Virtual Reality
The Quantum Mechanic led Alice down the road and through a wrought iron gate into an attractive park. Beautiful flower beds, full with an abundance of assorted blooms, lined both sides of the path, giving a most pleasing effect as they strolled along in the warm summer weather. In the sky the sun shone brilliantly, pouring out its light upon the idyllic scene. Beside the path colorful butterflies flitted from bright blossom to bright blossom and a small stream burbled downhill over a bed of rounded pebbles, while here and there along its path the water poured over a miniature waterfall. Alice thought it all very pretty and was looking around her in delight when she saw another figure approaching on a converging path.
The newcomer was plainly another little girl, but there was something very peculiar about her. She looked somewhat like Alice herself, but she resembled rather more the figure that Alice had occasionally seen in the negatives of her snapshots. Alice was reminded of the antielectrons which she had watched in the Bank. She noted to her surprise that, although the girl was coming toward her, she was facing in the opposite direction and walking along backward.
Alice was so absorbed in the remarkable appearance of this strange girl that she did not consider how quickly they were approaching one another. Before she had fully realized what was happening they had collided. There was a blinding flash which quite took her senses away. When she recovered from this she found herself walking alone down the path along which the other girl had come. Looking back she could see that the reverse-girl was walking away, still backward, along Alice's original path. Now, however, she was accompanied by another negative figure which was companionably walking along backward beside her. This second figure resembled her previous companion, the Quantum Mechanic.
When she looked around her, Alice was startled to discover that her surroundings had altered every bit as dramatically. Everything seemed to be reversed. In the sky the sun glowered darkly, draining the light from the scene below. Beside the path, dull butterflies flitted backward from dark blossom to dark blossom and a small stream burbled uphill over a bed of round pebbles, while here and there the water soared to the top of a miniature waterfall. Alice had never experienced anything like this before.
She was so fascinated by this remarkable scene that she did not observe that once again a small girl was bearing rapidly down upon her in reverse. Alice looked around just as they collided, with yet another blinding flash. When she recovered from her shock, she saw the girl was backing away along the path by which Alice had just come. She noticed furthermore that the scenery had now returned to normal. "Curiouser and curiouser," said Alice to herself. "The first collision somehow managed to make the whole countryside reverse itself, while the second one has put it back to normal. I'm sure I do not see how that could possibly happen. How can my colliding with that girl, however violently, affect the stream and the sun? It does not make any sense at all." Alice continued to debate with herself about the meaning of her recent experience. It had been so very remarkable that she paid hardly any attention when she heard a sharp detonation to one side of her, while shortly after an extremely energetic photon rushed across the path.
Alice had not reached any satisfactory explanation of her recent experience when the path led her out of the park and onto a wide, level plain. This seemed devoid of any feature, apart from a large, utilitarian building which stood facing her a little way ahead.
When she got close she could see that the building had a name board mounted centrally on the front, a little above the level of Alice's head. At one end this sign bore the words "State Agent." at the other "Virtual Realtor." In the center of the vast blank frontage were a door and a small window, which was full of notices.
As Alice could see no one outside, she opened the door and went in. Immediately inside the door was a short counter and behind this a huge room, almost empty apart from what seemed to be tiers of shelves rising up into the shadows in the distance. In the center of the room, a single figure was visible sitting at a desk and talking into a telephone. When he saw Alice he rose and hurried over.
He rested his hands on the counter and smiled widely in a toothy and rather insincere manner. "Come in, come in," he said, ignoring the fact that Alice had already come in. "What may I have the pleasure of showing you? Perhaps you are planning to move into your very first state? I am confident that we will be able to give you every satisfaction."
To tell you the truth," began Alice, not that she had been at all tempted to lie about it, "I am not actually looking for anything. I was told that you would be able to tell me something about how electrons and other particles move between states."
"Well, you have certainly come to the right place. We have long been established in the particle transition business. If you would care to come with me to one of our locations I will endeavor to clarify the situation to your complete satisfaction."
Alice understood this to mean that he would explain things, so she came around the counter and followed him to one of the sets of shelves, or whatever they were. Either they were a long way away and very large, or perhaps she and the State Agent shrank as they came closer, but however it happened Alice found as she drew near that they now looked much more like a tall block of apartment buildings. These bore a sign which read:
They were very open at the front, and she could see electrons moving around on each level.
"There you have a good example of quality states built on wellspaced energy levels. Each one is occupied by the permitted number of electrons, up to the highest occupied level. Above that there are many vacant states, but there is currently no room for any more electrons on the lower levels. When an electron is a sitting tenant in a state, there is of course no room for another electron. Usually if he is left to himself an electron has no inclination to move from a state once he has settled into it. However, if we wait for a little we may be lucky and see some forced movement."
