EASY LESSONS IN EINSTEIN. A DISCUSSION OF THE MORE INTELLIGIBLE FEATURES OF THE THEORY OF RELATIVITY

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EASY LESSONS IN EINSTEIN. A DISCUSSION OF THE MORE INTELLIGIBLE FEATURES OF THE THEORY OF RELATIVITY

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Wide World DR. ALBERT EINSTEIN IN His STUDY AT BERLIN.

Photos.

EASY LESSONS IN EINSTEIN A DISCUSSION OF THE MORE INTELLIGIBLE FEATURES OF THE THEORY OF RELATIVITY BY

EDWIN

E.

M.S., PH.D.

SLOSSON,

Literary Editor of The Independent, Associate in the Columbia School il of Journalism. Author of Great American Universities ,*' * *

Major

Prophets of To-day,

" " Six

Major

"Creative Chemistry,"

* *

Prophets,

etc.

With an Article by Albert Einstein and a Bibliography

ILLUSTRATED

NEW YORK HARCOURT, BRACE AND 1920

HOWE

COPYRIGHT, 1920, BY

HARCOURT, BRACE AND HOWK,

THE QUINN ft BOOEN COMPANY RAHWAY. N. J.

INC.

Appearcmces, for hiding Wonother ends, are your two grand fundamental world-enveloping Appearances, Space and Time.

Deepest of

der, as for

all illusory

many

CARLYLE.

Henceforth Space in itself and Time in itself sink mere shadows and only a kind of union of the two can be maintained as self -existent. MINKOWSKI.

into

045

A PREFATORIAL DIALOGUE (The Purpose of which is to Prevent the Prospective Reader from buying the Book under False Pretenses)

SCENE:

A

street car in

lation in

TIME

:

The

The Reader

uniform movement of trans-

direction.

any

present.

(looking over the top of a morning

paper)

Here's

:

something

queer

a

whole page taken with a new discovery " in physics Eclipse Observations Confirm Einstein's Theory of Relativity."

Anything about r

The Author:

Yes.

it

in

your paper?

Here's a cartoon on

it

by Mc-

Cutcheon.

The Reader: Must be something to it then. McCutcheon always knows what's news. (Reads on with audible fragments) "

Most

sensational discovery in the his" " Greatest achievetory of science ment of the human intellect " " Upsets " " Galileo,

Newton, and Euclid

Revo-

vi

EASY LESSONS IN EINSTEIN *

and theology/ It to someknow ought

lution in philosophy

looks as though

thing about

The Author:

I

I

this,

doesn't it?

And

think you will have to sometime.

you might as well do

now and

it

get

it

over with.

The Reader (running down the high spots)

the column and hitting " " Parallel lines

:

"a man moving light never

meet

with the speed of

grows old

due to a warp in space

"

"

"

"

gravitation

length of a

measuring depends upon direc" " tion of its motion mass is latent stick

"

"

energy "

sion

why, the man

The Author: Well,

crazy.

it is

But

madness

have

is

crazy, isn't

he?

definitions of insanity are so un-

certain that

his

fourth dimen-

time as a

it

not safe to say

who

is

seems there's method in otherwise

how

could he

upon the exact extent of the sun's attraction on light? hit

The Reader: (Picks up

his paper

and reads aloud

with concentrated attention)

"

Postu-

Every law of nature which holds good with respect to a coordilate

I.

nate system

K

must

also

hold good

EASY LESSONS IN EINSTEIN

vii

for any other system K', provided that

K

and K' are

uniform movement of

in

know any-

Say, do you

translation."

thing about this business?

The Author: Well,

a

yes,

The Reader: Can you it is all

The Author: Yes. is

have followed the

years.

tell

me

in plain language

what

about? I .can tell

Just that.

about, though I can't

is.

for a

at a safe distance

controversy

number of

I

little.

tell

you what you what

it it

Einstein says that there are only

men

twelve

the world capable of

in

understanding his

latest paper.

The Reader: Are you one of the twelve? The Author: No, nor the thirteenth. But without plunging into the mathematics of

might

talk over

some of the

it,

we

interesting

aspects of the theory of relativity and in the

end

I could

put you on track of

the twelve so you could read up on the subject

The Reader: All

if

right.

you

liked.

