Alice in Quantumland: An Allegory of Quantum Physics

by Robert Gilmore

  She commented on this to her companion, and he replied, "That is alpha particle clustering that you are describing. An alpha particle is a group of two protons and two neutrons which will bind together so tightly that they act as one particle. As it contains two protons the alpha particle is repelled by the overall positive charge of the protons and is trying to escape, but is prevented by the wall around the nucleus. The group is trying to tunnel out. They are planning to escape by barrier penetration, and sooner or later, of course, they will succeed."

  "How long is it likely to take them to manage it?" asked Alice curiously.

  "Oh a few thousand years, I should think."

  "Don't you think it is a bit premature to sound the alarm then?" inquired Alice. "It sounds to me as if you have plenty of time to deal with such an escape without having to panic!"

  "Ah, but we cannot be sure of that. It will probably take them thousands of years to escape, but they might get out at any moment. There is no way of being sure; it is all a matter of probability."

  "Are all escapes from the Nucleus by barrier penetration then?" asked Alice.

  "Not at all. Alpha emission is by barrier penetration, as I have just stated. We also get beta and gamma emission, and neither of those requires barrier penetration."

  "What are they, then?" asked Alice dutifully. She suspected that she was about to be told whether or not she asked, but it seemed more polite to inquire.

  "Gamma emission is photon emission, much as you get from the electrons in the atom. When an electron has been excited to a high state and then drops back to a lower one, it will emit a photon to carry off the energy released. The same thing happens when an excitation of the nucleus rearranges the charged protons: A photon is emitted when the nucleus returns to the state of lower energy. Because the interaction energies in the nucleus are so much greater than in the atom generally, the gamma photons have much higher energy than those from the atomic electrons. Indeed they will have some hundred thousand times more energy, but they are still photons.

  "Beta emission is the emission of an electron from the Nucleus," her informant continued.

  "I thought you said that there were no electrons in the Nucleus," protested Alice. "You said that the electrons were not aware of the strong interaction and just drifted through occasionally."

  "That is quite true. There are no electrons in the Nucleus."

  "If the Nucleus cannot hold electrons and there are no electrons in the Nucleus," said Alice patiently, "how can one escape from it? That does not make any sense. It cannot escape unless it is there to begin with."

  "It is because the Nucleus cannot hold electrons that they do escape from it so readily. The electrons are produced right inside the Nucleus in a weak interaction, and, of course, as the Nucleus cannot hold them they immediately escape. It is quite straightforward when you think about it," said the neutron kindly.

  "That may be," said Alice, who felt that it was not at all clear yet, "but what is a weak interaction? How do the electrons... ?"

  Once again a trumpet sounded and a herald somewhere in the top of the chamber cried out. "Attention everyone. The Castle is under attack! We are besieged by a hot plasma of charged particles."

  "Oh dear!" cried Alice. "That sounds serious."

  "No, it isn't really," replied a nearby neutron soothingly. "None of the charged particles in the plasma are likely to have enough energy to breach our defenses. Come and see."

  He led Alice up through the various galleries and energy levels within the Castle until they came to a position from which Alice could view the outside. She saw other nuclear castles in the distance and, spread across the plain, a number of protons moving quickly around. "Those protons are from a hot hydrogen plasma," Alice's companion told her. "In a plasma the atoms have lost some of their electrons and become positive ions with an overall positive charge. The nucleus of hydrogen contains only a single proton, so when a hydrogen atom loses its electron there is nothing left but a proton. Plasmas can be made very hot, and then the protons rush about with a lot of energy, but not enough for them to break in here," he finished complacently.

  Alice watched as some protons came running toward a nucleus and on up the curving base of its wall. As they rushed upward they moved more and more slowly as they lost their kinetic energy, eventually coming to a halt a short way up the wall. From that point they slipped back down again and rushed off in a different direction than that from which they had come.

  "You will see, even if I can't, that they are having no success at all at actually getting inside," continued Alice's guide.

  "Could they not get in by barrier penetration then?" asked Alice.

  "Well, yes. They could in principle, but they spend so little time near the Nucleus that it is really most unlikely."

  At this point Alice noticed a disturbance in the distance. Something was getting closer at a most remarkable speed. "What is that approaching?" she asked, rather anxiously.

  "I have no idea," answered the neutron. "Is there something approaching?"

  Alice realized that the neutron would naturally be unaware of the approach of the fast charged particle as it came galloping up, with plumes of scarcely seen virtual photons trailing from it in its whirlwind passage. As Alice was describing its appearance to the neutron, the newcomer arrived at a Castle in his path. With little apparent reduction in his mad onward rush, he ran up the barrier wall and over the top. A moment later Alice saw him galloping off into the distance, apparently little affected by his encounter. She could not say the same for the Nucleus he had entered. This had burst completely asunder, and large portions of it were flying off in different directions. Alice completed her description of the event.

  "Ah, that would be a Cosmic Ray-der. We very occasionally get one passing by. They come from somewhere way outside our world and they have enormous energy. To them the energy needed to cross the coulomb barrier of a Nucleus is as nothing and it presents no barrier at all. We have no defense against them, but fortunately they are, as I said, very rare."

