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Full text of "The Universe and Dr Einstein"






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INI UNIVERSE 

AND DR. 
EINJTEJN 



1: YOU 



—the average man— may now at last 
understand, by reading this most 
exciting book by Lincoln Barnett, 
how the universe appears in the light 
of modern scientific knowledge. This 
is the opinion-turn to his foreword-of 



EINSTEIN 

HINSEIf 



THE UNIVERSE 
AND DR. EINSTEIN 

by Lincoln Barnett 
with a foreword by 
Albert Einstein 

This book is an attempt— perhaps 
the most brilliantly successful of 
our time— to describe the universe 
as it now appears in the light of 
modern scientific and cosmological 
theory. 

Any portrait of the cosmos in 
which we live necessarily takes leave 
of pictures and analogies, and leads 
the reader deep into a series of 
ideas which are familiar and easy 
only to a small handful of the most 
speculative thinkers. It is Mr. Bar- 
nett's achievement that he makes 
advanced scientific thought not 
only lucid, but deeply exciting, to 
the intelligent layman. 

Against the background of the 
earlier laws of Newton and Galileo, 
we are shown how succeeding 
generations of physicists gradually 
added to the sum total of human 
knowledge, until in the first quarter 
of this century two great theore- 
tical systems were developed. One, 
the Quantum Theory, which has 
shaped all our concepts of the 
atom, the basic units of matter and 
energy, and the realities that are 
too small to be perceived ; and the 
other, Einstein's Theory of Rela- 
tivity, which has shaped all our 
concepts of space, time, gravita- 
tion, and the realities that are 
too remote and too vast to be 

[turn to second flap 



5'- 



net 



THE UNIVERSE AND DR. EINSTEIN 




THE UNIVERSE AND 
DR. EINSTEIN 

by 
LINCOLN BARNETT 

With a Foreword by 
ALBERT EINSTEIN 

Illustrated by 
ANTHONY SODARO 



LONDON 
VICTOR GOLLANCZ LTD. 

1949 



Copyright, 1948, by Harper & Brothers 
Copyriglit, 1948, by Lincoln Barnett 

First published June 1949 
Second impression October 1949 



TO 



J. K .B. and L. H. B. 



Printed in Great Britain by 
The Camelot Press Ltd., London and Southampton 



FOREWORD BY ALBERT EINSTEIN 

Anyone who has ever tried to present a 
rather abstract scientific subject in a popular manner 
knows the great difficulties of such an attempt. Either 
he succeeds in being intelligible by concealing the core 
of the problem and by offering the reader only 
superficial aspects or vague allusions, thus deceiving 
the reader by arousing in him the deceptive illusion of 
comprehension; or else he gives an expert account of 
the problem, but in such a fashion that the untrained 
reader is unable to follow the exposition and becomes 
discouraged from reading any further. 

If these two categories are omitted from to-day's 
popular scientific literature, surprisingly little re- 
mains. But the little that is left is very valuable indeed. 
It is of great importance that the general public be 
given an opportunity to experience — consciously and 
intelligently — the efforts and results of scientific 
research. It is not sufficient that each result be taken 
up, elaborated, and applied by a few specialists in the 
field. Restricting the body of knowledge to a small 
group deadens the philosophical spirit of a people and 
leads to spiritual poverty. 

Lincoln Barnett's book represents a valuable con- 
tribution to popular scientific writing. The main ideas 
of the theory of relativity are extremely well presented. 
Moreover, the present state of our knowledge in 
physics is aptly characterized. The author shows how 
the growth of our factual knowledge, together with 
the striving for a unified theoretical conception com- 
prising all empirical data, has led to the present 



situation which is characterized — notwithstanding all 
successes — by an uncertainty concerning the choice of 
the basic theoretical concepts. 
Princeton, New Jersey. 
September 10, 1948. 



THE UNIVERSE ANP DR. EINSTEIN 



Carved in the white walls of the Riverside 
Church in New York, the figures of six hundred 
great men of the ages — saints, philosophers, kings 
—stand in limestone immortality, surveying space 
and time with blank imperishable eyes. One panel 
enshrines the geniuses of science, fourteen of them, 
spanning the centuries from Hippocrates, who 
died around 370 B.C., to Albert Einstein, who was 
seventy years old in March, 1 949. It is noteworthy that 
Einstein is the only living man in this whole sculptured 
gallery of the illustrious dead. 

It is equally noteworthy that of the thousands of 
people who worship weekly at Manhattan's most 
spectacular Protestant church, probably 99 per 
cent, would be hard pressed to explain why 
Einstein's image is there. It is there because a 
generation ago, when the iconography of the 
church was being planned, Dr. Harry Emerson 
Fosdick wrote letters to a group of the nation's 
leading scientists asking them to submit lists of the 
fourteen greatest names in scientific history. Their 
ballots varied. Most of them included Archimedes, 
Euclid, Galileo, and Newton. But on every list 
appeared the name of Albert Einstein. 

The vast gap that has persisted for more than 
forty years — since 1905, when the Theory of 
Special Relativity was first published — between 
Einstein's scientific eminence and public under- 
standing of it is the measure of a gap in American 

7 






education. To-day most newspaper readers know 
vaguely that Einstein had something to do with the 
atomic bomb; beyond that his name is simply a 
synonym for the abstruse. While his theories form 
part of the body of modern science, they are not 
yet part of the modern curriculum. It is not sur- 
prising therefore that many a college graduate 
still thinks of Einstein as a kind of mathematical 
surrealist rather than as the discoverer of certain 
cosmic laws of immense importance in man's slow 
struggle to understand physical reality. He does 
not know that Relativity, over and above its 
scientific import, comprises a major philosophical 
system which augments and illumines the reflec- 
tions of the great epistemologists — Locke, Berkeley, 
and Hume. Consequently, he has very little notion 
of the vast, arcane, and mysteriously ordered 
universe in which he dwells. 



Dr. Einstein, now professor emeritus at the In- 
stitute for Advanced Study at Princeton, is cur- 
rently hard at work on a problem which has 
stumped him for more than a quarter-century and 
which he intends to solve before he dies. His 
ambition is to complete his "unified field theory," 
setting forth in one series of equations the laws 
governing the two fundamental forces of the 
universe, gravitation and electromagnetism. The 
significance of this task can be appreciated only 
when one realizes that virtually all the phenomena 
of nature are produced by these two primordial 
forces. Until a hundred years ago electricity and 
magnetism — while known and studied since early 
Greek times — were regarded as separate quantities. 
But the experiments of Oersted and Faraday in 
8 



the nineteenth century showed that a current of 
electricity is always surrounded by a magnetic field, 
and conversely that under certain conditions 
magnetic forces can induce electrical currents. From 
these experiments came the discovery of the electro- 
magnetic field through which light waves, radio 
waves, and all other electromagnetic disturbances are 
propagated in space. Thus electricity and magnetism 
may be considered as a single force. Save for gravita- 
tion, nearly all other forces in the material universe — 
frictional forces, chemical forces which hold atoms 
together in molecules, co-hesive forces which bind 
larger particles of matter, clastic forces which cause 
bodies to maintain their shape — are of electro- 
magnetic origin; for all of these involve the interplay 
of matter, and all matter is composed of atoms which 
in turn are composed of electrical particles. Yet the 
similarities between gravitational and electromagnetic 
phenomena are very striking. The planets spin in the 
gravitational field of the sun; electrons swirl in the 
electromagnetic field of the atomic nucleus. The earth, 
moreover, is a big magnet — a peculiar fact which 
is apparent to anyone who has ever used a compass. 
The sun is also a magnet. And so are all the stars. 

Although many attempts have been made to iden- 
tify gravitational attraction as an electromagnetic 
effect, all have failed. Einstein himself thought he had 
succeeded in 1 929 and published a unified field theory 
which he later scrapped as inadequate. His present 
objectives are more ambitious, for he is endeavouring 
now to formulate a set of universal laws that will 
encompass both the boundless gravitational and 
electromagnetic fields of interstellar space and the 
tiny, terrible field inside the atom. In this vast cosmic 
picture the abyss between macrocosmos and micro- 
cosmos — the very big and the very little — will be 
bridged, and the whole complex of the universe will 






resolve into a homogeneous fabric in which matter 
and energy are indistinguishable and all forms of 
motion from the slow wheeling of the galaxies to the 
wild night of electrons become simply changes in the 
structure and concentration of the primordial field. 

Since the aim of science is to describe and explain 
the world we live in, Einstein would, by thus defining 
the manifold of nature within the terms of a single 
harmonious theory, attain its loftiest goal. The mean- 
ing of the word "explain," however, suffers a contrac- 
tion with man's every step in quest of reality. Science 
cannot yet really "explain" electricity, magnetism, 
and gravitation; their effects can be measured and 
predicted, but of their ultimate nature no more is 
known to the modern scientist than to Thales of 
Miletus, who first speculated on the electrification of 
amber around 585 B.C. Most contemporary physicists 
reject the notion that man can ever discover what 
these mysterious forces "really" are. Electricity, 
Bcrtrand Russell says, "is not a thing, like St. Paul's 
Cathedral; it is a way in which things behave. When 
we have told how things behave when they are elec- 
trified, and under what circumstances they are 
electrified, we have told all there is to tell." Until 
recently scientists would have scorned such a thesis. 
Aristotle, whose natural science dominated Western 
thought for two thousand years, believed that man 
could arrive at an understanding of ultimate reality 
by reasoning from self-evident principles. It is, for 
example, a self-evident principle that every thing 
in the universe has its proper place, hence one can 
deduce that objects fall to the ground because 
that's where they belong, and smoke goes up because 
that's where it belongs. The goal of Aristotelian 
science was to explain why things happen. Modern 
science was born when Galileo began trying to explain 
how things happen and thus originated the method of 



' 



controlled experiment which now forms the basis of 
scientific investigation. 

Out of Galileo's discoveries and those of Newton in 
the next generation there evolved a mechanical uni- 
verse of forces, pressures, tensions, oscillations, and 
waves. There seemed to be no process of nature which 
could not be described in terms of ordinary experi- 
ence, illustrated by a concrete model or predicted by 
Newton's amazingly accurate laws of mechanics. But 
before the turn of the past century certain deviations 
from these laws became apparent; and though these 
deviations were slight, they were of such a funda- 
mental nature that the whole edifice of Newton's 
machine-like universe began to topple. The certainty 
that science can explain "how" things happen began 
to dim about twenty years ago. And right now it is a 
question whether scientific man is in touch with 
reality at all — or can ever hope to be. 



10 



II 



II 



I he factors that first led physicists to distrust 
their faith in a smoothly functioning mechanical uni- 
verse loomed on the inner and outer horizons of 
knowledge — in the unseen realm of the atom and in 
the fathomless depths of intergalactic space. To des- 
cribe these phenomena quantitatively, two great 
theoretical systems were developed between 1900 and 
1927. One was the Quantum Theory, dealing with 
the fundamental units of matter and energy. The 
other was Relativity, dealing with space, time, and 
the structure of the universe as a whole. 

Both are now accepted pillars of modern physical 
thought. Both describe phenomena in their fields in 
terms of consistent, mathematical relationships. They 
do not answer the Newtonian "how" any more than 
Newton's laws answered the Aristotelian "why." They 
provide equations, for example, that define with great 
accuracy the laws governing the radiation and propa- 
gation of light. But the actual mechanism by which 
the atom radiates light and by which light is propa- 
gated through space remains one of nature's supreme 
mysteries. Similarly the laws governing the phenom- 
enon of radioactivity enable scientists to predict that 
in a given quantity of uranium a certain number of 
atoms will disintegrate in a certain length of time. 
But just which atoms will decay and how they are 
selected for doom are questions that man cannot yet 
answer. 

In accepting a mathematical description of nature, 
physicists have been forced to abandon the ordinary 
world of our experience, the world of sense perceptions. 
12 



To understand the significance of this retreat it is 
necessary to step across the thin line that divides 
physics from metaphysics. Questions involving the 
relationship between observer and reality, subject and 
object, have haunted philosophical thinkers since the 
dawn of reason. Twenty-three centuries ago the Greek 
philosopher Dcmocritus wrote: "Sweet and bitter, 
cold and warm as well as all the colours, all these 
things exist but in opinion and not in reality; what 
really exists are unchangeable particles, atoms, and 
their motions in empty space." Galileo also was aware 
of the purely subjective character of sense qualities like 
colour, taste, smell, and sound, and pointed out that 
"they can no more be ascribed to the external objects 
than can the tickling or the pain caused sometimes by 
touching such objects." 

The English philosopher John Locke tried to pene- 
trate to the "real essence of substances" by drawing a 
distinction between what he termed the primary and 
secondary qualities of matter. Thus he considered that 
shape, motion, solidity, and all geometrical properties 
were real or primary qualities, inherent in the object 
itself; while secondary qualities, like colours, sounds, 
tastes, were simply projections upon the organs of 
sense. The artificiality of this distinction was obvious 
to later thinkers. 

"I am able to prove," wrote the great German 
mathematician, Leibnitz, "that not only fight, colour, 
heat, and the like, but motion, shape, and extension 
too are mere apparent qualities." Just as our visual 
sense, for example, tells us that a golf ball is white, so 
vision abetted by our sense of touch tells us that it is 
also round, smooth, and small — qualities that have 
no more reality, independent of our senses, than the 
quality which we define by convention as white. 

Thus gradually philosophers and scientists arrived 
at the startling conclusion that since every object is 

13 



simply the sum of its qualities, and since qualities 
exist only in the mind, the whole objective universe of 
matter and energy, atoms and stars, docs not exist 
except as a construction of the consciousness, an 
edifice of conventional symbols shaped by the senses of 
man. As Berkeley, the arch-enemy of materialism, 
phrased it: "All the choir of heaven and furniture of 
earth, in a word all those bodies which compose the 
mighty frame of the world, have not any substance 
without the mind. ... So long as they are not actually 
perceived by me, or do not exist in my mind, or that of 
any other created spirit, they must either have no 
existence at all, or else subsist in the mind of some 
Eternal Spirit." Einstein carried this train of logic to 
its ultimate limits by showing that even space and time 
are forms of intuition, which can no more be divorced 
from consciousness than can our concepts of colour, 
shape, or size. Space has no objective reality except as 
an order or arrangement of the objects we perceive in 
it, and time has no independent existence apart from 
the order of events by which we measure it. 



These philosophical subtleties have a profound 
bearing on modern science. For with the philosophers' 
reduction of all objective reality to a shadow-world of 
perceptions, scientists became aware of the alarming 
limitations of man's senses. Anyone who has ever 
thrust a glass prism into a sunbeam and seen the rain- 
bow colours of the solar spectrum refracted on a screen 
has looked upon the whole range of visible light. For 
the human eye is sensitive only to the narrow band of 
radiation that falls between the red and the violet. 
A difference of a few one hundred thousandths of 
a centimetre in wavelength makes the difference 
between visibility and invisibility. The wavelength of 

14 









red light is -00007 cm. and that of violet light 
•00004 cm. 

But the sun also emits other kinds of radiation. 
Infra-red rays, for example, with a wavelength of 
•00008 to -032 cm. are just a little too long to excite the 
retina to an impression of light, though the skin detects 
their impact as heat. Similarly ultra-violet rays with a 
wavelength of -00003 t0 • 00000 1 cm. are too short for 
the eye to perceive, but can be recorded on a photo- 
graphic plate. Photographs can also be made by the 
"light" of X-rays which are even shorter than ultra- 
violet rays. And there are other electromagnetic 
waves of lesser and greater frequency— the gamma 
rays of radium, radio waves, cosmic rays— which can 
be detected in various ways and differ from light only 
in wavelength. It is evident, therefore, that the human 
eye suppresses most of the "lights" in the world, and 
that what man can perceive of the reality around him 



VISIBLE LIGHT 




; J.. 1 ji ]l J«, ', l ^ 10l( J.. 1 (Ji 10 , -'io'-»iD>io , -'io- 1 w ,J io' 1 1 w to' '«' i°" w 1 »»* ,0 ' 1Q ' l0 * 
WAVELENGTH tCENTlMETRESI 

The electromagnetic spectrum reveals the narrow range of 
radiation visible to man's eye. From the standpoint of physics, the 
only difference between radio waves, visible light, and such high- 
frequency forms of radiation as X-rays and gamma rays lies in 
their wavelength. But out of this vast range of electromagnetic 
radiation, extending from cosmic rays with wavelengths of only 
one trillionth of a centimetre up to infinitely long radio waves, the 
human eye selects only the narrow band indicated in white on the 
above chart. Man's perceptions of the universe in which he dwells 
are thus restricted by the limitations of his visual sense. Wave- 
lengths are indicated on the chart by the denary system: i.e. io 3 
centimetres equals 10 X IO X 10 equals 1,000; and 10- 3 equals 
1/10 X 1/10 x j / 10 equals 1/1,000. 

15 






is distorted and enfeebled by the limitations of his 
organ of vision. The world would appear far different 
to him if his eye were sensitive, for example, to 
X-rays. 

Realization that our whole knowledge of the uni- 
verse is simply a residue of impressions clouded by our 
imperfect senses makes the quest for reality seem hope- 
less. If nothing has existence save in its being per- 
ceived, the world should dissolve into an anarchy of 
individual perceptions. But a curious order runs 
through our perceptions, as if indeed there might be 
an under] ayer of objective reality which our senses 
translate. Although no man can ever know whether 
his sensation of red or of Middle C is the same as 
another man's, it is nevertheless possible to act on the 
assumption that everyone sees colours and hears tones 
more or less alike. 

This functional harmony of nature, Berkeley, 
Descartes, and Spinoza attributed to God. Modern 
physicists who prefer to solve their problems without 
recourse to God (although this seems to become more 
difficult all the time) emphasize that nature mysteri- 
ously operates on mathematical principles. It is the 
mathematical orthodoxy of the universe that enables 
theorists like Einstein to predict and discover natural 
laws simply by the solution of equations. But the para- 
dox of physics to-day is that with every improvement 
in its mathematical apparatus the gulf between man 
the observer and the objective world of scientific 
description becomes more profound. 

It is perhaps significant that in terms of simple mag- 
nitude man is the mean between macrocosm and 
microcosm. Stated crudely this means that a super- 
giant red star (the largest material body in the 
universe) is just as much bigger than man as an 
electron (tiniest of physical entities) is smaller. It is not 
surprising, therefore, that the prime mysteries of 
16 




nature dwell in those realms farthest removed from 
sense-imprisoned man, nor that science, unable to 
describe the extremes of reality in the homely meta- 
phors of classical physics should content itself with 
noting such mathematical relationships as may be 
revealed. 



