"This is really too bad!" exclaimed Alice in frustration.
"I am afraid that it is what you have to expect," replied her companion sadly. "You see, you have only been given control of the intensity of the light and not its color. If light were a classical wave, then you would expect that as you increased its intensity, the associated disturbance would increase, and it would give more energy to the electrons that were emitted from the surface of the metal target. In fact, it is the color, or frequency, of the light that decides the energy of the individual photons which compose it. As you are not provided with any way to alter this, you cannot change the energy of the photons or for that matter the energy of the electrons which those photons will knock out of the metal surface. The stall has, of course, carefully been set up so that this energy is not quite enough to get through the retarding electric field. When you increased the intensity of the light, you directed more photons onto the surface, and these produced more electrons, but they all had the same energy, and in every case it was not quite enough for the electron to make it to the collector. I am afraid that you cannot win."
Alice felt somewhat cheated by her experience with this stall and looked around for something different to occupy her. Nearby was a small tent with a sign which read:
Alice and her companion slipped inside the tent, where the exhibitor was telling a small crowd how fortunate they were to see all six quarks captured and displayed for their entertainment. Alice looked at the exhibits. None of the quarks were present singly, of course. They were all assembled in pairs, each one bound unbreakably to his antiquark. Alice realized that this was as close to a collection of isolated quarks as it was possible to get. "And after all," she thought, "he did say that they were in captivity."
Alice looked at the assembled quark pairs. They were assembled on a platform which had various levels, with the heavier quark combinations standing on a higher energy level. She saw an up quark, wiggling his heavy eyebrows at her as before, a down quark, and, slightly higher up, a strange quark with flaming red curly hair.
As well as these three types, which she had already met at the MASSquerade, there were two others higher still. One projected a captivating personality, and she saw a quick flash of light as from a display of incredibly white teeth. "That is a charm quark," the Quantum Mechanic murmured in her ear. The other new quark was heavier yet. This one was placed quite high up, and Alice saw him even less clearly than other particles she had met, but she got the strangest impression that this one had a donkey's head. "That is a bottom quark," her companion informed her.
Alice now looked higher to see the sixth quark. There was the position on the platform, but it was empty. There was no sign of the sixth quark, which, she was informed, would be the top quark.
Other members of the audience also had noticed the absence of this sixth quark and were protesting noisily. "All right, all right!" said the exhibitor soothingly. "I know that he is in here somewhere. The top quark is the heaviest of them all, so we have to look for him at high energies, but he must be there." He picked up a large butterfly net which was leaning against a pole, climbed up a stepladder, and began making wide random sweeps of the net close beneath the roof of the tent.
During this, his audience became increasingly restless, with uncomplimentary remarks being made on all sides. Gradually, the mood of the crowd grew distinctly ugly and people began to slip away in order to write critical letters to their favorite technical journals. "Come away," said the Quantum Mechanic to Alice. "This is no place for us now."
They went outside and Alice's attention was caught by another stall at which people were clustered, throwing balls at various prizes which they would win if only they were able to knock them from their stands. It looked very much like the sort of fairground stall which she had seen near her home, except that in this one there was a sort of fence of thin, uniformly spaced wires between the competitors and their targets.
Alice watched for a while and noted that, as soon as a ball was thrown, it became quite blurred and it was impossible to see exactly where it had gone until it hit some point along the back wall of the booth. She saw that most of the balls did just that; they hit the wall rather than any of the prizes. Gradually piles of balls built up where they had hit, and Alice could see that these piles were positioned neatly in the spaces between the prizes.
"Exactly right," said a voice by her ear, echoing her thoughts. "The regularly spaced wires are acting to produce an interference pattern, with much greater probability for the balls being observed in some places than in others. Naturally the minima, the places where the probability of finding a ball is at its lowest, are arranged to fall where the prizes are."
"That doesn't seem very fair," remarked Alice.
"Well no, perhaps not, but in the Phun Phair you do not expect it to be fair. After all, the man who runs the stall has to make a living, so he does not want to give out prizes too often. Of course, there is still probability of the ball being observed even at the minima, so some prizes do get won, but not too many."
Alice still felt that it was not quite right somehow, but before she said anything further, her attention was caught by a large pavilion a little way off. It was surmounted by a huge glowing sign which said:
Below the sign there were a number of large posters strung across the front of the building:
Alice and her associate made their way to this exhibit and joined the crowd which was streaming in through the doorway. Within was a long, high-ceilinged enclosure with a raised platform in the center. On either side were a pair of short ramps leading up to doors at the two ends of the building. On each ramp stood a short metal cylinder with a pointed nose and stubby fins at the back.