That's

car anyhow.

Go

fair.

ahead.

The Author: (See following pages)

This

is

a slow

EASY LESSONS IN EINSTEIN "A

warp

No

in nature has been found,

line is straight,

no

circle

round;

For Isaac Newton had unsound Ideas of gravitation!'

Why

is it

that our newspapers are sending out their

reporters to interview astronomers as well as actresses

and devoting pages to speculations on the nature of space and time as well as on the state of the market? to get at the

It is

bottom of

it

merely because a few

photographs taken during the eclipse of the sun on

by two telescopes, one at Sobral in northern Brazil and the other on the island of Principe

May

29, 1919,

off the

west coast of Africa, showed an abnormal shift

of

than one-324,oooth of a right angle in the posi-

less

tion of the stars.

When

these photograph films were

laid over films taken before the eclipse

it

was found

that the star-images about the darkened disk of the

sun did not exactly coincide with the images when the sun was not in their midst. Measured with a micrometer the displacement of the stars

positions

was found

to be

i.

1

from

their ordinary

60 seconds of arc on the

EASY LESSONS IN EINSTEIN

2

African plates and 1.98 seconds on the Brazilian these

Average This

is

plates.

two observations and you get

extremely close to the 1.73 predicted

1.79.

by Pro-

and twice as large as the calculated according to Newton's law of

fessor Einstein of Berlin deflection

gravitation which

When

would be

.87 of a second.

the announcement of this result

the meeting of the Royal Society of

vember 6

all

Lodge, for

last

was made

at

London on No-

eyes were turned toward Sir Oliver

February he had been rash enough to

express the hope,

if

not the prediction, that the results

of the eclipse expedition would support Newton rather

But instead of taking part in the disIt was cussion Sir Oliver got up and walked out.

than Einstein.

suspected that he had

cans would put

it,

"

gone

off

mad/' as we Ameri-

because the starlight would not fol-

But he put a stop to any such rumors by a letter to The Times in which he explains that his departure was not due to any dissatisfaction with the universe but to the necessity of catching the

low

his preferred path.

6 o'clock

train.

He

frankly acknowledges that

eclipse result is a great victory for Einstein titative

doubt

"

;

"

the

the quan-

agreement is too close to allow much room for " but he adds a caution against a strengthen-

ing of great and complicated generalizations concern-

ing space and time on the strength of this splendid

A NEW VIEW OF GRAVITATION result

:

I trust that it

may

be accounted

for,

3

with reas-

onable simplicity in terms of the ether of space."

This caution till

1922,

when

is

wise, but

we

the next eclipse comes, to see

observations are verified and

consider

cannot hold our breath

some of the

we may

in the

if

these

meantime

implications of Einstein's theory

of relativity. Sir

Thomson, President of the Royal making the momentous announcement in

Joseph

Society, in

the session of the Society, said

If his theory is right, it If

view of gravitation. reasoning holds good

:

makes us take an it

is

entirely

new

sustained that Einstein's

and it has sustained two very severe tests in connection with the perihelion of Mercury and the present eclipse then it is the result of one of the highest achievements of human thought. The weak point in the theory is the great difficulty in expressing it. It would seem that no one can understand the new law of gravitation without a thorough knowledge of the theory of invariants and of the calculus of variations.

What

is this

important?

most of

theory of relativity and

The mathematics of

us, but

we

it

are

why is it so too much for

can get some notion of

it

by a

familiar illustration.

Suppose you wake up some morning in a Pullman berth and look fmt of the window to see where you are.

EASY LESSONS IN EINSTEIN

4

You

your view blocked by a passing train on the next track. Now if you do not feel any jar of your car find

and cannot catch sight of the landscape beyond the other train you cannot tell whether (i) your train is

moving forward and the other (2) your train

is

standing

still,

or

and the other train

is

train

still

is

standing

moving backward, or (3) whether both

in opposite directions, or (4) whether both

moving

trains are faster.

moving

It is

one another.

in the

same

You

But

the relative motion of the

to

wonder whether there

is

motion; whether there rest

your train

can measure their speed of parting

is

tween

direction, but

obvious that the trains are getting past

as accurately as you please.

lute

trains are

and motion.

you can perceive

all

two

trains.

