ed by Maxwell ana verified by Hertz, Albert proposed that ihere are no insTantaneous intemcilons at on in nature. Here is "the simple physical meaning of Alberfs 2nd postulaie:

Every interaction takes time it:' getfrom one place toihe

next.

{j

And if ihere are no insTantaneous interactions in nature then "there ,must be a maximum possible speed

ofi nterocllon.

I

.I

This is so im portant we will repeat it: Iffhere are no instantaneous interactions in Doture -then -there must be a maximum possible speed ot interaction. 101

he maximum possible speed of interaction in nature is the speed of the electromC?qnetic interaction - wliich is the speed cf light!

It's quite revolutionary really.

Now by the 8rinciple of

relotivity~ the

maximum

epeed or interaction must 1'~~I51' be the same for every J...l observer no ma1ter how they are moving.

e

~

The speed of Iighf(1he maximum speed of interaction) is a

universal constant.This is Albert5 2nd postulate.

102

Everyone sees ihe some speed 10r light no matler how th~ are movi n.9. 103

-This means ,of course;that nothing con go - foster than ,-.. speed of light . r; +L

..

me

Noihngluste~lrlon

the speed

~'~.

01

fi9ht?

Nonsense!

h

Un·American! ~ We crocked . ~~ tne 60und - berner

C~.

.

-

by qol~ the light: barrier.

and

we'll crdok

Nothinq

faster

~.---,.,.",,-

1tlanthe

.s-eed

~Iight!??

Now IVe heard ihing.

everj-

104-

The maximum poesible speed is a material

property of our world.

But how is it possible?

Well ... -L Alberl has lo show

that &omell1in.9

l:Jnexpected

IS gOIng on.

Albert has to show:

1 How everyone can ... the same speed for light (c). and

2 What happens when you try to get an object to move f88terthan c.

To do this Albert shows that:

The concept of time must be changed

The concept of length must be changed

The concept of ma.. must be changed

105

o ihis is A\beri~ position:

1

There ore no

instantaneous interactions

in nature.

2J Therefore fhere

must be a maximum Q05sible speed of interaction.

J The rnoxirnum poeeible speed

of interaction isibe speed .of

the electromagnetic inleroctlon.

4 lhe ~d ofihe electromagnetic Interaction is -the speed . of light

5 The speed of lioht;5 1tle maximum possible speed. The reoll" difficult part wos showinq how everyone couId see -the some speed fur light'.

Let·5 ioo

see how he

did it:

· Ibert nearly drove himself craz~until he real ized that TIME was 111e Joker In the ck! The time elapsed between events was no necessarilY the sorre fOrall observers!

Remem ber speed

is disTance ~one divided by me time

it takes. In symbols:

D

.5 = T

o the moving person could observe the Iiqht travel in,q a certain distance D in a certaif'l time T 10 give itie speed of light c ....

while a station.QIY person could observe the ligbT traveling a ditterent distance D in a arfferent time T in jusT such a way 1haT she would measure eJCQt.tly -the same spee~ 0 •••

..

~~ 10T

t is neat. Here's .how A\bert analyzed "the phenomenon of simultaneous events . 5imultaneous .. " ..

.... events?

Yes. Albert points out that any measurement of time uses "the idea of simultaneous events.

We have to understand that all our judgments in which time plays a part are always judgments of simultaneous events. If, for instance, I say "That train arrives here at 7 0' clock" I mean something like this: "The pointing of a small hand of my watch to 7 and the arrival of the train are simultaneous events."

A\bert arqued ihat simultaneous events in one frome of referer1te would nO(Iloces5cwily be simultaneous when viewed from 0 dittereni fmnie. Albert called this the RELATIVITY OF

SIMULTANEITY 8\bert suqqests. ihat we try to picture his argument In terms



113

ow, how for h05 our imaginary person gone?

Relative to the train ihe person has gone J1. a car length. But relative to the embankment the person hos gone farther. ----~

Distance

gone IS

a

relative

measure.

So you see, Albert argues that elapsed time is a relative measure also. To the person in the passenger car the opening of the doors is simultaneous; the time elapsed between the opening of the front door and the opening of the back door is zero. But to the person on the embankment the time elapsed between the opening of the doors is not zero and depends on how fast the train is moving.

