Arthur Eddington

“ He who doubts the reality of the four-dimensional world (for logical, as distinct from experimental, reasons) can only be compared to a man who doubts the reality of the penny, and prefers to regard one of its innumerable appearances as the real object.
Physical reality is the synthesis of all possible physical aspects of nature. An illustration may be taken from the phenomena of radiant-energy, or light. In a very large number of phenomena the light coming from an atom appears to be a series of spreading waves, extending so as to be capable of filling the largest telescope yet made. ”

“ Mind exalts the permanent and ignores the transitory; and it appears from the mathematical study of relations that the only way in which mind can achieve her object is by picking out one particular quality as the permanent substance of the perceptual world, partitioning a perceptual time and space for it to be permanent in, and, as a necessary consequence of this Hobson's choice, the laws of gravitation and mechanics and geometry have to be obeyed. Is it too much to say that mind's search for permanence has created the world of physics? ”

“ If atomicity depends on laws inherent in nature, it seems at first difficult to understand why it should relate to matter especially; since matter is not of any great account in the analytical scheme, and owes its importance to irrelevant considerations introduced by the mind. It has appeared, however, that atomicity is by no means confined to matter and electricity; the quantum, which plays so great a part in recent physics, is apparently an atom of action. ”

“ At present, there seems no ground for believing that discontinuity is a law due to the mind; indeed the mind seems rather to take pains to smooth the discontinuities of nature into continuous perception. We can only suppose that there is something in the nature of things that causes this aggregation into atoms. Probably our analysis into point-events is not final; and if it could be pushed further to reach something still more fundamental, then atomicity and the remaining laws of physics would be seen as identities. ”

“ So nature cannot be accused of connivance with mind in singling out matter for special distinction. Action is generally regarded as the most fundamental thing in the real world of physics, although the mind passes it over because of its lack of permanence; and it is vaguely believed that the atomicity of action is the general law, and the appearance of electrons is in some way dependent on this. But the precise formulation of the theory of quanta of action has hitherto baffled physicists. ”

“ In the relativity theory of nature the most elementary concept is the point-event. In ordinary language a point-event is an instant of time at a point of space; but this is only one aspect of the point-event, and it must not be taken as a definition. Time and space—the familiar terms—are derived concepts to be introduced much later in our theory. The first simple concepts are necessarily undefinable, and their nature is beyond human understanding. The aggregate of all the point-events is called the world. ”

“ This is how our theory now stands.—We have a world of point-events with their primary interval-relations. Out of these an unlimited number of more complicated relations and qualities can be built up mathematically, describing various features of the state of the world. These exist in nature in the same sense as an unlimited number of walks exist on an open moor. ”

“ It is one thing for the human mind to extract from the phenomena of nature the laws which it has itself put into them; it may be a far harder thing to extract laws over which it has had no control. ”

“ We see now that the choice of a permanent substance for the world of perception necessarily carries with it the law of gravitation, all the laws of mechanics, and the introduction of the ordinary space and time of experience. ”

“ We can conceive a world constituted otherwise. But our argument hitherto has been that, however the world is constituted, the necessary combinations of things can be found which obey the laws of mechanics, gravitation and electrodynamics, and these combinations are ready to play the part of the world of perception for any mind that is tuned to appreciate them; and further, any world of perception of a different character would be rejected by the mind as unsubstantial. ”

“ It must be recognised that the conservation of mass is not exactly equivalent to the permanence of matter. If a loaf of bread suddenly transforms into a cabbage, our surprise is not diminished by the fact that there may have been no change of weight. It is not very easy to define this extra element of permanence required, because we accept as quite natural apparently similar transformations—an egg into an omelette, or radium into lead. ”

“ The recorded games are our physical experiments. The rules of the game, ascertained by study of them, are the laws of physics. The hypothetical chess-board of 64 squares is the space and time of some particular observer or player; whilst the more general relations of two-fold order, are the absolute relations of order in space-time which we have been studying. The chessmen are the entities of physics—electrons, particles, or point-events ”

“ All the appearances can be accounted for if we are all looking at a three-dimensional object—a penny—and no reasonable person can doubt that the penny is the corresponding physical reality. Similarly, an observer on the earth sees and measures an oblong block; an observer on another star contemplating the same object finds it to be a cube. Shall we say that the oblong block is the real thing, and that the other observer must correct his measures to make allowance for his motion? ”

“ And he was no less convinced that these geometrical notions were only partial aspects of the relations of what he calls "elements of feeling."—"The reality corresponding to our perception of the motion of matter is an element of the complex thing we call feeling. What we might perceive as a plexus of nerve-disturbances is really in itself a feeling; and the succession of feelings which constitutes a man's consciousness is the reality which produces in our minds the perception of the motions of his brain. ”

“ But now it has been discovered that there are new points of view with new appearances; and the reality must contain them all. It is by bringing in all these new points of view that we have been able to learn the nature of the real world of physics.
Let us briefly recapitulate the steps of our synthesis. We found one step already accomplished. The immediate perception of the world with one eye is a two-dimensional appearance. But we have two eyes, and these combine the appearances of the world as seen from two positions ”

