There are also some longer, end-of-chapter, notes. These amplify some of the trickier points in t... more There are also some longer, end-of-chapter, notes. These amplify some of the trickier points in the text and are denoted thus: See end-of-chapter note 1 Much of the way that quantum theory describes the world may seem at first sight to be nonsenseand possibly it may seem so at the second, third, and twenty-fifth sight as well. It is, however, the only game in town. The old classical mechanics of Newton and his followers is unable to give any sort of explanation for atoms and other small systems. Quantum mechanics agrees very well with observation. The calculations are often difficult and tedious, but where they have been made, they have agreed perfectly with what has really been seen. As she fell forward she was amazed to see the screen grow enormously, and she found herself in among the swirling speckles, rushing with them down into the picture. "I cannot see anything with these dots swirling all around me," thought Alice. "It is just like being lost in a snowstorm; why I cannot even see my feet. I wish I could see just a little. I could be anywhere." At that moment Alice felt her feet strike something solid and she found herself standing on a hard, flat surface. All around her the swirling dots were fading away and she found that she was surrounded by a number of vague shapes. She looked more closely at the one nearest to her and observed a small figure, coming roughly up to her waist. It was exceedingly difficult to make out, as all the time it kept hopping rapidly to-andfro, moving so fast that it was very difficult to see at all clearly. The figure seemed to be carrying some sort of stick, or possibly a rolled umbrella, which was pointing straight up in the air. "Hello," Alice introduced herself politely. "I am Alice. May I ask who you are?" "I am an electron," said the figure. "I am a spin-up electron. You can readily tell me apart from my friend there who is a spin-down electron, so, of course, she is quite different." Under his breath he added something which sounded rather like "Vive la difference!" As far as Alice could see, the other electron looked very much the same, except that her umbrella, or whatever it was, was pointing down toward the ground. It was very difficult to tell for sure, as this figure also was jigging to-and-fro as rapidly as the first. "Oh please," said Alice to her first acquaintance. "Would you be good enough to stand still for a moment, as I really cannot see you at all clearly?" "I am good enough," said the electron, "but I am afraid there is not room enough. However I will try." So saying he slowed his rate of jiggling. But as he moved more slowly, he began to expand sideways and become more and more diffuse. Now, although he was no longer moving at all quickly, he looked so fuzzy and quite out of focus that Alice could no more see what he looked like than she had been able to before. "That is the best I can do," he panted. "I am afraid that the more slowly I move, the more spread out I become. That is the way things are here in Quantumland: The smaller the space you occupy, the faster you have to move. It is one of the rules, and there is nothing I can do about it." "There isn't really room to slow down here," continued Alice's companion as he began once more to leap rapidly around. "The platform is becoming so crowded that I have to be more compact." Sure enough, the space in which Alice stood had now become very crowded indeed, being closely packed with the small figures, each dancing feverishly to-and-fro. "What strange beings," thought Alice. "I do not think I shall ever be able to see quite what they look like if they will not stand still for a minute, and there does not seem to be much chance of that." Since it did not look as if she could get them to slow down she tried another topic. "Would you tell me please what sort of platform we are on?" she asked. "Why a railway platform, of course," replied one of the electrons cheerfully (it was very hard for Alice to say which had spoken; they really did all look very much the same). "We are going to take the wave train to the screen you see. You will change there to the photon express I expect, if you want to go any farther." "Do you mean the television screen?" asked Alice. "Why of course I do," cried one of the electrons. Alice could have sworn that it was not the same one which had just spoken, but it was very difficult to be certain. "Come on! The train is here and we have to get on." Sure enough, Alice could see a line of small compartments drawn up at the platform. They were very small. Some were empty, some had one electron in, and some two. All of the empty compartments were filling rapidly-in fact there did not seem to be any left-but Alice noticed that not one of the compartments held more than two electrons. As they passed by any of these compartments, the two occupants would cry out "No room! No room!" "Surely you could squeeze more than two into a compartment, seeing as the train is so crowded?" Alice asked her companion. "Oh no! Never more than two electrons together, that is the rule." "I suppose we shall have to get into different compartments then," declared Alice regretfully, but the electron reassured her. "There's no problem there for you, no problem at all! You can get into any compartment that you want, of course." "I am sure that I do not see why that should be," Alice replied. "If a compartment is too full to hold you, then it must surely be too full for me as well." "Not at all! The compartments are only allowed to hold two electrons, so almost all the places for electrons may be taken up, but you are not an electron! There is not a single other Alice on the train, so there is plenty of room for an Alice in any of the compartments." This did not seem to follow so far as Alice could see, but she was afraid that the train would start to move off before they got seats, so she began looking for an empty space that could take another electron. "How about this one?" she asked her associate. "Here is a compartment with only one other electron already in it. Can you get in here?" "Certainly not!" he snapped, sounding quite horrified. "That is another spin-up electron. I cannot share a compartment with another spin-up electron. What a suggestion! It is quite against my principle." "Don't you mean against your principles?" Alice asked him. "I mean what I say, against my principle, or rather Pauli's principle. It forbids any two of us electrons from doing exactly the same thing, which includes being in the same space and having the same spin," he responded crossly.
