Bergamini—Life Science
Magazine—Mathematics (1963)
Hoffmann—The
Strange Story of the Quantum (1947)
Lindley—Where Does the Weirdness Go?
(1996)
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A second
Enlightenment is now needed in which man can live in peace with his own
discoveries and creations—enabled by a fuller comprehension to use them for his
enrichment and pleasure. The realization
of this second Enlightenment cannot be fulfilled by ordinary educational
means. What we require are books with
sufficient appeal and persuasive power to enlighten the intelligent but
scientifically uninformed multitudes.
—Henry Margenau,
Mathematics—Life Science Library (1963)
Quantum
theory does not hold undisputed sway, but must share dominion with that other
rebel sibling—relativity. And although
these two bodies together have led to the most penetrating advances in the search
for knowledge—they must remain enemies.
Their fundamental disagreement will not be resolved until both are
subdued by a still more powerful theory that will sweep away our present
painfully won fancies concerning such things as space, time, matter, radiation
and causality. The nature of this theory
may only be surmised—but it will ultimately come down to the very same
certainty as to whether our civilization as a whole survives—no more no less.
—Banesh Hoffmann, The Strange Story of the Quantum (1947)
It seemed to Einstein as it has seemed to many others
over the years that if you take away from science the idea of a unique
underlying reality that all observers can agree on, then you are taking away
the very foundation of science itself.
Whether the collapse of the wavefunction
in quantum mechanics is a physical or a psychological event is not easy to say.
What’s the difference between the Moon and an
electron? I can’t be altogether sure the Moon is there if no one is looking at
it. But I can be sure—because of its constant and reliable utility over many
long years—that my theoretical Moon exists at all times.
Let me be
utterly skeptical. If someone asks me
whether I believe the Moon is there even when no one is looking at it, I am
obligated to say that the question makes no sense. If you want to verify that the Moon is there,
then go ahead and look—but then, of course, you are
not answering the question. If you want
an objective proof of the Moon’s existence, I will respond that I am a
physicist—and not a divine—and therefore have no interest in unanswerable
questions.
The idea that
physical quantities do not take on any practical reality until someone measures
them offended Einstein so much to the point where he asked the physicist
Abraham Pais whether he believed the Moon really
exists when no one is looking at it?
—David Lindley, Where Does the Weirdness Go?
(1996)
Einstein
always began with the simplest possible ideas, and then put them into their
proper context. But Einstein failed in
his attempt to create a unified field theory because he abandoned this simple
conceptual approach and instead resorted to the safety of obscure mathematics.
While
relativity uncovers the secrets of energy, gravity and spacetime—the other
theory that dominated the twentieth century, quantum theory, is the theory of
matter. What Einstein didn’t realize, as
physicists do now, is that the key to the unified field theory is found in the
marriage of relativity theory and quantum theory.
In many ways the
destinies of Einstein and Heisenberg were strangely interwoven, although the
theories they created, relativity and quantum theory, are universes apart. Both were revolutionary iconoclasts who
challenged the established wisdom of their predecessors.
—Michio Kaku, Beyond
Einstein (1995)
Knowledge
le savior.
—The Government of Canada, as depicted on the
2000 two-dollar coin
Introduction
Early man lived in fear and awe of natural events
because he could not explain them. Myth and magic dominated his thinking. Then,
gradually, he began to understand nature, and learned to enjoy and control her.
Historians speak of the epoch in which this understanding began to affect
Western culture as the Enlightenment.
Today that phrase has lost some of its meaning. The principles
of the Enlightenment, sufficient to let us live in peace with the beasts of the
forest, with the tides of the ocean, with thunder and lightning, are inadequate
to still our new disquietude about rockets, computers, bevatrons
and the superstrains of bacteria engendered by wonder
drugs. We live again in a world of magic, this time manmade, and we seek our
uncertain way among the robots which, some say, threaten our existence.