  Looking down on the area outside Alice could make out a few unobtrusive figures moving quite slowly and stealthily about. "Oh look!" she cried, forgetting who her companion was. "There are some neutrons moving about out there."

  "What?" cried the neutron by her side. "Are you sure? This is serious. Come, we must get down to the main hall at once."

  He rushed Alice back down through the successive energy levels to the hall she had first entered, ignoring her protest that there had not been very many neutrons outside and that they had not had much energy at all, really.

  Hardly had they arrived when, without warning, an invading neutron popped right through the wall and landed in the middle of the chamber, on top of all the other particles. This was not one of the normal occupants of the Nucleus, but one of the foreign neutrons which had come in from outside. Alice remembered that the virtual photon had told her how the coulomb barrier had no effect on neutral particles and how she herself had come in through the barrier without difficulty. In the same way this neutron had entered uninvited.

  There was immediately a great bustle and panic among all the nucleons. They rushed to-and-fro in consternation, surging from one gallery to the next, calling out that the stability of the nucleus had been totally upset by the addition of this excess neutron. As they surged to-and-fro, Alice was much alarmed to discover that the whole room was shaking violently in sympathy. The massive stone walls were quivering like a vibrating drop of liquid. One moment the chamber would be square and compact, the next it would stretch out very long and thin. A narrow neck formed in the middle close to where Alice was standing, so that the room was almost separated in two. Back and forth the walls swung, and each time the room became narrower and narrower at the midpoint. The room stretched out for a last time. Alice saw the far walls rushing away in opposite directions while the nearer walls came closing in as if they were going to crush her and the particles which were in her vicinity. Previously
the movement had always reversed before the gap closed, but this time the walls clashed together, just where Alice was standing together with a few neutrons.

  When the walls had moved through her, Alice found that she was back on the plain outside the Castle. She looked back toward it and saw that the tall, dark tower was split by a fissure which ran all the way down its middle. As she watched, the Castle was torn into two half towers, which slumped apart. Each one was shaking violently, its outer surface vibrating wildly like a bag full of jelly. High-energy photons soared from the two castles like some dramatic fireworks display as both of them shed their surplus energy. Gradually the shaking died down and both the irregular shapes flowed into the same tall soaring shape which she had first seen. Two smaller replicas of Castle Rutherford now stood before her, except that they did not stand but slid rapidly away from one another, driven by the positive charge which they had previously shared between them.

  "Come, I am glad that is over. It was really rather frightening," Alice admitted to herself. As she looked around the now quiet landscape she could see a few neutrons which had been ejected with her from the Castle when it had split in two. They spread out over the plane, rushing off in random directions. As she watched, one arrived by chance at the distant shape of another nuclear castle and promptly dived into it through its side.

  For a short time nothing appeared to happen. Then she could see this castle also begin to shake. The shaking increased until suddenly the castle split down the middle. "Oh no!" cried Alice in dismay as she saw the two halves thrust apart, spitting out energetic photons. Almost unnoticed, a fresh group of neutrons ran away from the scene of the catastrophe.

  Before much time had passed, a couple of the neutrons which were now roaming aimlessly around the plain had chanced upon and entered other nuclei. Again the process repeated, ending once again with these nuclei splitting, more gamma photons pouring onto the scene, and more neutrons being ejected to roam around in confusion. Again and again the process was repeated. Soon there were four nuclei all in the pangs of separation, then ten, twenty, fifty. All around her, Alice could see nuclear castles falling apart in fiery fission, while overhead the scene blazed with the intense, vivid radiation of high-energy photons.

  "This is terrible!" cried Alice in horror. "Whatever can be happening?"

  "Do not worry, Alice," said a calm voice by her side. "It is only induced nuclear fission. A chain reaction, you know. It is nothing for you to worry about. It is just that you are standing in the middle of what, in your world, would be called a nuclear explosion."

  Alice whirled around and saw the mild features of the Quantum Mechanic. "You do not have to worry," he said again. "The energies involved in a fission reaction are less than those you have already met within the Nucleus itself. The only problem is that they are no longer confined within the Nucleus. I have been looking for you," he continued, still calmly, "as I have an invitation to give you."

  He presented Alice with a stiff, ornately engraved invitation card. "It is an invitation to the Particle MASSquerade, a party which is being held for all the elementary particles," he said.

  Notes

  1. Almost everything in the physical world may be seen as caused by the interplay between electrons and photons, virtual or otherwise. The properties of solids, of individual atoms, and of the chemical behavior which comes from the interplay between atoms, all reduce to an electrical interaction between electrons. As well as the electrons which interact with the rest of the world, there is within the atom a positively charged nucleus. The nucleus is not held together by electrical forces, quite the reverse in fact.

