Atoms in the Void
Alice walked with the State Agent along the edge of the Void, looking out over the shimmering tenuous surface which was continuously aboil with the activity of the virtual particles as they were born and died unnoticed.
A little way out from the shore Alice saw a disturbance in the surface, some sort of circular depression in the general uniform level. Further out she could see other pits, and many of them were clumped together into groups. Some of the groups were very small and contained just a couple of the circular objects. Other collections were more extensive. She could see one group which contained a ring made up of six of the objects arranged in a circle, while others were attached around the outside. In the distance she could see some enormous assemblies spread across the surface. The largest contained many hundreds of the circular things, whatever they might be.
As Alice watched, she saw photons soar intermittently from one or another of the shapes which were spread out before her. The brilliantly colored photons looked rather like flares fired from ships at sea.
The Agent followed the direction of her gaze. "I see that you are watching the atoms as they swim in the Vacuum. Atoms provide us with much of our work in the electron state business, one way or another. You can see from here the various molecular partnerships that they have set up between them. These range from small two-atom businesses to huge organic conglomerates. Each different type of atom has its own distinctive spectrum of colors for the photons which it emits, so the photons act as signals which help you to identify the different types of atoms."
See end-of-chapter note 1
"I was wondering about all those things way out there," admitted Alice candidly. "I cannot see them very clearly from here. Is it possible to get any closer?"
"If you want to look closely at atoms we ought to go along to Mendeleev Moorings. There you will see every type of atom on display, with all the different elements laid out in a regular order."
The Agent led Alice along the shore until they came in sight of an extremely long, narrow jetty, which stretched far out over the Void. At the shore end there was an arched gate on top of which was a sign which read:
"There you are," announced the Agent. "That is where the atoms lie at dock before they set out to form their different chemical compounds. We usually call it the 'Mendeleev Marina' or the 'Atomic Pier,' though sometimes people talk of the 'Quay of the Universe.' You will find each different kind of atom represented here."
Together they walked beneath the sign and stepped onto the boards of the jetty. They strolled slowly out along the anchorage, while Alice looked at the long line of atoms moored in sequence to one side. Each of them appeared to her as a trumpet-shaped pit in the flat surface of the surrounding Void. The shape reminded her of the little whirlpool which she often saw forming over the drain whenever she emptied a bath, though these seemed to be quite still with no visible rotation. The surrounding surface of slick nothingness sloped down into each pit from the still flat level which stretched all around it. It sloped with almost imperceptible gradient at first, but ever more steeply as it funneled down toward the center. There were signs of activity taking place somewhere in the depths of the pit.
"Why is there such a deep hole?" Alice asked curiously. "As we are looking at Nothing, I would expect it to be all flat and featureless."
"That is a potential well," was the answer.
"What sort of well is that?" Alice continued curiously. "I know about garden wells which supply water and about oil wells, and I vaguely remember seeing something about a treacle well in a book I was reading recently, but what do you get in a potential well?"
"Why, the source of the potential, of course. You have to have a source to provide the water in a garden well. Here there is an electric charge as the source of electrical potential in the potential well. You should know by now what is in the well. It contains virtual photons. They provide the electrical attraction which would make the potential energy of a negative charge drop farther and farther below the surrounding vacuum level as it moves toward the potential source at the center of the atom. The potential source actually creates the well, you see."
The first pit was fairly shallow, but Alice could see that the others became successively deeper the farther they were positioned along the pier. The jetty stretched away ahead of her into the distance, with atom after atom moored along the side. Beside each one was a small notice to mark the mooring. The first of these read: 1H; the second, 2He; the third, 3Li. Each position had a different label. "Will these atoms all set out from here eventually to combine into groups like the ones already out on the surface of the Void?" asked Alice.
"Most of them will certainly, but there are a few which will not, like the one just here for example."
They paused beside an atom which carried the notice: 10Ne. "That is an atom of a Noble Gas element. They are an aristocratic lot and that means that they refuse to engage in commerce of any sort. They keep to themselves. They are perfectly satisfied with the way they are and will not mix with anyone else. They always travel around in splendid isolation. You never see them take part in any sort of compound."