114

Next, Albert argues, isihe relativity ofthe measurement of length. Albert asks'fwhat is the length a ihe passenger car?

An observer in the train measures the interval by marking off his measuring rod in a straight line. (This is the length measured by the moving observer) But it is a different matter when the distance has to be judged from the embankment.

115

Riqh.t Albert argues ihatto measure the length ofthe cat as seen from the embankment, we have to

mark the positions on ihe embankment which are being passed b~ the front door and the bock door

at the same timeT-as judqed from the embankment. The distance between ffiese points is tnen tneasured with a measuring rod.

(This is the length of the car as measured by the stationary observer)

116

· Ibert says: It is by no means evident that this last measurement will supply us with the same result as the first. Thus, the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself.

Albert i~'prep,aring the ground for a reconsider-

arion or Newton's analysis of space time t:t motion.

Classical mechanics assumes

"that:

1The time interval

between events if> independent oF-the motion of the observer.

Z

The spoce interval (length) of d bact' is . inde8endent offue motion of the observer.

Unjusiiflable!

11'1

ffewton 6aY{

Spoce and time Intervals ore. absolute ond the speed of light is relative.

Albert replaces Newton's metaphysical absolutes, the constructs of absolute space and time, with a material absolute: there are no instantaneous interactions in nature!

Albert's contribution was dramatic because it so fundamentally challenged the framework of classical physics that had been accepted for the previous 200 years.

dossicol

_

perfect

_ _ _\[_HtjJr------J 50?

How does

this aff€Ct us?

Quite rilrlht There's

no neecrto get

mat excited about relativity just

b~uee a bunch

at P0ysici5t~ got excited

118

by IT.

Relativity theory had nothing to do with the development of the A-bomb. The Anti-Nuclear Handbook tells the story. And we'll discuss this again later.

Mean whi Ie lets see what ihe -rest of Alberts argument consists or,

119

· Ibert didn't just argue that space and time intervals needed to Be reformulated. He showed exact~ how to do it. Albert's program: To find a place and time of an event relative to the railway embankment when we know the place and time of the event with respect to the train

such that

Every ray of light possesses the speed c relative to both the embankment and the train.

Since we ore iol~ing about ofdlstances

rneceurernenrs

and time, we are talk'ina about numbers. Alber"E needs to use the troditional lonqua~e of numbers to mo~e it

come our right

120

~

he nmtsfep of cwrse was counung.

lhere aro at least 1 more dinosaurs qround here. We'd better iell

me others.

Tallyinq has been dated t9 30,000 B.c.They used scmtcnee on bones to do It ((111

1 II}!I

I/J(I

VII;))!)}

JIII;}l;' 1ft) IJ II

And the next big step' was measurement, which got its real start wittllhe rise of the cities. 121

Hey tnan,howfur is "It to Gizeh?

he Eqyptian

ruler-priests needed measures of distance..Lorea, volume and weight 10 osse ss taxes

and run me state.

We'\1 need

o lot more groin and

beer to feed ihis lot.

122

o ~eep records of what "they were doinq they hod to write down -the accounts. 50 written l"Iumerals were 1he next step. And 1tlis if> where mathematics beqon 10 qet mystitled. Because 1he priests kepr wrlnng tor fnemselves. Hiero -glyph = priest's writing

Anyway, "\he Bobvloriion and Sumerian priests

gotrather

qood at you

~

Mary' ie 24years old. Mary is mice 05 old as

I

ask /

Ann.

Ann was when Mary was as old 65 Ann ·'s now. How old is Ann?

Now improved mathemqtics was needed tor

for noviqotion , fOr gunnery, for ship'buildinq, fOr hyaraulic engineering. for

astronomy,

building technology. 50 there

come: Algebraic notation Vieta (1580) Decimals Logarithms Slide rule

stevinus (1585) Napier (161-+) Gunter (1620)

AnalyTic geometry Adding machine Calculus calculus

Descorres(te37) Pascal (1642) NewTon (1665) Lei bn iz. 06S~) 133

ihere has been 0 long histor:Y c! nom ber mystics who were very Impreosea with 1helr own

• f course

cleverness

Ann 15

18

yoors old

0000

Fytha9oras:~PBle55 us divine number, who generated Gods and men. f\lumber containest the root and source of eternally flowing creation."

