Alice in Quantumland: An Allegory of Quantum Physics

by Robert Gilmore

  "What's a Not-a-Quark?" asked Alice.

  "An anti-Quark. And if you believe that, you should see my uncle. Part of the original string has vanished rapidly into the distance, carrying off the energy and connecting the absent Strangeo to the new antiQuark. So, you see, absence makes the part go yonder."

  "He may have escaped, but he still isn't free," protested Alice.

  "With a bound he was free. He is free of us now, but he is still bound. With his anti-Quark he is bound into a boson. That's like a pion, but pions can be deceiving and in this case they have formed a kaon instead. You do not see a free Quark-or even free a Quark sea, but that's another kettle of fish."

  "Are the fish in-a the Quark sea?" asked Downo.

  "No, there's nothing fishy about the Quark sea. Its sole purpose is to hold virtual Quark-Antiquark pairs."

  "The sole I understand, and the porpoise I understand, but why the pears in-a the sea?" argued Downo.

  "Forget the sea," replied Uppo, "or we will all be at sea. The point is that you will never find a Quark on his own."

  See end-of-chapter note 3

  "Does that mean that you have to stay here forever with no chance of a change?" asked Alice in concern.

  "Oh, we can have a change all right. They say a change is as good as a rest, but I feel quite at liberty to discuss the weak interaction."

  "I heard that mentioned when I was visiting the Nucleus. I believe it had something to do with beta decay of nuclei, whatever that may be."

  "It is the same thing. In fact it is a far, far beta thing. What happens is that a neutron inside the Nucleus changes into a proton and an electron, together with another particle called a neutrino. This neutrino has no charge, no mass, and no strong interaction. It doesn't do much of any thing really, like most of the folk I know. Anyway, that's the story we tell. What really happens is that a down Quark inside the neutron changes to an up Quark, an electron, and a neutrino. When the down Quark changes to an up Quark, then everything is on the up. It puts the charge up, the neutron becomes a proton, and there you are. Hang around, and you might get lucky."

  Hardly had he spoken when, by a most convenient coincidence, one of the two Downos became blurred and began to change and lose his identity. After a fleeting moment of transition, Downo was no longer there and in his place stood a duplicate of Uppo. As he moved aside, Alice saw an electron rush away from the same spot. This was followed by yet another particle. Alice caught only the briefest glimpse of this one, something barely perceived and very hard to see at all. This she assumed to have been the neutrino, performing its usual role of ignoring and being ignored by everything and everybody.

  The group of three Quarks now consisted of one Downo and two identical Uppos. Identical, that is, but for the fact that one was currently green and the other blue. "My," said Alice. "That was a most remarkable thing altogether."

  Obediently the two Uppos replied, in perfect unison, "That was a most remarkable thing."

  "But what can you expect," they added, "when the particles exchanged in an interaction have an electric charge? Photons don't have a charge, but this isn't the Charge of the Light Brigade. When a source emits one of these charged particles, it has to share the charge. There are no fluctuations allowed there, you know. When the particle's electric charge has changed then it counts as a different particle. You must have heard of charge accounts. That is how we Quarks get to change," they added.

  "But where does the electron come from?" asked Alice, who felt that the explanation was a little lacking.

  "The particles exchanged in the weak interaction are called W," began Uppo rather inconsequentially.

  "What?" responded Alice, temporarily forgetting her manners. "Not 'What,' just W. It is not much of a name, but it is all they have, poor things. There are two of them, you know: One is W Plus, and one is W Minus. No one has ever asked them what the W stands for," he finished thoughtfully. "Anyhow," he continued, "these W's, as their friends call them, are very friendly types. They will mix with anyone. They interact with both leptons and hadrons, with electrons as well as strongly interacting particles. So when a down Quark decides it is time to change into an up Quark, it gets all charged up. The electric charge of the Quark has increased, so it gives out a W Minus particle to balance the books. This W in turn plays it by the book and interacts with a passing neutrino, which has no electric charge at all, turning it into an electron, which does have an electric charge. The electron finds itself in company with a lot of strongly interacting particles, where it has no right to be, and leaves as rapidly as it can."

  See end-of-chapter note 4

  "But where does the W find a neutrino which it can change into an electron?" asked Alice in some puzzlement. "I didn't think there had been a neutrino there before. I thought that it was emitted after the decay, along with the electron."

  "Ah, that is where it fools you. You thought it should be there before, but instead it was there after. You are expecting it to arrive from the past, so it sneaks up on you, back from the future, and still arrives just when it is needed. Of course, because it came from the future, it is still around afterward, on its way to arrive. In this way it gets to be both the neutrino converted by the W and the one emitted after the decay. That cuts down on the overheads."

  "But how can it arrive from the future?" asked Alice. As she spoke she had a distinct feeling that she already knew the answer to this question.

  "It is an antineutrino, of course. One of my favorite anti's. Every particle has its antiparticle, which travels backward in time and so is opposite in every way. That's the great principle of antiparticles-' Whatever it is, I'm agin it."'