There are also some longer, end-of-chapter, notes. These amplify some of the trickier points in t... more There are also some longer, end-of-chapter, notes. These amplify some of the trickier points in the text and are denoted thus: See end-of-chapter note 1 Much of the way that quantum theory describes the world may seem at first sight to be nonsenseand possibly it may seem so at the second, third, and twenty-fifth sight as well. It is, however, the only game in town. The old classical mechanics of Newton and his followers is unable to give any sort of explanation for atoms and other small systems. Quantum mechanics agrees very well with observation. The calculations are often difficult and tedious, but where they have been made, they have agreed perfectly with what has really been seen. As she fell forward she was amazed to see the screen grow enormously, and she found herself in among the swirling speckles, rushing with them down into the picture. "I cannot see anything with these dots swirling all around me," thought Alice. "It is just like being lost in a snowstorm; why I cannot even see my feet. I wish I could see just a little. I could be anywhere." At that moment Alice felt her feet strike something solid and she found herself standing on a hard, flat surface. All around her the swirling dots were fading away and she found that she was surrounded by a number of vague shapes. She looked more closely at the one nearest to her and observed a small figure, coming roughly up to her waist. It was exceedingly difficult to make out, as all the time it kept hopping rapidly to-andfro, moving so fast that it was very difficult to see at all clearly. The figure seemed to be carrying some sort of stick, or possibly a rolled umbrella, which was pointing straight up in the air. "Hello," Alice introduced herself politely. "I am Alice. May I ask who you are?" "I am an electron," said the figure. "I am a spin-up electron. You can readily tell me apart from my friend there who is a spin-down electron, so, of course, she is quite different." Under his breath he added something which sounded rather like "Vive la difference!" As far as Alice could see, the other electron looked very much the same, except that her umbrella, or whatever it was, was pointing down toward the ground. It was very difficult to tell for sure, as this figure also was jigging to-and-fro as rapidly as the first. "Oh please," said Alice to her first acquaintance. "Would you be good enough to stand still for a moment, as I really cannot see you at all clearly?" "I am good enough," said the electron, "but I am afraid there is not room enough. However I will try." So saying he slowed his rate of jiggling. But as he moved more slowly, he began to expand sideways and become more and more diffuse. Now, although he was no longer moving at all quickly, he looked so fuzzy and quite out of focus that Alice could no more see what he looked like than she had been able to before. "That is the best I can do," he panted. "I am afraid that the more slowly I move, the more spread out I become. That is the way things are here in Quantumland: The smaller the space you occupy, the faster you have to move. It is one of the rules, and there is nothing I can do about it." "There isn't really room to slow down here," continued Alice's companion as he began once more to leap rapidly around. "The platform is becoming so crowded that I have to be more compact." Sure enough, the space in which Alice stood had now become very crowded indeed, being closely packed with the small figures, each dancing feverishly to-and-fro. "What strange beings," thought Alice. "I do not think I shall ever be able to see quite what they look like if they will not stand still for a minute, and there does not seem to be much chance of that." Since it did not look as if she could get them to slow down she tried another topic. "Would you tell me please what sort of platform we are on?" she asked. "Why a railway platform, of course," replied one of the electrons cheerfully (it was very hard for Alice to say which had spoken; they really did all look very much the same). "We are going to take the wave train to the screen you see. You will change there to the photon express I expect, if you want to go any farther." "Do you mean the television screen?" asked Alice. "Why of course I do," cried one of the electrons. Alice could have sworn that it was not the same one which had just spoken, but it was very difficult to be certain. "Come on! The train is here and we have to get on." Sure enough, Alice could see a line of small compartments drawn up at the platform. They were very small. Some were empty, some had one electron in, and some two. All of the empty compartments were filling rapidly-in fact there did not seem to be any left-but Alice noticed that not one of the compartments held more than two electrons. As they passed by any of these compartments, the two occupants would cry out "No room! No room!" "Surely you could squeeze more than two into a compartment, seeing as the train is so crowded?" Alice asked her companion. "Oh no! Never more than two electrons together, that is the rule." "I suppose we shall have to get into different compartments then," declared Alice regretfully, but the electron reassured her. "There's no problem there for you, no problem at all! You can get into any compartment that you want, of course." "I am sure that I do not see why that should be," Alice replied. "If a compartment is too full to hold you, then it must surely be too full for me as well." "Not at all! The compartments are only allowed to hold two electrons, so almost all the places for electrons may be taken up, but you are not an electron! There is not a single other Alice on the train, so there is plenty of room for an Alice in any of the compartments." This did not seem to follow so far as Alice could see, but she was afraid that the train would start to move off before they got seats, so she began looking for an empty space that could take another electron. "How about this one?" she asked her associate. "Here is a compartment with only one other electron already in it. Can you get in here?" "Certainly not!" he snapped, sounding quite horrified. "That is another spin-up electron. I cannot share a compartment with another spin-up electron. What a suggestion! It is quite against my principle." "Don't you mean against your principles?" Alice asked him. "I mean what I say, against my principle, or rather Pauli's principle. It forbids any two of us electrons from doing exactly the same thing, which includes being in the same space and having the same spin," he responded crossly.
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