A second Enlightenment is now needed in which man
can live in peace with his own discoveries and creations[Bek1]—enabled
by a fuller comprehension to use them for his enrichment and pleasure. The
shift of emphasis from the old-style humanities to science in our school
curricula indicates an awareness of this need. et it
cannot be fulfilled by ordinary educational means. I estimate optimistically
that, in my 30 years of college teaching, I may have inculcated what is called
the scientific spirit in perhaps 5,000 students. The scientific books
available, although large in number, are read by a relatively small group of
Americans. Clearly we require books with sufficient appeal and persuasive power
to enlighten the intelligent but scientifically uninformed multitudes.
When the Editors of LIFE decided to publish a series
of books on science, with the aid of their arsenal of editorial and graphic
talent and with a responsible concern befitting scholars, my hopes soared. Here
is promising evidence that the new Enlightenment may come to pass, that the
cultural gap between our technology and its meaning in terms of human values
may be narrowed and finally bridged.
With these high hopes I greet the publication of the
present volume, the first of a series on the physical and biological sciences.
It is particularly appropriate that it should deal with mathematics, which has a usefulness
and a prestige sufficient for it to merit the title “Queen of the Sciences,”
indispensable to all the rest.
Henry Margenau
Eugene Higgins Professor of Physics and Natural
Philosophy
Yale University
Preface
This book is designed to serve as a guide to those who
would explore the theories by which the scientist seeks to comprehend the
mysterious world of the atom. Nuclear fission and atomic bombs are not the
whole of atomic science. Behind them lie extraordinary ideas and stirring
events without which our understanding would be meager indeed.
The story of the quantum
is a confused and groping search for knowledge conducted by scientists of many
lands on a front far wider than the world of physics had ever seen before—illuminated
by flashes of insight, aided by accidents and guesses, and enlivened by
coincidences that one would only expect to find in works of fiction. It is the story of turbulent revolution—of
the undermining of a complacent physics that had long ruled a limited domain,
of a subsequent interregnum predestined for its own destruction by its inherent
contradictions, and of the tempestuous emergence of a much more chastened
regime—quantum theory. And while quantum theory rules newly
discovered land with a firm hand, its victory is not complete. What looks like mere scratches on the
brilliant surface of its domain reveal themselves as fascinating crevasses
betraying the darkness within and luring the intrepid on to new adventure. Nor does quantum theory hold undisputed sway
but must share domain with that
other rebel sibling—relativity.
And although together these two bodies have led to the most penetrating
advances in the search for knowledge—they must remain enemies. Their fundamental disagreement will not be
resolved until both are subdued by a still
more powerful theory that will sweep away our present painfully won fancies
concerning such things as space, time, matter, radiation and causality. The nature of this theory may only be
surmised—but it will ultimately come down to the very same certainty as to
whether our civilization as a whole survives—no more no less.[Bek2]
What are those potent wraiths we call space and time,
without which our universe would be inconceivable? What is that mystic essence,
matter, which exists within us and around in so many wondrous forms; which is
at once the servant and master of mind, and holds proud rank in the hierarchy
of the universe as a primary instrument of divine creation? And what is that
swiftest of celestial messengers, radiation, which leaps the empty vastnesses
of space with lightning speed?
Though true answers there can be none, science is
fated to fret about such problems. It must forever spin tentative theories
around them, seeking to entrap therewith some germ of truth upon which to poise
its intricate superstructure. The balance is delicate and every change sends
tremors coursing through the edifice to its uttermost tip. The story of relativity tells what
happened to science when one provisional theory of space and time yields to
another. The story of the quantum tells of adventures which recently befell our
theories of matter and radiation, and of their unexpected consequences.