You

begin

any such thing as absois

any

real difference be-

Is there

of telling whether your train

is

in

window

any possible way motion or not if all

some object that itself be moving? Suppose the windows were all curtained, how could you find out whether you were mov-

you can

see out of the

is

ing forward or backward or standing

You

still ?

discuss this curious question with your fellow

passengers at the breakfast table and one of them

makes the sible to

brilliant suggestion that

it

might be pos-

determine the absolute motion of the car by

reference to the

air.

If the car is

moving forward the

RELATIVE MOTION ON A TRAIN air

5

would stream from front to rear and the reverse

if it

were moving backward. "

genious experimentalist, of the car and

I at

"

Suppose," says the in-

you stand at one end

that

We

the other.

will shout at each

other alternately and time the passage of the sound

with our stop watches.

waves

it

Since sound

it

it

air

it,

go against and from that measure-

might be possible for us not only to determine

which way the car fast

by

will take longer for the shout to

the air current than with

ment

carried

is

is

moving but how

to calculate

travels, assuming, of course, that there

wind blowing."

That

strikes

you as a

ment, but you point out one possible

doors at the ends of the car

may

air inside is being carried along

how

is

no

crucial experi-

difficulty, that

the

be closed and the

with the car, so no

difference would be observable in the speed of the " All right," sound even though the car were moving. replies

your

scientific friend,

liminary test to see

with the

car,

and

if

if

"

we

will

the enclosed air

we

find that

it is

is

make a

pre-

carried along

not then

we

will

try the second experiment with the sound signals to

which way the air current is moving. These two experiments must settle it, for either the air is moving see

with the car or

it is

moving through the

you conceive of any other

car.

possibility than these

No, you cannot, so you proceed

to try the

Can

two?

"

two experi-

EASY LESSONS IN EINSTEIN

6

First

ments.

you

visit

both ends of the car and find

both doors open ; the air then with the

You

car.

not being carried along

turn then with confidence to the

second experiment and you is

is

find,

of course, that there

a difference in the speed of sound whether

with the air drift or against

There might,

way

I

it

moves

it.

admit, be practical

difficulties in

the

of carrying out such a delicate experiment on a

moving

train,

but

we need not

bother with them, for

probably the current of air through the car would be so strong as to blow your hat out of the back door

and that would or at least

it

settle

would

the question to your satisfaction settle the

question in the affirma-

tive.

But imagine your amazement if this second experiment should give negative results like the first one; if you could detect no difference in time whether the sound was sent forward or back or across the car.

You would

then have proved by experiment (i) that

the air did not

did not

from

move with

move through

the car and (2) that the air

the car.

You might

suppose

at rest, but suppose the your car on the other train people passing yours tried the same experiments and got the same result, namely, that they, too,

this that

were

is

at rest as regards the air.

You would

then

be in a quandary, for your two indisputable experi-

CONTRADICTORY EXPERIMENTS ments had apparently given contradictory

7

You

results.

might get out of it by saying that there was no air, but if not what carried the sound waves and the hat?

CONTRADICTORY EXPERIMENTS

Now

this is the

been in for the

way

quandary

in

which physicists have

We

enly bodies ?

Is there

last thirty-three years.

of discovering absolute motion

The sun

pass across the sky from east to west and

assumed that the earth was This

it.

tion, for

is

the

years

seen to

man

at first

and the sun went

first

glance out of your Pullman

get the impression that the other train

moving it

still

is

the natural and instinctive assump-

is

when you

window you

the heav-

among

can observe and measure with great

accuracy their relative motion.

around

any

But for the

one.

last three

hundred

has been the fashion to assume the earth was

moving and not the

sun.

That assumption has the

advantage of simplifying the calculations of the asI

tronomers, though

never could see

why we

should

have to give up our simple notions of sunrise and sunset to save

The

them a

earth

silently that

little

moves

we

feel

trouble figuring.

if it

does

move

so quietly

no jar or engine-beat

to

tell

and

us of

EASY LESSONS IN EINSTEIN

8 its

by clouds could we or even

And do we

actually get any from observation of the heavenly see them moving about relatively to each

this point

We

bodies ?

find

rotation?

its

proof on

were perpetually shrouded out its motion through space

If the earth

motion.

other and

we can

movements most

represent their

moon

easily by supposing that the

goes around the

earth and that the earth and the rest of the planeta

go around the sun. But is this whole solar system in motion? So it seems when we compare it with the stars.