They walked a little farther and the Agent explained that, even apart from the aloof Noble atoms, there was considerable variation in the enthusiasm with which different elements joined into compounds. "For example, this is a particularly active concern," he remarked, as they came to a notice which read: 17Cl.
Alice decided that it was time to examine one of these atoms more closely, so she tentatively extended one foot off the edge of the jetty. To her delight she did not sink. Her foot stood on a tiny dimple in the surface, rather like some pond-skating insects she had once watched. When she tried to walk toward the atom, however, she discovered that there was no friction in the void. The surface was extremely slippery, and she was quite unable to keep her footing. With a small cry she skidded down the increasingly steep slope and toppled into the deep pit.
As she fell, Alice found that she had plenty of time to look around her. The sides of the well became ever steeper as they closed in upon her, and she soon noticed that she was falling through the ghostly outline of a series of rooms which had low, closely spaced ceilings. The first few rooms were very low indeed, scarcely tall enough for a doll's house, but as she fell the rooms became steadily taller. Initially they were all completely empty and deserted, but then she came to a room which contained a large, round table surrounded by chairs. On the floor below this she could see desks and filing cabinets, as if she was passing through some sort of office.
As the time passed she became increasingly amazed to find that she was still falling, without any sign of reaching the bottom. Down, down, down; would the fall never come to an end?
Alice gradually began to realize that her fall was not going to come to an end. She had not reached the bottom of the hole, but she was not getting any lower. She was floating quite unsupported in the center of the funnel, on a level with one of the shadowy rooms. She looked around her and noted that she was not alone. Near her were two electrons who were involved in a hectic flurry of activity. Around them she could discern the faint outline of an extremely tiny and cramped office. "Excuse me," she called. "Do you think that you could stop for a moment and tell ine where I am?"
"No room, no room," they called.
"I beg your pardon, what do you mean?" cried Alice, to whom this reply did not seem particularly relevant.
"There is not enough room here for us to slow down at all, let alone stop," they answered her. "As you know, when the position of a particle is restricted, the Heisenberg relation forces its momentum to be large, and it is so cramped here that we have no choice but to keep moving. If we had as much room as they have on some of the higher levels we could afford to move in a more leisurely way, but not here. This is the lowest level, you see, so we must expect to be kept busy."
"Really?" inquired Alice. "What is it that you do that is so important?"
"We do not do anything in particular. No one is particularly interested in what the electrons in the ground state are doing, just as long as we keep moving."
"In that case, do you think you could tell me where I am, without stopping?" Alice asked. "For I do not know where I have come to. What is preventing any of us from falling farther down into the well."
"You are in the lowest level of a chlorine atom, as we have already told you. Here, we are so close to the potential source that there is very little room, so we have to move very quickly as our momentum is forced to be high. This means that our kinetic energy is also high. None of us is in a particularly virtual state, you see. Electrons have secure positions in atoms, with very good tenure. Most atoms have been around for a long time and the quantum energy fluctuations are small, so for us electrons the energy and momentum are properly related.
"You probably know that when an electron, or anything else, falls farther into a potential, it loses potential energy, and this will be converted to kinetic energy," they went on.
"Yes, that was explained to me when I visited the Heisenberg Bank," agreed Alice.
"Here in this potential well, though, when we get closer to the center, there is less and less room, so we need to have more kinetic energy. If we were to fall even closer we would need to have more kinetic energy than we can possibly get from converting potential energy, so we are unable to fall any further. In fact, paradoxically, we just do not have enough energy to be able to fall any lower and we cannot borrow the energy as a quantum fluctuation because we would need it for a long time.
"There are only two states on this level so there is only room for two electrons, one being in a spin-up and one in a spin-down state. There are more states available as you move up to higher energy levels, so you will find more electrons on the levels above. The next two levels can hold up to eight electrons on each level. In any atom, the lowest levels, the ones with the lowest potential energy, are the first to be filled. The Pauli principle allows only one electron in each state, so when all the states on one level already have an electron, any extra electrons have no choice but to move into levels higher up. The levels are filled from the bottom until all the electrons are accommodated. The highest level which contains any electrons is called the valence level. That is where the valence electrons live, though there are plenty of unoccupied states higher up in the attic. The valence electrons make all the decisions and control the compounds our atom can join. If you want to discover how an atom operates, your best plan would be to go up and talk to them."