So abstract a matter as the quantum
theory serves well as the basis for learned treatises whose pages overflow with
the unfriendly symbols of higher mathematics. Here in this
book is its story without
mathematics yet without important omission of concept. Here too is a
glimpse of the scientific theorist at work, pen and paper his implements, as he
experiments with ideas. Not the least of his gifts is a talent for reaching
valuable conclusions from what later prove to be faulty premises. For his
insight is penetrating. Be it a hint here or a clue there, a crude analogy or a
wild guess, he fashions working hypotheses from whatever material is at hand,
and, with the divine gift of intuition for guide, courageously follows the
faintest will-o’-the-wisp till it show him a way toward truth.
The magnificent rise of the quantum to a dominant
position in modern science and philosophy is a story of drama and high
adventure often well-nigh incredible. It is a chaotic tale, but amid the apparent chaos one gradually
discerns a splendid architecture, each discovery, however seemingly irrelevant
or nonsensical, falling
cunningly into its appointed place till the whole intricate jigsaw is revealed
alone of the major discoveries of the human mind.
Does the Moon really exist?
The idea that physical quantities do not take on any
practical reality until someone measures them offended Einstein so much to the
point where he asked the
physicist Abraham Pais whether he believed the Moon
really exists when no one is looking at it?
This is not an easy
question to answer. I have in my mind a theoretical moon. This
theoretical moon, a purely mental construct, has certain hypothetical or
proposed physical properties: it is a more or less spherical piece of rock, it
follows a certain orbit around Earth, its surface has
a certain reflectivity, and so on. If someone asks me at any time where the
Moon is in the sky, and what phase it presents, I turn to my theoretical moon,
make the necessary calculations based on the time of day, the position of the
Sun, the latitude and longitude of the observer, et cetera, and I tell my
questioner—If you raise your eyes to this position in the sky, you will find
the image of the Moon, and it will have a certain crescent shape whose precise
details I can specify, if you wish.
And then my questioner looks upwards, and finds a real
Moon in the real sky, just where I said it would be, and with just the shape I
predicted. If, over a period of time, many people test my knowledge of the Moon
in this way, they will find I am infallible. My theoretical moon, following its
theoretical orbit, always tells me where anyone needs to look in the sky to
find the real Moon. Of course, if it happens to be overcast, I could say that
the image of the Moon would be in such and such a place, were it not for the
clouds, but since the sky is obscured on this occasion I cannot prove the Moon
really is there, and my questioner could not prove that it is not.
Or another more ingenious questioner might tell me
that he does not plan to look at the Moon directly, but wishes to observe the
shadows cast by the Moon on the ground nearby (it happens to be a clear, bright
night). Then I can predict just as reliably as before that the shadows will
fall in a certain direction. If this questioner asks me, do I think that a
correct prediction of the positions of shadows proves that the Moon is really
there, I can only respond that I, as a pure theoretician, have nothing to say
on whether the Moon is really there or not, and that if you, my questioner, do
not care to look up in the sky for yourself to see if the Moon is there, then
the question is moot.
Let me be utterly skeptical. If someone asks me whether I believe the Moon
is there even when no one is looking at it, I am obligated to say that the question makes no sense. If you want to verify that the Moon is there,
then go ahead and look—but then of course you are not answering the
question. If you want an objective proof
of the Moon’s existence, I will respond that I am a physicist—and not a divine—and therefore have no
interest in unanswerable questions.
In fact, I am not really as stern as this. Over the
years I have developed a certain faith in my theoretical moon, the one I carry
around in my head; its properties are constant, reliable, and predictable, and
I can use it with absolute confidence to predict at any time where a moonlike
image is to be found in the sky. I trust my theoretical moon, and so does
everyone else, so if anyone asks me if the Moon really there when no one is
looking at it?—I respond warmly—Sure, why not, it might as well be.
But when I turn to my theoretical electron—the mental
construct, possessed of certain attributes and qualities,
that I also carry around in my head—things are not so amiable. It’s true
that if anyone asks me a question about the behavior of an actual electron in a
real experiment, I can turn to my theoretical electron and use it to make
predictions. But the best predictions I can come up with are merely
probabilities. If someone asks—Will the electron’s spin point up or down?—I
have to say there’s a fifty-fifty chance of either result; and if someone else
asks—Will it point left or right?—I have to say there’s a fifty-fifty chance of
that too. And if someone asks—Does the electron’s spin point in any particular
direction when no one is measuring it?—I have to say, unequivocally, no.