On the central platform stood the Great Paradoxus, a tall figure with glossy black hair, a spiky waxed moustache, and a flowing black cloak. "Good evening, Ladies and Gentlemen," he greeted them. "Tonight I plan to conduct a little experiment on the reduction of amplitudes, which you may find to be of some interest. Here on the platform beside me," he continued, "you see a source of transitions, transitions which will release two photons in exactly opposite directions. As you know, if you were to measure the spin of the photons along some direction of your choice, you would find them to have a spin either up or down, with no intermediate choice possible." Alice had not known that, though she had heard talk of spin-up and spin-down electrons, but all the other people present were nodding their heads wisely, so she assumed it must be all right.
"As I say, if you were to measure the spin, you would find it to be spin-up or spin-down, but if you do not measure it, then there will be a mixture, a superposition of states having different directions for the spin. Only when you make a measurement of the spin will the amplitudes reduce. One will be selected, and one will no longer be present. Now," he said abruptly, "the source which you see here makes its transitions from states which have no spin at all, so the total spin of the two particles produced must also be zero. That means," he explained kindly, "that the spins of the two photons must be opposite: If one has spin-up then the other must have spin-down. But, mark you, the spin direction of the photons is only selected from the superposition of states when a measurement is made-that is the usual understanding. Thus, you see that when a measurement is made on one photon with the discovery, let us say, that it has spin-up, then the amplitude superposition for that photon will reduce to the appropriate state.
"However," Paradoxus continued, drawing himself up to his full height, "at the same time, the superposition for the other photon must reduce also, because we know that this photon must have the opposite spin. This must happen however far apart the photons might be at the time, even if they had arrived at different stars in the sky. In this demonstration we will not be making our measurements quite so far apart as that," he smiled at his audience. "I now call for two volunteers, two trusty and reliable experimenters who will agree to travel to the opposite ends of Quantumland and make our observations for us."
/> See end-of-chapter note 1
There was a buzz of argument and discussion from the assembled crowd. Eventually, two people were pushed forward. Both were dressed in long frock coats and narrow trousers, and both had bushy side whiskers. Both wore waistcoats, each with a gold chain attached to a watch which its owner had obviously checked recently against a reliable standard clock. These two were not actually identical to one another, since only particles are completely identical, but they were certainly very much alike. They were obviously both honorable, honest, and reliable as well as being competent and conscientious observers. If they were to say that they had seen something, no one would dream of disputing it.
Paradoxus handed to each a polarimeter, a device with which they might measure the spin directions of the particles. With military precision each stripped the instrument he had been given, examined it to make sure that it had no unusual features, and quickly reassembled it. The showman then summoned two attractive female assistants, who escorted the volunteers to the metal cylinders and opened a door in the side of each. For some reason each of the two observers then put on a tall top hat before he squeezed himself into the cramped space within. The assistants closed the doors, lit a fuse at the rear of each cylinder, and stepped hastily back. With a roar the stubby rockets rushed up the ramps, through the doors at the end of the pavilion and arced over the horizon, making for the opposite ends of Quantumland.
"And now we wait for them to arrive," remarked the impresario. "As soon as each is in position he will send a message through his telegraph line." He indicated two bells which stood on small tables at either end of the platform. Everyone looked at them, waiting for them to ring as a signal that the show might proceed. It was a long wait.
"Everyone seems very patient," remarked Alice, who was beginning to feel a bit restless herself.
"They have to be," replied the Quantum Mechanic. "Experimental scientists all learn to develop patience."
Finally the bells rang, first one and then shortly after the other. This indicated that both observers were in position, and, with a dramatic gesture, Paradoxus opened windows at either end of his photon source. Two by two the photons went rushing off in opposite directions.
After some time he closed the windows again and there was another long pause. "I wonder what we are waiting for now," thought Alice, who felt that the entertainment might move just a little faster. There was a flapping of wings and through the door at one end of the building flew a carrier pigeon, which was expertly caught by one of the assistants. Not long after, a pigeon arrived through the other door, and the messages carried by both could be compared. Paradoxus displayed the two messages, which showed a perfect correlation, with a spin-up photon going to one side invariably accompanied by a spin-down version detected at the other, even though the two detectors were too far apart to have had time to exchange any information.
"That's no mystery!" shouted someone from the other side of the large room. The voice had come from a tall figure whom Alice could not see very clearly, but he did look rather like the Classical Mechanic. "It is obvious," he went on, "that the photons are not in fact completely uncertain whether they are really spin-up or spin-down when they leave the source. In some way they know which they will be, and they know also that the two of them must be opposite. It does not matter then how long they wait before they are detected; they will be found to have that spin direction which was already decided when they were emitted."
"That sounds a very reasonable argument, does it not?" beamed the impresario, looking not in the least dismayed. "We shall have to extend our demonstration a little. You say that it has been decided at the time of emission whether the photons shall have spin upward or downward, and they carry this information with them as they travel. What would happen if our two observers were to measure the spin in other directions, say to the left and to the right, or at some other angle in between? And what would happen if our observers were to rotate their polarimeters as and when they felt like it, without referring back to us or collaborating with one another? Would it be possible for the source to know in advance what information it should transmit along with the particles such that their spins would match properly whatever the angles our friends chose for their measurements? I think not!"
