Alice in Quantumland: An Allegory of Quantum Physics

by Robert Gilmore

  It was a really beautiful sight, if rather peculiar. The virtual photons were moving in every way conceivable, while some photons seemed to have mastered the art of traveling from one position to another without actually requiring any time to elapse between the two events.

  As Alice was watching this strange scene with interest, the helmet emitted a whirring noise beside her ear, followed immediately by a loud "clunk." The view in front of her shimmered and returned to the mundane view she had seen before she put on the helmet. Alice exclaimed aloud in annoyance at losing the fascinating picture. "I am sorry," said the Agent. "I am afraid that there is a timer built into the mechanism. I had intended to make it coin-operated, you see."

  Alice was still too much enthralled by the vision she had just been watching to pay much attention to the Agent's apology and tried to describe to him what she had seen. As with all the people she had met in this odd world, he immediately began a lengthy explanation.

  "That is just another aspect of the way that virtual particles do things which real particles cannot. It is a bit like barrier penetration in a way. I expect you have seen some cases of barrier penetration by now."

  "I was told that I had," answered Alice carefully. "I saw someone penetrate through a door when I first came here and I was told that he could do this because his wave function spread into and through the door, to give a small probability of his being observed on the other side."

  "That is quite true. That part of his wave function allowed your friend to penetrate into a barrier which would have stopped a real classical particle. He did not have enough energy to cross the barrier, so when he was penetrating the door he was in a sort of virtual condition. There are very few particles, if any, which are entirely real. They almost all have some virtual aspects, though some are more virtual than others. The exchange photons you have just been looking at are almost totally virtual.

  "It is the general rule that virtual particles do not obey the rules, even though they cannot manage to escape them for very long. This means that they can do things for which they do not actually have enough energy. These exchanged virtual particles, such as the photons you saw, produce interactions between other particles. They can penetrate through barriers which would stop a real classical particle, and this includes the barrier of time itself. They can move in a spacelike way, while real particles can only be timelike. This means that, although a real particle can sit at the same position while the time changes, it is unable to sit at the same time while its position changes. A virtual particle is able to do both. It can move sideways in time if it chooses."

  "That sounds very curious indeed," said Alice. "I am not surprised that real particles are unable to do that and that they only move from the past to the future."

  See end-of-chapter note 2

  "Well, actually that is not quite true," said the Agent a little apologetically. "It is certainly true that most particles move forward in time, just as you suppose. However most particles become a little virtual on occasion, during collisions for example, so it is possible for a real particle to revert. One moment it is moving forward through time in a respectable, lawabiding way. The next moment it finds that it has been quite turned around and that it is moving backward toward the past. Though it might surprise you to hear me say so, this is an allowable way for a real particle to behave."

  "Oh!" cried Alice suddenly, startling the Agent in the middle of his careful description. "I think that must have been what happened to me earlier. I could not imagine what had become of me when I was walking through the park and everything seemed to reverse around me, but now I see that it was not the stream and the butterflies which were going backward. It was I who was traveling backward in time!"

  Alice told her companion all she could remember about the incident, and he agreed with her interpretation. "It certainly sounds to me like a clear case of antiparticle production," he said.

  "Antiparticle!" exclaimed Alice. "I did not know that this had anything to do with antiparticles. I remember seeing them at the Heisenberg Bank, but I do not understand why they should have anything to do with the present case."

  "I would have thought it was obvious," said the Agent, though Alice did not feel it was in the least obvious. "Why, don't you see that when a particle moves backward in time it appears to an onlooker to be something totally opposite, moving forward through time in the normal way. Take the case of an electron. It has a negative electric charge, so when it moves from the past to the future in the normal way it carries its negative charge into the future. If, on the other hand, it moves from the future into the past, then it carries this negative charge from the future to the past, which is like a positive charge going from the past, to the future. Either way it is making the overall charge in the future more positive. It looks to an outside observer like a positron, or antielectron.

  "What happened to you would have appeared to the rest of the world as an unusually high-energy photon giving up its energy to create an Alice and an anti-Alice. The anti-Alice would travel along until it collided with an Alice and the two mutually annihilated one another, converting their energy back to photons."

  "How can that be?" cried Alice in some dismay. "I do not see how this anti-Alice could ever have found a second Alice to collide with anyway. There is only one of me and I certainly haven't been annihilated," she concluded defiantly.

  "Ah, but what I have just described is how it would appear to the rest of the world. How it would appear to you is quite different, quite different altogether. For you the annihilation would come before the creation of course."

  "I do not see any 'of course' about it," answered Alice rather sharply. "How can anything be destroyed before it is created?"

  "Why, that is the natural order of things when you are going backward in time. Normally, when you move forward in time you expect creation to come before destruction don't you?"