17 



Ill 



1 he first step in science's retreat from 
mechanical explanation toward mathematical ab- 
straction was taken in 1900, when Max Planck put 
forth his Quantum Theory to meet certain problems 
that had arisen in studies of radiation. It is common 
knowledge that when heated bodies become incandes- 
cent they emit a red glow that turns to orange, then 
yellow, then white as the temperature increases. Pains- 
taking efforts were made during the past century to 
formulate a law stating how the amount of radiant 
energy given off by such heated bodies varied with 
wavelength and temperature. All attempts failed until 
Planck found by mathematical means an equation 
that satisfied the results of experiment. The extra- 
ordinary feature of his equation was that it rested on 
the assumption that radiant energy is emitted not in 
an unbroken stream, but in discontinuous bits or por- 
tions which he termed quanta. 

Planck had no evidence for such an assumption, for 
no one knew anything (then or now) of the actual 
mechanism of radiation. But on purely theoretical 
grounds he concluded that each quantum carries an 
amount of energy given by the equation, E = Av, where 
v is the frequency of the radiation and h is Planck's 
Constant, a small but inexorable number (roughly 
•000000000000000000000000006624) which has since 
proved to be one of the most fundamental constants 
in nature. In any process of radiation the amount of 
emitted energy divided by the frequency is always 
equal to h. Although Planck's Constant has dominated 
the computations of atomic physics for half a century, 
18 



its magnitude cannot be explained any more than the 
magnitude of the speed of light can be explained. Like 
other universal constants, it is simply a mathematical 
fact for which no explanation can be given. Sir Arthur 
Eddington once observed that any true law of nature 
is likely to seem irrational to rational man; hence 
Planck's quantum principle, he thought, is one of the 
few real natural laws science has revealed. 



The far-reaching implications of Planck's conjecture 
did not become apparent till 1905, when Einstein, 
who almost alone among contemporary physicists 
appreciated its significance, carried the Quantum 
Theory into a new domain. Planck had believed he 
was simply patching up the equations of radiation. But 
Einstein postulated that all forms of radiant energy — 
light, heat, X-rays— actually travel through space in 
separate and discontinuous quanta. Thus the sensa- 
tion of warmth we experience when sitting in front of a 
fire results from the bombardment of our skin by innu- 
merable quanta of radiant heat. Similarly sensations 
of colour arise from the bombardment of our optic 
nerves by light quanta which differ from each other 
just as the frequency v varies in the equation E = hv. 

Einstein substantiated this idea by working out a 
law accurately defining a puzzling phenomenon 
known as the photoelectric effect. Physicists had been 
at a loss to explain the fact that when a beam of pure 
violet light is allowed to shine upon a metal plate the 
plate ejects a shower of electrons. If light of lower 
frequency, say yellow or red, falls on the plate, elec- 
trons will again be ejected but at reduced velocities. 
The vehemence with which the electrons are torn 
from the metal depends only on the colour of the light 
and not at all on its intensity. If the light source is 

19 



removed to a considerable distance and dimmed to a 
faint glow the electrons that pop forth are fewer in 
number, but their velocity is undiminished. The 
action is instantaneous even when the light fades to 
imperceptibility. 

Einstein decided that these peculiar effects could be 
explained only by supposing that all light is composed 



LIGHT SOURCE 







ELECTRONS 



METAL PLATE 

The photolectric effect was interpreted by Einstein in 1905. When 
light falls on a metal plate, the plate ejects a shower of electrons. 
This phenomenon cannot be explained by the classic wave theory 
of light, Einstein deduced that light is not a continuous stream of 
energy but is composed of individual particles or bundles of 
energy which he called photons. When a photon strikes an electron 
the resulting action is analogous to the impact of billiard balls as 
shown in the simplified conception above. 

of individual particles or grains of energy which he 
called photons, and that when one of them hits an elec- 
tron the resulting action is comparable to the impact 
of two billiard balls. He reasoned further that photons 
of violet, ultra-violet, and other forms of high fre- 
quency radiation pack more energy than red and 
infra-red photons, and that the velocity with which 
each electron flies from the metal plate is proportional 
to the energy content of the photon that strikes it. He 
expressed these principles in a series of historic equa- 
tions which won him the Nobel Prize and profoundly 
so 



influenced later work in quantum physics and spec- 
troscopy. Television and other applications of the 
photoelectric cell owe their existence to Einstein's 
Photoelectric Law. 



In thus adducing an important new physical prin- 
ciple Einstein uncovered at the same time one of the 
deepest and most troubling enigmas of nature. No one 
doubts to-day that all matter is made up of atoms 
which in turn are composed of even smaller building 
blocks called electrons, neutrons, and protons. But 
Einstein's notion that light too may consist of discon- 
tinuous particles clashed with a far more venerable 
theory that light is made up of waves. 

There are indeed certain phenomena involving light 
that can only be explained by the wave theory. For 
example the shadows of ordinary objects like build- 
ings, trees, and telegraph poles appear sharply 
defined; but when a very fine wire or hair is held 
between a light source and a screen it casts no dis- 
tinct shadow whatsoever, suggesting that light rays 
have bent around it just as waves of water bend 
around a small rock. Similarly a beam of light passing 
through a round aperture projects a sharply-defined 
disk upon a screen; but if the aperture is reduced 
to the size of a pinhole, then the disk becomes 
ribbed with alternating concentric bands of light 
and darkness, somewhat like those of a conven- 
tional target. This phenomenon is known as diffrac- 
tion and has been compared with the tendency of 
ocean waves to bend and diverge on passing through 
the narrow mouth of a harbour. If instead of one 
pinhole, two pinholes are employed very close 
together and side by side, the diffraction patterns 
merge in a series of parallel stripes. Just as two wave 

21 






1 



systems meeting in a swimming pool will reinforce 
each other when crest coincides with crest and annul 
each other when the crest of one wave meets the 
trough of another, so in the case of the adjacent pin- 
holes the bright stripes occur where two light waves 
reinforce each other and the dark stripes where 
two waves have interfered. These phenomena— dif- 
fraction and interference — are strictly wave character- 
istics and would not occur if light were made up of 
individual corpuscles. More than two centuries of 
experiment and theory assert that light must consist of 
waves. Yet Einstein's Photoelectric Law shows that 
light must consist of photons. 

This fundamental question — is light waves or is it 
particles? — has never been answered. The dual 
character of light is, however, only one aspect of a 
deeper and more remarkable duality which pervades 
all nature. 



The first hint of this strange dualism came in 1925, 
when a young French physicist named Louis de 
Broglie suggested that phenomena involving the inter- 
play of matter and radiation could best be understood 
by regarding electrons not as individual particles, but 
as systems of waves. This audacious concept flouted 
two decades of quantum research in which physicists 
had built up rather specific ideas about the elementary 
particles of matter. The atom had come to be pictured 
as a kind of miniature solar system composed of a 
central nucleus surrounded by varying numbers of 
electrons (1 for hydrogen, 92 for uranium) revolving 
in circular or elliptical orbits. The electron was less 
vivid. Experiments showed that all electrons had 
exactly the same mass and the same electrical charge, 
so it was natural to regard them as the ultimate 
22 






foundation stones of the universe. It also seemed 
logical at first to picture them simply as hard, elastic 
spheres. But little by little, as investigation progressed, 
they became more capricious, defiant of observation 
and measurement. In many ways their behaviour 
appeared too complex for any material particle. "The 
hard sphere," declared the British physicist, Sir James 
Jeans, "has always a definite position in space; the 
electron apparently has not. A hard sphere takes up a 
very definite amount of room; an electron — well, it is 
probably as meaningless to discuss how much room an 
electron takes up as it is to discuss how much room a 
fear, an anxiety, or an uncertainty takes up." 

Shortly after de Broglie had his vision of "matter 
waves," a Viennese physicist named Schrodinger 
developed the same idea in coherent mathematical 
form, evolving a system that explained quantum 
phenomena by attributing specific wave functions to 
protons and electrons. This system, known as "wave 
mechanics," was corroborated in 1927 when two 
American scientists, Davisson and Germer, proved 
by experiment that electrons actually do exhibit 
wave characteristics. They directed a beam of elec- 
trons upon a metal crystal and obtained diffraction 
patterns analogous to those produced when light 
is passed through a pinhole. * Their measurements 
indicated, moreover, that the wavelength of an 
electron is of the precise magnitude predicted 
by de Broglie's equation, A-A/ros, where P is the 
velocity of the electron, m is its mass, and h is Planck's 
Constant. But further surprises were in store. For sub- 
sequent experiments showed that not only electrons 
but whole atoms and even molecules produce wave 
patterns when diffracted by a crystal surface, and that 
1 A crystal, because of the even and orderly agreement of its 
component atoms and the closeness of their spacing, serves as a 
diffraction grating for very short wavelengths, such as those ot 
X-rays. 

23 






their wavelengths are exactly what de Broglie and 
Schrodinger forecast. And so all the basic units of 
matter — what J. Clerk Maxwell called "the imperish- 
able foundation stones of the universe" — gradually 
shed their substance. The old-fashioned spherical elec- 
tron was reduced to an undulating charge of electrical 
energy, the atom to a system of superimposed waves. 
One could only conclude that all matter is made of 
waves and we live in a world of waves. 

The paradox presented by waves of matter on the 
one hand and particles of light on the other was 
resolved by several developments in the decade before 
World War II. The German physicists, Heisenberg 
and Born, bridged the gap by developing a new 
mathematical apparatus that permitted accurate 
descripdon of quantum phenomena either in terms of 
waves or in terms of particles as one wished. The idea 
behind their system had a profound influence on the 
philosophy of science. They maintained it is pointiess 
for a physicist to worry about the properties of a single 
electron; in the laboratory he works with beams or 
showers of electrons, each containing billions of indi- 
vidual particles (or waves) ; he is concerned therefore 
only with mass behaviour, with statistics and the laws 
of probability and chance. So it makes no practical 
difference whether individual electrons are particles or 
systems of waves — in aggregate they can be pictured 
either way. For example, if two physicists are at the 
seashore one may analyse an ocean wave by saying, 
"Its properties and intensity are clearly indicated by 
the positions of its crest and its trough"; while the 
other may observe with equal accuracy, "The section 
which you term a crest is significant simply because 
it contains more molecules of water than the area you 
call a trough." Analogously Born took the mathe- 
matical expression used by Schrodinger in his equa- 
tions to denote wave function and interpreted it as a 

H 



"probability" in a statistical sense. That is to say, he 
regarded the intensity of any part of a wave as a 
measure of the probable distribution of particles at 
that point. Thus he dealt with the phenomena of dif- 
fraction, which hitherto only the wave theory could 
explain, in terras of the probability of certain corpuscles 
— light quanta or electrons — following certain paths 
and arriving at certain places. And so "waves of 
matter" were reduced to "waves of probability." It 
no longer matters how we visualize an electron or 
an atom or a probability wave. The equations of 
Heisenberg and Born fit any picture. And we can, if 
we choose, imagine ourselves living in a universe of 
waves, a universe of particles, or as one facetious 
scientist has phrased it, a universe of "wavicles." 






25 



IV 



While quantum physics thus defines with 
great accuracy the mathematical relationships govern- 
ing the basic units of radiation and matter, it further 
obscures the true nature of both. Most modern 
physicists, however, consider it rather naive to 
speculate about the true nature of anything. They are 
"positivists" — or "logical empiricists" — who contend 
that a scientist can do no more than report his observ- 
ations. And so if he performs two experiments with 
different instruments and one seems to reveal that 
light is made up of particles and the other that light 
is made up of waves, he must accept both results, 
regarding them not as contradictory, but as comple- 
mentary. By itself neither concept suffices to explain 
light, but together they do. Both are necessary to des- 
cribe reality and it is meaningless to ask which is 
really true. For in the abstract lexicon of quantum 
physics there is no such word as "really." 

It is futile, moreover, to hope that the invention of 
more delicate tools may enable man to penetrate 
much farther into the microcosm. There is an 
indeterminacy about all the events of the atomic uni- 
verse which refinements of measurement and observa- 
tion can never dispel. The element of caprice in 
atomic behaviour cannot be blamed on man's coarse- 
grained implements. It stems from the very nature of 
things, as shown by Heisenberg in 1927 in a famous 
statement of physical law known as the "Principle of 
Uncertainty." To illustrate his thesis, Heisenberg 
pictured an imaginary experiment in which a physicist 

26 



r 

attempts to observe the position and velocity 1 of a 
moving electron by using an immensely powerful 
super-microscope. Now, as has already been sug- 
gested, an individual electron appears to have no 
definite position or velocity, A physicist can define 
electron behaviour accurately enough so long as he is 
dealing with great numbers of them. But when he tries 
to locate a particular electron in space the best he can 
say is that a certain point in the complex superim- 
posed wave motions of the electron group represents 
the probable position of the electron in question. The 
individual electron is a blur— as indeterminate as the 
wind or a sound wave in the night— and the fewer the 
electrons with which the physicist deals, the more 
indeterminate his findings. To prove that this indeter- 
minacy is a symptom not of man's immature science 
but of an ultimate barrier of nature, Heisenberg pre- 
supposed that the imaginary microscope used by his 
imaginary physicist is optically capable of magnifying 
by a hundred billion diameters, i.e. enough to 
bring an object die size of an electron within the 
range of human visibility. But now a further diffi- 
culty is encountered. For, inasmuch as an electron 
is smaller than a light wave, the physicist can "illu- 
minate" his subject only by using radiation of shorter 
wavelength. Even X-rays are useless. The electron can 
be rendered visible only by the high-frequency gamma 
rays of radium. But the photoelectric effect, it will be 
recalled, showed that photons of ordinary light exert 
a violent force on electrons; and X-rays knock them 
about even more roughly. Hence the impact of a still 
more potent gamma ray would prove disastrous. 

The Principle of Uncertainty asserts therefore that 
it is absolutely and forever impossible to determine the 
position and the velocity of an electron at the same 

1 In physics the term "velocity" connotes direction as well aa 
speed. 

27 



time — to state confidently that an electron is "right 
here at this spot" and is moving at "such and such a 
speed." For by the very act of observing its position, 
its velocity is changed; and, conversely, the more 
accurately its velocity is determined, the more in- 
definite its position becomes. And when the physicist 
computes the mathematical margin of uncertainty in 
his measurements of an electron's position and velocity 
he finds it is always a function of that mysterious 
quantity — Planck's Constant, L 



Quantum physics thus demolishes two pillars of the 
old science, causality and determinism. For by deal- 
ing in terms of statistics and probabilities it abandons 
all idea that nature exhibits an inexorable sequence 
of cause and effect. And by its admission of margins 
of uncertainty it yields up the ancient hope that 
science, given the present state and velocity of every 
material body in the universe, can forecast the history 
of the universe for all time. One by-product of 
this surrender is a new argument for the existence 
of free will. For if physical events are indeterminate 
and the future is unpredictable, then perhaps the 
unknown quantity called "mind" may yet guide 
man's destiny among the infinite uncertainties of a 
capricious universe. But this notion invades a realm of 
thought with which the physicist is not concerned. 
Another conclusion of greater scientific importance is 
that in the evolution of quantum physics the barrier 
between man, peering dimly through the clouded 
windows of his senses, and whatever objective reality 
may exist has been rendered almost impassable. For 
whenever he attempts to penetrate and spy on the 
"real" objective world, he changes and distorts its 
workings by the very process of his observation. And 
28 






when he tries to divorce this "real" world from his 
sense perceptions he is left with nothing but a mathe- 
matical scheme. He is indeed somewhat in the position 
of a blind man trying to discern the shape and texture 
of a snowflake. As soon as it touches his fingers or his 
tongue it dissolves. A wave electron, a photon, a wave 
of probability, cannot be visualized; they are simply 
symbols useful in expressing the mathematical rela- 
tionships of the microcosm. 

To the question, Why does modern physics employ 
such abstract methods of description? the physicist 
answers: because the equations of quantum physics 
define more accurately than any mechanical model 
the fundamental phenomena beyond the range of 
vision. In short, they work, as the calculations which 
hatched the atomic bomb spectacularly proved. The 
aim of the practical physicist, therefore, is to enunciate 
the laws of nature in ever more precise mathematical 
terms. Where the nineteenth-century physicist en- 
visaged electricity as a fluid and, with this metaphor 
in mind, evolved the laws that generated our present 
electrical age, the twentieth-century physicist tends to 
avoid metaphors. He knows that electricity is not a 
fluid, and he knows that such pictorial concepts as 
"waves" and "particles," while serving as guide- 
posts to new discovery, must not be accepted as 
accurate representations of reality. In the abstract 
language of mathematics he can describe how things 
behave though he does not know — or need to know — 
what they are. 

Yet there are present-day physicists for whom the 
void between science and reality presents a challenge. 
Einstein has more than once expressed the hope that 
the statistical method of quantum physics would 
prove a temporary expedient. "I cannot believe," he 
says, "that God plays dice with the world." He 
repudiates the positivist doctrine that science can only 



report and correlate the results of observation. He 
believes in a universe of order and harmony. And he 
believes that questing man may yet attain a know- 
ledge of ultimate reality. To this end he has looked not 
within the atom, but outward to the stars, and beyond 
them to the vast, drowned depths of empty space 
and time. 



' 



3° 



In his great treatise, On Human Understanding, 
philosopher John Locke wrote three hundred years 
ago: "A company of chessmen standing on the same 
squares of the chessboard where we left them, we say, 
are all in the same place or unmoved: though perhaps 
the chessboard has been in the meantime carried out 
of one room into another. . . . The chessboard, we also 
say, is in the same place if it remain in the same part of 
the cabin, though perhaps the ship which it is in sails 
all the while; and the ship is said to be in the same 
place supposing it kept the same distance with the 
neighbouring land, though perhaps the earth has 
turned around; and so chessmen and board and ship 
have every one changed place in respect to remoter 
bodies." 