But who knows

visible stars are

if

the solar system and

all

the

not altogether moving off through

space at the rate of a mile or a thousand miles a

second? that It

How

can

we

tell

we have something

unless

and fixed to measure the motion by? seemed until recently that we had such a fixture, is still

the ether.

We

know of

the light that comes

the sun and stars only from

from them

Light, as

to us.

we

can prove by simple experiments, consists of wave motion. Now, can you have wave motion without

Sound waves are conveyed by

something to wave? air but there is

no

air

between the earth and the sun.

So as nothing could be found scientists

to

had to invent something

fill

this

empty space

to satisfy their sense

of the fitness of things.

The

their excogitations.

was a British invention,

It

ether

was

the product of

THE GALA OF THE ETHER vised in the Royal Institution, whence have

many useful theories and discoveries. The ether, as Salisbury said, is simply tive of the verb

"

to undulate."

a sort of transparent than any

solid,

more

easily penetrateci than

than

steel

passes through

come

so

the nomina-

was conceived of as

jelly filling all space,

more

rigid

than any

fluid,

more

frictionless

any

and yet so it

It

9

gas.

It

must be more

elastic

rarefied that ordinary matter

The

without the slightest effort

between the particles of the rushing earth as the wind blows through the branches

ether

is

supposed to

slip

of a tree.

For many years after its invention the ether had nothing to do except to carry light about from one But when the electro-magnetic place to another. waves of the wireless telegraph were produced something was needed also to carry them and this new task

was

upon the shoulders of the uncomplaining When Rontgen discovered the X-rays, whose

laid

ether.

waves are 10,000 times shorter than the shortest

light

waves, these were turned over to the ether to run. fact, it

In

got so that whenever a physicist found any

action that he could not explain by ordinary matter " Let the ether do it," and that hypothetical he said :

substance apparently answered every purpose until

came

to this question of relative motion.

it

EASY LESSONS IN EINSTEIN

10

Now

whatever we

would seem that

if

may

there

is

think about the ether

any such thing

it

filling all

"

"

space we might use it for measuring the empty motion of the earth through it as we did the air curIf the earth is really revolving

rent in the car.

the sun the ether must be whizzing through

around

its

pores

at the rate of about nineteen miles a second.

But wait ries

there

along with

is

the possibility that the earth car-

in its flight through space a sort of

it

atmosphere of ether as

it

does of

We

air.

must

first

get rid of this possibility by a preliminary experiment to see if a swiftly

moving mass of matter does catch

up and carry along with it a little of the ether. would cause a sort of an eddy or disturbance ether in the neighborhood of the disturbs the water.

For

moving mass

it

as a boat

would be a

and show a distorted image. Sir Oliver this experiment and got negative results.

deflected

Lodge tried That is, moving matter does not the ether.

left

in the

instance, a ray of light pass-

ing close to a rapidly revolving wheel little

This

to

Consequently,

it

disturb or carry with

would seem, we are

the only other logical alternative, that the

ether drifts through matter and detect this drift

we

should expect to

by measuring the speed of

the direction of the earth's motion.

It

light in

ought to take

longer for light to travel from one point to another

NEGATIVE RESULTS if

the earth meantime

point and

is

11

moving away from the

first

ought to take less time if the earth is moving toward it. Well, Michelson and Morley tried and also got negative results! It this experiment did not

was

it

make any

difference whether the ray of light

sent in the direction of the earth's

the reverse or across the line,

the

same

it

movement or

traveled invariably at

speed, 186,000 miles a second.

Here then

were two unquestionable experiments apparently con-

One proved that the ether The other proved that earth.

tradicting each other.

did

not travel with the

the

ether did not

through

stand

still

while the earth traveled

it.

Now when we get contradictory answers to the questions

we

Nature

is

questions.

put to Nature "we must assume nonsensical

that

we

unless

are asking nonsensical

If in the trial of a pickpocket

one witness

swears that the thief did not run up the street and another witness that he did not run down the street the lawyer does not necessarily say that one of

must be a

He

liar.

meditates a

them

moment and then

occurs to him that possibly the pickpocket did not

it

move

or that perhaps he disappeared into the third dimension

by climbing up a

fire-escape or dropping into a coal-

hole.

