Table of Contents

Quotes

Bergamini—Life Science Magazine—Mathematics (1963)

Hoffmann—The Strange Story of the Quantum (1947)

Lindley—Where Does the Weirdness Go? (1996)

Kaku—Beyond Einstein (1995)


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Quotes

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

 


Bergamini—Life Science Magazine—Mathematics (1963)

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

 


Hoffmann—The Strange Story of the Quantum (1947)

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.


Lindley—Where Does the Weirdness Go? (1996)

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.


Kaku—Beyond Einstein (1995)

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.


 

 


 [Bek1]No kidding.

 [Bek2]T1 baby.