Embodied in this little picture of the moving but 
unmoved chessmen is one principle of relativity — 
relativity of position. But this suggests another idea — 
relativity of motion. Anyone who has ever ridden on a 
railroad train knows how rapidly another train 
flashes by when it is travelling in the opposite direc- 
tion, and conversely how it may look almost motion- 
less when it is moving in the same direction. A varia- 
tion of this effect can be very deceptive in an enclosed 
station, like Grand Central Terminal in New York. 
Once in a while a train gets under way so gently that 
passengers feel no recoil whatever. Then if they 
happen to look out the window and see another train 
slide past on the next track, they have no way of know- 
ing which train is in motion and which is at rest; 
nor can they tell how fast either one is moving or in 

31 



. 



what direction. The only way they can judge then- 
situation is by looking out the other side of the car for 
some fixed body of reference, like the station platform 
or a signal light. Sir Isaac Newton was aware of these 
tricks of motion, only he thought in terms of ships. 
He knew that on a calm day at sea a sailor can shave 
himself or drink soup as comfortably as when his 
ship is lying motionless in harbour. The water 
in his basin, the soup in his bowl, will remain unruffled 
whether the ship is making 5 knots, 15 knots, or 25 
knots. So unless he peers out at the sea it will be 
impossible for him to know how fast his ship is moving 
or indeed if it is moving at all. Of course, if the sea 
should get rough or the ship change course abruptly, 
then he will sense his state of motion. But granted 
the idealized conditions of a glass-calm sea and a 
silent ship, nothing that happens below decks — no 
amount of observation or mechanical experiment per- 
formed inside the ship — will disclose its velocity 
through the sea. The physical principle suggested by 
these considerations was formulated by Newton in 
1687. "The motions of bodies included in a given 
space," he wrote, "are the same among themselves, 
whether that space is at rest or moves uniformly for- 
ward in a straight line." This is known as the 
Newtonian or Galilean Relativity Principle. It can 
also be phrased in more general terms: mechanical 
laws which are valid in one place are equally valid in 
any other place which moves uniformly relative to 
the first. 



The philosophical importance of this principle lies 
in what it says about the universe. Since the aim of 
science is to explain the world we live in, as a whole 
and in all its parts, it is essential to the scientist that he 



32 






have confidence in the harmony of nature. He must 
believe that physical laws revealed to him on earth are 
in truth universal laws. Thus in relating the fall of an 
apple to the wheeling of the planets around the sun 
Newton hit upon a universal law. And although he 
illustrated his principle of relative motion by a ship 
at sea, the ship he actually had in mind was the earth. 
For all ordinary purposes of science, the earth can be 
regarded as a stationary system. We may say if we 
choose that mountains, trees, houses, are at rest, and 
animals, automobiles, and aeroplanes move. But to 
the astrophysicist, the earth, far from being at rest, is 
whirling through space in a giddy and highly com- 
plicated fashion. In addition to its daily rotation about 
its axis at the rate of 1,000 miles an hour, and its 
annual revolution about the sun at the rate of 20 
miles a second, the earth is also involved in a number 
of other less familiar gyrations. Contrary to popular 
belief, the moon does not revolve around the earth; 
they revolve around each other — or, more precisely, 
around a common centre of gravity. The entire solar 
system, moreover, is moving within the local star 
system at the rate of 13 miles a second; the local star 
system is moving within the Milky Way at the rate of 
200 miles a second; and the whole Milky Way is drift- 
ing with respect to the remote external galaxies at the 
rate of 100 miles a second — and all in different 
directions ! 

Although he could not then know the full com- 
plexity of the earth's movements, Newton was never- 
theless troubled by the problem of distinguishing rela- 
tive motion from true or "absolute" motion in a 
confusingly busy universe. He suggested that "in the 
remote regions of the fixed stars or perhaps far beyond 
them, there may be some body absolutely at rest," but 
admitted there was no way of proving this by any 
celestial object within man's view. On the other hand, 

Btu 33 



I. 



it seemed to Newton that space itself might serve as a 
fixed frame of reference to which the wheeling of the 
stars and galaxies could be related in terms of absolute 
motion. He regarded space as a physical reality, 
stationary and immovable; and while he could not 
support this conviction by any scientific argument, he 
nevertheless clung to it on theological grounds. For to 
Newton space represented the divine omnipresence of 
God in nature. 

In the next two centuries it appeared probable that 
Newton's view would prevail. For with the develop- 
ment of the wave theory of light scientists found it 
necessary to endow empty space with certain mechan- 
ical properties — to assume, indeed, that space was 
some kind of substance. Even before Newton's time 
the French philosopher, Descartes, had argued that 
the mere separation of bodies by distance proved the 
existence of a medium between them. And to 
eighteenth- and nineteenth-century physicists it was 
obvious that if light consisted of waves, there must be 
some medium to support them, just as water propa- 
gates the waves of the sea and air transmits the vibra- 
tions we call sound. Hence when experiments showed 
that light can travel in a vacuum, scientists evolved a 
hypothetical substance called "ether" which they 
decided must pervade all space and matter. Later on 
Faraday propounded another kind of ether as the 
carrier of electric and magnetic forces. When Maxwell 
finally identified light as an electromagnetic distur- 
bance the case for the ether seemed assured. 



A universe permeated with an invisible medium in 
which the stars wandered and through which light 
travelled like vibrations in a bowl of jelly was the 
end product of Newtonian physics. It provided a 



34 



mechanical model for all known phenomena of nature, 
and it provided the fixed frame of reference, the ab- 
solute and immovable space, which Newton's cosmo- 
logy required. Yet the ether presented certain problems, 
not the least of which was that its actual existence had 
never been proved. To discover once and for all 
whether there really was any such thing as ether, two 
American physicists, A. A. Michelson and E. W. 
Morley, performed a classic experiment in Cleveland 
in the year 1881. 

The principle underlying their experiment was 
quite simple. They reasoned that if all space is simply 
a motionless sea of ether, then the earth's motion 
through the ether should be detectable and measur- 
able in the same way that sailors measure the velocity 
of a ship through the sea. As Newton pointed out, 
it is impossible to detect the. movement of a ship 
through calm waters by any mechanical experi- 
ment performed inside the ship. Sailors ascertain a 
ship's speed by throwing a log overboard and watch- 
ing the unreeling of the knots on the log-line. Hence, 
to detect the earth's motion through the ether sea, 
Michelson and Morley threw a "log" overboard, 
and the log was a beam of light. For if light really 
is propagated through the ether, then its velocity 
should be affected by the ether stream arising from 
the earth's movement. Specifically, a light ray pro- 
jected in the direction of the earth's movement 
should be slightly retarded by the ether flow, just 
as a swimmer is retarded by a current when going 
upstream. The difference would be slight, for the 
velocity of light (which was accurately determined in 
1849) is 186,284 miles a second, while the velocity of 
the earth in its orbit around the sun is only 20 miles 
a second. Hence a light ray sent against the ether 
stream should travel at the rate of 186,264 miles a 
second, while one sent with the ether stream should 

35 




--- — t* — - 



The Michelson-Morley interferometer consisted of an arrange- 
ment of mirrors, so designed that a beam transmitted from a light 
source (above, left) was divided and sent in two directions at the 
same time. This was done by a mirror, A, the face of which was 
only thinly silvered, so that part of the beam was permitted to pass 
through to mirror C (right) and the remainder reflected at right 
angles toward miiror B. Mirrors B and C then reflected the rays 
back to mirror A wheie, reunited, they proceeded to an observing 
telescope T. Since the beam ACT had to pass three times 
through the thickness of glass behind the reflecting face of mirror 
A, a clear glass plate of equal thickness was placed between A and 
B to intercept beam ABT and compensate for this retardation. 
The whole apparatus was rotated in different directions so that 
the beams ABT and ACT could be sent with, against, and at right 
angles to the postulated ether stream. At first glance it might 
appear that a trip "downstream" — for example from B to A — 
should compensate in time for an "upstream" trip from A to B. 
But this is not so. To row a boat one mile upstream and another 
mile downstream takes longer than rowing two miles in still 
water, or across current, even with allowance for drift. Had there 
been any acceleration or retardation of either beam by the ether 
stream, the optical apparatus at T would have detected k. 

36 



be clocked at 186,304 miles a second. With these ideas 
in mind, Michelson and Morley constructed an instru- 
ment of such great delicacy that it could detect a vari- 
ation of even a fraction of a mile per second in the 
enormous velocity of light. This instrument, which 
they called an "interferometer," consisted of a group 
of mirrors so arranged that a light beam could be split 
in two and flashed in different directions at the same 
time. The whole experiment was planned and 
executed with such painstaking precision that the 
result could not be doubted. And the result was simply 
this: there was no difference whatsoever in the velocity 
of the light beams regardless of their direction. 

The Michelson-Morley experiment confronted 
scientists with an embarrassing alternative. On the 
one hand, they could scrap the ether theory which had 
explained so many things about electricity, mag- 
netism, and light. Or, if they insisted on retaining the 
ether, they had to abandon the still more venerable 
Copernican theory that the earth is in motion. To 
many physicists it seemed almost easier to believe that 
the earth stood still than that waves — light waves, 
electromagnetic waves — could exist without a medium 
to sustain them. It was a serious dilemma and one that 
split scientific thought for a quarter century. Many 
new hypotheses were advanced and rejected. The 
experiment was tried again by Morley and by others, 
with the same conclusion; the apparent velocity of the 
earth through the ether was zero. 



37 















VI 

Among those who pondered the enigma of the 
Michelson-Morley experiment was a young patent 
office examiner in Berne, named Albert Einstein. In 
1905, when he was just twenty-six years old, he pub- 
lished a short paper suggesting an answer to the riddle 
in terms that opened up a new world of physical 
thought. He began by rejecting the ether theory and 
with it the whole idea of space as a fixed system or 
framework, absolutely at rest, within which it is 
possible to distinguish absolute from relative motion. 
The one indisputable fact established by the 
Michelson-Morley experiment was that the velocity 
of light is unaffected by the motion of the earth. 
Einstein seized on this as a revelation of universal law. 
If the velocity of light is constant regardless of the 
earth's motion, he reasoned, it must be constant 
regardless of the motion of any sun, moon, star, 
meteor, or other system moving anywhere in the 
universe. From this he drew a broader generalization, 
and asserted that the laws of nature are the same 
for all uniformly moving systems. This simple state- 
ment is the essence of Einstein's Special Theory of 
Relativity. It incorporates the Galilean Relativity 
Principle which stated that mechanical laws are the 
same for all uniformly moving systems. But its phras- 
ing is more comprehensive; for Einstein was thinking 
not only of mechanical laws but of the laws governing 
light and other electromagnetic phenomena. So he 
lumped them together in one fundamental postulate: 
all the phenomena of nature, all the laws of nature, 
are the same for all systems that move uniformly 
relative to one another. 

38 



On the surface there is nothing very startling in this 
declaration. It simply reiterates the scientist's faith in 
the universal harmony of natural law. It also advises 
the scientist to stop looking for any absolute, station- 
ary frame of reference in the universe. The universe is 
a restless place; stars, nebulae, galaxies, and all the vast 
gravitational systems of outer space are incessantly in 
motion. But their movements can be described only 
with respect to each other, for in space there are no 
directions and no boundaries. It is futile, moreover, for 
the scientist to try to discover the "true" velocity of 
any system by using light as a measuring rod, for the 
velocity of light is constant throughout the universe 
and is unaffected either by the motion of its source or 
the motion of the receiver. Nature offers no absolute 
standards of comparison; and space is — as another 
great German mathematician, Leibnitz, clearly saw 
two centuries before Einstein — simply "the order or 
relation of things among themselves." Without things 
occupying it, it is nothing. 

Along with absolute space, Einstein discarded the 
concept of absolute time — of a steady, unvarying, 
inexorable universal time flow, streaming from the 
infinite past to the infinite future. Much of the 
obscurity that has surrounded the Theory of 
Relativity stems from man's reluctance to recognize 
that sense of time, like sense of colour, is a form of 
perception. Just as there is no such thing as colour 
without an eye to discern it, so an instant or an hour 
or a day is nothing without an event to mark it. And 
just as space is simply a possible order of material 
objects, so time is simply a possible order of events. 
The subjectivity of time is best explained in Einstein's 
own words. "The experiences of an individual," he 
says, "appear to us arranged in a series of events; in 
this series the single events which we remember 
appear to be ordered according to the criterion of 



'earlier* and 'later.' There exists, therefore, for the 
individual, an I-time, or subjective time. This in itself 
is not measurable. I can, indeed, associate numbers 
with the events, in such a way that a greater number 
is associated with the later event than with an earlier 
one. This association I can define by means of a clock 
by comparing the order of events furnished by the 
clock with the order of the given series of events. We 
understand by a clock something which provides a 
series of events which can be counted." 

By referring our own experiences to a clock (or a 
calendar), we make time an objective concept. Yet the 
time intervals provided by a clock or a calendar are 
by no means absolute quantities imposed on the entire 
universe by divine edict. All the clocks ever used by 
man have been geared to our solar system. What we 
call an hour is actually a measurement in space — an 
arc of 15 degrees in the apparent daily rotation of the 
celestial sphere. And what we call a year is simply a 
measure of the earth's progress in its orbit around the 
sun. An inhabitant of Mercury, however, would have 
very different notions of time. For Mercury makes its 
trip around the sun in 88 of our days, and in that same 
period rotates just once on its axis. So on Mercury a 
year and a day amount to the same thing. But it is 
when science ranges beyond the neighbourhood of the 
sun that all our terrestrial ideas of time become mean- 
ingless. For Relativity tells us there is no such thing as 
a fixed interval of time independent of the system to 
which it is referred. There is indeed no such thing as 
simultaneity, there is no such thing as "now," inde- 
pendent of a system of reference. For example, a man 
in New York may telephone a friend in London, and 
although it is 7 p.m. in New York and midnight in 
London, we may say that they are talking "at the 
same time." But that is because they are both resi- 
dents of the same planet, and their clocks are geared to 
40 






the same astronomical system. A more complicated 
situation arises if we try to ascertain, for example, 
what is happening on the star Arcturus "right now." 
Arcturus is 38 light years away. A light year is the dis- 
tance light travels in one year, or roughly six trillion 
miles. If we should try to communicate with Arcturus 
by radio "right now" it would take 38 years for our 
message to reach its destination and another 38 years 
for us to receive a reply. 1 And when we look at 
Arcturus and say that we see it "now," we are actually 
seeing a ghost — an image projected on our optic 
nerves by light rays that left their source in 1 9 1 1 . 
Whether Arcturus even exists "now," nature forbids 
us to know until 1987. 



Despite such reflections it is difficult for earthbound 
man to accept the idea that this very instant which he 
calls "now" cannot apply to the universe as a whole. 
Yet in the Special Theory of Relativity Einstein 
proves by an unanswerable sequence of example and 
deduction that it is nonsense to think of events taking 
place simultaneously in unrelated systems. His argu- 
ment unfolds along the following lines. 

To begin with, one must realize that the scientist, 
whose task it is to describe physical events in objective 
terms, cannot use subjective words like "this," "here," 
and "now." For him concepts of space and time take 
on physical significance only when the relations 
between events and systems are defined. And it is con- 
stantiy necessary for him, in dealing with matters 
involving complex forms of motion (as in celestial 
mechanics, electrodynamics, etc.) to relate the magni- 
tudes found in one system with those occurring in 
another. The mathematical laws which define these 
1 Radio waves travel at the same speed as light waves. 












relationships are known as laws of transformation. 
The simplest transformation may be illustrated by a 
man promenading on the deck of a ship: if he walks 
forward along the deck at the rate of 3 miles an hour 
and the ship moves through the sea at the rate of 1 2 
miles an hour, then the man's velocity with respect to 
the sea is 15 miles an hour; if he walks aft his velocity 
relative to the sea is of course 9 miles an hour. Or as a 
variation one may imagine an alarm bell ringing at a 
railway crossing. The sound waves produced by the 
bell spread away through the surrounding air at the 
rate of 400 yards a second. A railroad train speeds 
toward die crossing at the rate of 20 yards a second. 
Hence the velocity of the sound relative to the train is 
420 yards a second so long as the train is approaching 
the alarm bell and 380 yards a second as soon as the 
train passes the bell. This simple addition of velocities 
rests on obvious common sense, and has indeed been 
applied to problems of compound motion since the 
time of Galileo. Serious difficulties arise, however, 
when it is used in connection with light. 

In his original paper on Relativity, Einstein empha- 
sized these difficulties with another railway incident. 
Again there is a crossing, marked this time by a signal 
light which flashes its beam down the track at 186,284 
miles a second — the constant velocity of light, denoted 
in physics by the symbol c. A train steams toward the 
signal light at a given velocity v. So by the addition of 
velocities one concludes that the velocity of the light 
beam relative to the train is c plus v when the train 
moves toward the signal light, and c minus v as soon 
as the train passes the light. But this result conflicts 
with the findings of the Michelson-Morlcy experi- 
ment, which demonstrated that the velocity of light is 
unaffected either by the motion of the source or the 
motion of the receiver. This curious fact has also been 
confirmed by studies of double stars which revolve 

42 









around a common centre of gravity. Careful analysis 
of these moving systems has shown that the light from 
the approaching star in each pair reaches earth at 
precisely the same velocity as the light from the reced- 
ing star. Since the velocity of light is a universal con- 
stant, it cannot in Einstein's railway problem be 
affected by the velocity of the train. Even if we 
imagine that the train is racing toward die signal light 
at a speed of 10,000 miles a second, the principle 
of the constancy of the velocity of light tells us 
that an observer aboard the train will still clock 
the speed of the oncoming light beam at precisely 
186,284 miles a second, no more, no less. 

The dilemma presented by this situation involves 
much more than a Sunday morning newspaper 
puzzle. On the contrary it poses a deep enigma of 
nature. Einstein saw that the problem lay in the 
irreconcilable conflict between his belief in (1) the 
constancy of the velocity of light, and (2) the principle 
of the addition of velocities. Although the latter 
appears to rest on the stern logic of mathematics (i.e. 
that two plus two makes four), Einstein recognized in 
the former a fundamental law of nature. He con- 
cluded, therefore, that a new transformation rule 
must be found to enable the scientist to describe the 
relations between moving systems in such a way that 
the results, satisfy the known facts about light. 