See end-of-chapter note 2
"How shall I get up to that level from here?" asked Alice.
"Well, if you were an electron you would have to wait here until you were excited to the higher level by a photon which could give you the extra energy you would need. In your case, however, I expect that you can be carried up by the Ladder Operator."
"Don't you mean the elevator operator?" queried Alice. "I have been in an elevator in a large department store and it had an operator who took people from floor to floor, but I have never heard of a ladder that needed one."
When she looked around, however, she could see a sort of ladder with very widely separated rungs. Beside it stood a rather indistinct figure. "May I ask who you are?" said Alice curiously.
"I am the Ladder Operator. I am not a physical creature, but merely a mathematical construct. It is my job to transform a system from one state to a higher or lower one." He performed some complicated operation which Alice completely failed to understand but resulted in her being carried rung by rung up to the higher level.
In due course Alice arrived at the level on which she had seen the large, round table. This level contained more electrons than the first. She managed to count eight in all, though with some difficulty. As with all the electrons she had seen so far, they were moving energetically around. Several of them were circling around the table, some in one direction and some in the other. The others were not obviously rotating but were nonetheless in motion. None of them was sitting quietly on any of the chairs around the table, but they were leaping up and down, and some were stepping on and off the table. The electrons were never still, though on this level they were not moving quite so frantically as they had been on the lowest one.
"Hello Alice," they cried as she appeared. "Come, and let us show you how a reliable, medium-sized atom operates. The way in which Chlorine Corporation conducts its business is decided by us seven electrons in the valence level."
"But there are eight of you!" protested Alice.
"That is because we have entered into a partnership with another atom, Sodium Syndicate, to form a sodium chloride molecule. Working together in this way we like to think that we are the Salt of the Earth. An atom runs much more harmoniously when all of its levels that hold any electrons are filled completely. On our own we have only seven electrons in the valence level and Sodium has but the one, although there is room for eight. It helps both of us if the Sodium valence electron comes over here to sit on our valence level and give us a full board. This means of course that we now have an extra electron, and so we have a negative charge. The Sodium atom has an electron less than normal, which gives them a positive charge, and the electrical force between these opposite charges holds the two atoms together. That is known as ionic bonding between the atoms and is one of the common forms of corporate structure."
"That sounds very cooperative on both sides," agreed Alice tactfully. "Which of you is the electron that has come over from the Sodium atom then?" she asked.
"I am," they all cried, talking together. They paused for a moment and looked at one another. "No, he is the one," they now said, still speaking in perfect unison. Alice realized that there was absolutely no point in asking any question which tried to distinguish between the identical electrons.
"Could you explain to me, please, why you say that the sodium atom has a positive electric charge when it has lost one of its electrons," she asked instead. "Surely it still has quite a few electrons left, and they will presumably have negative charges also."
"That is quite true, all we electrons do have the same amount of negative charge, as we are all identical. Normally in an atom this charge is balanced and neutralized by an equal amount of positive charge carried by the Nucleus. Atoms are usually neutral, with no net electrical charge either way. So you see, when an atom has one electron more than usual, it will be negatively charged. It is known as a negative ion. If it has one electron fewer than normal, the positive charge on the Nucleus will dominate, and the atom becomes a positive ion."
"I see," said Alice thoughtfully, "but what is this Nucleus that you are talking about?"
"Every atom has one," was the evasive answer, "but you do not want to know too much about it. You really don't!" he added nervously.
At this point the conversation was interrupted by a faint cry which started somewhere below them, passed through the valence level close at hand, and finally stopped somewhere above. Alice looked up and saw that it was due to an electron which had apparently been excited by a photon from its position in a lower level and was now looking uncomfortably remote in one of the empty higher levels. The electron wandered rather slowly around the high wide level until eventually it gave a brief cry and toppled to the level below. As it did a photon rushed out of the atom, carrying away the energy released by the fall. Alice watched with interest as the electron fell in succession from one level to the next, in each case emitting a photon. As the lower energy levels were more widely separated than those above, each fall was farther than the one before, so the photons created had higher energy arising from each successive fall. As their energy increased, the color of the light moved farther toward the blue end of the spectrum.