Quickly he wrote out new instructions for the observers, bound the notes to the pigeons' legs, and sent them back to whence they had come. After a pause the telegraph bells rang once more to show that the messages had been received and understood. Again, with a flourish, he opened the windows on the central source and let the photons stream outward. After a suitable period, he closed the windows again, and then it was back to waiting. Alice was feeling distinctly tired of waiting for something to happen when, at last, there was a rushing noise from both sides. This grew steadily louder, and then the two rockets came arcing back down through the doors at the two ends of the building and landed back on the ramps from which they had departed.
As the stubby cylinders sat smoking gently, the doors opened and from each vehicle descended one of the observers, still wearing his tall formal hat. They both marched over to the impresario, removed their hats, bowed, and presented him with their notes. As far as Alice could tell, everyone in the audience apart from herself immediately crowded around to try to be the first to get a glimpse of the results. There was a tremendous hubbub of discussion and argument, and they all began to make their own calculations. Alice saw people with tiny portable computers, with electronic calculators, and with slide rules. She also saw someone with a strange mechanical calculator which had scores of tiny cogwheels. The Chinese folk whom she had noticed earlier had each produced an abacus, and their deft fingers slipped the beads to-and-fro along the wires more quickly than her eyes could follow. Even the hairy gentleman in the animal skins was involved. He had abandoned his wheel and was going through some complicated procedure with several little piles of bleached knucklebones.
Finally the arguing groups quieted down and came together in a common conclusion. It was true, they said, that there was a quite inexplicable agreement between the spin directions of the two photons. Even when arbitrary changes were made in the directions along which the two spins were measured, the observed correlations were greater than could be explained by any information sent out along with the particles. It was all quite clear, they agreed; in fact, it was clear as a bell. It didn't look all that clear to Alice, but if everyone was agreed, she supposed it must be correct.
"That is a very interesting result," remarked the Quantum Mechanic as he returned from the middle of the crowd. Most of the other people present were still arguing excitedly, despite the fact that they were apparently all in agreement. "It shows that the behavior of the wave function in different places cannot be caused by messages passed from one position to the other. There simply isn't enough time for that. It presents a whole new Aspect of quantum nature."
See end-of-chapter note 2
Interesting it might be, but Alice felt that there had been too much sitting and waiting and that she would like more action, so they left the pavilion and went off to investigate the rides.
"You will have to behave as a charged particle if you want to take any of the rides," remarked the Quantum Mechanic. "The rides all operate by electrical acceleration, so they will only work for charged particles. As you are just a sort of honorary particle, I see no reason why you should not be a charged particle just as readily as an uncharged one."
They had come to a very long, narrow building on which was a sign reading:
There was an excited line of electrons outside, waiting their turn to get on, but Alice did not think that this was quite the ride she wanted at the moment. She would rather go on something like the Big Wheel, which she had ridden in a fair near her home.
She mentioned this to her companion, who said that he would take her to the circular machines. As they headed in that direction they were passed by a parade. There was a succession of little carts, on each of which was bal
anced a huge apparatus built around a vast iron magnet with copper coils wound around it and various intriguing devices embedded in its center. From all of these snaked great bundles of wires and cables.
"How do those little carts manage to support all that weight?" asked Alice. "Surely they should be squashed flat under such huge masses of metal?"
"Oh, they would be if the pieces of equipment were real, but this is the Experiment Funding Parade, so each one is only a proposal. They are rather like the experiments we did in our gedanken room. They are just ideas at the moment, not real at all, so they are not very heavy. In fact, most of them carry very little weight indeed."
Alice looked at the procession and observed that the second cart carried an apparatus exactly like the first, the third carried another exactly the same, so did the fourth, the fifth, the sixth, and on and on as far as the parade was visible. "There doesn't seem to be a great deal of variety," remarked Alice.
"That is because multiple copies of each proposal must be submitted," replied her associate. "There will be a different one along in due course."
As they watched the floats go by the air was filled with a snowstorm of irregular scraps of paper. "Torn-up unsuccessful grant applications," said the Quantum Mechanic before Alice could ask. "Come along, we had better find your ride."
They passed a succession of Big Wheels. They were all lying on their side instead of being upright as they would be in a normal fair, and Alice's companion told her that in the Phun Phair they called them rings rather than wheels. There was the Big Ring, the Much Bigger Ring, and the CERN Truly Enormous Ring. Alice decided that she would like to ride on this last one.
She lined up with a jostling bunch of protons, and soon she was entering the machine and being seated, or "injected" as they termed it, in a beam bucket. This was a sort of electrical enclosure which Alice shared with a large crowd of protons who were milling around excitedly in all directions. They moved off, accelerated forward by strong fields which pulled on their electric charges. As they gathered speed, the protons quieted down, and they all rushed forward together.
Alice in Quantumland: An Allegory of Quantum Physics Page 18
