"Then I must ask your permission to continue my attempt; perhaps something useful may yet result from it. I now picture to myself a human being who lived in classical times and who, following Ovid and the great majority of his contemporaries, regards the earth as a disc. On this disc, each inhabitant of the earth has his own particular position, for the disc has a centre with reference to which the position of a person can be specified if his distance and his angular displacement from a given initial radius is specified. Thus, there is a variation of position if various persons are considered. On the other hand, the Above and the Below is absolutely invariable for all persons, for the lines running between Above and Below are all parallel for them, since they all have uniformly the same disc under their feet and the same heaven above their heads. Ovid would therefore have refused to entertain for a moment the suggestion that Above-Below is a variable. But his distant descendants accepted the view that the earth is spherical and that there are antipodes as self-evident, and they found not the slightest difficulty in considering the line Above-Below to vary with their own position, making all possible angles with an initial line extending to direct oppositeness. Referred to the centre of the sphere, all people have now an 'invariant' position, whereas, in compensation, the Above-Below is subject to every conceivable variation. And now I again address myself to the average reader, and say that the meaning of these analogies is that every doctrine that leads to a great uniformity converts what was formerly invariant into a variable quantity, and vice versa. The theory of relativity makes all considerations about the physical world independent of all co-ordinate systems; it establishes completely invariable uniformity, removed from all changes due to varying points of view. Hence what was previously invariable—such as a rigid measuring-rod—will now become variable. It is not surprising that this requires a new method of thought, a revision of our mode of reasoning, for the above analogies show that these radical adjustments are characteristically necessary in the case of comprehensive theories, and that such theories are able to overcome apparently firmly established ideas. The parallels that I drew above will at least inspire the average reader with a certain confidence, for they show him how results of reasoning that were once considered incredible were regarded as self-evident by later generations."
I have already emphasized sufficiently that Einstein regards as inadequate these auxiliary pictures that have presented themselves to me. Yet in the course of the conversation I gained the impression that his judgment grew somewhat milder, and that, with certain reservations, he was disposed to let them pass as tolerably useful helps—and they are not intended to be more than this. I think, therefore, that I am not acting counter to his wishes in citing these allegorical examples here, particularly as they arose in the course of our talks.
Since then, I have had many opportunities of testing these examples on certain persons, and may mention that they proved quite useful. Analogies of this kind may offer a friendly help in moments when the uninitiated feel themselves in peril, and encounter a difficulty which they imagine to be insurmountable. They do not remove the difficulty, but they impart a certain power of expansion to the intellect and encourage a continuation of effort, which would probably otherwise be relaxed at the first sign of something which is imagined to be inconceivable. There is thus no room in textbooks for such helps, but they may justifiably find a place in a book that departs from the methodical route, and hopes to discover in by-ways things that are suggestive and instructive.
CHAPTER X
DISCONNECTED SUGGESTIONS
Conditionality and Unconditionality of Physical Laws.—Conception of Temperature.—Grain of Sand and Universe.—Are Laws unalterable?—Paradoxes of Science.—Rejuvenation by Motion.—Gain of a Second.—Deformed Worlds.—Atomic Model.—Researches of Rutherford and Niels Bohr.—Microcosmos and Macrocosmos.—Brief Statement of the Principle of Relativity.—Science with reduced Sense-Organs.—Eternal Repetition.—Higher Types of Culture.
IN all branches of reasoning, no word and no conception has played a more important part than that of law. Physical laws denote the barrier that separates strictly chance and arbitrariness from necessity, and it seems to us that the region of the latter must ever extend so that finally nothing will be left of the former, which will have become amalgamated with necessity. We shall be constrained to believe more and more in a supreme law that will be a complete expression of all the partial laws which science presents to us as more or less permanent results of individual researches.
Our conversation was centred about these individual laws, such as those that are taught in the theory of gases, optics, etc., and that are associated with the names, Boyle, Gay-Lussac, Dalton, Marriotte, Huyghens, Fresnel, Kirchhoff, Boltzmann, and others. In connexion with these I asked Einstein whether he regarded the laws as things unconditioned in themselves, and capable of proof under every set of circumstances; and whether absolutely valid laws existed or could exist.
Einstein's answer was essentially in the negative. "A law cannot be final, if only for the reason that the conceptions, which we use to formulate it, show themselves to be imperfect or insufficient as science progresses. Let us consider, for example, an elementary law such as Newton's Law of Force. From our more recent point of view we find the conception of direct action at a distance to be inexact in Nature. For it has been shown that action at a distance is not an ultimate factor, but must be resolved into a multiplicity of actions between immediately neighbouring points (The Theory of Action by Contact or Contiguous Action). Another example is provided by the conception Temperature. This conception becomes meaningless if we endeavour to apply it to molecules: it leads to no result if we try to impose it on the smallest parts of matter as such. The reason is that the state, the velocity, and the inner energy of the individual molecules fluctuates between very wide limits. The conception 'temperature' is applicable only to a configuration composed of many molecules, and even then it is not applicable quite generally. For let us picture to ourselves an extremely rarefied gas contained in a closed receiver. Two opposite walls are to be at different temperatures, the one being cold and the other being hot In a gas at such very low pressure the molecules come into collision so seldom that, practically, we have to take into account only the collisions of the molecules with the confining walls. The molecules that rebound from the hot wall have greater velocities than those coming from the colder wall, and hence the conception of temperature becomes untenable for this gas."
"Would the temperature-scale on the thermometer then denote nothing?" I asked. "The greater or lesser degree of warmth of a body, in this case of the mass of gas, depends on the more rapid or less rapid motion of its smallest parts. The motions are in any case present, so what would a thermometer indicate?"
"It would betray only that it had nothing to indicate. If a thermometer that is blackened on one side were inserted into the vessel containing the gas, then different temperatures would be recorded if the thermometer were gradually turned about its own axis; and this signifies that the conception of temperature has become meaningless for this configuration of molecules. And passing beyond the quoted examples, I should maintain that all our conceptions, however subtly they may have been thought out, are shown in the course of progressive knowledge to be too rough hewn, that is, too little differentiated."