What’s the difference between the Moon and an
electron? I can’t be altogether sure the Moon is there if no one is looking at
it. But I can be sure—because of its constant and reliable utility over many
long years—that my theoretical Moon exists at all times. But my theoretical
electron is not nearly so independent a creature. If someone asks me whether
the electron’s spin is pointing up or down, I should really ask my
questioner—Are you planning to measure whether it is up or down, or were you
just making a casual inquiry?—It all depends.
This is what makes quantum mechanics, and in
particular the Copenhagen interpretation of it, so disconcerting to physicists
brought up to believe in the existence of a dependable, objective reality.
Always in science, we conduct experiments, obtain data, and make inferences
from the data. In classical physics you can infer, for example, a lunar orbit
from observations taken over a number of nights, and this inferred orbit will
correctly give the position of the Moon on any other night.
But in quantum mechanics, this doesn’t work. If you
have an unmeasured electron, its spin is entirely uncertain; if you measure its
spin using a Stern-Gerlach magnet of some particular
orientation, you will obtain a specific result; you can then say with
confidence that the spin-state of the electron is, for the time being,
definitely in the direction it was found to be in, and you can use that datum
as a baseline to predict (with the appropriate probabilities) the result of
another spin measurement in a different direction. And so on. But at each
measurement the spin is reset, loosely speaking, to a new value, and loses all
memory of its previous value. This would be like saying that if I observed the
position of the Moon on Monday, Tuesday, and Wednesday nights, then I could
predict the Tuesday position from the Monday observation, and the Wednesday
position from the Tuesday observation, but not the Wednesday position from the
Monday observation, because the intervening Tuesday observation would have
reset the Moon’s position and made the earlier observation irrelevant.
It was an article of faith in classical physics that
all observations, taken together, refer to a single, consistent reality.
Quantum mechanics disallows this certainty—a series of measurements of a single
object or system does not, in general, yield a set of results that can be
consistently referred to a single underlying model of what is really
going on.
It seemed to Einstein as it has seemed to many others
over the years that if you take away from science the idea of a unique
underlying reality that all observers can agree on, then you are taking away
the very foundation of science itself. This was why Einstein worked so hard to
prove that quantum mechanics was at best an incomplete theory of the world.
Einstein’s Mistake
By the early 1900s, the scientific world was thrown
into turmoil by a series of new experiments that challenged three centuries of
Newtonian physics. The world was witnessing the birth pangs of a new physics
emerging from the ashes of the old order. Out of this chaos, however, emerged
not one but two theories.
Einstein pioneered the first theory of relativity and
concentrated his efforts on understanding the nature of forces such as gravity
and light. The foundation for understanding the nature of matter, however, was
laid by the second theory, quantum mechanics, which governs the world of
subatomic phenomena. It was created by Werner Heisenberg and his collaborators.
In many ways, the destinies of Einstein and Heisenberg
were strangely interwoven, although they created theories that are universes
apart. Both of German origin, they were revolutionary iconoclasts who
challenged the established wisdom of their predecessors. They so thoroughly
dominated modern physics that their discoveries would determine the course of
physics for over half a century.
Some have argued that Einstein made the biggest
blunder of his life by rejecting quantum mechanics. This, however, is a myth
perpetuated by scores of science historians and journalists who are largely
ignorant of Einstein’s scientific thought. This myth survives only because most
of these historians are not fluent in the mathematics used to describe the
unified field theory.
Instead of showing how outdated he was, a careful
scientific reading of Einstein’s work published fifty years ago reveals that he
was surprisingly modern in his approach. These papers show clearly that
Einstein eventually accepted the validity of quantum mechanics. However, his
personal belief was that quantum mechanics was an incomplete theory,
in the same way that Newton’s theory of gravity was not incorrect, merely
incomplete.
