from PRIMER OF QUANTUM MECHANICS, Wiley, N.Y. 1987 and Dover, N.Y. 2003 by Marvin Chester
PREFACE
Quantum mechanics is the fundamental theoretical infrastructure upon which all understanding of the nature of the physical world is built. This book is an exposition of that theory presented at the level of a junior·year undergraduate physics student.
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In writing this book, I set as my primary task this one: to fuse the mathematical machinery of quantum mechanics with the philosophical world view embedded in it. That the mathematics appear to grow organically out of the philosophy was my aim. The object was to present a consistent physical imagery that tightly parallels the mathematics and thus, with verbal threads, to weave the philosophical tapestry into the mathematical formalism.
It is incontrovertible that quantum mechanics faithfully describes nature’s behavior. To accommodate one’s world view to what is nature’s behavior is the reason for a philosophical tapestry. The tapestry allows us to have a way of perceiving nature as natural.
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EPILOGUE
THE SIGNATURE OF UNDERSTANDING:
PERCEIVING NATURE AS NATURAL
It is possible to feel uncomfortable with the picture of reality that issues from quantum mechanics. Much of it appears to contradict the intuition of direct physical experience: it seems to defy understanding. Yet the purpose of studying the physical world is surely to gain understanding.
The quest for understanding hangs on the meaning of the word, understanding. One understands when one perceives a satisfying structure. For a scientist, a satisfying structure is one that, with few axioms, accounts for and quantitatively matches the behavior of nature.
Understanding is the perception of nature as natural. You have understood something when its behavior is just what you expect it to be, when it appears that what is, ought to be. A bubble rises because the heavier liquid surrounding it falls down from above to below it. We see the bubble rise and so it ought to do. We understand the phenomenon.
Understanding is lacking when things seem to be different from what they ought to be. That incontrovertible facts appear to make no sense reveals a faulty structure of understanding. The structure is no longer satisfying.
Under these conditions to achieve understanding requires a revision in the conceptual structure. Recognizing that they are also your prejudices, you question your axioms. You cast off some old ones and take on some new ones. You alter your philosophy. To achieve understanding is to go through a conceptual metamorphosis.
UNDERSTANDING MATERlALIZES
BY CONCEPTUAL METAMORPHOSIS
The history of physics provides striking examples of the process. Consider the introduction of gravity, that all masses pull on one another, even from afar. Newton called it an action-at-a-distance force.
The phrase echoes the incomprehensibility of the concept to people of Newton’s time. Only between touching bodies could forces be envisioned. That forces could reach out invisibly from one body to pull on another seemed beyond comprehension. It was not understood.
A century passed before the term force field was introduced to describe action-at-a-distance forces. Today every child is familiar with force fields. What in Newton’s time puzzled the minds of sages is now the comfortable self-evident perception of little boys and girls.
What happened to the profound questions perceived by the sages? They lost their meaning; they became meaningless. No one now expects that forces require touching. We recognize the expectation to be a prejudice. The problem of how forces could act at a distance was never resolved. It was dissolved. A conceptual metamorphosis dissolved it.
Understanding consisted in perceiving the question to be meaningless. According to quantum mechanics, one cannot know both position and momentum simultaneously. Why are we denied this knowledge? To perceive this question as inherently meaningless is what quantum mechanics teaches us. What has a definite momentum does not have a position. To demand both together is like demanding dry wetness. It is denied us, not by nature’s perversity, but rather, because the demand is meaningless.
When the picture of nature that Newton presented proved to be indisputably correct, the sages of his time had to undergo a conceptual metamorphosis. Modem physics confronts us with the same task: to embrace the picture of nature presented by quantum mechanics.
It has been my aim in this book to paint that picture.