Einstein found what he wanted in a series of equa- 
tions developed by the great Dutch physicist, H. A. 
Lorentz, in connection with a specific theory of his 
own. Although its original application is of interest 
now chiefly to scientific historians, the Lorentz trans- 
formation lives on as part of the mathematical frame- 
work of Relativity. To understand what it says, 
however, it is first necessary to perceive the flaws in 

43 



the old principle of the addition of velocities. These 
flaws Einstein pointed out by means of still another 
railway anecdote. Once again he envisaged a straight 
length of track, this time with an observer sitting on 
an embankment beside it. A thunderstorm breaks, and 
two bolts of lightning strike the track simultaneously at 




separate points, A and B. Now, asks Einstein, what 
do we mean by "simultaneously"? To pin down this 
definition, he assumes that the observer is sitting pre- 
cisely half way between A and B, and that he is 
equipped with an arrangement of mirrors which 
enable him to see A and B at the same time without 
moving his eyes. Then if the lightning flashes are 
reflected in the observer's mirrors at precisely the same 
instant, the two flashes may be regarded as simul- 
taneous. Now a train roars down the track, and a 
second observer is sitting precariously perched atop 
one of the cars with a mirror apparatus just like the 
one on the embankment. It happens that this moving 
observer finds himself directly opposite the observer 
on the embankment at the precise instant the light- 
ning bolts hit A and B. The question is: will the light- 
ning flashes appear simultaneous to him? The answer 
is: they will not. For if his train is moving away from 
lightning bolt B and toward lightning bolt A, then it is 
obvious that B will be reflected in his mirrors a frac- 

44 






tion of a second later than A. Lest there be any doubt 
about this, one may imagine temporarily that the 
train is moving at the impossible rate of 186,284 
miles a second, the velocity of light. In that event, 
flash B will never be reflected in the mirrors because it 
can never overtake the train, just as the sound from a 
gun can never overtake a bullet travelling with super- 
sonic speed. So the observer on the train will assert 
that only one lightning bolt struck the track. And 
whatever the speed of the train may be the moving 
observer will always insist that the lightning flash 
ahead of him has struck the track first. Hence the 
lightning flashes which are simultaneous relative 
to the stationary observer are not simultaneous 
relative to the observer on the train. 

The paradox of the lightning flashes thus drama- 
tizes one of the subtlest and most difficult concepts in 
Einstein's philosophy: the relativity of simultaneity. 
It shows that man cannot assume that his subjective 
sense of "now" applies to all parts of the universe. For, 
Einstein points out, "every reference body (or co- 
ordinate system) has its own particular time; unless we 
are told the reference body to which the statement of 
time refers, there is no meaning in a statement of the 
time of an event." The fallacy in the old principle of 
the addition of velocities lies therefore in its tacit 
assumption that the duration of an event is indepen- 
dent of the state of motion of the system of reference. 
In the case of the man pacing the deck of a ship, for 
example, it was assumed that if he walked three miles 
in one hour as timed by a clock on the moving ship, 
his rate would be just the same timed by a stationary 
clock anchored somehow in the sea. It was further 
assumed that the distance he traversed in one horn- 
would have the same value whether it was measured 
relative to the deck of the ship (the moving system) or 
relative to the sea (the stationary system). This con- 

45 



stitutes a second fallacy in the addition of velocities — 
for distance, like time, is a relative concept, and there 
is no such thing as a space interval independent of the 
state of motion of the system of reference. 

Einstein asserted, therefore, that the scientist who 
wishes to describe the phenomena of nature in terms 
that are consistent for all systems throughout the uni- 
verse must regard measurements of time and distance 
as variable quantities. The equations comprising the 
Lorentz transformation do just that. They preserve the 
velocity of light as a universal constant, but modify all 
measurements of time and distance according to the 
velocity of each system of reference, A 

1 The Lorentz transformation relates distances and times 
observed on moving systems with those observed on systems 
relatively at rest. Suppose, for example, that a system, or refer- 
ence body, is moving in a certain direction, then according to the old 
principle of velocities, a distance or length x', measured with respect 
to the moving system along the direction of motion, is related to 
length x, measured with respect to a relatively stationary system, 
by the equation x 1 =• x i vt, where v is the velocity of the moving 
system and / is the time. Dimensions y 1 and z\ measured with 
respect to the moving system at right angles to x' and at right 
angles to each other (i.e., height and breadth}, are related to 
dimensions y and z on the relatively stationary system by y* 
=y, and z? = z* And finally a time interval t', clocked with respect 
to the moving system, is related to time interval J, clocked with 
respect to the relatively stationary system, by t' =» (. In other 
words, distances and times are not affected, in classical physics,, by 
the velocity of the system in question. But it is this presupposition 
which leads to the paradox of the lightning Jlaslies. The Lorentz trans- 
formation reduces the distances and times observed on moving 
systems to the conditions of the stationary observer, keeping the 
velocity of light c a constant for all observers. Here are the 
equations of the Lorentz transformation which have supplanted 
the older and evidendy inadequate relationships cited above: 

x — vt 

/■•J 

t - (vffix 

t' = v i - («W 

It will be noted that, as in the old transformation law, dimen- 
sions y' and z' are unaffected by motion. It will also be seen that 

46 






So although Lorentz had originally developed his 
equations to meet a specific problem, Einstein made 
them the basis of a tremendous generalization, and to 
the edifice of Relativity added another axiom: the 
laws of nature preserve their uniformity in all systems 
when related by the Lorentz transformation. Stated 
thus, in the abstract language of mathematics the sig- 
nificance of this axiom can scarcely be apparent to the 
layman. But in physics an equation is never a pure 
abstraction; it is simply a kind of shorthand expression 
which the scientist finds convenient to describe the 
phenomena of nature. Sometimes it is also a Rosetta 
Stone in which the theoretical physicist can decipher 
secret realms of knowledge. And so by deduction from 
the message written in the equations of the Lorentz 
transformation, Einstein discovered a number of new 
and extraordinary truths about the physical universe. 

if the velocity of the moving system v is small relative to the 
velocity of light c, then the equations of the Lorentz transforma- 
tion reduce themselves to the relations of the old principle of the 
addition of velocities. But as the magnitude of v approaches that 
of c, then the values of at' and t' are radically changed. 



47 



VII 

1 hese truths can be described in very concrete 
terms. For once he had evolved the philosophical and 
mathematical bases of Relativity, Einstein had to 
bring them into the laboratory, where abstractions 
like time and space are harnessed by means of clocks 
and measuring rods. And so translating his basic ideas 
about time and space into the language of the 
laboratory, he pointed out some hitherto unsuspected 
properties of clocks and rods. For example: a clock 
attached to any moving system runs at a different 
rhythm from a stationary clock: and a measuring rod 
attached to any moving system changes its length 
according to the velocity of the system. Specifically 
the clock slows down as its velocity increases, and the 
measuring rod shrinks in the direction of its motion. 
These peculiar changes have nothing to do with 
the construction of the clock or the composition of 
the rod. The clock can be a pendulum clock, a spring 
clock, or on hour-glass. The measuring rod can be a 
wooden ruler, a metal yardstick, or a ten-mile cable. 
The slowing of the clock and the contraction of the rod 
are not mechanical phenomena; an observer riding 
along with the clock and the measuring rod would 
not notice these changes. But a stationary observer, 
i.e. stationary relative to the moving system, would 
find that the moving clock has slowed down with 
respect to his stationary clock, and that the moving 
rod has contracted with respect to his stationary units 
of measurement. 

This singular behaviour of moving clocks and yard- 
sticks accounts for the constant velocity of light. It 
explains why all observers in all systems everywhere, 
48 









regardless of their state of motion, will always find that 
light strikes their instruments and departs from their 
instruments at precisely the same velocity. For as then- 
own velocity approaches that of light, their clocks slow 
down, their yardsticks contract, and all their measure- 
ments are reduced to the values obtained by a rela- 
tively stationary observer. The laws governing these 
contractions are defined by the Lorentz transforma- 
tion and they are very simple: the greater the speed, 
the greater the contraction. A yardstick moving with 
90 per cent, the velocity of light would shrink to about 
half its length; thereafter the rate of contraction 
becomes more rapid; and if the stick could attain the 
velocity of light, it would shrink away to nothing at 
all. Similarly, a clock travelling with the velocity of 
light would stop completely. From this it follows that 
nothing can ever move faster than light, no matter 
what forces are applied. Thus Relativity reveals 
another fundamental law of nature: the velocity of light 
is the top limiting velocity in the universe. 

At first meeting, these facts are difficult to digest, but 
that is simply because classical physics assumed, 
unjustifiably, that an object preserves the same 
dimensions whether it is in motion or at rest and that a 
clock keeps the same rhythm in motion and at rest. 
Common sense dictates that this must be so. But as 
Einstein has pointed out, common sense is actually 
nothing more than a deposit of prejudices laid down in 
the mind prior to the age of eighteen. Every new idea 
one encounters in later years must combat this 
accretion of "self-evident" concepts. And it is because 
of Einstein's unwillingness ever to accept any 
unproven principle as self-evident that he was able to 
penetrate closer to the underlying realities of nature 
than any scientist before him. Why, he asked, is it any 
more strange to assume that moving clocks slow down 
and moving rods contract, than to assume that they 

49 



don't? The reason classical physics took the latter view 
for granted is that man, in his everyday experience, 
never encounters velocities great enough to make these 
changes manifest. In an automobile, an aeroplane, 
even in a V-2 rocket, the slowing down of a watch is 
immeasurable. It is only when velocities approximate 
that of light that relativistic effects can be detected. 
The equations of the Lorentz transformation show 
very plainly that at ordinary speeds the modification 
of time and space intervals amounts practically to 
zero. Relativity does not therefore contradict classical 
physics. It simply regards the old concepts as limiting 
cases that apply solely to the familiar experiences 
of man. 



Einstein thus surmounts the barrier reared by man's 
impulse to define reality solely as he perceives it 
through the screen of his senses. Just as the Quantum 
Theory demonstrated that elementary particles of 
matter do not behave like the larger particles we dis- 
cern in the coarse-grained world of our perceptions, so 
Relativity shows that we cannot foretell the phe- 
nomena accompanying great velocities from the slug- 
gish behaviour of objects visible to man's indolent eye. 
Nor may we assume that the laws of Relativity deal 
with exceptional occurrences; on the contrary, they 
provide a comprehensive picture of an incredibly com- 
plex universe in which the simple mechanical events 
of our earthly experience are the exceptions. The 
present-day scientist, coping with the tremendous* 
velocities that prevail in the fast universe of the atom 
or with the immensities of sidereal space and time, 
finds the old Newtonian laws inadequate. But 
Relativity provides him in every instance with a com- 
plete and accurate description of nature. 

50 






Whenever Einstein's postulates have been put to 
test, their validity has been amply confirmed. 
Remarkable proof of the relativistic retardation 
of time intervals came out of an experiment per- 
formed by H. E. Ives of the Bell Telephone Labora- 
tories in 1936. A radiating atom may be regarded 
as a kind of clock in that it emits light of a definite 
frequency and wavelength which can be measured 
with great precision by means of a spectroscope. 
Ives compared the light emitted by hydrogen 
atoms moving at high velocities with that emitted by 
hydrogen atoms at rest, and found that the frequency 
of vibration of the moving atoms was reduced in 
exact accordance with the predictions of Einstein's 
equations. Some day science may devise a far more 
interesting test of the same principle. Since any 
periodic motion serves to measure time, the human 
heart, Einstein has pointed out, is also a kmd of clock. 
Hence, according to Relativity, the heartbeat of a per- 
son travelling with a velocity close to that of light 
would be relatively slowed, along with his respiration 
and all other physiological processes. He would not 
notice this retardation because his watch w ^iWr|ip w 
down in the same degree. But, judged by a^tatiom 
timekeeper, he would "grow old" less rapidly. In a 
Buck Rogers realm of fantasy, it is possible to imagine 
some future cosmic explorer boarding an atom- 
propelled space ship, ranging the void at 167,000 
miles per second, and returning to earth after ten 
terrestrial years to find himself physically only five 
years older. 









VIII 

In order to describe the mechanics of the 
physical universe, three quantities are required: 
time, distance, and mass, Since time and distance are 
relative quantities, one might guess that the mass of 
a body also varies with its state of motion. And indeed 
the most important practical results of Relativity have 
arisen from this principle — the relativity of mass. 

In its popular sense, "mass" is just another word for 
"weight." But as used by the physicist, it denotes a 
rather different and more fundamental property of 
matter — namely, resistance to a change of motion. 
A greater force is necessary to move a freight car than 
a velocipede; the freight car resists motion more stub- 
bornly than the velicopede because it has greater 
mass. In classical physics the mass of any body is a 
fixed and unchanging property. Thus the mass of a 
freight car should remain the same whether it is 
at rest on a siding, rolling across country at 60 
miles an hour, or hurtling through outer space at 
60,000 miles a second. But Relativity asserts that the 
mass of a moving body is by no means constant, but 
increases with its velocity. The old physics failed 
to discover this fact simply because man's senses 
and instruments are too crude to note the infini- 
tesimal increases of mass produced by the feeble 
accelerations of ordinary experience. They become 
perceptible only when bodies attain velocities close to 
that of light. (This phenomenon, incidentally, does 
not conflict with the relativistic contraction of length. 
One is tempted to ask: how can an object become 
smaller and at the same time get heavier? The con- 
traction, it should be noted, is only in the direction of 

52 



motion: width and breadth are unaffected. Moreover 
mass is not "heaviness" but resistance to motion.) 

Einstein's equation giving the increase of mass with 
velocity is similar in form to the other equations of 
Relativity but vastly more important in its conse- 
quences: 



ML 



m = 



V 1 - v 2 fc* 



Here m stands for the mass of a body moving with 
velocity v, m for its mass when at rest, and c for the 
velocity of light. Anyone who has ever studied elemen- 
tary algebra can readily see that if v is small, as are all 
the velocities of ordinary experience, then the differ- 
ence between m and m is practically zero. But when 
8 approaches the value of c then the increase of mass 
becomes very great, reaching infinity when the 
velocity of the moving body reaches the velocity of 
light. Since a body of infinite mass would offer infinite 
resistance to motion the conclusion is once again 
reached that no material body can travel with the 
speed of light. 1 

Of all aspects of Relativity the principle of increase 
of mass has been most often verified and most fruit- 
fully applied by experimental physicists. Electrons 
moving is powerful electrical fields and beta particles 
ejected from the nuclei of radioactive substances attain 
velocities ranging up to 99 per cent, that of light. For 
atomic physicists concerned with these great speeds, 
the increase of mass predicted by Relativity is no argu- 
able theory but an empirical fact their calculations 
cannot ignore. In fact the mechanics of the proton- 
synchrotron and other new super-energy machines are 
designed to allow for the increasing mass of particles 
as their speed approaches the velocity of light. 

By further deduction from his principle of Relativity 
1 See Appendix. 

53 



of mass, Einstein arrived at a conclusion of incal- 
culable importance to the world. His train of reason- 
ing ran somewhat as follows: since the mass of a 
moving body increases as its motion increases, and 
since motion is a form of energy (kinetic energy), then 
the increased mass of a moving body comes from its 
increased energy. In short, energy has mass! By a few 
comparatively simple mathematical steps, Einstein 
found the value of the equivalent mass m in any unit of 
energy E and expressed it by the equation m = £/c 2 . 
Given this relation a high school freshman can take 
the remaining algebraic step necessary to write the 
most important and certainly the most famous equa- 
tion in history: E= mc 2 . 

The part played by this equation in the develop- 
ment of the atomic bomb is familiar to most news- 
paper readers. It states in the shorthand of physics that 
the energy contained in any particle of matter is equal 
to the mass of that body (in grammes) multiplied by 
the square of the velocity of light (in centimetres per 
second). This extraordinary relationship becomes 
more vivid when its terms are translated into con- 
crete values, i.e. i kilogram of coal (about 2 lb.), 
if converted entirely into energy, would yield 25 
billion kilowatt hours of electricity or as much as all 
the power plants in the U.S. could generate by run- 
ning steadily for two months. 

£ = mc i provides the answer to many of the long- 
standing mysteries of physics. It explains how 
radioactive substances like radium and uranium 
are able to eject particles at enormous velocities and to 
go on doing so for millions of years. It explains how 
the sun and all the stars can go on radiating light and 
heat for billions of years; for if our sun were being con- 
sumed by ordinary processes of combustion, the earth 
would have died in frozen darkness aeons ago. It 
reveals the magnitude of the energy that slumbers 

54 



1 






in the nuclei of atoms, and forecasts how many 
grammes of uranium must go into a bomb in order 
to destroy a city. Finally, it discloses some funda- 
mental truths about physical reality. Prior to Rela- 
tivity scientists had pictured the universe as a vessel 
containing two distinct elements, matter and energy — 
the former inert, tangible, and characterized by a 
property called "mass," and the latter active, 
invisible, and without mass. But Einstein showed that 
mass and energy are equivalent: the property called 
mass is simply concentrated energy. In other words, 
matter is energy and energy is matter, and the distinc- 
tion is simply one of temporary state. 

In the light of this broad principle many puzzles 
of nature are resolved. The baffling interplay of 
matter and radiation which appears sometimes to be a 
concourse of particles and sometimes a meeting of 
waves, becomes more understandable. The dual role 
of the electron as a unit of matter and a unit of elec- 
tricity, the wave electron, the photon, waves of matter, 
waves of probability, a universe of waves — all these 
seem less paradoxical. For all these concepts simply 
describe different manifestations of the same under- 
lying reality, and it no longer makes sense to ask what 
any one of them "really" is. Matter and energy are 
interchangeable. If matter sheds its mass and travels 
with the speed of light we call it radiation or energy. 
And conversely if energy congeals and becomes inert 
and we can ascertain its mass we call it matter. 
Heretofore science could only note their ephemeral 
properties and relations as they touched the percep- 
tions of earthbound man. But since July 16, 1945, 
man has been able to transform one into the other. 
For on that night at Alamogordo, New Mexico, man 
for the first time transmuted a substantial quantity of 
matter into the light, heat, sound, and motion which 
we call energy. 

55 



Yet the fundamental mystery remains. The whole 
march of science toward the unification of concepts — 
the reduction of all matter to elements and then to a 
few types of particles, the reduction of "forces" to the 
single concept "energy," and then the reduction of 
matter and energy to a single basic quantity — leads 
still to the unknown. The many questions merge into 
one, to which there may never be an answer: what is 
the essence of this mass-energy substance, what is the 
underlying stratum of physical reality which science 
seeks to explore? 

Thus Relativity, like the Quantum Theory, draws 
man's intellect still farther away from the Newtonian 
universe, firmly rooted in space and time and 
functioning like some great, unerring, and manage- 
able machine. Einstein's laws of motion, his basic 
principles of the relativity of distance, time, and mass, 
and his deductions from these principles comprise 
what is known as the Special Theory of Relativity. In 
the decade following the publication of this original 
work, he expanded this scientific and philosophical 
system into the General Theory of Relativity, through 
which he examined the mysterious force that guides 
the whirling of the stars, comets, meteors, and 
galaxies, and all the moving systems of iron, stone, 
vapour, and flame in the immense, inscrutable void. 
Newton called this force "universal gravitation." 
From his own concept of gravitation Einstein attained 
a view of the vast architecture and anatomy of the 
universe as a whole. 



