WHAT IS A QUANTUM? (Dec, 1930)

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By PAUL R. HEYL, Ph.D. Physicist United States Bureau of Standards, Author of “The New Frontier of Physics”, Contributing Editor Scientific American

“Do you remember,” said the visitor, “when I came here some time ago, asking you to tell me what an atom was?”

“Yes,” said the scientist, “and I could not do it.”

“Perhaps you did better than you thought. Now I have another question to ask you.”

“I hope it is something easier this time.”

“Well, it isn’t about Einstein. I only want to know what the quantum theory is all about. What is a quantum, anyway?”

“You do not seem to be getting any more moderate in your demands,” said the scientist. “How much do you know about it, to begin with?”

“Very little. All I have gathered is that a quantum has something to do with energy, and that it is considered a very important thing nowadays.”

“Then so far you have nothing to unlearn,” said the scientist. “We may as well start at the beginning. The quantum theory is a good illustration of the fact that history is prone to repeat itself as well in scientific thought as elsewhere.”

“How is that?” asked the*visitor. “Is not science always progressive?”

“Yes, certainly; but some parts of it progress faster than others, principally because they had an earlier start. Our ideas regarding energy, for example, have recently undergone a change similar to that suffered by our concept of matter a great many years ago.”

“In what way?”

MATTER has been studied by man for thousands of years. It was at first supposed to be continuous in its structure, as indeed it appears to be; but our present idea is that it is really discontinuous in its structure, built up of atoms and molecules and actually consisting principally of empty interspaces. This concept grew up gradually, but we may perhaps take the work of Dalton at the opening of the 19th Century as marking a time when the atomic theory was rather generally accepted.” “Yes,” said the visitor. “I have heard him called the father of the atomic theory.”

“Still,” continued the scientist, “there were men of scientific standing all through the 19th Century who clung to the older continuous theory. The last great disbeliever in atoms, Ernst Mach, died as lately as 1916.”

“You surprise me!” said the visitor. “I did not know that the past projected so far into the present.”

“Such are the facts of the case,” replied the scientist. “This last opponent of the atomic theory lived to see the doctrine against which he so hopelessly fought conquer not only the domain of matter but also that of energy.”

“Are there then atoms of energy?”

“Something very like it; only we call them quanta. Energy is a comparatively new concept, dating back only to the middle of the 19th Century. When it first took shape it was regarded as continuous.”

“Of course,” said the visitor. “I have always understood it that way. The continuous stream of light and heat from the sun illustrates that.”

“How do you know that the stream of light from the sun is continuous?”

“Why,” said the visitor, “there are no dark spaces perceptible—but then,” he added with a smile, “I suppose the same might be said of matter.”

“Exactly. The cases are parallel. For good reasons we believe in the existence of atoms, though no one has ever seen them; and also for sufficient reasons we have come to recognize the discontinuous nature of energy. History is repeating itself in scientific thought.”

“So that is what the quantum theory is all about!” said the visitor. “But how did this change in our ideas of energy come to pass?”

“Very much as the atomic theory of matter came to supersede the continuous theory. One was found to fit the facts of experiment better than the other. The historical parallel is perfect.”

“This is getting interesting,” said the visitor. “Tell me how it happened.”

“IT began over 30 years ago, shortly after the discovery of the X rays. It was soon found that air or any other gas exposed to the passage of X rays became electrically conducting. Bring a charged electroscope near an X-ray tube in action, and the divergent gold leaves will collapse at once; the charge leaks away through the air, which under normal conditions is one of the best of insulators. It was found that this conducting property of the air was caused by the fact that some of its atoms were split up by the X rays into two parts, bearing opposite electrical charges, though the original atom was electrically neutral. This is called ionization of the gas. And the surprising thing was that so few of the atoms were ionized. Although the gas was swept through and through by successive waves of X rays, only about one atom in a million million was thus broken up.” “I should say,” said the visitor, “that that net must have had a lot of big holes in it.”

“Exactly,” said the scientist, smiling. “Put into scientific language, that was just what J. J. Thomson thought about it. He was forced to the conclusion that the advancing wave of X rays was not uniform, but of a beady or lumpy structure, the energy of the wave being concentrated mostly in spots and spread

out thinly elsewhere. His explanation was that only these intense spots of energy were equal to the task of splitting up an atom, and from the fact that so few atoms were ionized he reasoned that the wave front must be made up principally of thin places.”

“A perfectly natural conclusion,” said the visitor. “But where do the atoms of energy come in—and the empty spaces between them? This thick-and-thin structure is just as continuous as if it were uniform.”

“True enough,” answered the scientist. “The quantum theory carries things to the limit of supposing all the energy to be concentrated in the spots with the interspaces empty. This extreme the X-ray evidence that I have mentioned did not require, and it is a principle of scien-tific thought that we are never to assume more than is necessary to explain the facts. It required evidence of another sort to force us farther. This next step is due to Planck, who in 1900 suggested the modern form of the quantum theory.”

“On X-ray evidence?”

“No; the evidence was of a different nature. It had to do with light. Theory and experiment had, in a certain field, failed to agree. Planck brought them into agreement by supposing energy to be atomic in its structure.”

“Was the discrepancy between theory and experiment so serious as to require this radical step?”

“IT would have been serious, no matter what its magnitude, provided that it was great enough to be sure of; but judge for yourself. What happens when a piece of iron is heated?” “It becomes red hot.” “And then—?”

“Yellow, and finally white hot.” “But suppose I should tell you that it should not act that way; that on theoretical grounds it ought to show a blue color from the start, no matter how hot it was?”*J “I should consider that a very serious discordance. Was it really as bad as that?”