Looking downward Alice saw that the space that had been left by the electron which was excited from the lower level had been filled and that one of her companions in the valence level was missing. Before long the electron falling from above had dropped to the valence level and filled the vacant place. The atom was now back to its original state. Two electrons had exchanged levels, but as they were identical that was no difference at all.
See end-of-chapter note 3
"You will have noticed all the different colors of the photons which I emitted," said one of the electrons proudly. This remark tended to suggest that it was the electron which had fallen that had just spoken, but Alice was now too experienced with the effects of electron identity to fall into that trap. "That is the way that atoms emit light you know: when electrons change from one level to another. All the photons were of different energy, and hence different color, because the levels are all different distances apart. They are very closely spaced at the top of the well but are farther and farther apart as you get lower down. This level spacing is different in atoms of different types, so the set of photon energies is completely distinctive for each type of atom-as distinctive as a human fingerprint."
Hardly had the eight electrons settled down, or got as settled as they could ever be while they were all in continuous frantic motion, when there was a tremor which seemed to run through the whole atom. "What was that!" cried Alice in some alarm.
"It was an interaction of some sort. We have been separated from our Sodium partner and are drifting through the void as a free negative ion. But do not worry. I do not anticipate that we shall drift about aimlessly for very long. We shall very soon be back in business if the Exchange is agreeable."
"What Exchange is that?" asked Alice. "Do you mean the Stock Exchange? I understand that controls business in my world."
"In our case we mean the Electron Exchange. All of our activities are governed by electron interactions of some sort, so it is electron exchange which is significant. Perhaps you would like to visit the Exchange?"
"Yes, I should think so," replied Alice. "How would I get there from here? Is it a long journey?"
"Oh no. Not really. In fact it is not really a journey at all. As you are in an interacting atom, you are already there in a sense; you just need a different representation. It is all a question of how you look at things. Just follow me."
As the electron had told her, they did not seem actually to go anywhere else, but still Alice found herself in company with an electron on the edge of a broad room. The floor was crowded with electrons which clustered around a large table in the middle of the room. It looked to Alice rather like one of the tables which she had seen in old war films, where commanders moved around various counters which represented aircraft, or ships, or armies. On this table also, she saw a great selection of counters which were being moved around into different groupings.
She looked more closely at some of these counters and saw that they bore the same labels as the atom moorings on the Periodic Pier. In fact, as she looked really closely, she was no longer so sure that they were merely counters. They looked like reduced versions of the atoms which she had seen along the side of that jetty. "Perhaps they are the same," she thought. "Maybe those are the same atoms which I am seeing differently. I suppose that instead of the Periodic Pier, that would make this the Periodic Table."
Around the side of the room, the walls carried rows of display screens on which she could see columns of numbers that changed as atoms were moved from group to group.
"Are those the prices for the various atoms?" asked Alice.
"Yes, after a fashion. Those numbers tell us the energies of the various electrons which are taking part in chemical combinations. They quote the binding energies of the electrons: the amount by which an electron's energy has been reduced below the value it would have if it were free. The larger is the value quoted, the lower is the potential energy that the electron has, and so the more stable and successful is the compound which it binds. The job of the Exchange is to make these binding energies as large as possible."
"And is this all done by moving electrons from one atom to another?" queried Alice, who remembered the explanation she had been given of ionic bonding in Sodium Chloride.
"Not always, no. Sometimes that is the most effective method and then the binding is done in that way. The Electron Exchange can get an advantage by moving electrons around because the electron states that are available within an atom are arranged in levels, or shells, with quite large gaps between. The binding energy for the last electron in a lower shell level is much greater than for the first electron that has to go into the next shell higher. This means that there is an easy method of improving the overall energy score for an atom which has only one electron in its highest shell. If this electron can move from its splendid but extravagant isolation into an almost full lower shell in some other atom, then there is almost certain to be an overall gain in binding energy.
"It is equally true that, when an atom has but one space remaining in its highest occupied shell, this state will have an unusually low energy, and any electron which transfers into it will be likely to improve its energy balance sheet. It is generally true that atoms with just one electron too many or too few are the most active―the most likely to take part in transactions and to form compounds. Atoms with two electrons alone in a high state and those with only two spaces left in a lower one may engage in similar electron transfers, but the gain in binding energy for the second electron is usually a lot less than for the first one, and it is much less effective."