Alice stood and looked at the edifice, and after a short wait she saw a photon rush into the front. There was a commotion, and one of the electrons in the lowest level soared up and out of sight. Alice looked around to see where the photon had come from. Parked nearby there was a small truck with, painted on its side, the slogan:
"I am in luck," cried the State Agent joyfully. "A photon has given its energy to an electron in the lowest level and excited it right up to one of the vacant levels at the top. It is not so often that we get a removal from the ground state. That leaves a very attractive vacancy. I must see to it at once."
He rushed off and soon came back carrying a notice board on a post, which he planted in the ground. The notice read:
Hardly had he got the board in position than one of the electrons in the second level gave a short cry and toppled down to the empty state. Once there he settled in and carried on as if nothing untoward had happened. As he fell Alice saw a photon rush out. Since the electron had not fallen very far, the energy carried by this photon was much less than the energy carried by the photon which had released the original electron.
The State Agent sighed, picked up a paintbrush from a pot he had brought out when he fetched the sign, and proceeded to cross out the word "Ground" and write "Second" in its place. The paint was hardly dry when Alice heard another sharp cry. An electron in the third level had fallen into the empty place in the second. The State Agent cursed and altered his board again to read "Third." He slammed the brush back into the paint pot and glared at the building.
There was another sharp cry. An electron from still higher up had fallen into the third level. The State Agent tore his notice from its post, flung it on the ground and stamped on it.
See end-of-chapter note 1
"Excuse me," said Alice, rather hesitant at interrupting this display of passion. "I had thought you said that the electrons would stay in their states indefinitely if they were left alone, but those ones appear to have fallen down quite spontaneously."
"So it may seem," replied the Agent, quite glad to be distracted from his momentary fit of temper. "Actually all of those electron transitions have in fact been stimulated by photons, but you did not notice them because they were virtual photons. Virtual photons play a very important part in all electron interactions. They not only give these apparently spontaneous transitions between states, but they also help to create the states themselves in the first instance. So you see, the very particles which keep an electron in its steady state are also the ones which force the electron to leave it.
"Before I tell you about virtual particles we ought to look at normal particles, the ones which are not virtual. They are commonly known as real particles. The distinctive thing about them is that there is a very strict relation between their particular masses and the energy and momentum that they can have. That is what the notice there is about."
The agent pointed to a small sticker, printed on fluorescent green paper, which was attached to the front of the building. It said:
"They are certainly very fond of notices here," Alice thought to herself. "That one does sound rather suggestive, though I must admit that I do not know what it means."
"The mass shell," continued the agent, as if answering her thoughts, "is the region where energy and momentum are related in the strict way required for real particles. It is the straight and narrow path followed by conventional, hidebound particles.
"If you want to be a force in the community and to push things around, then you have to be able to transfer momentum. If you want something to move from where it is, or if you want to keep something from moving away, then you must transfer momentum. In each case you are concerned with moving, and moving means momentum. Whether you want to start a movement or to stop one makes little difference. It is changes in momentum which deflect objects from their paths and make things change, and it is control of momentum which makes particles take a particular path, for that matter.
"On the mass shell, you cannot have momentum without supplying the appropriate kinetic energy that befits your mass. A really massive particle, one with a lot of energy already invested in its rest mass, does not need so much extra kinetic energy to provide it with a given amount of momentum as would a lighter particle. All real particles must have the appropriate amount of energy if they are to have momentum. This is true even for photons, which do not have any rest mass at all."
The Agent reached into his pocket and took out a number of legallooking documents. "The conditions are quite precise. Provided that real particles obey them, they are free, free of any energy debt. They can move around as they wish, as far as they wish. They are quite free to come and go. You may have seen the rule: 'What is not forbidden is compulsory,"' he remarked.
"Yes, I did," replied Alice, anxious to air her knowledge. "I saw that in the Heisenberg Bank, and the manager told me about momentum and...."
"There is another rule," continued the agent enthusiastically, without actually stopping to listen to Alice's reply. "It says 'What is forbidden had better be done pretty quickly.' This is the rule followed by the virtual particles. These are not usually discussed much in polite, classical society, but they have a very important part to play in the world. Virtual particles behave in ways that classical laws say are simply not allowed."
"How can that be?" asked Alice, a little naively. "Surely if something is not allowed then no particle will be able to do it."