  "Yes, of course I do," replied Alice.

  "Well in that case, if you move backward in time you naturally expect the creation to come after destruction from your point of view. You are experiencing events in reverse order after all. I would have expected you to see that for yourself.

  "In this case you were walking quietly along with the Quantum Mechanic and suddenly you collided with the anti-Alice. As far as your companion was concerned you and the anti-Alice were both utterly destroyed and your mass energy was carried off by high-energy photons."

  "Oh dear! The poor Mechanic," exclaimed Alice. "He must believe that I have been destroyed then! How can I find him to set his mind at rest?"

  "I shouldn't worry too much about that," the Agent assured her. "Naturally, the Quantum Mechanic knows about antiparticle annihilation, so he will know that you have simply gone back in time. He will no doubt expect to bump into you later, or perhaps earlier, depending on how far back you went. Anyway, the annihilation process converted you to an anti-Alice and you traveled backward in time until you were created, together with an Alice, by a high-energy photon. That is how it would have seemed to any onlooker. To you it just appeared that suddenly you were no longer traveling back in time, but had started to move forward as normal. You would not have seen the photon which caused this. You couldn't because it ceased to exist at the instant when you reversed your passage through time, so both as Alice and anti-Alice you were in a future which it never reached.

  "You see now that, although anyone looking on would say that for a time there were three of you, two Alices and one anti-Alice, in fact they were all the same you. Because you had gone back in time you were living through the same period that you had already lived through as you walked along with the Quantum Mechanic. When you were returned to normal by the pair-creation process, you lived through the same period for a third time, now once again moving forward in time.

  "That part of your life was rather like a road which zigzags up the side of a hill, climbing first to the east, then doubling sharply back to run toward the west before turning to the east agai
n. If you climbed due north up the side of such a hill you might think that you crossed three different roads, while in fact you would have crossed the same road three times. It is the same sort of thing with antiparticle production. The antiparticle is a section of the road which goes the other way."

  At that point there was a faint buzzing from the helmet and a small green light glowed in the corner of the visor. "I think the helmet is sufficiently recharged for another demonstration," said the Agent. "If you look carefully this time you should be able to make out some of the secondorder effects."

  He adjusted the side of the helmet, and once again the view clouded over....

  The view cleared again to reveal that the landscape everywhere was strung together by an all-pervading net of photon lines. When Alice looked more carefully at one particular region, she could see that a few of the bright links were interrupted. In the middle of a shining photon strand she could see a sort of loop, where the photon changed in midposition into what she could just recognize as an electron and a positron, an antielectron. These two combined together again almost immediately to form a photon strand which went on to attach itself to a real electron.

  Peering still more closely, Alice could see another photon faintly issuing from the electron in the loop. Partway along the path of this photon she could see the dim outline of another electron-positron loop. From this emerged even fainter photons, and, if she peered really closely, she could just make out faint electron-positron loops along these. As far as she was able to distinguish she could see photons creating closed electronpositron loops and electrons or positrons emitting photons which created more electron-positron pairs. This went on and on, in apparently infinite profusion, but becoming fainter and fainter with each extra stage of complexity. Alice was becoming quite dizzy as she strained her eyes to try and see some end to this sequence. Finally an end came. She heard the whir and clunk from the helmet, and the entire pattern vanished from her sight.

  "I thought that you said that electrons were joined by photon exchange," she said in a rather accusing tone. "I am sure that I saw electrons among the virtual particles. Quite a lot of them in fact."

  "Oh yes, you would. The original real electrons act as the sources of the electric field, though it is more correct to say that the electric charges carried by the electrons are what produce the field. Photons do not really care about anything but electric charge, but wherever there is such a charge you will always get a cloud of virtual photons hanging about it. If another charged particle comes by, these photons are available to be exchanged and to produce a force between the two particles. Exchanged particles have to be created in order to be exchanged and they are destroyed afterward when they have been captured. Their number is obviously not conserved, so they have to be bosons.

  "The relationship between photons and charge works both ways. Just as charged particles produce photons, so photons would like to produce charged particles, but they cannot produce just one charged particle because the amount of electric charge present is not allowed to change. That is another of the rules, and one that does not allow any uncertainty. What the photons can do however is to produce both an electron and an antielectron, or positron, at the same time. Since one has a negative charge and the other a positive one, the total charge in the universe has not changed. That was what you saw. The virtual photons produce virtual electron-positron pairs, which annihilate one another and return to being a photon. During the brief life of the pair, however, since they are both charged particles, they may produce more photons; those photons may produce more electron-positron pairs, and so on."

  "My goodness," said Alice. "It does sound excessively complicated. Where does it all end?"