56 



IX 



"The non-mathematician," says Albert 
Einstein, "is seized by a mysterious shuddering when 
he hears of "four-dimensional things, by a feeling not 
unlike that awakened by thoughts of the occult. And 
yet there is no more commonplace statement than that 
the world in which we live is a four-dimensional space- 
time continuum." 

A non-mathematician might question Einstein's 
use of the term "commonplace" in this connection. 
Yet the difficulty lies more in the wording than in 
ideas. Once the meaning of the word "continuum" is 
properly grasped, Einstein's picture of the universe as 
a four-dimensional space-time continuum — and this 
is the view that underlies all modern conceptions 
of the universe — becomes perfectly clear. A con- 
tinuum is something that is continuous. A ruler, 
for example, is a one-dimensional space continuum. 
Most rulers are divided into inches and fractions, 
scaled down to one-sixteenth of an inch. 

But it is possible to imagine a ruler calibrated to a 
millionth or a billionth of an inch. In theory there is 
no reason why the steps from point to point should not 
be even smaller. The distinguishing characteristic of 
a continuum is that the interval separating any two 
points may be divided into an infinite number of 
arbitrarily small steps. 

A railroad track is a one-dimensional space con- 
tinuum, and on it the engineer of a train can describe 
his position at any time by citing a single co-ordinate 
point, i.e. a station or a milestone. A sea captain, how- 
ever, has to worry about two dimensions. The surface 

57 



of the sea is a two-dimensional continuum and the 
co-ordinate points by which a sailor fixes his position 
in his two-dimensional continuum are latitude and 
longitude. An aeroplane pilot guides his plane through 
a three-dimensional continuum, hence he has to con- 
sider not only longitude and latitude, but also his 
height above the ground. The continuum of an aero- 
plane pilot constitutes space as we perceive it. In other 
words, the space of our world is a three-dimensional 
continuum. 

To describe any physical event involving motion, 
however, it is not enough simply to indicate position in 
space. It is necessary to state also how position changes 
in time. Thus to give an accurate picture of the opera- 
tion of a New York-Chicago express, one must men- 
tion not only that it goes from New York to Albany to 
Syracuse to Cleveland to Toledo to Chicago, but also 
the times at which it touches each of those points. This 
can be done either by means of a timetable or a visual 
chart. If the miles between New York and Chicago 
are plotted horizontally on a piece of ruled paper 
and the hours and minutes are plotted vertically, 
then a diagonal line properly drawn across the page 
illustrates the progress of the train in a two- 
dimensional space-time continuum. This type of 
graphic representation is familiar to most newspaper 
readers; a stock market chart, for example, pictures 
financial events in a two-dimensional dollar-time con- 
tinuum. In the same way the flight of an aeroplane from 
New York to Los Angeles can best be pictured in a 
four-dimensional space-time continuum. The fact that 
the plane is at latitude x, longitude j, and altitude z 
means nothing to the traffic manager of the airline 
unless the time co-ordinate is also given. So time is the 
fourth dimension. And if one wishes to envisage the 
flight as a whole, as a physical reality, it cannot be 
broken down into a series of disconnected take-offs, 

58 









climbs, glides, and landings. Instead it must be 
thought of as a continuous curve in a four-dimensional 
space-time continuum. 



Since time is an impalpable quantity it is not pos- 
sible to draw a picture or construct a model of a four- 



ARRIVE CHICAGO 1 00 PM CSX 



12:00 PM - 



9:00 AM - 



6:00 AM 



3:00 AM 



12.1X1 AM 



9:00 PM 




300 400 500 600 
DISTANCE IN MILES 



700 800 900 



The westbound run of a New York-Chicago express pictured in a 
two-dimensional space-time continuum. 

dimensional space-time continuum. But it can be 
imagined and it can be represented mathematically. 
And in order to describe the stupendous reaches of the 
universe beyond our solar system, beyond the clusters 
and star clouds of the Milky Way, beyond the lonely 
outer galaxies burning in the void, the scientist must 
visualize it all as a continuum in three dimensions of 
space and one of time. In our minds we tend to 
separate these dimensions; we have an awareness of 
space and an awareness of time. But the separation is 

59 



purely subjective; and as the Special Theory of Rela< 
tivity showed, space and time separately are relative 
quantities which vary with individual observers. In 
any objective description of the universe, such as 
science demands, the time dimension can no more be 
detached from the space dimension than length can be 
detached from breadth and thickness in an accurate 
representation of a house, a tree, or Betty Grable. 
According to the great German mathematician, 
Herman Minkowski, who developed the mathe- 
matics of the space-time continuum as a convenient 
medium for expressing the principles of Relativity, 
"space and time separately have vanished into the 
merest shadows, and only a sort of combination of the 
two preserves any reality." 

It must not be thought, however, that the space- 
time continuum is simply a mathematical construc- 
tion. The world is a space-time continuum; all reality 
exists both in space and time, and the two are indi- 
visible. All measurements of time are really measure- 
ments in space, and conversely measurements in space 
depend on measurements of time. Seconds, minutes, 
hours, days, weeks, months, seasons, years, are 
measurements of the earth's position in space relative 
to the sun, moon, and stars. Similarly latitude and 
longitude, the terms whereby man defines his spatial 
position on earth, are measured in minutes and 
seconds, and to compute them accurately one must 
know the time of day and the day of the year. Such 
"landmarks" as the Equator, the Tropic of Cancer, or 
the Arctic Circle are simply sundials which clock the 
changing seasons; the Prime Meridian is a co-ordinate 
of daily time; and "noon" is nothing more than an 
angle of the sun. 

Even so, the equivalence of space and time becomes 
really clear only when one contemplates the stars. 
Among the familiar constellations, some are "real" in 
60 



T 



that their component stars comprise true gravitational 
systems, moving in an orderly fashion relative to one 
another; others are only apparent — their patterns are 
accidents of perspective, created by a seeming 
adjacency of unrelated stars along the line of sight. 
Within such optical constellations one may observe 
two stars of equal brightness and assert that they are 
"side by side" in the firmament, whereas in actuality 
one may be 40 light years and the other 400 light years 
away. 

Obviously the astronomer has to think of the uni- 
verse as a space-time continuum. When he peers 
through his telescope he looks not only outward in 
space, but backward in time. His sensitive cameras 
can detect the glimmer of island universes 500 million 
light years away — faint gleams that began their 
journey at a period of terrestrial time when the 
first vertebrates were starting to crawl from warm 
Paleozoic seas on to the young continents of Earth. His 
spectroscope tells him, moreover, that these huge 
outer systems are hurtling into limbo, away from our 
own galaxy, at incredible velocities ranging up to 
35,000 miles a second. Or, more precisely, they were 
receding from us 500 million years ago. Where they are 
"now," or whether they even exist "now," no one can 
say. If we break down our picture of the universe into 
three subjective dimensions of space and one of local 
time, then these galaxies have no objective existence 
save as faint smudges of ancient enfeebled light on a 
photographic plate. They attain physical reality only 
in their proper frame of reference, which is the four- 
dimensional space-time continuum. 



In man's brief tenancy on earth he egocentrically 
orders events in his mind according to his own feelings 
of past, present, and future. But except on the reels of 



61 



one's own consciousness, the universe, the objective 
world of reality, does not "happen" — it simply exists. 
It can be encompassed in its entire majesty only by a 
cosmic intellect. But it can also be represented sym- 
bolically, by a mathematician, as a four-dimensional 
space-time continuum. An understanding of the 
space-time continuum is requisite to a comprehension 
of the General Theory of Relativity and of what it says 
about gravitation, the unseen force that holds the 
universe together and determines its shape and size. 



62 



X 



In the Special Theory of Relativity, Einstein 
studied the phenomenon of motion and showed that 
there appears to be no fixed standard in the universe 
by which man can judge the "absolute" motion of the 
earth or of any other moving system. Motion can be 
detected only as a change of position with respect to 
another body. We know, for example, that the earth is 
moving around the sun at the rate of twenty miles a 
second. The changing seasons suggest this fact. But 
until four hundred years ago men thought the shifting 
position of the sun in the sky revealed the sun's move- 
ment around the earth; and on this assumption 
ancient astronomers developed a perfectly practical 
system of celestial mechanics which enabled them to 
predict with great accuracy all the major phenomena 
of the heavens. Their supposition was a natural one, 
for we cajCtfeel our motion through space; nor has 
any physical experiment ever proved that the earth 
actually is in motion. And though all the other 
planets, stars, galaxies, and moving systems in the uni- 
verse are ceaselessly, restlessly changing position, their 
movements are observable only with respect to one 
another. If all the objects in the universe were 
removed save one, then no one could say whether that 
one remaining object was at rest or hurtling through 
the void at 100,000 miles a second. Motion is a relative 
state; unless there is some system of reference to which 
it may be compared, it is meaningless to speak of the 
motion of a single body. 

Shortly after publishing the Special Theory of 

63 



Relativity, however, Einstein began wondering if 
there is not indeed one kind of motion which may be 
considered "absolute" in that it can be detected by the 
physical effect it exerts on the moving system itself — 
without reference to any other system. For example, 
an observer in a smoothly running train is unable to tell 
by experiments performed inside the train whether he 
is in motion or at rest. But if the engineer of the train 
suddenly applies the brakes or jerks open the throttle, 
he will then be made aware, by the resulting jolt, of a 
change in his velocity. And if the train rounds a turn, 
he will know by the outward tug of his own body, 
resisting a change of direction, that the train's course 
has been altered in a certain way. Therefore, Einstein 
reasoned, if only one object existed in the entire uni- 
verse — the earth, for example — and it suddenly began 
to gyrate irregularly, its inhabitants would be uncom- 
fortably aware of their motion. This suggests that 
non-uniform motion, such as that produced by forces 
and accelerations, may be "absolute" after all. It also 
suggests that empty space can serve as a system of 
reference within which it is possible to distinguish 
absolute motion. 

To Einstein, who held that space is nothing and 
motion is relative, the apparendy unique character of 
non-uniform motion was profoundly disturbing. In 
the Special Theory of Relativity he had taken as his 
premise the simple assertion that the laws of nature 
are the same for all systems moving uniformly relative 
to one another. And as a steadfast believer in the 
universal harmony of nature he refused to believe that 
any system in a state of non-uniform motion must be a 
uniquely distinguished system in which the laws of 
nature are different. Hence as the basic premise of his 
General Theory of Relativity, he stated : the laws of 
nature are the same for all systems regardless of their 
state of motion. In developing this thesis he worked 

64 



out new laws of gravitation which upset most of the 
concepts that had shaped man's picture of the uni- 
verse for three hundred years. 



Einstein's springboard was Newton's Law of 
Inertia which, as every schoolboy knows, states that 
"every body continues in its state of rest, or of uniform 
motion in a straight line, unless it is compelled to 
change that state by forces impressed thereon." 
It is inertia, therefore, which produces our peculiar 
sensations when a railroad train suddenly slows 
down or speeds up or rounds a curve. Our body 
wants to continue moving uniformly in a straight 
line, and when the train impresses an opposing 
force upon us the property called inertia tends 
to resist that force. It is also inertia which 
causes a locomotive to wheeze and strain in order to 
accelerate a long train of freight cars. 

But this leads to another consideration. If the cars 
are loaded the locomotive has to work harder and 
burn more coal than if the cars are empty. To his Law 
of Inertia Newton therefore added a second Jaw stat- 
ing that the amount of force necessary to accelerate a 
body depends on the mass of the body; and that if the 
same force is applied to two bodies of different masses, 
then it will produce a greater acceleration in the 
smaller body than in the bigger one. This principle 
holds true for the whole range of man's everyday 
experience— from pushing a baby carriage to firing a 
cannon. It simply generalizes the obvious fact that one 
can throw a baseball farther and faster than one can 
throw a cannon-ball. 

There is, however, one peculiar situation in which 
there appears to be no connection between the 
acceleration of a moving body and its mass. The base- 
ball and the cannon-ball attain exactly the same rate 
Gru 65 



of acceleration when they are falling. This phe- 
nomenon was first discovered by Galileo, who proved 
by experiment that, discounting air resistance, bodies 
all fall at precisely the same rate regardless of their 
size or composition. A baseball and a handkerchief 
fall at different speeds only because the handker- 
chief offers a larger surface to the resistance of the 
air. But objects of comparable shape, such as a 
marble, a baseball, and a cannon-ball, fall at the 
same rate. (In a vacuum the handkerchief and 
the cannon-ball would fall side by side.) This phe- 
nomenon appears to violate Newton's Law of Inertia. 
For why should all objects travel vertically at the 
same velocity regardless of their size or mass, if those 
same objects, when projected horizontally by an equal 
force, move at velocities that are strictly determined 
by their mass? It would appear as though the factor of 
inertia operates only in a horizontal plane, 

Newton's solution to this riddle is given in his Law 
of Gravitation, which states simply that the mysteri- 
ous force by which a material body attracts another 
body increases with the mass of the object it attracts. 
The bigger the object, the stronger the call of gravity. 
If an object is small, its inertia or tendency to resist 
motion is small, but the force that gravity exerts upon 
it is also small. If an object is big, its inertia is great, 
but the force that gravity exerts upon it is also great. 
Hence gravity is always exerted in the precise degree 
necessary to overcome the inertia of any object. And 
that is why all objects fall at the same rate, regardless 
of their inertial mass. 

This rather remarkable coincidence— the perfect 
balance of gravitation and inertia— was accepted on 
foith, but never understood or explained, for three 
centuries after Newton. All of modern mechanics and 
engineering grew out of Newtonian concepts, and the 
heavens appeared to operate in accordance with his 

66 



laws. Einstein, however, whose discoveries have all 
sprung from an inherent distrust of dogma, disliked 
several of Newton's assumptions. He doubted that the 
balance of gravitation and inertia was merely an acci- 
dent of nature. And he rejected the idea of gravitation 
being a force that can be exerted instantaneously over 
great distances. The notion that the earth can reach 
out into space and pull an object toward it with a force 
miraculously and invariably equal to the inertial 
resistance of that object seemed to Einstein highly 
improbable. So out of his objections he evolved a new 
theory of gravitation which, experience has shown, 
gives a more accurate picture of nature than Newton's 
classical law. 



67 









XI 



In accordance with his usual mode of creative 
thought, Einstein set the stage with an imaginary situ- 
ation. The details have doubtless been envisaged by 
many another dreamer m restless slumber or in 
moments of insomnia fancy. He pictured an im- 
mensely high building and inside it an elevator that 
had slipped from its cables and is falling freely. Within 
the elevator a group of physicists, undisturbed by any 
suspicion that their ride might end in disaster, are per- 
forming experiments. They take objects from their 
pockets, a fountain pen, a coin, a bunch of keys, and 
release them from their grasp. Nothing happens. The 
pen, the coin, the keys appear to the men in the ele- 
vator to remain poised in mid-air — because all of them 
are falling, along with the elevator and the men, at 
precisely the same rate in accordance with Newton's 
Law of Gravitation. Since the men in the elevator are 
unaware of their predicament, however, they may 
explain these peculiar happenings by a different 
assumption. They may believe they have been magic- 
ally transported outside the gravitational field of the 
earth and are in fact poised somewhere in empty 
space. And they have good grounds for such a belief. 
If one of them jumps from the floor he floats smoothly 
toward the ceiling with a velocity just proportional to 
the vigour of his jump. If he pushes his pen or his keys 
in any direction, they continue to move uniformly in 
that direction until they hit the wall of the car. Every- 
thing apparently obeys Newton's Law of Inertia, and 
continues in its state of rest or of uniform motion in a 
68 



straight line. The elevator has somehow become an 
inertial system, and there is no way for the men inside 
it to tell whether they are falling in a gravitational 
field or are simply floating in empty space, free from 
all external forces. 

Einstein now shifts the scene. The physicists are still 
in the elevator, but this time they really are in empty 
space, far away from the attractive power of any celes- 
tial body. A cable is attached to the roof of the ele- 
vator; some supernatural force begins reeling in the 
cable; and the elevator travels "upward" with con- 
stant acceleration, i.e. progressively faster and faster. 
Again the men in the car have no idea where they are, 
and again they perform experiments to evaluate their 
situation. This time they notice that their feet press 
solidly against the floor. If they jump they do not float 
to the ceiling, for the floor comes up beneath them. If 
they release objects from their hands, the objects 
appear to "fall." If they toss objects in a horizontal 
direction they do not move uniformly in a straight 
line, but describe a parabolic curve with respect to the 
floor. And so the scientists, who have no idea that their 
windowless car actually is climbing through inter- 
stellar space, conclude that they are situated in quite 
ordinary circumstances in a stationary room rigidly 
attached to the earth and affected in normal measure 
by the force of gravity. There is really no way for them 
to tell whether they are at rest in a gravitational field 
or ascending with constant acceleration through outer 
space where there is no gravity at all. 

The same dilemma would confront them if their 
room were attached to the rim of a huge rotating 
merry-go-round set in outer space. They would feel 
a strange force trying to pull them away from the 
centre of the merry-go-round, and a sophisticated out- 
side observer would quickly identify this force as 
inertia (or, as it is termed in the case of rotating 

69 






objects, centrifugal force). But the men inside the 
room, who as usual are unaware of their odd predica- 
ment, would once again attribute the force to gravity. 
For if the interior of their room is empty and 
unadorned, there will be nothing to tell them which is 
the floor and which is the ceiling except the force that 
pulls them toward one of its interior surfaces. So what 
a detached observer would call the "outside wall" of 
the rotating room becomes the "floor" of the room for 
the men inside. A moment's reflection shows that there 
is no "up" or "down" in empty space. What we on 
earth call "down" is simply the direction of gravity. 
To a man on the sun it would appear that the 
Australians, Africans, and Argentines are hanging by 
their heels from the southern hemisphere. By the same 
token, Admiral Byrd's flight over the South Pole was 
a geometrical fiction; actually he flew under it — ■ 
upside down. And so the men inside the room on the 
merry-go-round will find that all their experiments 
produce exactly the same results as the ones they per- 
formed when their room was being swept "upward" 
through space. Their feet stay firmly on the "floor." 
Solid objects "fall." And once again they attribute 
these phenomena to the force of gravity and believe 
themselves at rest in a gravitational field. 