  "And is there no way any of you can ever get free?" asked Alice, to be quite sure on this point.

  "No, no way at all," they assured her.

  "Does that mean that I cannot escape either?" asked Alice in dismay, as she did not really wish to be trapped with them forever. "Not at all. You have no color so the gluons don't hold you. You are one of the most colorless people we have ever met, so there is nothing to keep you; you can leave whenever you wish. We won't even notice. You can get up and walk away. Just don't forget to leave a tip."

  This sounded much too simple, but Alice tried it anyway. She stood up and found that indeed there had been nothing to prevent her from leaving the group at any time. She stretched after her cramped confinement in such a small space, looked around her, and found that she was standing face to mask with the Master of Ceremonies. His grinning mask was just a few feet from her face. She stared at him, hypnotized by his wide, fixed grin and the dark eyeholes above. Deep within their black depths where his eyes should have been, she thought she could see an intense blue spark, like a distant star on a clear, frosty night.

  "And how did you enjoy your meeting with the Quarks?" he asked her merrily.

  "It was very interesting," she replied truthfully. "They were most colorful characters, but I did find them rather changeable.

  "Was that the last unmasking that will take place tonight," Alice continued, "or are there further layers to be stripped away before I can see what is really there?"

  "Who can say?" he replied. "How can you ever know if you are finally looking on the naked face of Nature or if you are simply looking at yet another mask? Tonight however there is but one more unmasking to come. I have yet to remove my own mask."

  As he was speaking, the bright spotlight which had followed him all through the evening began to dim, and the light from the chandeliers overhead became even fainter than it had been before. As the light died, the Master of Ceremonies lifted both hands to his face and slowly pulled off his mask.

  In the rapidly fading light Alice looked at the face behind the mask. She could see nothing but a smooth oval, a total blank with no features of any sort discernible. She stared in astonishment at this enigmatic visage, and, as the last gleam of light died, she saw the mask wink at her.

  Notes

  1. The protons and neutrons which in
habit the nucleus (known collectively as nucleons) are examples of strongly interacting particles, also known as hadrons. There are many other hadrons, though not all particles interact strongly. The class of particles which are known as leptons do not feel the strong interaction at all. Electrons belong to this class and so are not bound inside the nucleus together with the nucleons. They are aware of the nucleus only as a positive electric charge which holds them loosely bound within the atom.

  Experiments in high-energy physics have discovered hundreds of strongly interacting particles. This situation presents a fairly familiar scenario in physics. Whenever a class contains a very large number of members, they usually turn out to be built up as composites of something more basic. The various chemical compounds identified are all composed of atoms. There are 92 naturally occurring varieties of atoms that are stable, and they are all composed of electrons arranged in differing numbers around a central nucleus. Nuclei in turn are composed of neutrons and protons bound by the ex-change of pions. These are mentioned in the previous chapter. Now the neutron and proton are found to be just two members of a class with hundreds of others: Κ, ρ, ω, Λ, Σ, Ξ, Ω, Δ, and so on. These particles have now been shown all to be composed of quarks.

  2. Quarks are held together by forces like, but yet unlike, the electrical interaction. These forces do not act on electrical charge, but on something else which is called color charge or just color. This has nothing to do with color as we normally understand it; it is just a name which has been given to something completely new. The fact that the word color is already in use is perhaps unfortunate, though it is not the first time that a word has had two different meanings.

  The interaction between two electrically charged particles is due to the exchange of virtual photons. The interaction between quarks is caused by the exchange of a new class of particles which have been named gluons. There are differences between the interactions: Electrical charges come in only two forms, positive and negative, or charge and anticharge. The photons which are exchanged between electrical charges are themselves electrically neutral; they carry no charge and so do not emit more virtual photons in their own right.

  The gluons exchanged between quarks are emitted by a form of charge carried by the quarks, but completely different from the normal electrical charge. It is called color charge, though it has nothing whatsoever to do with the colors that we can see. While there is only one form of electrical charge, together with its opposite, or anticharge, there are three different forms of color charge, given the names blue, green, and red. Again it should be stressed that these names are just conventions and have nothing to do with ordinary color. Associated with each color charge there is an anticolor, and there are two ways of producing color-neutral objects. With electrical charge you can only produce an electrically neutral object by combining charge and anticharge (positive and negative charge). There are two ways to produce color-neutral particles: a combination of color and anticolor (as in bosons) or a combination of all three colors of quarks (as in fermions).

  3. When particles are bound together by the electrical interaction, the potential energy in the binding decreases rapidly as they move far apart. If a particle is given enough energy, it can break free completely, as a rocket which has reached escape velocity has then enough energy to break free of the earth's potential. When a gluon string has already been stretched, however, it takes just as much energy to stretch it a little farther as it did initially. It is like stretching an elastic string; it does not get any easier the farther you stretch it. It is also like an elastic string in that, when you stretch it, it can break.