"So what can an atom do if it has several electrons in its outer shell?" asked Alice, as this seemed to be expected of her.
"Such an atom has to change to a different kind of binding, one which is known as a covalent bond. An atom such as carbon, for instance, has four electrons in its outer shell. This means it has four electrons too many to be an empty shell and four electrons too few to be a full one. It is too nicely balanced to gain anything by actually transferring electrons to or from another atom, so instead it shares them. It turns out that if the electrons from two atoms are in a superposition of states such that each may be in either atom, then the energy of the two atoms may be lowered and this serves to bind them together.
"The ionic bond, in which an electron is completely moved from one atom to another, can only work between very different atoms, one of which has an electron too many, the other an electron too few. The covalent bond, on the other hand, can work when both atoms are of the same type. The most remarkable example is given by the covalent bonding of carbon atoms, the basis of the huge Organic Conglomerates." Alice could sense an atmosphere of awed respect emanating from the electron manipulators around the table as the Organics were mentioned.
"A carbon atom has four electrons in its outer, or valence, level. If each of these electrons is combined with electrons from other atoms, then all of the eight electron states contribute to the superposition and the shell is effectively filled. In this way a carbon atom can attach itself to as many as four other atoms, which may also be carbon. The carbon atom may also exchange two of its electrons with another carbon atom to give a double bond, in which case it will not be connected to so many other atoms, though the connection will be stronger.
"The ionic bond at its strongest connects but one atom to one other, so it does not produce large molecules. Where there are two electrons to transfer, things can get more complex. Even then the situation does not compare with that of carbon, where one atom may connect to four others and each of those may be connected to several others. Carbon-based compounds can form into enormous organic molecules of great complexity, which may contain hundreds of atoms in all."
"Do all of the different atom types that I can see there form compounds in the ways you describe?" Alice asked.
"Yes, apart from the noble gases. With the noble gases, the atoms have filled valence shells already and so do not stand to gain by any electron transfers. All of the others do form compounds to a degree, though some are more active than others and some are encountered much more often. The chlorine atom which you visited, for example, is very active. It will form compounds with the simplest atom, hydrogen, which employs only one electron in total, and also with the largest natural element, uranium. That is a very large establishment indeed. It employs almost a hun dred electrons, but only the ones in the outer valence level really affect its chemical behavior. It is so large that there have been rumors that its Nucleus is unstable," he added confidentially.
"I wanted to ask about that," said Alice firmly. "You have mentioned the nucleus again. Please, would you tell me: What is the nucleus?"
All of the electrons looked somehow uncomfortable, but reluctantly answered. "The Nucleus is the hidden master of the atom. We electrons conduct all the business of forming chemical compounds and emitting light from the atom and so on, but it is the Nucleus which really controls the sort of atom we are. It makes the final policy decisions, and fixes the number of electrons that we can have and the levels that are available to put them in. The Nucleus contains the nuclear family, the hidden underground of Organized Charge."
Alarmed by this outburst of candor, the electrons around the room all tried to shrink unobtrusively into one corner, or at least as far as they were able without becoming too localized. Too late, the harm was done! Alice became aware of a new menacing presence nearby.
Amongst the scurrying electrons there was now a hulking shape, looming over Alice and her companions. She realized that it was a photon, but distinctly more massive than any she had seen before. Like all the photons she had seen it was glowing, but in a peculiarly dim and furtive way. Alice also noticed that, surprisingly for something which was itself the essence of light, this photon was wearing a pair of very dark glasses.
"It is a heavy virtual photon," gasped the electrons, "Very heavy, a long way off its mass shell. It is one of the enforcers for the Nucleus. Photons such as him transmit the Nucleus's electrical control to its client electrons."
"I hear that someone is asking questions," said the photon, in a menacing tone. "The nucleons are the sort of particles that do not like to hear that questions are being asked by any other person whatever. I am taking that same person for a little ride to meet certain parties, or rather certain particles. They want to meet her very badly indeed."