“Yes, the classical theory insisted on predict all the keys of an organ in succession, beginning at the lowest. To the lowest frequencies would be added successively those higher in the scale, until at last the whole range (or spectrum) would be present. But the classical theory demanded that the high frequencies should appear from the start, and always be more intense than the lower ones.”

“And Planck’s theory straightened out this discrepancy?”

“Perfectly. On the quantum theory we suppose that energy is made up of atoms or quanta. Less than one quantum can not be absorbed or emitted by a body, and all emission or absorption must be in multiples of this fundamental quantum.”

The visitor looked blank.

“It is something like our money system,” continued the scientist. “The smallest amount we can pay anybody is one cent, and any amount that changes hands must be a multiple of one cent. Now suppose your income was small, say one cent per hour, and that your creditors were pressing you. All you could do would be to pay out one cent now and then. This corresponds to the case of iron slightly heated. The influx of heat is not rapid, and the iron can emit only quanta of low frequencies—coins of low value. If your income was more rapid you might be able to pay out nickels or even dimes occasionally along with the cents. So as the iron is more intensely heated it is able to emit quanta of higher frequencies along with the lower ones.”

“Is there only one fundamental quantum?”

“No, matters are more complicated than that. It is like having several different kinds of currency circulating together; English, French, German, as well as our own. The smallest coins of each kind would be different in value, and not exact multiples of each other; and we would have a series of multiples •’ of each kind in circulation together. There may be many quanta of different frequencies, and a radiating body may emit multiples of any of them.”

“But nothing but exact multiples? No fractional quantities?”

“Apparently not.”

“Why is that?”

“We do not know.”

THE visitor was silent for some moments. Then he said:

“The only reason why I can not pay out or receive anything but exact multiples of one cent is because the mint in this country does not coin anything else. It is not a limitation on my part. In England I would not find the slightest difficulty in paying out multiples of a half penny, although that is not exactly equal to one cent.”

The scientist nodded approvingly.

“I agree with you. This curious restriction to multiples of a quantum in exchanges of energy may be a limitation arising from Something in the structure of the molecule, or it may be that Nature’s mint coins nothing but “even multiples of a quantum. I am inclined to the latter view. The fact that a molecule can actually emit almost any quantity of energy that can be imagined, provided that there is a fundamental quantum of which it is a multiple, suggests that the limitation is not in the molecule.”

The visitor smiled.

“I have read that Sir John Herschel once compared atoms to manufactured articles, because of their close similarity. Now it seems that we must think of energy likewise. Nature coins quanta and multiples of quanta, and it is against the law to clip or debase the coinage.”

“Yes,” said the scientist. “A quantum seems to be indivisible.”

“Just as it used to be thought the atom was.”

“Your point is well taken,” answered the scientist. “But up to the present we have no experimental evidence requiring us to assume the contrary.”

“Well,” said the visitor, “to return to my original question, what is a quantum? If we magnified a light wave sufficiently what would we see?”

“It is no more possible to magnify a light wave sufficiently to perceive its structure than to magnify matter enough to see the molecules; but if we could sufficiently enlarge an advancing front of a light wave it would probably appear as a lot of bright specks on a dark background.”

“That rather suggests Newton’s corpuscular theory of light.”

“Quite so, except for the important difference that each quantum is vibrating with a certain definite frequency.”

“And what is it that vibrates? What is a quantum?”

“Nobody knows. Some have thought it to be a little train of waves, something like a dart; others have pointed

out that it is more probably a three-dimensional affair. We have no more idea of what a quantum is than we have of the nature of an atom; and, as you know, our concept of an atom is a good deal like a moving picture.”

“Three dimensional?” said the visitor. “How big is a quantum?”

“That question has been asked by others. The answer seems to depend on the direction by which we approach the question. For instance, a quantum of light must enter the eye as a whole to excite vision. Less than a quantum will not do. And yet, from astronomical considerations, a quantum of starlight must have about the dimensions of a barrel.”

“And all that has to get into the pupil of the eye? That is something like packing the genie into a bottle.”

“We frequently encounter contradictions of this sort in the early stages of scientific thinking about any subject. It indicates usually that our ideas are as yet incomplete and fragmentary. We must attain a broader and more general concept, of which these contradictory pictures may be seen to be special cases.”

“The philosophers of old,” remarked the visitor, “used to say that Nature makes no jumps; but what with atoms and quanta it begins to look as if discontinuity was the first law of Nature.”

“There is a curious consequence of this discontinuity,” said the scientist, “which probably you have not heard of. Suppose that you took a pocket full of pennies and went to visit an orphan asylum, and on your arrival found that there were more children than pennies. Even allowing only one cent to each child some would have to go without. But perhaps you see what I am coming to,” said the scientist, breaking off as the visitor began to smile.

“Not exactly,” said the visitor. “But I can see that for ‘children’ we must read ‘molecules’ and for ‘pennies’, ‘quanta of energy.'”

EXACTLY,” said the scientist. “We have a pretty good idea of the energy value of a quantum just as we have of the size and mass of a molecule, though we can not tell just what either looks like. And it works out in this way: the total heat energy in a body may consist of fewer quanta than the number of its molecules. This is possibly the case in red hot iron. It is a curious thought that in such a body there may be molecules here and there as devoid of energy as if the whole body were at absolute zero.”

“Poverty and riches rub elbows among molecules as with men,” said the visitor. “Very human little fellows, these.”

“Perhaps,” said the scientist, “the molecules of which we are made up might view the matter oppositely, and with more reason.”

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