The agent heard her then and answered her question. It is the quantum fluctuations which permit it," he said. "If you have been to the Bank, you will remember that particles may have a loan of energy for a short time. The larger the amount of energy the shorter the time of course. You may have heard the expression The difficult we do immediately, the impossible takes a little longer.' Well, in quantum mechanics the impossible does not take a little longer, but it does last a little shorter. Virtual particles can enjoy all the benefits of energy which they do not possess, on a short-term free trial. This includes being able to transfer momentum."
"It must be a rather short free trial," said Alice thoughtfully.
"Oh, it is; it is. But it is something for nothing you see, so they all want it. You will have a better appreciation of virtual particles once you have seen them."
"But I can't see them," complained Alice. "Surely that is the point."
"You cannot see them at the moment," the Agent replied sternly, "but you will when you put on my virtual reality helmet." He walked quickly away in the direction from which they had come, and Alice hoped that she had not offended him. She was relieved when he returned soon after, carrying a large and highly technical looking helmet. This had a transparent visor which entirely covered the front, and there was a long cable attached to a socket at the back. The cable snaked away along the path by which he had come until it was lost from sight in the distance. "Here it is," he said triumphantly, "a marvel of modern technology. Just put this on, and you will see the world of virtual particles."
Alice felt a little nervous as she contemplated the helmet. It was large, and it looked very complicated and even, she felt, a little sinister. However, if this was going to reveal the virtual particles she had heard mentioned so often, she was prepared to try it. She put the helmet on her head. It was very heavy. The Agent reached across to the helmet and made some adjustment at the side of her head, where Alice was unable to see. The view through the visor clouded over with little sparkling dots and....
When her view through the visor cleared, it had dramatically changed. Alice could still see the electrons in their various levels, but now instead of their appearing to be within a tall building she saw them as enmeshed in a network of vivid lines which joined one electron to another, so that they looked as much as anything like flies caught in some great spider's web of shining strands. As she looked more carefully at these strands she could see that they were actually composed of photons, but photons distinctly different from the ones she had seen before at the Academy.
All the photons which she had met before had been moving very rapidly, but they had at least been moving in a normal fashion. They had started at one position and a little time later they were at a new position, even if their positions were never precisely defined, while in the intervening period they passed through all the points between the two positions. It had never occurred to Alice that it was possible to travel in any other way, but some of these virtual photons seemed to manage it. As she looked at them she found it very difficult to say in which direction they were moving, or indeed if they were moving at all in any normal fashion. A given strand in the net, which represented the behavior of one photon, would seem to appear at the same moment at the positions of both the electrons which it joined, without apparently moving in the normal way from one to another. This link would then fade while others appeared elsewhere in the great mesh of photons which coupled together the electric charges of all the electrons.
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 again. 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.
Although the helmet had gone, Alice's head was still full of the remarkable sights she had seen and she turned them over in her mind as she walked in silence beside the State Agent, along the shore of the infinite Void.
Notes
1. Within atoms, the allowed states for electrons have widely spaced energy levels and electrons may occupy only these levels. An electron can only transfer from one of these states if it goes to another (empty) one and in so doing its energy changes by a definite amount, the difference in the energies of the two states. An atom in its normal, or ground, state has its lowest energy levels uniformly filled with electrons, but there are levels of higher energy which are normally empty. When an electron is excited from its initial position it will end up in one of these empty higher levels or leave the atom completely.
An electron which has been excited to a higher level can decay back to a level of lower energy if there is an empty state available. As the electron transfers to a level of lower energy, it must rid itself of the surplus energy, which it does by emitting a photon. This is how atoms come to give off light. Since the electrons all occupy definite states within the atom, any photon that is emitted can only have an energy equal to the difference of that possessed by the initial and final states of the electron. This gives a large number of possibilities, but nevertheless imposes a restriction on the energy which a photon may have. The photon energy is proportional to the frequency of the light and thus to its color, so the spectrum of the light produced by an atom consists of a set of colored "lines" of specific frequencies. The spectrum for a given type of atom is completely distinctive.
Classical physics can give no explanation for these spectra.
2. Virtual particles have a distinct fuzziness, both in time and in energy. This fuzziness shows itself as energy fluctuations, in which the particles behave as if they had more (or less) energy than they should. It can equally appear as an uncertainty in time. In a quantum system particles seem to be able to be in two places at the same time (or at least they have amplitudes which are).
The particles can even turn time around. The physicist Richard Feynman explains antiparticles as being "particles traveling backward in time."* This explains the way in which the properties of antiparticles are opposite to those of the particles: A negative electric charge carried backward in time is equivalent to a positive charge moving toward the future. In both cases the positive charge in the future is being increased, and a negatively charged electron traveling toward the past is seen as a positively charged positron, which is its antiparticle.
All particles have their antiparticles, as is to be expected if they are in effect the same particle behaving in a different way.