  "Oh, it doesn't. It goes on like that forever, getting more and more complicated. But the probability of an electron producing a photon, or of the photon producing an electron-positron pair, is rather small. This means that the more complicated amplitudes are weaker and eventually they are too weak to be noticeable. You must have seen that."

  "Well," said Alice, whose head was spinning as she tried to follow what she had just observed and been told, "all I can say is that I have seen nothing like it before."

  "You may well have done so," returned the Agent. "What you have just seen is like Nothing anywhere else. Though I am a little surprised that you have managed to see Nothing before you came here."

  "I am sure that I wouldn't say that," replied Alice indignantly. "I may not have traveled very much, but I have still seen something, I would have you know."

  "I have no doubt that you have," said the State Agent. "I am sure that you came from a very desirable location, but it is relatively easy to see Something, you know. It is much more difficult to see Nothing. I do not know how you could have done it without the aid of my virtual reality helmet."

  "Just a minute," interrupted Alice, who had begun to suspect that they were talking at cross-purposes. "Would you tell me please what you mean by Nothing?"

  "Why yes, certainly. I mean Nothing: the complete absence of any real particles whatever. You know: the Vacuum, the Void, the oblivion of all things, whatever you like to call it."

  Alice was quite taken aback by the extent of this negative concept. "Would that look any different through your helmet? I should have thought that Nothing would look like nothing however you looked at it."

  "Why, of course it makes a difference. The void is not the best neighborhood, perhaps, but there is plenty of undercover activity. Come and see for yourself."

  The Agent set off at a smart pace and Alice followed him across the floor of his office. It was becoming increasingly difficult for her to believe that they were still inside an office, or a building of any sort, for it seemed remarkably large. They walked for some time, with Alice struggling under the weight of the helmet and of the cable which was still stretching out behind her. "I wonder how long this connection can be," she said to herself. "I am sure I must come to the end of it soon."

  The Periodic Mansions, in which she had watched the electron states, were soon out of sight behind them, and still they marched on. Just as Alice was about to beg that they stop for a rest, she saw ahead of them what looked rather like the shore of a lake, or of a remarkably calm sea. As they came closer she could see that it was a very large lake, that is, if it was a lake. It stretched ahead of them as far as she was able to see, an apparently limitless expanse. But if it was the sea, it was the strangest seascape that Alice had ever seen. It was very calm, completely and utterly still apart from a faint, hardly seen, quivering around the surface. It was not blue, or green, or wine-dark, or any other color Alice had heard used to describe water. It was completely without color. It was like a deep, clear night but without the stars.

  "What is that?" gasped Alice, overcome by the eye-devouring emptiness of the sight.

  "Nothing," replied the Agent. "That is Nothing. It is the Void!"

  "Come now," he continued. "Let me switch on the helmet, and you may observe the activity in the Void."

  He reached out to the helmet and once again did whatever he had done before. Alice's view, her view of Nothing, clouded over....

  Her view cleared to reveal a scene very similar to the last one she had seen through the helmet. Once more she saw a mesh of glowing strands. This time, however, she did not see the strands ending on the real electrons, which before had seemed to be trapped in the web but were in reality its source. Now there were no real particles present, only the virtual ones. Photons created electron-positron pairs. Electrons and positrons produced more photons, just as she had seen before. Previously the network had originated from the real electrons, which were its source and anchor in the world of real particles. Where was its source now? The electron-positron pairs were produced by the photons; the photons were produced by the electron-positron pairs, which were produced by the photons. Alice tried to trace back along the lines of particles to find their source, but she found that she was going around and around in circles. She felt
that she must have lost her thread and was trying again to follow the lines more carefully when she heard the familiar buzzing and the loud clunk, and the whole scene vanished.

  Alice once more explained what she had seen to the Agent and told him how she had been unable to decide which particles had been creating which others. "I am not surprised," replied the Agent. "They all create one another, you know. It is a chicken and egg situation, with them all laying and hatching at the same time."

  "How can that be?" asked Alice. "There must be a source. They cannot have come from nowhere."

  "I am afraid that they can and they have," was the answer. "All that prevents particle-antiparticle production normally is the need to provide energy for the particles' rest mass, and virtual particles are not even inhibited by that. The whole thing is a great big quantum fluctuation."

  "Is it real then?" asked Alice. "Are all those particles really there at all."

  "Oh yes, they are quite real, even if not in the technical sense of real particles. They are just as vital a part of the world as anything else. I should think, though, you have now seen as much through the helmet as you need," he continued and lifted the heavy device from Alice's head. "We shall not be needing it any more, so I shall engage the cable rewind mechanism." He touched a button on its side and the helmet began to rewind itself along its cable, scuttling over the ground in the direction from which they had come, like a mechanical spider, until it vanished from sight.