This did not sound like a very promising start for a new encounter, and Alice was considering whether she might safely refuse. She could never quite make out, in thinking it over afterward, how it was that they began: All she could remember was that they were running side by side and the photon was continuously crying "faster," and Alice felt that she could not go faster, though she had no breath left to say so. They rushed across the surface of the table and dived into one of the atoms represented on its surface. It was one of the uranium atoms and it grew enormously as it rushed up to meet them.
The most curious part of the experience once they were inside the atom was that the things around them never changed in position: However fast they went they never seemed to pass anything. What Alice did note was that her surroundings, the busy electrons and the outlines of the levels which contained them seemed to be getting steadily larger as she ran.
"Is everything really growing, or am I shrinking?" thought poor puzzled Alice.
"Faster!" cried the photon. "Faster! Do not try to talk."
Alice felt that she would never be able to talk again; she was getting so out of breath: and still the photon cried "Faster! Faster!" and dragged her along.
"Are we nearly there?" Alice managed to pant out at last.
"Nearly there!" the photon repeated. "Why, we are there all the time and no other place, but we are not sufficiently localized, not hardly. Faster!" They ran on for a time in silence, going faster and faster while the surrounding scene ballooned in size around them, spreading upward and outward until everything she had seen before was too large to be readily appreciated.
"Now! Now!" cried the photon. "Faster! Faster! Your momentum is now nearly so large as will localize you within the Nucleus." They went so fast that they seemed to skim through the air, until suddenly, just as Alice was getting quite exhausted, she found herself standing in front of a tall, dark tower which rose smoothly in front of her, curving up from the ground and narrowing steadily as it rose. It was dark and featureless at the lower levels, though somewhere at the top Alice could see that it finished in a confusion of turrets and battlements. The overall effect Alice found extremely forbidding.
"There you see Castle Rutherford, the home of the Nuclear Family," said the heavy virtual photon.
Notes
1. Atoms had been found to contain light negative electrons and, later, were found to contain a positively charged nucleus. This suggested that they might be tiny versions of the solar system, with planetary electrons in orbit around a nuclear sun. The notion gave rise to fantasies in which the electrons were indeed miniature planets, with still more miniature people living on them, and so on ad infinitum. Unfortunately for such schemes, the "solar system" picture is clearly wrong.
? The only reason planets do not fall directly into the sun is because they are orbiting around it. There is definite evidence that many electrons do not have any rotation the nucleus.
? According to classical physics, the orbiting electrons within atoms should radiate energy and their motion should run down. Something as small as an atom would do this rather quickly, in less than a millionth of a second, and atoms do not collapse in this way. (The solar system is, in fact, running down, but rather slowly, on a time scale of millions of years.)
2. Because of the Pauli principle you can have only one electron in each state. As electrons are available in spin-up and spin-down versions, this effectively doubles the number of states. Electrons will fall into the atomic states because they have lower energy there and it is a general rule that things tend to fall to lower energy levels (as you may discover by holding a cup over a tiled floor and releasing it). Any atom has a large number of levels which could hold electrons; in fact, the number of states is infinite, though the upper ones are very close together in energy. An atom will continue to attract electrons into its levels only until it contains the correct number to compensate the positive charge of its nucleus, after which the atom no longer has any surplus positive charge with which to attract further electrons. When an atom has reached its full complement of electrons, it will in almost all cases contain more than there are room for in the state of lowest energy. Some electrons must then be accommodated in states of higher energy.
3. When people looked at the light given off by atoms of a single type, they found that the spectrum was not a uniform spread of colors like a rainbow, but a set of sharp lines, each of a distinct color. Every type of atom showed these line spectra, which were a complete mystery to classical physics.
The set of energy levels for the electrons is unique to any given type of atom. When electrons transfer from one level to another they emit photons which have an energy that corresponds to the difference in the energy of the two levels. As the energy of photons is proportional to the frequency and color of the light, this gives an optical line spectrum for the atoms which is as distinctive as a fingerprint.
The explanation of the existence of a line spectrum was the first major success of the developing quantum theory. The theory fitted the observed line frequencies and predicted other line spectra which had not been seen. These where all found in due course and showed that the quantum theory could not readily be dismissed.