So with our

ether quandary.

If the ether does not

EASY LESSONS IN EINSTEIN

12

move and does not stand ether or perhaps there

is

perhaps there isn't any a fourth dimension. These still

are two conceivable ways out of the dilemma though they are not easy to accept, either of them. If there is

no ether what

carries the light

waves?

a fourth dimension in what direction does it is

no harder

dimension than that he needs

it

If there is it lie ?

to believe in or conceive of it is

But

a fourth

the ether, and if the physicist finds

in his business

he will have to have

it.

Einstein says that he needs a fourth dimension for his

formulas.

THE CONUNDRUM OF THE AGES For twenty-four hundred years philosophic thought has been concerned with the problem of the relation of space and time. societies of

Drop

into

today and you will

any of the scientific find them discussing

whether space is finite or infinite, whether there is any difference between rest and motion, whether length is absolute or relative, whether time and space have

which are the very questions discussed by Pythagoras and Zeno in the Greek cities of Asia real existence,

Minor.

Now

the time spent in these speculations has

not been wasted, although conclusion, for out of

it

it

has led to no definite

have grown our mathematics

THE CONUNDRUM OF THE AGES and

physics.

The Wandering Jew, who

is

13

the only

mortal having the privilege of attending the schools of the Eleatics and those of the present day, would ob-

modern

serve one difference, that

them

Of

put

experiment wherever poswhile the ancients were content with thinking

their theories to the test sible,

scientists try to

of,

out. all

the guesses that have been given to this rid-

dle of the universe

none has been more bold and revo-

lutionary than that contained in a paper of four or

pages contributed in 1905 to the 'Annalen der Physik by Albert Einstein. The controversy it precipifive

tated has not altogether been confined to the realm

of pure reason, for scientists are but

human and

as such

are not entirely uninfluenced by patriotic prejudice.

In this brief paper he proposed a

new theory of the The first was

universe based upon two postulates.

the principle of relativity; that 3.llmotion is relative.

This means, for instance, that the motion of a smoothly

we would

moving

never

train if the

know

windows

were darkened and that we could never discover the forward movement of the earth

if

we

could not see the

heavenly bodies. Einstein's second postulate light is independent of the is

was

that the velocity of

motion of the source.

a hard one for our reason to swallow, for

it

This

means

EASY LESSONS IN EINSTEIN

14

that nothing can travel faster than light, 186,000 miles

a second, and that you cannot make light travel faster than that by giving it a swift send-off. It is the same as saying that

if

man

a

an engine threw a

ball

standing on the cowcatcher of

forward,

it

would not make any

difference with the velocity of the ball whether the train

was running

at full speed

forward or backward or

But the experiments of the American Michelson and Morley, who measured the physicists, standing

still.

speed of light and found

was moving toward it,

it

the

same whether the earth

the source of the ray or

or at right angles to

its direction,

away from

confirm Einstein's

second assumption.

we

accept Einstein's two primary postulates and " " his later his theory clears Principle of Equivalence If

up

this ether-drift difficulty as well as various other

riddles of the universe.

orbit of

Mercury

account for.

that

It explains the shifting

Newton's theory could never

It foretold the deflection

sun's gravitation that the observations

of last

May

confirmed.

of the

A

of light by the

on the

eclipse

third test, the shifting of

the lines of the solar spectrum toward the red end in a gravitational

field,

has not been met.

nical points concern only physicists

Such tech-

and astronomers,

but Einstein's relativity theory, which two out of the three experiments support, carries with

it

certain

PARADOXES OF RELATIVITY

15

speculations as to time and space that are upsetting to

current conceptions.

PARADOXES OF RELATIVITY

now

All three of Newton's laws of motion are

questioned and the world

called

is

the lesson which Euclid taught

never meet.

it

upon

to unlearn

that parallel lines

According to Einstein they

may

meet.

