It is an especial pleasure to me that George Gamow's two gems—concerning the two adventures of Mr Tompkins in the wonderful worlds conjured up when the speed of light is made small or Planck's constant large—are now reprinted in paperback. Whilst, with hindsight, one may find details to quibble about, the excitement of these deeply delightful tales remains as fresh with me as it was some fifty years ago when I first encountered them. Though physics has moved on in many ways, the basic physics of relativity and quantum theory has not changed. By his ingenuity and narrative skills, Gamow is able to transform some of the puzzling and obscure mysteries of this basic physics—a physics which, indeed, is still modern—into magical and enthralling stories for children.

I remember reading (or being read) the Tompkins stories as a quite young child, and I am sure that their magic was responsible, to a very considerable extent, for the great excitement that fundamental physics has held for me for the rest of my life. I still vividly recall the tigers of the quantum jungle, and the old woodcarver's boxes of mysterious coloured balls (the nucleons), the relativistically flattened bicycle, and the professor calling out ‘Just lie down and observe’ as he and Mr Tompkins see their miniature universe collapse inwards upon them.

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.’

PERMANENCE UNEXPLAINABLE BY CLASSICAL PHYSICS

Thus, aided by the marvellously subtle instrument of X-rays (which, as the physicist remembers, revealed thirty years ago the detailed atomic lattice structures of crystals), the united efforts of biologists and physicists have of late succeeded in reducing the upper limit for the size of the microscopic structure, being responsible for a definite large-scale feature of the individual – the ‘size of a gene’ – and reducing it far below the estimates obtained on pp. 29–30. We are now seriously faced with the question: How can we, from the point of view of statistical physics, reconcile the facts that the gene structure seems to involve only a comparatively small number of atoms (of the order of 1,000 and possibly much less), and that nevertheless it displays a most regular and lawful activity – with a durability or permanence that borders upon the miraculous?

Let me throw the truly amazing situation into relief once again. Several members of the Habsburg dynasty have a peculiar disfigurement of the lower lip (‘Habsburger Lippe’). Its inheritance has been studied carefully and published, complete with historical portraits, by the Imperial Academy of Vienna, under the auspices of the family.

From early childhood onwards we grow accustomed to the surrounding world as we perceive it through our five senses; in this stage of mental development the fundamental notions of space, time and motion are formed. Our mind soon becomes so accustomed to these notions that later on we are inclined to believe that our concept of the outside world based on them is the only possible one, and any idea of changing them seems paradoxical to us. However, the development of exact physical methods of observation and the profounder analysis of observed relations have brought modern science to the definite conclusion that this ‘classical’ foundation fails completely when used for the detailed description of phenomena ordinarily inaccessible to our everyday observation, and that, for the correct and consistent description of our new refined experience, some change in the fundamental concepts of space, time, and motion is absolutely necessary.

The deviations between the common notions and those introduced by modern physics are, however, negligibly small so far as the experience of ordinary life is concerned. If, however, we imagine other worlds, with the same physical laws as those of our own world, but with different numerical values for the physical constants determining the limits of applicability of the old concepts, the new and correct concepts of space, time and motion, at which modern science arrives only after very long and elaborate investigations, would become a matter of common knowledge.

One weekend Maud went away to visit her aunt in Yorkshire, and Mr Tompkins invited the professor to have dinner with him in a famous sukiyaki restaurant. Sitting on the soft cushions at a low table, they were enjoying all the delicacies of the Japanese kitchen and sipping sake from little cups.

‘Tell me,’ said Mr Tompkins. ‘The other day I heard Dr Tallerkin saying in his lecture that the protons and the neutrons in a nucleus were held together by some kinds of nuclear forces. Are those the same forces which hold electrons in an atom?’

‘Oh, no!’ answered the professor. ‘Nuclear forces are something quite different. Atomic electrons are attracted to the nucleus by ordinary electrostatic forces first studied in detail by a French physicist, CHARLES AUGUSTIN DE COULOMB, toward the end of the eighteenth century. They are comparatively weak and decrease in inverse proportion to the square of the distance from the centre. Nuclear forces are quite different. When a proton and a neutron come close to each other but not yet in direct contact, there are practically no forces between them. But as soon as they come into contact, there appears an extremely strong force which holds them together’.

SPACE AND TIME IN COSMOLOGY

The question about the nature of space and time is intimately linked with the question of cosmology: Did space and time have a beginning? Do they go on forever? Space and time form the framework for our picture of cosmology, while our large-scale view of the Universe puts the limits on what space and time are.