  The atomic nucleus contains neutrons, which have no electrical charge, and protons which are positively charged. Within the small space of the nucleus, whose radius is typically a hundred thousand times smaller than the overall size of an atom, the mutual repulsive force of the protons is enormous. This electrical force tends to tear the nucleus apart, so there must be an even stronger force which holds the nucleus together, one that, for some reason, is not evident elsewhere. Such a force exists, and it is called the strong nuclear interaction. Although it is strong, it has a very short range, so that its effects are not obvious outside the nucleus. This strong interaction is produced by the exchange of virtual particles, just as the electrical interaction is produced by photon exchange. Photons have no rest mass, but the exchanged particles in the strong interaction are relatively heavy. They must get their rest mass energy through a particularly large quantum fluctuation, which is only possible for a very short time. Such heavy virtual particles are very short-lived and unable to travel far from their source, so that the interaction they produce is consequently of short range.

  lutching her invitation, Alice climbed up the broad stone steps which led to the tall polished door. She could not remember how she had come to be there, though she remembered being given the invitation. "So I expect this is probably the right place for the MASSquerade, whatever that may be," she said to herself encouragingly. "I always seem to end up somehow where people want me to be."

  She stopped outside the door and examined it. Its paint was very smooth and glossy, deep red in color. It had a shiny brass doorknob and an equally shiny brass knocker in the shape of a grotesque face. It was also closed and locked. Cheerful candlelight streamed from the keyhole and Alice could hear loud music being played within.

  How was she to enter? The answer seemed obvious enough, so she firmly grasped the knocker and hammered loudly.

  "Ow! Do you mind!" exclaimed an anguished voice from close at hand. Literally at hand, in fact. Alice stared in surprise at the door, to meet the furious glare of an irate door knocker.

  "That was my nose!" it exclaimed indignantly. "What do you want anyway?"

  "I am really sorry," said Alice, "but I thought that, as you are a door knocker, I might use you to knock at the door. How am I to get in if I do not knock?" she asked plaintively.

  "There's no use in knocking," said the knocker huffily. "They are making such a noise inside no one could possibly hear you." And certainly there was a great deal of noise going on within: a buzz of conversation, a louder voice speaking above the rest, but still not quite audible through the door, and, above it all, the sound of the music.

  "How am Ito get in then?" asked Alice, in some frustration.

  "Are you to get in at all?" said the door knocker. "That's the first question, you know."

  It was, no doubt, but Alice did not like to be told so. "It is really dreadful," she muttered to herself, "the way everyone will argue so." Raising her voice she addressed the knocker, though she felt a little self-conscious in talking to a door knocker at all. "I have an invitation," she said, holding it up in front of his face.

  "So I see," replied the knocker. "That is an invitation to the Particle MASSquerade, which is a function for particles only. Are you a particle?"

  "I am sure that I don't know," declared Alice. "I did not think that I was, but with all the things that have happened to me, I am beginning to feel that I must be."

  "Well, let me see if you meet the requirements," said the knocker, rather more agreeably now that its nose felt recovered. "Let me just look at my notes for a moment." Alice did not see how a door knocker could keep notes, let alone look at them, but after a short pause the knocker continued. "Ah, yes. Here we are. The list of specifications to define a particle."

  "One," it read out. "Whenever you are observed, are you invariably observed in a reasonably well-defined position?"

  "Yes, I think so, as far as I know," answered Alice.

  "That's fine," said the knocker encouragingly.

  "Two. Do you have a unique and well-defined mass―apart from the normal fluctuations, of course."

  "Well, yes. My weight has not changed very much for some time." That was what Alice believed, at any rate.

  "Good, that is a very important requirement. All the different particles have their particular masses. It is one of their most distinctiv
e features and very useful when it comes to telling one particle from another." Alice was rather taken with the notion that people might be identified by weighing them rather than looking at their faces, but she realized that particles did not on the whole have anything very definite in the way of faces.

  "Three. Are you stable?"

  "I beg your pardon?" said Alice, feeling distinctly affronted.

  "I said, 'Are you stable?' It is a simple enough question. Or at least it ought to be: The requirement has become increasingly blurred recently. It used to mean quite simply, 'Do you decay to something else?' If you were likely to decay at any time in the future, then you were unstable, and that was that. But that wasn't good enough! People started to say, 'We cannot be sure that anything lives forever, so a distinct state that exists for a long enough time can be classed as a particle.' Then the question is, 'What counts as long enough?' Is it years, or seconds, or what? At the moment they accept lifetimes of less than a hundred million millionth of a second as being stable," he finished disgustedly. "So, I must now ask you: Do you expect to survive for longer than a hundred million millionth of a second?"

  "Oh yes, I should think so," answered Alice confidently.

  "Good, then I can count you as a stable particle. You had better go inside. You may not have anything better to do than stand about out here, but I have," grumbled the door knocker. There was a click and the door swung open. Alice lost no time in passing through it.

  Inside she walked through an elegant entrance hall, with pale paneled walls, chandeliers, and alcoves containing statues. As they were all statues of notable particles, it was rather difficult for Alice to make out much detail. She thought it was rather clever the way the sculptor had managed to make the features of a statue appear so vague and unlocalized. In fact, to the uninitiated, they looked much like shapeless pieces of stone.