According to Newton the action of gravitation instantaneous throughout

all

space.

is

According to

Einstein no action can exceed the velocity of light. If the theory of relativity

thing as absolute time or

is

right there can be

way

of finding whether clocks

Our

in different places are synchronous.

vary according to

may

weight of a body shortest; distance

straight line.

how we

yardsticks

hold them and the

may depend upon

its velocity.

between two points

may

These are a few of the

The

not be a

startling im-

plications of Einstein's theory of relativity.

put

no such

If he

had

forward as a mere metaphysical fancy, as a posbut unverifiable hypothesis, it would have aroused

it

sible

mere

idle curiosity.

But he deduced from

it

mathe-

governing physical phenomena which could be put to the test of experiment. They have been tested in these two crucial cases and prove to be true. matical laws

EASY LESSONS IN EINSTEIN

16

In the preceding pages we have discussed the question of the relativity of motion and seen how impossible it is

are

to

on

for instance, whether a train or a ship you

tell,

is

moving or not

unless you can compare

something that you are

what are you sure

is

"

sure

"

is

stationary?

it

stationary.

with

But

Nothing on earth "

" compared with the fixed stars is spinning around at the rate of about a thousand miles an hour and rushing around the sun at the rate of surely, for the earth

nearly 70,000 miles an hour.

But are we sure the

we have nothing else to compare them with? You may remember Herbert Spencer's illustration of the sea captain who was walking west on stars are fixed since

the deck of a ship sailing east at the

same

Is

rate.

he

you are in the same boat, you say he is. If you are on shore when the ship is passing " you say he is standing still and marking time." It

moving or not?

all

If

depends on the point of view.

Now you may tive,

readily admit that

not absolute, and yet you

that space

and time are

But motion

is

all

may

motion

is

rela-

balk at the idea

also relative, not absolute.

merely simultaneous change of position

and time, and why should we feel so certain about space and time when we have never seen either ? in space

You may desk

is

you are sure your ask you how long you have

say, for instance, that

so long.

But

if I

ARE YOU SURE OF YOUR SHAPE? to say as long as something else.

You may

say

17 it is

a

But how long is a yard ? It is as long as " stick marked one yard," and this in

yard long.

some tape or

turn has been taken from some other yardstick, until

you get back to the brass rod in London that is just as long as the distance from the tip of the nose of

King Henry

I to

the end of his royal thumb.

a standard of absolute measurement

difficulty

But such

unsatisfactory

an absolute monarchist.

to everyone except

from the

is

But apart

of the present inaccessibility of

King Henry's nose and thumb, can we be confident that our yardstick keeps the same length while we are measuring with

it?

We

must admit indeed that

it is

summer day than on a winter day, but can that it does not alter in length when we hold

longer on a

we it

be sure

upright or lay

tell if it

it

horizontally ?

did change in length as

Or, rather, could it is

we

changed in direc-

tion?

ARE YOU SURE OF YOUR SHAPE? If

you have ever been

in

any of those funny places at

the amusement parks you will have noticed the convex

mirrors there and

how

ridiculous they

make

other

you cannot afford the nickel necessary for the study of optics in such an establishment you can contemplate your reflection in the side of a people look.

If

EASY LESSONS IN EINSTEIN

18

shiny tin cup or can.

who

man

looks as you suppose yourself to be except that

somehow you seem

when you look right

you

into the

man

become left-handed.

to have

convex cylindrical mirror

into a

see a

Look a

In a plane mirror you see a

man

thinner than you

same mirror

shorter than

you

"

"

But up-

really are."

and you see

set horizontal

You

really are."

set

grin at

the sight of such queer-looking creatures, but you notice that they are equally

Now how

amused

at

your shape.

are you going to prove to the

men

in the

curved glasses that they are mere caricatures and that

you are not images?

really built

You

on the plan of

either of these

naturally resort to measurement, as a

You cannot get into the mirror world tall man who pretends to represent you,

scientist should.

to

measure the

but you can explain to him in the sign language what

do and he instantly complies. You stand up a measuring rod at your side and show him that you are exactly 72 inches tall. He also sets up a

you want him

to

rod and that also reads 72 inches. use any kind of measure he

when stick. it

it

you

let

will catch

him

him

comes to measurement of width with the same

You

hold your rule across your shoulders and

reads 18 inches, that

But he also measures it

likes,

Never mind,

his

is,

one- fourth your height.

width with his rule and makes

just the same, 18 inches, although as

you

see

him he

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