Einstein believed that quantum mechanics,
while highly successful, was not a final theory. His later scientific work,
which has been largely ignored by nonscientists and historians, shows that he
believed his unified field theory, as a by-product, would account automatically
for the features of quantum mechanics. Subatomic particles and atoms, Einstein
thought, would only appear as solutions to his geometric theory of gravity and
light.
Einstein, however, died in the midst of his pursuit of
the notion that the forces of nature ultimately must be united by some physical
principle or symmetry. Even four decades after his death, most of his
biographers skip over the last years of his physics research, ignoring the
blind alleys he explored in his search for the unified field theory and
concentrating instead on his devotion to nuclear disarmament.
Although physicists do not fully comprehend all the
details necessary to unite the four fundamental forces into one theory, they do
understand why Einstein had so much trouble wrestling with the unified field
theory. We understand where Einstein went wrong.
Einstein once said that in his relativity theory he
placed clocks everywhere in the universe, each beating at a different rate, but
in reality he couldn’t afford to buy a clock for his home. In this way,
Einstein revealed a clue to the way he arrived at his great discoveries—he
thought in physical pictures. The mathematics, no matter how
abstract or complex. always came later, mainly
as a tool by which to translate these physical pictures into a precise
language. The pictures, he was convinced, were so simple and elegant that they
could be understood by the general public. The mathematics might be obscure and
complex, but the physical picture always should be elemental.
One of Einstein’s biographers noted, “Einstein always
began with the simplest possible ideas and then, by describing how he saw the
problem, he put it into the appropriate context. This intuitive approach was
almost like painting a picture. It was an experience that taught me the
difference between knowledge and understanding.”
Because of Einstein’s keen insight, he was able to see
farther than others. It was Einstein’s great pictorial insight that led him to
propose the relativity theory. For three decades, he was a towering figure in
physics because his physical pictures and conceptual ability were unerringly
correct. The irony is, however, that in the last three decades of his life,
Einstein failed to create the unified field theory largely because he abandoned
this conceptual approach, resorting to the safety of obscure mathematics
without any clear visual picture.
Of course, Einstein was aware of the fact that he
lacked a guiding to physical principle. He once wrote, “I believe that in order
to make real progress one must again ferret out some general principle from nature.”
No matter how hard he tried, however, he could not think of a new physical
principle, so he gradually became obsessed with purely mathematical concepts,
such as “twisted” geometries, which are bizarre mathematical structures devoid
of physical content. He ultimately failed to create the unified field theory,
which was to have been the centerpiece of his research, because he strayed from
his original path.
In retrospect, we see that the superstring theory may
be the physical framework that eluded Einstein for so many years. The
superstring theory is very graphic, encompassing the infinite number of
particles as modes of a vibrating string. If the theory lives up to its
promise, then we see that, once again, the most profound physical theories can
be summarized pictorially in a surprisingly simple fashion.
Einstein was correct in his pursuit of unification. He
believed that an underlying symmetry was at the root of the unification of all
forces. However, he used the wrong tactic, trying to unite the force of
gravitation with the electromagnetic force (light) rather than with the nuclear
force. It was natural that Einstein would try to unite these two forces,
because they were the subject of intense investigation during his lifetime.
However, he consciously chose to neglect the nuclear force, which is perhaps
understandable because it was the most mysterious of the four forces at that
time. He also felt uncomfortable with the theory that describes the nuclear
force—quantum theory.
While relativity uncovers the secrets of energy,
gravity, and spacetime, the other theory that dominated the twentieth century,
quantum mechanics, is a theory of matter. In simple terms, quantum mechanics
successfully describes atomic physics by uniting the dual concepts of waves and
particles. But Einstein didn’t realize, as physicists do now, that the key to
the unified field theory is found in the marriage of relativity and quantum
theory.