One day Mr Tompkins was going home, feeling very tired after the long day's work in the bank, which was doing a land office business. He was passing a pub and decided to drop in for a glass of ale. One glass followed the other, and soon Mr Tompkins began to feel rather dizzy. In the back of the pub was a billiard room filled with men in shirt sleeves playing billiards on the central table. He vaguely remembered being here before, when one of his fellow clerks took him along to teach him billiards. He approached the table and started to watch the game. Something very queer about it! A player put a ball on the table and hit it with the cue. Watching the rolling ball, Mr Tompkins noticed to his great surprise that the ball began to ‘spread out’. This was the only expression he could find for the strange behaviour of the ball which, moving across the green field, seemed to become more and more washed out, losing its sharp contours. It looked as if not one ball was rolling across the table but a great number of balls, all partially penetrating into each other. Mr Tompkins had often observed analogous phenomena before, but today he had not taken a single drop of whisky and he could not understand why it was happening now. ‘Well,’ he thought, ‘let us see how this gruel of a ball is going to hit another one.’
One day Mr Tompkins was going home, feeling very tired after the long day's work in the bank, which was doing a land office business. He was passing a pub and decided to drop in for a glass of ale. One glass followed the other, and soon Mr Tompkins began to feel rather dizzy. In the back of the pub was a billiard room filled with men in shirt sleeves playing billiards on the central table. He vaguely remembered being here before, when one of his fellow clerks took him along to teach him billiards. He approached the table and started to watch the game. Something very queer about it! A player put a ball on the table and hit it with the cue. Watching the rolling ball, Mr Tompkins noticed to his great surprise that the ball began to ‘spread out’. This was the only expression he could find for the strange behaviour of the ball which, moving across the green field, seemed to become more and more washed out, losing its sharp contours. It looked as if not one ball was rolling across the table but a great number of balls, all partially penetrating into each other. Mr Tompkins had often observed analogous phenomena before, but today he had not taken a single drop of whisky and he could not understand why it was happening now. ‘Well,’ he thought, ‘let us see how this gruel of a ball is going to hit another one.’
One day Mr Tompkins was going home, feeling very tired after the long day's work in the bank, which was doing a land office business. He was passing a pub and decided to drop in for a glass of ale. One glass followed the other, and soon Mr Tompkins began to feel rather dizzy. In the back of the pub was a billiard room filled with men in shirt sleeves playing billiards on the central table. He vaguely remembered being here before, when one of his fellow clerks took him along to teach him billiards. He approached the table and started to watch the game. Something very queer about it! A player put a ball on the table and hit it with the cue. Watching the rolling ball, Mr Tompkins noticed to his great surprise that the ball began to ‘spread out’. This was the only expression he could find for the strange behaviour of the ball which, moving across the green field, seemed to become more and more washed out, losing its sharp contours. It looked as if not one ball was rolling across the table but a great number of balls, all partially penetrating into each other. Mr Tompkins had often observed analogous phenomena before, but today he had not taken a single drop of whisky and he could not understand why it was happening now. ‘Well,’ he thought, ‘let us see how this gruel of a ball is going to hit another one.’
The billiard ball rolls smartly along the baize, aimed for another ball at the far end of the table. The player watching its trajectory anticipates the solid tlock! of contact, to be followed by the familiar textbook demonstration of the conservation of energy and momentum. But something has gone awry on this billiards table. The moving ball passes right through the stationary one, without altering its own motion or disturbing the repose of its target. And then the rolling ball glides wraithlike through the rail at the edge of the table and continues imperturbably sailing across the room, with no inclination to fall to the floor. What’s going on here? It’s not quantum tunneling;
Next morning Mr Tompkins was dozing in bed, when he became aware of somebody's presence in the room. Looking round, he discovered that his old friend the professor was sitting in the armchair, absorbed in the study of a map spread on his knee. ‘Are you coming along?’ asked the professor, lifting his head. ‘ Coming where?’ said Mr Tompkins, still wondering how the professor had got into his room. ‘To see the elephants, of course, and the rest of the animals of the quantum jungle. The owner of the billiard room we visited recently told me his secret about the place where the ivory for his billiard-balls came from. You see this region which I've marked with red pencil on the map? It seems that everything within it is subject to quantum laws with a very large quantum constant. The natives think that all this part of the country is populated by devils, and I am afraid it will hardly be possible for us to find a guide. But if you want to come along, you had better hurry up. The boat is sailing in an hour's time and we still have to pick up Sir Richard on our way.’ ‘Who is Sir Richard?’ asked Mr Tompkins. ‘ Haven't you ever heard about him?’ The professor was evidently surprised. ‘He is a famous tiger-hunter, and decided to go with us, when I promised him some interesting shooting.’
Next morning Mr Tompkins was dozing in bed, when he became aware of somebody's presence in the room. Looking round, he discovered that his old friend the professor was sitting in the armchair, absorbed in the study of a map spread on his knee. ‘Are you coming along?’ asked the professor, lifting his head. ‘Coming where?’ said Mr Tompkins, still wondering how the professor had got into his room. ‘To see the elephants, of course, and the rest of the animals of the quantum jungle. The owner of the billiard room we visited recently told me his secret about the place where the ivory for his billiard-balls came from. You see this region which I've marked with red pencil on the map? It seems that everything within it is subject to quantum laws with a very large quantum constant. The natives think that all this part of the country is populated by devils, and I am afraid it will hardly be possible for us to find a guide. But if you want to come along, you had better hurry up. The boat is sailing in an hour's time and we still have to pick up Sir Richard on our way.’ ‘Who is Sir Richard?’ asked Mr Tompkins. ‘Haven't you ever heard about him?’ The professor was evidently surprised. ‘He is a famous tiger-hunter, and decided to go with us, when I promised him some interesting shooting.’
A few days later, while finishing his dinner, Mr Tompkins remembered that it was the night of the professor's lecture on the structure of the atom, which he had promised to attend. But he was so fed up with his father-in-law's interminable expositions that he decided to forget the lecture and spend a comfortable evening at home. However, just as he was getting settled with his book, Maud cut off this avenue of escape by looking at the clock and remarking, gently but firmly, that it was almost time for him to leave. So, half an hour later, he found himself on a hard wooden bench in the university auditorium together with a crowd of eager young students. ‘Ladies and gentlemen,’ began the professor, looking at them gravely over his spectacles, ‘In my last lecture I promised to give you more details concerning the internal structure of the atom, and to explain how the peculiar features of this structure account for its physical and chemical properties. You know, of course, that atoms are no longer considered as elementary indivisible constituent parts of matter, and that this role has passed now to much smaller particles such as electrons, protons, etc.’
I distinguish between two conceptually different kinds of physical space: a space of ordinary material bodies, which is the space of points at which I could imaginably place (say) the tip of my finger, or the center of a billiard-ball, and a space of elementary physical determinables, which is the smallest space of points such that stipulating what is happening at each one of those points, at every time, amounts to an exhaustive physical history of the universe. In all classical physical theories, these two spaces happen to coincide – and what we mean by calling a theory “classical”, and all we mean by calling a theory “classical”, is (I will argue) precisely that these two spaces coincide. But once the distinction between these two spaces in on the table, it becomes clear that there is no logical or conceptual reason why they must coincide – and it turns out (and this is the main topic of the present paper) that a very simple way of pulling them apart from one another gives us quantum mechanics.