From these fanciful occurrences Einstein drew a 
conclusion of great theoretical importance. To physi- 
cists it is known as the Principle of Equivalence of 
Gravitation and Inertia. It simply states that there is 
no way to distinguish the motion produced by inertial 
forces (acceleration, recoil, centrifugal force, etc.) 
from motion produced by gravitational force. The 
validity of this principle will be evident to any aviator; 
for in an aeroplane it is impossible to separate the 
70 



effects of inertia from those of gravitation. The 
physical sensation of pulling out of a dive is exactly the 
same as that produced by executing a steeply banked 
turn at high speed. In both cases the factor known to 
flyers as a "G-load" (Gravity load) appears, blood is 
drawn away from the head, and the body is pulled 
heavily down into the seat. But in one case the effects 
are produced by gravity, in the other by inertia. 

In this principle, which is the keystone of General 
Relativity, Einstein found an answer both to the riddle 
of gravitation and the problem of "absolute" motion. 
It showed that there is nothing unique or "absolute" 
about non-uniform motion after all; for the effects of 
non-uniform motion which can supposedly reveal the 
state of motion of a body, even if it exists alone in 
space, are indistinguishable from the effects of gravita- 
tion. Thus in the case of the merry -go-round, what one 
observer identified as the pull of inertia or centrifugal 
force and therefore an effect of motion, another 
observer identified as the familiar tug of gravitation. 
And any other inertial effect produced by a change of 
speed or a change of direction can equally well be 
ascribed to a changing or fluctuating gravitational 
field. So the basic premise of Relativity holds true; 
motion, both uniform and non-uniform, can only be 
judged with respect to some system of reference — 
absolute motion does not exist. 

The sword with which Einstein slew the dragon of 
absolute motion was gravitation. But what is gravita- 
tion? The gravitation of Einstein is something entirely 
different from the gravitation of Newton. It is not a 
"force." The idea that bodies of matter can "attract" 
one another is, according to Einstein, an illusion that 
has grown out of erroneous mechanical concepts of 
nature. So long as one believes that the universe is a 
big machine, it is natural to think that its various parts 
can exert a force on one another. But the deeper 

71 



science probes toward reality, the more clearly it 
appears that the universe is not like a machine at all. 
So Einstein's Law of Gravitation contains nothing 
about force. It describes the behaviour of objects in a 
gravitational field — the planets, for example — not in 
terms of "attraction" but simply in terms of the paths 
they follow. To Einstein, gravitation is simply part of 
inertia; the movements of the stars and the planets 
arise from their inherent inertia; and the courses they 
follow are determined by the metric properties of 
space — or, more properly speaking, the metric pro- 
perties of the space-time continuum. 

Although this sounds very abstract and even para- 
doxical, it becomes quite clear as soon as one dismisses 
the notion that bodies of matter can exert a physical 
force on each other across millions of miles of empty 
space. This concept of "action-at-a-distance" has 
troubled scientists since Newton's day. It led to par- 
ticular difficulty, for example, in understanding elec- 
tric and magnetic phenomena. To-day scientists no 
longer say that a magnet "attracts" a piece of iron by 
some kind of mysterious but instantaneous action-at-a- 
distance. They say rather that the magnet creates a 
certain physical condition in the space around it, 
which they term a magnetic field; and that this 
magnetic field then acts upon the iron and makes it 
behave in a certain predictable fashion. Students 
in any elementary science course know what a 
magnetic field looks like, because it can be rendered 
visible by the simple process of shaking iron filings 
on to a piece of stiff paper held above a magnet. 
A magnetic field and an electrical field are physical 
realities. They have a definite structure, and 
their structure is described by the field equations 
of James Clerk Maxwell which pointed the way 
toward all the discoveries in electrical and radio 
engineering of the past century. A gravitational field 
72 



is as much of a physical reality as an electromagnetic 
field, and its structure is defined by the field equations 
of Albert Einstein. 




/ f 6 WTO* -^ 

1 \ V o*^T 






of a bar magnet. 



Just as Maxwell and Faraday assumed that a mag- 
net creates certain properties in surrounding space, so 
Einstein concluded that stars, moons, and other celes- 
tial objects individually determine the properties of 
the space around them. And just as the movement of a 
piece of iron in a magnetic field is guided by the 
structure of the field, so the path of any body in a 
gravitational field is determined by the geometry of 
that field. The distinction between Newton's and 
Einstein's ideas about gravitation has sometimes been 
illustrated by picturing a litde boy playing marbles in 
a city lot. The ground is very uneven, ridged with 
bumps and hollows. An observer in an office ten 
stories above the street would not be able to see these 

73 



irregularities in the ground. Noticing that the marbles 
appear to avoid some sections of the ground and move 
toward other sections, he might assume that a "force" 
is operating which repels the marbles from certain 
spots and attracts them toward others. But another 
observer on the ground would instantly perceive that 
the path of the marbles is simply governed by the cur- 
vature of the field. In this little fable Newton is the 
upstairs observer who imagines that a "force" is at 
work, and Einstein is the observer on the ground, who 
has no reason to make such an assumption. Einstein's 
gravitational laws, therefore, merely describe the field 
properties of the space-time continuum. Specifically, 
one group of these laws sets forth the relation between 
the mass of a gravitating body and the structure of 
the field around it; they are called structure laws. A 
second group analyses the paths described by moving 
bodies in gravitational fields; they are the laws of 
motion. 

It should not be thought that Einstein's theory of 
gravitation is only a formal mathematical scheme. For 
it rests on assumptions of deep cosmic significance. 
And the most remarkable of these assumptions is that 
the universe is not a rigid and immutable edifice 
where independent matter is housed in independent 
space and time; it is on the contrary an amorphous 
continuum, without any fixed architecture, plastic 
and variable, constantly subject to change and distor- 
tion. Wherever there is matter and motion, the con- 
tinuum is disturbed. Just as a fish swimming in the sea 
agitates the water around it, so a star, a comet, or a 
galaxy distorts the geometry of the space-time through 
which it moves. 

When applied to astronomical problems, Einstein's 
gravitational laws yield results that are close to those 
given by Newton. If the results paralleled each other 
in every case, scientists might tend to retain the 

74 



familiar concepts of Newtonian law and write off 
Einstein's theory as a weird if original fancy. But a 
number of strange new phenomena have been dis- 
covered, and at least one old puzzle solved, solely on 
the basis of General Relativity. The old puzzle 
stemmed from the eccentric behaviour of the planet 
Mercury. Instead of revolving in its elliptical orbit 




The rotation of Mercury's elliptical orbit, greatly exaggerated. 

Actually the ellipse advances only 43 seconds of an arc per 

century. 

with the regularity of the other planets, Mercury 
deviates from its course each year by a slight but exas- 
perating degree. Astronomers explored every possible 
factor that might cause this perturbation, but found 
no solution within the framework of Newtonian 

75 



theory. It was not until Einstein evolved his laws of 
gravitation that the problem was solved. Of all the 
planets Mercury lies closest to the sun. It is small and 
travels with great speed. Under Newtonian law these 
factors should not in themselves account for the 
deviation; the dynamics of Mercury's movement 
should be basically the same as those of any other 
planet. But under Einstein's laws, the intensity of 
the sun's gravitational field and Mercury's enormous 
speed make a difference, causing the whole ellipse of 
Mercury's orbit to execute a slow but inexorable 
swing around the sun at the rate of one revolution in 
3,000,000 years. This calculation is in perfect agree- 
ment with actual measurements of the planet's course. 
Einstein's mathematics are thus more accurate than 
Newton's in dealing with high velocities and strong 
gravitational fields. 

An achievement of far greater importance, however, 
than this solution of an old problem was Einstein's 
prediction of a new cosmic phenomenon of which no 
scientist had ever dreamed — namely, the effect of 
gravitation on light. 






76 



XII 

1 he sequence of thought which led Einstein 
to prophesy this effect began with another imaginary 
situation. As before, the scene opens in an elevator 
ascending with constant acceleration through empty 
space, far from any gravitational field. This time some 
roving interstellar gunman impulsively fires a bullet at 
the elevator. The bullet hits the side of the car, passes 
clean through and emerges from the far wall at a 
point a little below the point at which it penetrated 
the first wall. The reason for this is evident to the 
marksman on the outside. He knows that the bullet 
flew in a straight line, obeying Newton's Law of 
Inertia; but while it traversed the distance between 
the two walls of the car, the whole elevator travelled 
"upward" a certain distance, causing the second 
bullet hole to appear not opposite the first one but 
slightly nearer the floor. However, the observers inside 
the elevator, having no idea where in the universe they 
are, interpret the situation differently. Aware that on 
earth any missile describes a parabolic curve toward 
the ground, they simply conclude that they are at rest 
in a gravitational field and that the bullet which 
passed through their car was describing a perfectly 
normal curve with respect to the floor. 

A moment later as the car continues upward 
through space a beam of light is suddenly flashed 
through an aperture in the side of the car. Since the 
velocity of light is great, the beam traverses the dis- 
tance between its point of entrance and the opposite 
wall in a very small fraction of a second. Nevertheless, 

77 



the car travels upward a certain distance in that inter- 
val, so the beam strikes the far wall a tiny fraction of 
an inch below the point at which it entered. If the 
observers within the car are equipped with sufficiently 
delicate instruments of measurement, they will be able 
to compute the curvature of the beam. But the ques- 
tion is, how will they explain it? They arc still 
unaware of the motion of their car and believe them- 
selves at rest in a gravitational field. If they cling 
to Newtonian principles, they will be completely 
baffled because they will insist that light rays always 
travel in a straight line. But if they are familiar with 
the Special Theory of Relativity they will remember 
that energy has mass in accordance with the equation 
m = Ejc 2 . Since light is a form of energy they will 
deduce that light has mass and will therefore be 
affected by a gravitational field. Hence the curvature 
of the beam. 

From these purely theoretical considerations 
Einstein concluded that light, like any material object, 
travels in a curve when passing through the gravita- 
tional field of a massive body. He suggested that his 
theory could be put to test by observing the path of 
starlight in the gravitational field of the sun. Since the 
stars are invisible by day, there is only one occasion 
when sun and stars can be seen together in the sky, 
and that is during an eclipse. Einstein proposed, there- 
fore, that photographs be taken of the stars immediately 
bordering the darkened face of the sun during an 
eclipse and compared with photographs of those same 
stars made at another time. According to his theory, 
the light from the stars surrounding the sun should be 
bent inward, toward the sun, in traversing the sun's 
gravitational field; hence the images of those stars 
should appear to observers on earth to be shifted out- 
ward from their usual positions in the sky. Einstein 
calculated the degree of deflection that should be 

78 



observed and predicted that for the stars closest to the 
sun the deviation would be about 1 -75 seconds of an 
arc. Since he staked his whole General Theory of 
Relativity on this test, men of science diroughout the 
world anxiously awaited the findings of expeditions 
which journeyed to equatorial regions to photograph 




_ ' EARTH 

The deflection of starlight in the gravitational field of the sun. 
Since the light from a sf ar in the neighbourhood of the sun's disk 
is bent inward, toward the sun, as it passes through the sun s 
gravitational field, the image of the star appears to observers on 
earth to be shifted outward and away from the sun. 

the eclipse of May 29, 191 9. When their pictures were 
developed and examined, the deflection of the star- 
light in the gravitational field of the sun was found to 
average 1-64 seconds — a figure as close to perfect 
agreement with Einstein's prediction as the accuracy 
of instruments allowed. 



Another prediction made by Einstein on the basis 
of General Relativity pertained to time. Having 
shown how the properties of space are affected by a 

79 



gravitational field, Einstein reached the conclusion by 
analogous but somewhat more involved reasoning 
that time intervals also vary with the gravitational 
field. A clock transported to the sun should run at a 
slighdy slower rhythm than on eardi. And a radiating 
solar atom should emit light of slighdy lower fre- 
quency than an atom of the same element on earth. 
The difference in wavelength would in this case be 
immeasurably small. But there are in the universe 
gravitational fields stronger than the sun's. One of 
these surrounds the freak star known as the "com- 
panion of Sirius"— a white dwarf composed of matter 
in a state of such fantastic density that I cubic inch of 
it would weigh a ton on earth. Because of its great 
mass, this extraordinary dwarf, which is only three 
times larger than the earth, has a gravitational field 
potent enough to perturb the movements of Sirius, 
seventy times its size. Its field is also powerful enough 
to slow down the frequency of its own radiation by a 
measurable degree, and spectroscopic observations 
have indeed proved that the frequency of fight 
emitted by Sirius' companion is reduced by the exact 
amount predicted by Einstein. The shift of wave- 
length in the spectrum of this star is known to 
astronomers as "the Einstein Effect" and constitutes 
an additional verification of General Relativity. 



80 






XIII 

Up to this point, the concepts of General 
Relativity have dealt with the phenomena of the 
individual gravitational field. But the universe is 
filled with incomputable bodies of matter — meteors, 
moons, comets, nebulae, and billions on billions of 
stars grouped by the interlocking geometry of their 
gravitational fields in clusters, clouds, galaxies, and 
supergalactic systems. One naturally asks, what then 
is the over-all geometry of the space-time continuum 
in which they drift? In cruder language, what is the 
shape and size of the universe? All modem replies to 
the question have been derived directly or indirectly 
from the principles of General Relativity. 

Prior to Einstein the universe was most commonly 
pictured as an island of matter afloat in the centre of 
an infinite sea of space. There were several reasons for 
this concept. The universe, most scientists agreed, had 
to be infinite; because as soon as they conceded that 
space might come to an end somewhere, they were 
faced with the embarrassing question: "And what lies 
beyond that?" Yet Newtonian law prohibited an 
infinite universe containing a uniform distribution of 
matter, for then the total gravitational force of all die 
masses of matter stretching away to infinity would be 
infinite, and the heavens would be ablaze with infinite 
light. To man's feeble eye, moreover, it appeared that 
beyond the rim of our Milky Way the lamps of space 
became sparser and sparser, diffusing gradually in 
attenuated outposts like lonely lightiiouses on the fron- 
tiers of the fathomless void. But the island universe 
presented difficulties too. The amount of matter it 



held was so small by contrast with an infinity of space 
that inevitably the dynamic laws governing the move- 
ments of the galaxies would cause them to disperse 
like the droplets of a cloud and the universe would 
become entirely empty. 

To Einstein this picture of dissolution and disap- 
pearance seemed eminently unsatisfactory. The basic 
difficulty, he decided, derived from man's natural but 
unwarranted assumption that the geometry of the uni- 
verse must be the same as that revealed by his senses 
here on earth. We confidently assume, for example, 
that two parallel beams of light will travel through 
space for ever without meeting, because in the infinite 
plane of Euclidean geometry parallel lines never meet. 
We also feel certain that in outer space, as on a tennis 
court, a straight line is the shortest distance between 
two points. And yet Euclid never actually proved that 
a straight line is the shortest distance between two 
points; he simply arbitrarily defined a straight line as 
the shortest distance between two points. 

Is it not then possible, Einstein asked, that man is 
being deceived by his limited perceptions when he pic- 
tures the universe in the garb of Euclidean geometry? 
There was a time when man thought the earth was 
fiat. Now he accepts the fact that the earth is round, 
and he knows that on the surface of the earth the 
shortest distance between two such points as New 
York and London is not a straight line across the 
Atlantic, but a "great circle" that veers northward 
past Nova Scotia, Newfoundland, and Iceland. So 
far as the surface of the earth is concerned, Euclid's 
geometry is not valid. A giant triangle drawn on the 
earth's surface from two points on the Equator to the 
North Pole would not satisfy Euclid's theorem that 
the sum of the interior angles of a triangle is always 
equal to two right angles or 180 degrees. It would 
contain more than 180 degrees, as a glance at the 
82 



globe will quickly show. And if someone should 
draw a giant circle on the earth's surface he 
would find that the ratio between its diameter 
and its circumference is less than the classic value 
pi. These departures from Euclid are due to the curva- 
ture of the earth. Although no one doubts to-day that 
the earth has a curvature, man did not discover this 




fact by getting off the earth and looking at it. The 
curvature of the earth can be computed very comfort- 
ably on terra firma by a proper mathematical inter- 
pretation of easily observable facts. In the same way, 
by a synthesis of astronomical fact and deduction, 
Einstein concluded that the universe is neither 
infinite nor Euclidean, as most scientists supposed, but 
something hitherto unimagined. 

83 



It has already been shown that Euclidean geometry 
does not hold true in a gravitational field. Light rays 
do not travel in straight lines when passing through a 
gravitational field, for the geometry of the field is such 
that within it there are no straight lines; the shortest 
course that the light can describe is a curve or great 
circle which is rigorously determined by the geometri- 
cal structure of the field. Since the structure of a 
gravitational field is shaped by the mass and velocity 
of the gravitating body — star, moon, or planet — it 
follows that the geometrical structure of the universe 
as a whole must be shaped by the sum of its material 
content. For each concentration of matter in the uni- 
verse there is a corresponding distortion of the space- 
time continuum. Each celestial body, each galaxy 
creates local irregularities in space-time, like eddies 
around islands in the sea. The greater the concentra- 
tion of matter, the greater the resulting curvature of 
space- time. And the total effect is an over-all curva- 
ture of the whole space-time continuum: the com- 
bined distortions produced by all the incomputable 
masses of matter in the universe cause the continuum 
to bend back on itself in a great closed cosmic curve. 

The Einstein universe therefore is non-Euclidean 
and finite. To earthbound man a light ray may appear 
to travel in a straight line to infinity, just as to an 
earthworm crawling "straight" ahead for ever and 
ever the earth may seem both flat an infinite. But 
man's impression that the universe is Euclidean in 
character, like the earthworm's impression of the 
earth, is imparted by the limitations of his senses. In 
the Einstein universe there are no straight lines, there 
are only great circles. Space, though finite, is 
unbounded; a mathematician would describe its 
geometrical character as the four-dimensional ana- 
logue of the surface of a sphere. In the less abstract 
words of the late British physicist, Sir James Jeans: 
84 



"A soap-bubble with corrugations on its surface is 
perhaps the best representation, in terms of simple 
and familiar materials, of the new universe revealed 
to us by the Theory of Relativity. The universe is 
not the interior of the soap-bubble, but its surface, 
and we must always remember that while the sur- 
face of the soap-bubble has only two dimensions, 
the universe bubble has four — three dimensions of 
space and one of time. And the substance out of 
which this bubble is blown, the soap-film, is empty 
space welded on to empty time." 

Like most of the concepts of modern science, 
Einstein's finite, spherical universe cannot be visual- 
ized — any more than a photon or an electron can be 
visualized. But as in the case of the photon and 
the electron, its properties can be described mathe- 
matically. By taking the best available values of 
modern astronomy and applying them to Einstein's 
field equations, it is possible to compute the size of the 
universe. In order to determine its radius, however, it 
is first necessary to ascertain its curvature. Since, as 
Einstein showed, the geometry or curvature of space is 
determined by its material content, the cosmological 
problem can be solved only by obtaining a figure for 
the average density of matter in the universe. 