The nature of space and time underwent a radical change from Newton to Einstein. As Newton set out in his Principia Mathematica, space and time was an unchanging Aristotelian background to the unfolding play of particles and waves. But even this seemingly innocuous assumption caused Newton problems. Gravity acted instantaneously everywhere (action at a distance); a radical idea for the 1770s used to the idea that every effect had a direct cause. If the Universe was infinite in extent, the forces acting on any given point would depend instantaneously on the influence of all of the matter throughout the Universe. But because the volume of space increases rapidly with distance these forces would accumulate and increase without limit in an infinite Universe. These problems were mainly swept under the carpet as Newtonian gravity clearly gave an excellent local approximation to the motion of the moon and planets.

NEW LAWS TO BE EXPECTED IN THE ORGANISM

What I wish to make clear in this last chapter is, in short, that from all we have learnt about the structure of living matter, we must be prepared to find it working in a manner that cannot be reduced to the ordinary laws of physics. And that not on the ground that there is any ‘new force’ or what not, directing the behaviour of the single atoms within a living organism, but because the construction is different from anything we have yet tested in the physical laboratory. To put it crudely, an engineer, familiar with heat engines only, will, after inspecting the construction of an electric motor, be prepared to find it working along principles which he does not yet understand. He finds the copper familiar to him in kettles used here in the form of long, long wires wound in coils; the iron familiar to him in levers and bars and steam cylinders is here filling the interior of those coils of copper wire. He will be convinced that it is the same copper and the same iron, subject to the same laws of Nature, and he is right in that.

Ladies and Gentlemen:

Tonight I will request your special attention, since the problems which I am going to discuss are as difficult as they are fascinating. I am going to speak about new particles, known as ‘positrons’, possessing more than unusual properties. It is very instructive to notice that the existence of this new kind of particle was predicted on the basis of purely theoretical considerations several years before they were actually detected, and that their empirical discovery was largely helped by the theoretical preview of their main properties.

The honour of having made this prediction belongs to a British physicist, Paul Dirac, of whom you have heard and who arrived at his conclusions on the basis of theoretical considerations so strange and fantastic that most physicists refused to believe them for quite a long time. The basic idea of Dime's theory can be formulated in these simple words: ‘There should be holes in empty space.’ I see you are surprised; well, so were all physicists when Dirac uttered these significant words. How can there be a hole in an empty space? Does this make any sense? Yes, if one implies that the so-called empty space is actually not so empty as we believe it to be.

In this last chapter I wish to demonstrate in a little more detail the very strange state of affairs already noticed in a famous fragment of Democritus of Abdera – the strange fact that on the one hand all our knowledge about the world around us, both that gained in everyday life and that revealed by the most carefully planned and painstaking laboratory experiments, rests entirely on immediate sense perception, while on the other hand this knowledge fails to reveal the relations of the sense perceptions to the outside world, so that in the picture or model we form of the outside world, guided by our scientific discoveries, all sensual qualities are absent. While the first part of this statement is, so I believe, easily granted by everybody, the second half is perhaps not so frequently realized, simply because the non-scientist has, as a rule, a great reverence for science and credits us scientists with being able, by our ‘fabulously refined methods’, to make out what, by its very nature, no human can possibly make out and never will be able to make out.

If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electro-magnetic waves of wave-length in the neighbourhood of 590 millimicrons.

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.’

Ladies and Gentlemen:

Today I am going to discuss the problem of curved space and its relation to the phenomena of gravitation. I have no doubt that any one of you can easily imagine a curved line or a curved surface, but at the mention of a curved, three-dimensional space your faces grow longer and you are inclined to think that it is something very unusual and almost supernatural. What is the reason for this common ‘horror’ for a curved space, and is this notion really more difficult than the notion of a curved surface? Many of you, if you will think a little about it, will probably say that you find it difficult to imagine a curved space because you cannot look on it ‘from outside’ as you look on a curved surface of a globe, or, to take another example, on the rather peculiarly curved surface of a saddle. However, those who say this convict themselves of not knowing the strict mathematical meaning of curvature, which is in fact rather different from the common use of the word. We mathematicians call a surface curved if the properties of geometrical figures drawn on it are different from those on a plane, and we measure the curvature by the deviation from the classical rules of Euclid. If you draw a triangle on a flat piece of paper the sum of its angles, as you know from elementary geometry, is equal to two right angles.