Plato:

rr

Galileo:

lIThe book ofihe Universe

Hertz:

(Jad ever geometrizes

It

is wri1ten in molhemoticol language" without which one wanders.in vain throv9h a dork, labyrlnth.55 re One cannot escape the fuelinq that Theoo math em aticaI funnulas haye an independent eXIstence and intelliqence of their own, thatffleyore

wiser than we am. wiser even ihan

-theirdiscoverers.mot we get rnor:e out ef'them than was orisinally put ,Onto them."

.00

0

ond who forgot

the onqinol impulses "that led them to

mathematics

in the first place.

134

-( p5SST.. ,.. ever since 111e mattlematicians have started on relativity, I myself no longer understand it.'

But in reoli~ mo1hemarics is only a Iqnqu9Qe

51Z~ and and re atiol16hips between meosuroble

invented by human Ibelnqs to describe

Q~antitie5

ttl1n95. And ihat's.exactly how Albe.rt used moth

to express the relaTionshIp between the place and time cfon event in relotion to -the embankment when we know ire ploce and i1me of the event with respect to the train. 0 •• 0

And now let's have that passenger car O!jQin Mike.

135

Actually this pa5senger car is a bit complex" can we have oomelhing 0 Iitle simpler lookin.9?

Thafs better. You knowJwe could do awoy with ihe car altoqether and just "IndIcate a movi ng frame of reference. HoW"about trylf'1g that?

X' isthe distance along

me CQr.

y'is the distance up the car. v i5 the speed of the

moving frame.

136

>

y'?» x·

V

here,that's ~ifT}pler. Now we have a moving finme of reference y x .

And a stationary frame of reference

x

1r

rx isihe distance along the embonkment

zr

ism distance up the embankment

y'

m >V x: x

Which corresponds to ihe p056e!]qer car and the emboDkment. We marl< ,an eyent in lfIe movlrJQ fume by its coordinotes y'x'and tim~ t and we mark ffle same event In:fue J.sTationary trame by \ts coordinates ti- x

and

a

Its ttrf1e-t-,

Albert noworgues(u.5lng

olqebra) thafthe relationship

between the coordinates

ofevents in "the two systems is x' = x-vt VI-V/c2.'

y'''~ t , ,.

;..::L

1.- - C,.X

VI-V/~,.,

137

The sy5lem of

~uatlons on page 137 15

Known

'My name.

by

!f~Uztzphysic~tJ 19fj-(3fB Dutch iheoretlcol

discovered

the

.

senior 51otesmon of

phxsics end friend Of Einstein.

Right. Now we must show what's going on here

0 tJ 0 0 0

Imooine ihat both frome5 df reference ore at rest (rslofive to each other ofeourse). And we hove two idenhccl rather spec·IQI I~qht docks in them (designed byihe U.s. physicr5r R.P.feyrnman).

X'

x

138

1he liqht bulb gives out regular pulses ofliqm- which qo up tottle mi rrortjqet retlocted and . . bounce bark to ~ counter which goes dickfclick.

y'

S'

Now we imagine that the s' system

is q iven a verocity V50tnat it if> a movinq system W"lttl respect to ire SY6tem .e.

5'-+

v-+

y

The observer in

s' Bees her clock work exactly the eorre as when she was at reer,

x

otherwise ihe principle of relativity would be wrong. If her clock chonqed when she was moving she could then tell she 'NQS moving by notiCln9

ihe change.

-eut -the stationary observer, /C). \ooking at fue

moving 5'clock

sees someihin9 completely

different.

14-0

I

",,=--=,

l

fEV}

j

,--- n • "" n D1 ~.:!j }zl':!---r~ ~

&1

PULSE

PULSE

EMITTED

AP>50RBED

Mov'lng frame of reference 5 as seen by the coservenn-c'

Albert points out

that the veloeity

of Iiqht isthe some fur c:r1\ observers. Thus ihe stationary observer hears more time elapse between clicks on

the moving dock thon onthe statlona ry

dod