Fortunately, this figure is available, for astronomer 
Edwin Hubble of the Mt. Wilson Observatory con- 
scientiously studied sample areas of the heavens over 
a period of years and painstakingly computed the 
average amount of matter contained in them. The 
conclusion he reached was that in the universe as a 
whole there is • 00000000000000000000000000000 1 
gramme of matter per cubic centimetre of space. 
Applied to Einstein's field equations, this figure 
yields a positive value for the curvature of the 
universe, which in turn reveals that the radius 

85 






years, or 
Einstein's 



of the universe is 35 billion light 
2 1 0,000,000,000,000,000,000,000 miles, 
universe, while not infinite, is nevertheless sufficiently 
enormous to encompass billions of galaxies, each con- 
taining hundreds of millions of flaming stars and incal- 
culable quantities of rarefied gas, cold systems of iron 
and stone and cosmic dust, A sunbeam, setting out 
through space at the rate of 186,000 miles a second 
would, in this universe, describe a great cosmic circle 
and return to its source after a little more than 200 
billion terrestrial years. 






86 



XIV 

At the time Einstein evolved his cosmology, 
he was unaware, however, of a strange astronomical 
phenomenon which was only interpreted several 
years later. He had assumed that the motions of the 
stars and galaxies were random, like the aimless drift- 
ing of molecules in a gas. Since there was no evidence 
of any unity in their wanderings, he had ignored them 
entirely and regarded the universe as static. But 
astronomers were beginning to notice signs of a 
systematic movement among the outer galaxies at the 
extreme limits of telescopic vision. All these outlying 
galaxies, or "island universes," are, apparently, 
receding from our solar system and from each other. 
This organized flight of the distant galaxies — the 
remotest of them being about 500 million light years 
away — is an entirely different affair from the indolent 
wheeling of the nearer gravitational systems. For such 
a systematic movement would have an effect on the 
curvature of the universe as a whole. 

The universe is, therefore, not static; it is expanding 
in somewhat the same manner as a soap bubble or a 
balloon expands. The analogy is not quite exact, how- 
ever, for if we conceive of the universe as a kind of 
spotted balloon — the spots representing matter — one 
would expect the spots to expand too. But this cannot 
be, because then we would never notice the expansion, 
just as Alice in Wonderland would have been unaware 
of her sudden changes in stature if all her surround- 
ings had grown and contracted along with her. There- 
fore, as cosmologist H. P. Robertson of the California 
Institute of Technology has pointed out, in visualizing 

87 



the universe as a spotted balloon, we must think of the 
spots as inelastic patches sewn upon the surface. 
Material bodies retain their dimensions while space 
stretches out between them, Like the skin of the balloon 
between the patches. 

This extraordinary phenomenon greatly compli- 
cates cosmology. If the spectroscopic analysis that 
indicates the recession of these outer galaxies is correct 
(as most astronomers believe it to be) then the veloci- 
ties at which they are vanishing into limbo are almost 
beyond belief. Their speed appears to increase with 
distance. While the nearer galaxies, about one million 
light years away, are travelling at a mere 100 miles a 
second, those 250 million light years away are flying 
off at the fantastic rate of 25,000 miles a second, 
almost one-seventh the velocity of light. Since all of 
these remote galaxies, without exception, are moving 
away from us and from each other, one must conclude 
that at some epoch of cosmic time all of them were 
clustered together in one fiery, inchoate mass. And if 
die geometry of space is shaped by its material con- 
tent, then the universe in this pregalactic phase must 
have been an uncomfortably cramped and crowded 
receptacle, characterized by an excessive curvature 
and packed with matter in a state of inconceivable 
density. Calculations based on the velocities of die 
receding galaxies show that they must have separated 
and started their flight from the "centre" of this 
shrunken universe about two billion years ago. 



Several theories have been advanced by 
astronomers and cosmologists to explain the enigma of 
the expanding universe. One, put forth by the Belgian 
cosmologist,- Abbe Lemaitre, proposes that the uni- 
verse originated from a single stupendous primordial 
88 



atom which exploded and thus precipitated the 
expansion which we still perceive. An analogous 
theory, made public recendy by Dr. George Gamow 
of George Washington University, reconstructs in 
detail how the constituent elements might have been 
forged in the dense, flaming core of the universe 
before it started to expand. In the beginning, says Dr. 
Gamow, the nucleus of the universe was an inferno of 
homogenous primordial vapour seething at unimagin- 
able temperatures such as no longer exists even in the 
interiors of stars. (The temperature of the sun, which 
is an average star, ranges from 5,500° Centigrade 
at the surface up to 40,000,000° in the interior.) 
There were no elements in such heat, no molecules, 
no atoms — nothing but free neutrons in a state 
of chaotic agitation. When the cosmic mass began to 
expand, however, the temperature began to fall; and 
when it had dropped to about one billion degrees the 
neutrons condensed into aggregates; electrons were 
emitted which attached themselves to nuclei, and 
atoms were formed. All the elements in the universe 
were thus created within the space of a few critical 
moments in the cosmic dawn and their roles fixed for 
the two billion years of continuing expansion that 
ensued. 

An earlier theory of the expanding universe, put 
forth some years ago by Dr. R. C. Tolman of the 
California Institute of Technology, suggests that the 
cosmic expansion may be simply a temporary con- 
dition which will be followed at some future epoch of 
cosmic time by a period of contraction. The universe 
in this picture is a pulsating balloon in which cycles of 
expansion and contraction succeed each other through 
eternity. These cycles are governed by changes in the 
amount of matter in the universe; for as Einstein 
showed, the curvature of the universe is dependent on 
its content. The difficulty with this theory is that it 



rests on the assumption that somewhere in the uni- 
verse matter is being formed. Although it is true that 
the amount of matter in the universe is perpetually 
changing, the change appears to be all in one direc- 
tion — toward dissolution. All the phenomena of 
nature, visible and invisible, within the atom and in 
outer space, indicate that the substance and energy of 
the universe are inexorably diffusing like vapour 
through the insatiable void. The sun is slowly but 
surely burning out, the stars are dying embers, and 
everywhere in the cosmos heat is turning to cold, 
matter is dissolving into radiation, and energy is being 
dissipated into empty space. 

The universe is thus progressing toward an ultimate 
"heat-death," or as it is technically defined, a con- 
dition of "maximum entropy." When the universe 
reaches this state some billions of years from now all 
the processes of nature will cease. All space will be at 
the same temperature. No energy can be used because 
all of it will be uniformly distributed through the 
cosmos. There will be no light, no life, no warmth — 
nothing but perpetual and irrevocable stagnation. 
Time itself will come to an end. For entropy points the 
direction of time. Entropy is the measure of random- 
ness. When all system and order in the universe have 
vanished, when randomness is at its maximum, and 
entropy cannot be increased, when there no longer is 
any sequence of cause and effect — in short, when the 
universe has run down, there will be no direction to 
time, there will be no time. And there is no way of 
avoiding this destiny. For the fateful principle known 
as the Second Law of Thermodynamics, which stands 
to-day as virtually the only pillar of classical physics 
left intact by the march of science, proclaims that the 
fundamental process of nature are irreversible. 
Nature moves just one way. 

There are a few contemporary theorists, however, 

90 



who propose that somehow, somewhere beyond man's 
meagre ken the universe may be rebuilding itself. In 
the light of Einstein's principle of the equivalence of 
mass and energy, it is possible to imagine the diffused 
radiation in space congealing once more into particles 
of matter — electrons, atoms, and molecules — which 
may then combine to form larger units, which in turn 
may be collected by their own gravitational influence 
into diffuse nebulae, stars, and, ultimately, galactic 
systems. And thus the life cycle of the universe may 
be repeated for all eternity. Laboratory experiments 
have indeed demonstrated that photons of high- 
energy radiation, such as gamma rays, can, under cer- 
tain conditions, interact with matter to produce pairs 
of electrons and positrons. Astronomers have also 
determined recentiy that atoms of the lighter ele- 
ments, drifting in space — hydrogen, helium, oxygen, 
nitrogen, and carbon — may slowly coalesce into 
molecules and microscopic particles of dust and gas. 
And still more recently Dr. Fred L. Whipple of 
Harvard has described in his "Dust Cloud 
Hypothesis," published in 1948, how the rarefied 
cosmic dust that floats in interstellar space in quan- 
tities equal in mass to all the visible matter in the uni- 
verse could in the course of a billion years condense 
and coagulate into stars. According to Whipple, 
these tiny dust particles, barely one fifty-thousandth 
of an inch in diameter, are blown together by the 
delicate pressure of starlight, just as the fine-spun 
tail of a comet is deflected away from the sun by 
the impact of solar photons. As the particles cohere, 
an aggregate is formed, then a cloudlet, and 
then a cloud. When the cloud attains gigantic 
proportions (i.e. when its diameter exceeds six trillion 
miles), its mass and density will be sufficient to set a 
new sequence of physical processes into operation. 
Gravity will cause the cloud to contract, and its 

9i 



contraction will cause its internal pressure and temper- 
ature to rise. Eventually, in the last white-hot stages of 
its collapse, it will begin to radiate as a star. Theory 
shows that our solar system might have evolved, 
in special circumstances, from such a process — our 
sun being the star in question and the various planets 
small cold by-products condensed from subsidiary 
cloudlets spiralling within the main cloud. 

Presupposing the possibility of such events as these, 
one might arrive ultimately at the concept of a self- 
perpetuating pulsating universe, renewing its cycles 
of formation and dissolution, light and darkness, 
order and disorder, heat and cold, expansion and con- 
traction, through never-ending aeons of time. And yet 
this picture has not been widely accepted because no 
definite evidence has been found to support it. 
Although dust clouds of all dimensions and degrees 
of density can be seen hanging in the abyss of inter- 
stellar space, no one can state from man's brief tem- 
poral perspective that they are proto-stars, any more 
than one can say with assurance that a white cumulus 
cloud riding the blue atmosphere of our earth on any 
given day is to-morrow's thunder storm or simply an 
evanescent wraith of mist that winds have gathered 
and will presently disperse. But apart from conjec- 
ture on the origins of our solar system or the indi- 
vidual stars or any component part of the system of 
nature in which we stand, there are theoretical as well 
as empirical difficulties inherent in every suggestion 
that the universe as a whole may still be a-building. 
Nothing in all inanimate nature can be unmistakably 
identified as a pure creative process. At one time, for 
example, it was thought that the mysterious cosmic 
rays which continually bombard the earth from outer 
space might be by-products of some process of atomic 
creation. But there is greater support for the opposite 
view that they are by-products of atomic annihilation. 

92 



Everything indeed, everything visible in nature or 
established in theory, suggests that the universe is 
implacably progressing toward final darkness and 
decay. 

There is an important philosophical corollary to 
this view. For if the universe is running down and 
nature's processes are proceeding in just one direction, 
the inescapable inference is that everything had a 
beginning: somehow and sometime the cosmic processes 
were started, the stellar fires ignited, and the whole 
vast pageant of the universe brought into being. Most 
of the clues, moreover, that have been discovered at 
the inner and outer frontiers of scientific cognition 
suggest a definite time of Creation. The unvarying 
rate at which uranium expends its nuclear energies 
and the absence of any natural process leading to its 
formation indicate that all the uranium on earth must 
have come into existence at one specific time, which, 
according to the best calculations of geophysicists, was 
about two billion years ago. The tempo at which the 
wild thermo-nuclear processes in the interiors of stars 
transmute matter into radiation enables astronomers 
to compute with fair assurance the duration of stellar 
life, and the figure they reach as the likely average 
age of most stars visible in the firmament to-day is two 
billion years. The arithmetic of the geophysicists and 
astrophysicists is thus in striking agreement with that 
of the cosmogonists who, basing their calculations on 
the apparent velocity of the receding galaxies, find 
that the universe began to expand two billion years 
ago. And there are other signs in other areas of science 
that submit the same reckoning. So all the evidence 
that points to the ultimate annihilation of the universe 
points just as definitely to an inception fixed in time. 
Even if one acquiesces to the idea of an immortal 
pulsating universe, within which the sun and earth 
and super-giant red stars are comparative newcomers, 



the problem of initial origin remains. It merely pushes 
the time of Creation into the infinite past. For while 
theorists have adduced mathematically impeccable 
accounts of the fabrication of galaxies, stars, star dust, 
atoms, and even of the atom's components, every 
theory rests ultimately on the a priori assumption that 
something was already in existence — whether free 
neutrons, energy quanta, or simply the blank inscrut- 
able "world stuff," the cosmic essence, of which the 
multifarious universe was subsequently wrought. 






94 



XV 



Cjosmolooists for the most part maintain 
silence on the question of ultimate origins, leaving that 
issue to the philosophers and theology. Yet only the 
purest empiricists among modern scientists turn their 
backs on the mystery that underlies physical reality. 
Einstein, whose philosophy of science has some- 
times been criticized as materialistic, once said: 

"The most beautiful and most profound emotion 
we can experience is the sensation of the mystical. It 
is the sower of all true science. He to whom this 
emotion is a stranger, who can no longer wonder 
and stand rapt in awe, is as good as dead. To know 
that what is impenetrable to us really exists, mani- 
festing itself as the highest wisdom and the most 
radiant beauty which our dull faculties can compre- 
hend only in their most primitive forms — this know- 
ledge, this feeling is at the centre of true 
religiousness." 

And on another occasion he declared, "The cosmic 
religious experience is the strongest and noblest main- 
spring of scientific research." Most scientists, when 
referring to the mysteries of the universe, its vast 
forces, its origins, and its rationality and harmony, 
tend to avoid using the word God. Yet Einstein, who 
has been called an atheist, has no such inhibitions. 
"My religion," he says, "consists of a humble admira- 
tion of the illimitable superior spirit who reveals 
Himself in the slight details we are able to perceive 
with our frail and feeble minds. That deeply 

95 



emotional conviction of the presence of a superior 
reasoning power, which is revealed in the incompre- 
hensible universe, forms my idea of God." 

So far as science is concerned, there are at the 
moment two gateways which offer the promise of 
closer access to physical reality. One is the great new 
telescope which soon, from Palomar Mountain, 
California, will project man's vision into deeper 
abysses of space and time than ever were dreamed by 
astronomers a generation ago. Till now the extreme 
range of telescopic perception has essentially ter- 
minated at the faint hurrying galaxies 500 million 
light years away. But the two-hundred-inch reflector 
of Palomar will double that range, enabling man to 
look upon whatever lies beyond. Perhaps it will 
reveal only new homogeneous oceans of space and new 
myriads of far galaxies whose antique light has swum 
to earth through a billion years of terrestrial time. But 
it may reveal other things — variations in the density of 
matter or visual evidence of a cosmic curvature from 
which man can accurately compute the dimensions of 
the universe in which he so insignificantly dwells. 

The other gateway to this knowledge may be 
opened by the Unified Field Theory upon which 
Einstein has been at work for a quarter century. 
To-day the outer limits of man's knowledge are 
defined by Relativity, the inner limits by the 
Quantum Theory. Relativity has shaped all our con- 
cepts of space, time, gravitation, and the realities that 
are too remote and too vast to be perceived. The 
Quantum Theory has shaped all our concepts of the 
atom, the basic units of matter and energy, and the 
realities that are too elusive and too small to be per- 
ceived. Yet these two great scientific systems rest on 
entirely different and unrelated theoretical founda- 
tions. The purpose of Einstein's Unified Field Theory 
is to construct a bridge between them. Believing in the 
96 



harmony and uniformity of nature. Einstein hopes to 
evolve a single edifice of physical laws that will encom- 
pass both the phenomena of the atom and the phe- 
nomena of outer space. Just as Relativity reduced 
gravitational force to a geometrical peculiarity of the 
space-time continuum, the Unified Field Theory will 
reduce electromagnetic force — the other great uni- 
versal force — to equivalent status. "The idea that 
there are two structures of space independent of each 
other, the metric-gravitational and the electromag- 
netic," Einstein observed a few years ago, "is intoler- 
able to the theoretical spirit." Moreover, as Relativity 
showed that energy has mass and mass is congealed 
energy, the Unified Field Theory will regard matter 
simply as a concentration of field. From its perspec- 
tive, the entire universe will be revealed as an 
elemental field in which each star, each atom, each 
wandering comet and slow-wheeling galaxy and flying 
electron is seen to be but a ripple or tumescence in the 
underlying space-time unity. And so a profound 
simplicity will supplant the surface complexity of 
nature; the distinction between gravitational and 
electromagnetic force, between matter and field, 
between electric charge and field will be for ever lost; 
and matter, gravitation, and electromagnetic force 
will all thus resolve into configurations of the four- 
dimensional continuum which is the universe. 

Completion of the Unified Field Theory will climax 
the long march of science towards unification of con- 
cepts. For within its framework all man's perceptions 
of the world and all his abstract intuitions of reality — 
matter, energy, force, space, time — merge finally into 
one. It touches the "grand aim of all science," which, 
as Einstein defines it, is "to cover the greatest number 
of empirical facts by logical deduction from the 
smallest possible number of hypotheses or axioms." 
The urge to consolidate premises, to unify concepts, to 

Dtu 97 






penetrate the variety and particularity of the manifest 
world to the undifferentiated unity that lies beyond is 
not only the leaven of science; it is the loftiest passion 
of the human intellect. The philosopher and mystic, as 
well as the scientist, have always sought through 
their various disciplines of introspection to arrive at a 
knowledge of the ultimate immutable essence that 
undergirds the mutable illusory world. More than 
twenty-three hundred years ago Plato declared, 
"The true lover of knowledge is always striving after 
being. . . , He will not rest at those multidinous phe- 
nomena whose existence is appearance only." 



But the irony of man's quest for reality is that as 
nature is stripped of its disguises, as order emerges 
from chaos and unity from diversity, as concepts 
merge and fundamental laws assume increasingly 
simpler form, the evolving picture becomes ever more 
abstract and remote from experience — far stranger 
indeed and less recognizable than the bone structure 
behind a familiar face. For where the geometry of a 
skull predestines the outlines of the tissue it supports, 
there is no likeness between the image of a tree tran- 
scribed by our senses and that propounded by wave 
mechanics, or between a glimpse of the starry sky on 
a summer night and the four-dimensional continuum 
that has replaced our perceptive Euclidean space. 