“ There is a striking contrast between the triumph of the scientific mind in formulating the great general scheme of natural laws, nowadays summed up in the principle of least action, and its present defeat by the newly discovered but equally general phenomena depending on the laws of atomicity of quanta. ”

“ So the mind surveying the world of point-events looks for the permanent things. The simpler relations, the intervals and potentials, are transient, and are not the stuff out of which mind can build a habitation for itself. But the thing that has been identified with matter is permanent, and because of its permanence it must be for mind the substance of the world. ”

“ The fact that in nature a ring has atomic and not continuous structure is scarcely relevant. A conception of motion which affords a distinction between a rotating and non-rotating continuous ring must be possible; otherwise this would amount to an a priori proof that matter is atomic. According to the conception now proposed, velocity of matter is as much a static quality as density. Generally velocity is accompanied by changes in the physical state of the world, which afford the usual means of recognising its existence ”

“ Is not the real world that which comprehends the appearances to all real observers? Whether or not it is a tenable hypothesis that that which no one observes does not exist, science uncompromisingly rejects it. ”

“ Our brains are constituted of matter, and they feel and think—or at least feeling and thinking are closely associated with motions or changes of the matter of the brain. It would be difficult to say that any hypothesis as to the nature of matter makes this process less or more easily understood; and a brain constituted out of differential coefficients of 's can scarcely be said to be less adapted to the purposes of thought than one made, say, out of tiny billiard balls! ”

“ A definition of the velocity of matter in some such terms as "wind divided by air" does not correspond to the way in which motion primarily manifests itself in our experience. Motion is generally recognised by the disappearance of a particle at one point of space and the appearance of an apparently identical particle at a neighbouring point. ”

“ So far as we know, the different possible impersonal points of view have been exhausted—those for which the observer can be regarded as a mechanical automaton, and can be replaced by scientific measuring-appliances. A variety of more personal points of view may indeed be needed for an ultimate reality; but they can scarcely be incorporated in a real world of physics. There is thus justification for stopping at this point but not for stopping earlier. ”

“ Here is a hint of aspects deep within the world of physics, and yet unattainable by the methods of physics. And, moreover, we have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature. ”

“ The law of gravitation is not a law in the sense that it restricts the possible behaviour of the substratum of the world; it is merely the definition of a vacuum. We need not regard matter as a foreign entity causing a disturbance in the gravitational field ”

“ The kinematical conception of motion implies change—disappearance at one point and reappearance at another point—but no change is detectable. The state at any one moment is the same as at a previous moment, and the matter occupying one position now is indistinguishable from the matter in the same position a moment ago. At the most it can only differ in a mysterious non-physical quality—that of identity ”

“ It is postulated that the world is four-dimensional, which means that a particular point-event has to be specified by the values of four variables or coordinates, though there is entire freedom as to the way in which these four identifying numbers are to be assigned.
The meaning of the statement that the world is four-dimensional is not so clear as it appears at first. An aggregate of a large number of things has in itself no particular number of dimensions. ”

“ This definition of velocity enables us to understand why velocity except in reference to matter is meaningless, whereas acceleration and rotation have a meaning. The philosophical argument, that velocity through space is meaningless, ceases to apply as soon as we admit any kind of structure or aether in empty regions; consequently the problem is by no means so simple as is often supposed. But our definition of velocity is dynamical, not kinematical. Velocity is the ratio of certain components of , and only exists when is not zero. ”

“ Secondly, familiar objects belong not to the real world of physics, but to a much earlier stage in the synthesis of appearances. The ultimate elements in a theory of the world must be of a nature impossible to define in terms recognisable to the mind. ”

“ The two equations are accordingly merely definitions—definitions of the way in which certain states of the world (described in terms of the indefinables) impress themselves on our perceptions. When we perceive that a certain region of the world is empty, that is merely the mode in which our senses recognise that it is curved no higher than the first degree. ”

“ But if the law of quanta do indeed differentiate the actual world from other worlds possible to the mind, we may expect the task of formulating them to be far harder than anything yet accomplished by physics. ”

“ The primary interval relation is of an undefined nature, and the 's contain this undefinable element. The expression is therefore of defined form, but of undefined content. By its form alone it is fitted to account for all the physical properties of matter; and physical investigation can never penetrate beneath the form. The matter of the brain in its physical aspects is merely the form; but the reality of the brain includes the content. ”

“ In actual fact, however, if the hypotheses as stated were correct, the objective counterparts would form a world having the same structure as the phenomenal world.... In short, every proposition having a communicable significance must be true of both worlds or of neither: the only difference must lie in just that essence of individuality which always eludes words and baffles description, but which for that very reason is irrelevant to science. ”

“ Hence the interval is at once identified with something familiar to experience, namely the thing that a scale and a clock measure. However advantageous that may be for the sake of bringing the theory into touch with experiment at the outset, we can scarcely hope to build up a theory of the nature of things if we take a scale and clock as the simplest unanalysable concepts. The result of this logical inversion is that by the time the equation is encountered, both sides of the equation are well-defined quantities. ”