  The gluon string is capable of absorbing more and more energy as the quarks separate and the string stretches. Eventually the energy in the string is more than is necessary to create a quark-antiquark pair. The string breaks and its broken ends are terminated on the color charges of the new quark and antiquark. In place of the original bound system of three quarks there are now two separate systems, one of three quarks and one of a quark and an antiquark. Instead of releasing a free quark the energy has created a new particle, a boson. This will always happen and free quarks are never produced.

  4. Though the quarks cannot escape from the "particles" within which they are bound, they can change from one type to another. This is caused by a peculiar process called the weak interaction. The weak interaction is a broad-minded process which will interact with virtually everything. The electromagnetic interaction affects only particles that have electric charge. The strong interaction affects only the strongly interacting particles (or hadrons) and not leptons. The weak interaction will affect them all, though the effect is rather slow and weak because it is a weak interaction.

  The weak interaction is peculiar in that it can change quarks. It can change either a down quark or a strange quark to an up quark. In the process, the electric charge of the quark is changed, with the surplus charge carried off by the "W boson," the type of particle which is exchanged in the weak interaction. This charge may then be handed over to newly created leptons, an electron and a massless electrically neutral lepton known as an antineutrino. This happens in the process of nuclear β decay, in which a radioactive nucleus emits a fast electron. This process had been known for many years, but was odd in that it was quite clear that there were not any electrons available within the nucleus to be so emitted. The electron is created in the decay process and, as it is not bound, leaves the nucleus immediately.

  he darkness slowly cleared from about Alice. The shadows lifted from her eyes, which were immediately dazzled by a chaos of bright lights and colors. At the same time her ears were assaulted by an assertive cacophony of sounds. She looked around her and found that she was in the midst of a merry and diverse throng of people. There appeared to be all manner of folk present, in every kind of dress. She could see that some of them were wearing white coats, such as one imagines scientists to wear in their laboratories, while others in the crowd were dressed in very casual clothes or in formal suits. She could see costumes from countries all over the world and indeed from many different times in the past.

  There were men in Victorian frock coats, with impressive bushy side whiskers, and others in burnooses, or traditional Chinese costume, with wide flowing sleeves and long pigtails. She saw one particularly hairy-looking individual who staggered past dressed in untreated animal skins and carrying what looked rather like a roughly formed wheel, which appeared to have been chipped out of stone. One the side of the wheel the words Patent applied for had been carefully chiseled. One man in particular caught her attention for some reason. She sensed some special quality about him, without being able to pin down exactly what it might be. He had a pale, intense face and was dressed in the breeches, waistcoat, and wide frock coat of the seventeenth century. He was walking along absentmindedly taking a large bite out of a bright red apple.

  "Where am I?" she asked herself, speaking aloud but hardly expecting to be noticed in the hubbub which arose all around her.

  "You are in the Experimental Physics Phun Phair," came the unexpected response. Alice looked to see who had spoken, and found that, once again, she was accompanied by the Quantum Mechanic, who was walking quietly by her side. He indicated a banner stretched across a gateway by which they had, apparently, just entered. It bore the slogan:

  "It does seem to be spelled rather strangely," commented Alice, this being the first thing which struck her about it.

  "Well, what do you expect? They are all scientists here, you know. This is the great carnival of empirical observation. Here you will find many demonstrations of physical phenomena and sideshows of experimental results."

  Alice gazed around her and saw a splendid variety of tents and stalls, with here and there a more substantial looking building. They all carried large, brightly colored posters which vied with one another for the attention of the crowd. She read a few of them:

  There was a disturbance of some sort in the crowd nearby. Alice looked across and saw
a balding bearded man wrapped in what appeared to be a large white bath towel. He was shouldering his way through the crowd, hampered by the fact that he was carrying a large posterboard in one hand and an incredibly long pole or lever of some sort in the other. She peered carefully at the notice he was carrying. At the top, roughly painted out, she could just make out the words:

  Below the erased words she read the modified message:

  "Who is that," asked Alice, "and what is he planning to do?"

  "Oh, that is a well-known Greek philosopher. He is obviously intending to go into his old 'Moving the World' routine."

  "Really?" exclaimed Alice. "Does he often move the world then?"

  "Oh no, he never does. He can never find a fixed place to stand while he uses his lever, you see."

  As this did not appear to offer much immediate entertainment, Alice looked around for something more promising. Her attention was attracted by a stall nearby which bore the name "Photoelectric Canon." There was a sort of stylized gun from which the player could direct a beam of light onto a metal surface. The light caused electrons to be emitted where it struck, and the idea, as explained by the stall's occupant, was to get the electrons to move a little distance to a sort of bucket, where they would be collected. This seemed easy enough to Alice, even when it was explained that, to make things a little more interesting, there was a weak electric field which resisted the passage of the electrons and turned them back just before they reached the collector. After all, as the stall owner explained, there was a control which would allow Alice to increase the intensity of the beam of light to many times its present value. However hard she tried, though, she found that she could not get any of the electrons to travel that last little distance. She turned the intensity of the light higher and higher. More and more electrons came streaming out, but every one was turned back at the last minute by the electric field.