In trying to distinguish appearance from reality 
and lay bare the fundamental structure of the uni- 
verse, science has had to transcend the "rabble of the 
senses." But its highest edifices, Einstein has pointed 
out, have been "purchased at the price of emptiness of 
content." A theoretical concept is emptied of content 
to the very degree that it is divorced from sensory 
experience. For the only world man can truly know 
98 



is the world created for him by his senses. If he 
expunges all the impressions which they translate and 
memory stores, nothing is left. That is what the philos- 
opher Hegel meant by his cryptic remark: "Pure 
Being and Nothing are the same." A state of existence 
devoid of associations has no meaning. So paradox- 
ically what the scientist and the philosopher call the 
world of appearance — the world of light and colour, 
of blue skies and green leaves, of sighing wind and 
murmuring water, the world designed by the 
physiology of human sense organs — is the world in 
which finite man is incarcerated by his essential 
nature. And what the scientist and the philosopher 
call the world of reality — the colourless, soundless, 
impalpable cosmos which lies like an iceberg beneath 
the plane of man's perceptions — is a skeleton structure 
of symbols. 

And the symbols change. While physicists of the last 
century knew, for example, that the crimson of a rose 
was a subjective, esthetic sensation, they believed 
that "in reality" the quality they termed crimson was 
an oscillation of the luminiferous ether. To-day it is 
conventional to identify crimson as a wavelength. But 
it is equally proper to think of it as the value of the 
energy content of photons. Such considerations led a 
famous physicist to remark cynically that on 
Mondays, Wednesdays, and Fridays one uses the 
quantum theory, and on Tuesdays, Thursdays, and 
Saturdays the wave theory. In either case the concepts 
employed are abstract constructions of theory. And 
upon examination such concepts as gravitation, 
electron] agnetism, energy, current, momentum, the 
atom, the neutron, all turn out to be theoretical 
substructures, inventions, metaphors which man's 
intellect has contrived to help him picture the true, the 
objective reality he apprehends beneath the surface of 
things. So in place of the deceitful and chaotic 

99 



representations of the senses science has substituted 
varying systems of abstract representation. While 
these systems are distinguished by constantly increas- 
ing mathematical accuracy, it would be difficult 
to-day to find any scientist who imagines himself, 
because of his ability to discern previous errors, in a 
position to enunciate final truths. On the contrary, 
modern theorists are aware, as Newton was, that they 
stand on the shoulders of giants and- that their partic- 
ular perspective may appear as distorted to posterity 
as that of their predecessors seemed to them. 



For all the promise of future revelation it is possible 
that certain terminal boundaries have already been 
reached in man's struggle to understand the manifold 
of nature in which he finds himself. In his descent into 
the microcosm he has encountered indeterminacy, 
duality, paradox — barriers that seem to admonish him 
he cannot pry too inquisitively into the heart of things 
without altering and vitiating the processes he seeks to 
observe. And in exploring the macrocosm he comes at 
last to a final featureless unity of space-time, mass- 
energy, matter-field — an ultimate, undiversified, 
and eternal ground beyond which there appears 
to be nowhere to progress. "The prison house," 
said Plato, "is the world of sight." Every seeming 
avenue of escape from this prison house that science 
has surveyed leads only deeper into a misty realm of 
symbolism and abstraction. 

It may be that the extreme and insurmountable 
limit of scientific knowledge will be reached in the 
attainment of perfect isomorphic representation — 
that is, in a final flawless concurrence of theory and 
natural process, so complete that every observed phe- 
nomenon is accounted for and nothing is left out of 
ioo 






the picture. In its approach to this goal, science has 
hitherto achieved its most notable pragmatic and 
operational triumphs. For while telling nothing of the 
true "nature" of things, it nevertheless succeeds in 
defining their relationships and depicting the events 
in which they are involved. "The event," Alfred 
North Whitehead declared, "is the unit of things 
real." By this he meant that however theoretical 
systems may change and however empty of content 
their symbols and concepts may be, the essential and 
enduring facts of science and of life are the happen- 
ings, the activities, the events. The implications of this 
idea can best be illustrated by contemplating a simple 
physical event such as the meeting of two electrons. 
Within the frame of modern physics one can depict 
this event as a collision of two elementary grains of 
matter or two elementary units of electrical energy, as 
a concourse of particles or of probability waves, or as 
a commingling of eddies in a four-dimensional space- 
time continuum. Theory does not define what the 
principals in this encounter actually are. Thus in 
a sense the electrons are not "real" but merely 
theoretical symbols. On the other hand, the meeting 
itself is "real" — the event is "real." It is as though 
the true objective world lies forever half-concealed 
beneath a translucent, plastic dome. Peering through 
its cloudy surface, deformed and distorted by the ever- 
changing perspectives of theory, man faintly espies 
certain apparently stable relationships and recurring 
events. A consistent isomorphic representation of these 
relationships and events is the maximal possibility of 
his knowledge. Beyond that point he stares into the 
void. 

In the evolution of scientific thought, one fact has 
become impressively clear: there is no mystery of the 
physical world which does not point to a mystery 
beyond itself. All high-roads of the intellect, all 

101 



by-ways of theory and conjecture lead ultimately to an 
abyss that human ingenuity can never span. For man 
is enchained by the very condition of his being, his 
finiteness and involvement in nature. The farther he 
extends his horizons, the more vividly he recognizes 
the fact that, as the physicist Neils Bohr puts it, "we 
are both spectators and actors in the great drama of 
existence." Man is thus his own greatest mystery. He 
does not understand the vast veiled universe into 
which he has been cast for the reason that he does not 
understand himself. He comprehends but little of his 
organic processes and even less of his unique capacity 
to perceive the world about him, to reason and to 
dream. Least of all does he understand his noblest and 
most mysterious faculty; the ability to transcend him- 
self and perceive himself in the act of perception. 

Man's inescapable impasse is that he himself is part 
of the world he seeks to explore; his body and proud 
brain are mosaics of the same elemental particles that 
compose the dark, drifting dust clouds of interstellar 
space; he is, in the final analysis, merely an ephemeral 
conformation of the primordial space-time field. 
Standing midway between macrocosm and micro- 
cosm, he finds barriers on every side and can perhaps 
but marvel, as St. Paul did nineteen hundred years 
ago, that "the world was created by the word of God 
so that what is seen was made out of things which do 
not appear." 






102 



READING LIST 

1 his list does not include all the sources 
consulted in the preparation of this book; it does, how- 
ever, encompass the major sources of material plus 
some related volumes that might be of interest and 
value to the reader who wishes to explore further areas 
of this field. 

The Development of Physical Thought, by Leonard B. 
Leob and Arthur S. Adams. John Wiley & Sons, 
Inc., 1933. A survey course of modern physics. 
Comprehensive, beautifully written, and as enjoy- 
able to the lay reader as valuable to the student. 
Specific discoveries of the last decade are, of course, 
not represented; otherwise a superior history of 
science. 

"The Dust Cloud Hypothesis," by Fred L. Whipple, 
Scientific American, May, 1948. It should be noted 
that the new Scientific American is no longer a gadget 
and hobby magazine. Under new management, it 
now presents articles of fundamental scientific 
importance, brilliantly edited for intelligent 
laymen. 

Einstein, His Life and Times, by Phillipp Frank. Alfred 
A. Knopf, 1947. The best biogrophy of Einstein by 
a former colleague and eminent physicist. Detailed 
exposition of Einstein's scientific contributions as 
well as lively biographical and personal details. 

The Evolution of Physics, by Albert Einstein and Leopold 
Infeld. Simon and Schuster, 1942. The growth of 
ideas from early concepts to Relativity and Quanta, 
simply and fascinatingly described. No mathe- 
matics. 

103 






The Expanding Universe, by H. P. Robertson, Reprint 
from Science in Progress, Second Series. A clear, 
detailed, and interesting discussion of the structure 
of the universe by a famed cosmologist. 

Explaining the Atom, by Selig Hecht. The Viking Press, 
I 947- Unsurpassed as an exposition of the history 
and the theory of the atom. Written by a famous 
biophysicist for the layman. 

Flights from Chaos, by Harlow Shapley. Whittlesey 
House, 1930. A fascinating survey of the universe 
and its component parts from atoms to galaxies by 
Harvard's distinguished astronomer. This book is 
unfortunately out of print, but should not be. 

"Galaxies in Flight," by George Gamow, Scientific 
American, July, 1948. See note under "The Dust 
Cloud Hypothesis," above. 

Meet the Atoms, by O. R. Frisch. A. A. Wyn, Inc., 1947. 
A popular guide to modern physics. Amusingly 
written by a noted atomic physicist. 

Mind and Nature, by Hermann Weyl, University of 
Pennsylvania Press, 1934. The epistemological 
implications of modern physics set forth by a great 
theorist and colleague of Dr. Einstein. The philo- 
sophical standpoint from which the present volume 
is written is derived in great measure from this small 
but remarkable book, comprising five lectures de- 
livered by Dr. Weyl at Swarthmore College in 1933. 

Modern Physics, by G. E. M. Jauncey. D. Van Nostrand 
Company, Inc., 1948. Up-to-the-minute text, 
including sections on nuclear physics, radioactivity, 
cosmic rays, and the like. Also chapters on astro- 
physics, Relativity, and the philosophical implica- 
tions of modern science. 

Mr. Tompkins in Wonderland, by George Gamow. 
The Macmillan Company, 1947. Principles of 
Relativity and Quantum Theory set forth in an 
ingenious framework of narrative fiction. 

104 



The Mysterious Universe, by Sir James Jeans. The 
Macmillan Company, 1932. A classic which has 
awakened thousands of readers to the relationship 
between science and philosophy. 

The Nature of the Physical World, by A. S. Eddington. 
The Macmillan Company, 1928. Required reading 
for anyone interested in this field. 

One Two Three . . . Infinity, by George Gamow. The 
Viking Press, 1947. An eclectic account of facts and 
theories about the universe in its microscopic and 
macroscopic manifestations, described by a top- 
flight theoretical physicist who is also the ablest and 
most entertaining expositor of science writing 
to-day. & 

Physics and Philosophy, by Sir James Jeans. The 
Macmillan Company, 1943. A further discussion of 
the changing concepts of modern physics and their 
philosophical implications. 

Relativity, the Special and General Theory, by Albert 
Einstein. Henry Holt & Co., 1920. Lucid and 
detailed. Some mathematics, but not too difficult. 

Science and the Modern World, by Alfred North 
Whitehead. The Macmillan Company, 1925. 
Another classic, also required reading. 



105 



APPENDIX 



In theoretical physics there are often several 
avenues of approach to a given concept. The exposi- 
tion of the principle of the increase of inertial mass 
on pages 52-4 follows a quickly comprehended 
pattern analogous to those employed by many college 
physics texts. Readers with some mathematical equip- 
ment may wish to read Dr. Einstein's development of 
this principle as set forth in his book, Relativity, the 
Special and General Theory. Some essential excerpts 
follow, quoted with permission from Peter Smith, 
Publisher. 

"The most important result of a general character 
to which the Special Theory of Relativity has led is 
concerned with the conception of mass. Before the 
advent of relativity, physics recognized two conser- 
vation laws of fundamental importance — namely, 
the law of the conservation of energy and the law 
of the conservation of mass; these two fundamental 
laws appeared to be quite independent of each other. 
By means of the theory of relativity they have been 
united into one law. . . . 

"In accordance with the theory of relativity the 
kinetic energy of a material point of mass m is no 

longer given by the well-known expression m— 

2> 



me* 



but by the expression V 



1 --^" 



"By means of comparatively simple considerations 
we are led to draw die following conclusion: A body 
106 



moving with the velocity v } which absorbs an amount 
of energy E in the form of radiation without suffer- 
ing an alteration in velocity in the process, has, as a 
consequence, its energy increased by an amount 



V 



1 - 



"In consideration of the expression given above for 
the kinetic energy of the body, the required energy of 
the body comes out to be 



( m 



c 2 / 



»'-> 



mass 



"Thus the body has the same energy as a bodv of 

(E\ 
m + ~<?) movm S with the velocity v. Hence we 

can say: If a body takes up an amount of energy E 0) 
then its inertial mass increases by an amount — • 

the inertial mass of a body is not a constant, but 
varies according to the change in the energy of the 
body. The inertial mass of a system of bodies can 
even be regarded as a measure of its energy. The 
law of the conservation of the mass of a system 
becomes identical with the law of conservation of 
energy. ..." 



107 



ACKNOWLEDGEMENT 

Tor their help and advice in the preparation 
of this book I wish to thank Dr. Allen G. Shenstone of 
the Department of Physics, Princeton University; Dr. 
Hermann Weyl and Dr. Valentin Bargmann of the 
Institute for Advanced Study, Princeton, N. J.; and 
Dr. H. P. Robertson of the California Institute of 
Technology. 

I also wish to express my appreciation to Dr. 
Harlow Shapley of the Harvard Observatory, who 
read the original manuscript and made valuable sug- 
gestions and criticisms, with particular reference to 
the sections dealing with astronomy. 

I owe my very special gratitude to Dr. William W. 
Havens, Jr., of the Department of Physics, Columbia 
University, who read and checked both the original 
manuscript, prior to its publication in Harpefs maga- 
zine, and the expanded version that appears here; and 
who patiendy and cordially contributed his time and 
knowledge to the solution of many difficulties pre- 
sented by the exposition of this material. 



INDEX 



1 08 






Acceleration and mass, ^2 
6 5 fT. ' 5 ' 

Action-at-a-distance, 72 

Age and relativity, 5 1 

Archimedes, 7 

Arcturus, 41 

Aristotle, 10 

Atom, 9) la , 22j 24j 50 ffi| 55j 

B 9> 9i, 92, 93, 97, 100 

Berkeley, 8, 14, 16 
Beta particles, 53 
Bohr, Niels, 102 
Born, Max, 24 
de Broglie, Louis 22-4 

Cause and effect, 28, 90 
Centrifugal force, 69, 70 
Colour perception, 39, 99 
Companion of Sirius, 80 
Continuum, 57 ff. 
Cosmic rays, 15, 93 
Cosmology. See Universe. 
Creation of universe, 93 

Davisson, C. J., 23 
Democritus, 13 
Denary system, 15 
Descartes, 16, 34 
Determinism, 28 
Duality of nature, 22 ff. 
Dust cloud hypothesis, 91 

Eddingtom, Sir Arthur, 19 

Einstein, Albert, 7 ff. 
beliefs about universe, 29, 81 ff. 
on common sense, 49 
on religion, 29, 95-6 
on time perception, 39 ff. 
photoelectric law, 20-2 
rejection of ether theory, 38 
theory of general relativity, 

56 ff. 
theory of special relativity, 7 
38 ff., 5 6 *' 7 ' 

unified field theory, 8, 9, 96 ff. 



Einstein effect, 80 
Electrical field, 72, 97 
Electricity, 9, 10, 37, 72 
Electromagnetic field, g, 73 % nj 
Electromagnetic waves, 15 
Electromagnetism, 9, 97) 98, 99 
Electron ,6 20, ff, 27, 29, 53, 

55, °5, 89, 91, 101 
Energy, lo , 53 ff, 97, IOO 

of quantum, 18, 99 

radiant, 18, 19 
Entropy, 90 ff. 
Equation, 

E - Av, 18 

E m m&, 54 

A => kjnw t 23 

m = Ejc 2 , 54 

Tito 

Vi - J^/c 2 ' 53 
Equations, de Broglie's, 23 
Lorentz transformation, 46-7 
mass-energy relation, 54 
mass-velocity relation, 52 
quantum energy, 18 
Equivalence of gravitation and 

inertia principle, 70 ff. 
Ether theory, 34 ff. 
Michelson-Morley experiment, 
35-7 
Euclid, 7, 82-98 

Faraday, Michael, 8, 94. ?» 
Force, inertial, 70 ff. 
Fosdick, H. E, 7 
Four-dimensional space-time 

continuum, 57, 97 ff 
Fourth dimension, 59 ff. 
Free will and modern science, 28 

Galileo, 7, u, 13,32,38,66 
Jjamma rays, 15, 27, 91 
Gamow, George, 89 
General theory of relativity, 56 ff. 
Germer, L. H., 23 

109 



Time-space continuum, gr 

97 ff- 

Tolman, R, C, 89 
Transformation laws, 43 ff. 



ff., 



Ultraviolet rays, 15 
Uncertainty, principle of, 26-7 
Unifield field theory, 7, 8, 96 ff. 
Universe and Euclidean geom- 
etry, 82 ff. 
and mathematical principles, 

1 6, 28-9, 98 ff. 
average density of matter in, 

85 , 
expansion of, 87 ff. 
fundamental forces, 8, 56, 96 
infinity of, 84 ff. 
in light of Einstein's theories, 

38, 50, 56 ff, 71, 74, 81 ff. 
mechanical, 10 ff., 32, 34, 71 
Newtonian, 32, 34-5, 50, 56, 

81 
origin, theories, 88 ff. 



radius of, 85 
Uranium, 12, 54, 93 

Velocity of light, 35-6, 38, 39, 
42-3, 44, 48 
of earth through ether, 37 
of electron, 53 
of sound, 42 

Wavelength of electron, 23 
of molecule, 23 
of various types of radiation, 

of visible light, 15 
Wave mechanics, 23, 98 
Wave theory, 21, 22, 34, 55, 99 
Waves, electromagnetic, 15 
Weight, 52 
Whipple, F. L., 91 
Whitehead, A. N., ior 

X-rays, 15, 27 



112 



perceived. It is on these two theories 
that the whole of our modern 
knowledge of the world is based. 

Mr. Barnett gives a fascinating 
account of the steady growth of 
Einstein's ideas, and of the way in 
which he put them to the test. For 
instance, how he brought the philo- 
sophical and mathematical bases 
of relativity into the laboratory, so 
to speak, translating them into 
terms of clocks and measuring 
rods and moving bodies. Or the 
triumphant demonstration of the 
correctness of his belief (on which 
he staked the whole of his General 
Theory of Relativity) that light 
travels in a curve when it passes 
near any massive object. Every- 
body who reads Mr. Baraett's 
story of these and many other en- 
thralling experiments will want to 
explore more deeply into the 
mysterious laws of creation which 
govern the life and evolution of 
our planet. 

Here is, we believe, the popular 
scientific book for which everyone 
has been waiting— accurate in 
every detail, and yet written with 
such clarity that the lay reader wiH 
begin to understand, perhaps for 
the first time, the basic laws which, 
according to our present know- 
ledge, govern our universe. There 
are a number of diagrams to help 
him. 

Einstein himself thinks so highly 
of the book that he has consented 
to write a foreword. 



OS 
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