Arthur Eddington

“ The negation of absolute motion is thus associated with the possibility of choosing the time-direction in any way we please. What determines the separation of space and time for any particular observer can now be seen. Let the observer place himself so that he is, to the best of his knowledge, at rest. If he is a normal human being, he will seat himself in an arm-chair; if he is an astronomer, he will place himself on the sun or at the centre of the stellar universe. ”

“ It is through experiment that we have been led back to the principle of relativity for uniform motion. In seeking some kind of extension of this principle to accelerated motion, we are led by the feeling that, having got so far, it is difficult and arbitrary to stop at this point. We now try to conceive a system of nature for which all kinds of motion of the observer are indifferent. It will be a completion of our synthesis of what is perceived by observers having all kinds of motions with respect to one another, removing the restriction to uniform motion. ”

“ Force, as known to us observationally, is like the other quantities of physics, a relation. The force, measured with a spring-balance, for example, depends on the acceleration of the observer holding the balance; and the term may, like length and duration, have no exact counterpart in a description of nature independent of the observer. Newton's view assumes that there is such a counterpart, an active cause in nature which is identical with the force perceived by his standard unaccelerated observer. ”

“ The object of the relativity theory, however, is not to attempt the hopeless task of apportioning responsibility between the observer and the external world, but to emphasise that in our ordinary description and in our scientific description of natural phenomena the two factors are indissolubly united. All the familiar terms of physics—length, duration of time, motion, force, mass, energy, and so on—refer primarily to this relative knowledge of the world ”

“ Sometimes by instinctive habit, sometimes by design, we attempt to eliminate our own share in the observation, and so form a general picture of the world outside us, which shall be common to all observers. ”

“ Nevertheless, it would almost seem that such motion must logically exist, if the aether exists; and, even at the expense of formal simplicity, it ought to be exhibited in any theory which pretends to give a complete account of what is going on in nature. If a substantial aether analogous to a material ocean exists, it must rigidify, as it were, a definite space; and whether the observer or whether nature pays any attention to that space or not, a fundamental separation of space and time must be there. ”

“ Just as the observer by changing his orientation makes a new division of the two-dimensional plane into right-and-left, backwards-and-forwards—just as the observer by changing his longitude makes a new division of three-dimensional space into vertical and horizontal—so the observer by changing his motion makes a new division of the four-dimensional order into time and space. ”

“ More personal idiosyncracies disappear if, instead of relying on his crude senses, he employs scientific measuring apparatus. But scientific apparatus has position, motion and size, so that these are still involved in the results of any observation. There is no essential distinction between scientific measures and the measures of the senses. In either case our acquaintance with the external world comes to us through material channels; the observer's body can be regarded as part of his laboratory equipment, and, so far as we know, it obeys the same laws. ”

“ We have two eyes, which have dinned into our minds from babyhood that the world has to be looked at from more than one position. Our brains have so far responded as to give us the idea of solid relief, which enables us to appreciate the three-dimensional world in a vivid way that would be scarcely possible if we were only acquainted with strictly two-dimensional pictures. ”

“ We not merely deduce the three-dimensional world; we see it. But we have no such aid in synthesising different motions. Perhaps if we had been endowed with two eyes moving with different velocities our brains would have developed the necessary faculty; we should have perceived a kind of relief in a fourth dimension so as to combine into one picture the aspect of things seen with different motions. ”

“ The only definition of this epithet that can be given is that an "unaccelerated" observer is one for whom Newton's laws of motion hold. On this theory, the phenomena are not indifferent to an acceleration or non-uniform motion of the whole system. Yet an absolute non-uniform motion through space is just as impossible to imagine as an absolute uniform motion. The partial relativity of phenomena makes the difficulty all the greater. If we deny a fundamental medium with continuous identity of its parts, motion uniform or non-uniform should have no significance ”

“ What we mean by the equivalence of all frames is that they are not differentiated by any qualities formerly supposed to be intrinsic in the frames themselves—rest, rectangularity, acceleration—independent of the absolute structure of the world that is referred to them. Accordingly the objection to attributing absolute properties to Newton's frame of reference is not that it is impossible for a frame of reference to acquire absolute properties, but that the Newtonian frame has been laid down on the basis of relative knowledge without any attempt to follow the lines of absolute structure. ”

“ It would be unreasonable to limit our thought of nature to what can be comprised in sense-pictures. As Lodge has said, our senses were developed by the struggle for existence, not for the purpose of philosophising on the world. ”

“ The most formidable objection to this relativist view of the world is the aether difficulty. We have seen that uniform motion through the aether cannot be detected by experiment, and therefore it is entirely in accordance with experiment that such motion should have no counterpart in the four-dimensional world. ”

“ An observer on the sun considers that they do not occur at the same place; they are separated by about 70,000 miles, that being the distance travelled by the earth in its orbital motion with respect to the sun. It is clear that he is not resolving in quite the same directions as the terrestrial observer, since he finds the space-component to be 70,000 miles instead of zero. But if he alters one component he must necessarily alter the other ”

“ But this assumes that the observed effects of centrifugal force cannot be produced in any other way than by rotation of the observer's frame of reference. If once it is admitted that centrifugal force may not be completely distinguishable by experiment from another kind of force—gravitation—perceived even by Newton's unaccelerated observer, the argument ceases to apply. We can never determine exactly how much of the observed field of force is centrifugal force and how much is gravitation; and we cannot find experimentally any definite standard that is to be considered absolutely non-rotating. ”

“ They explore the new field and bring back their spoils—a few simple generalisations—to apply them to the practical world of three-dimensions. Some guiding light will be given to the attempts to build a scheme of things entire. For the rest, physics will continue undisturbedly to explore the relative world, and to employ the terms applicable to relative knowledge, but with a fuller appreciation of its relativity. ”

“ Our present point is that there is but one separation of two events in four dimensions, which can be resolved in any number of ways into the components length and duration.
We see further how motion must be purely relative. Take two events and in the history of one particle. We can choose any direction as the time-direction; let us choose it along . Then and are separated only in time and not in space, so the particle is at rest. If we choose a slightly inclined time-direction, the separation will have a component in space ”

“ We see the starry heavens revolve round the earth, but decide that it is really the earth that is revolving, and so picture the state of the universe in a way which would be acceptable to an astronomer on any other planet.
The first step in throwing our knowledge into a common stock must be the elimination of the various individual standpoints and the reduction to some specified standard observer. The picture of the world so obtained is none the less relative. We have not eliminated the observer's share ”

“ A small speck on the horizon of the sea is interpreted as a giant steamer. From the window of our railway carriage we see a cow glide past at fifty miles an hour, and remark that the creature is enjoying a rest. ”

“ Our first task is a description of the world independent of the motion of the observer. The question of the elimination of his gauge of magnitude belongs to a later development of the theory discussed in Chapter xi. Let us draw a square on a sheet of paper, making the sides equal, to the best of our knowledge. We have seen that an aviator flying at 161,000 miles a second in the direction , would judge that the sides , had contracted to half their length, so that for him the figure would be an oblong. ”

“ It will be seen that we are not fully equipped by our senses for forming an impersonal picture of the world. And it is because the deficiency is manifest that we do not hesitate to advocate a conception of the world which transcends the images familiar to the senses. ”

“ Accordingly Newton's laws of mechanics are not of the general type in which it is unnecessary to particularise the observer; they hold only for observers with a special kind of motion which is described as "unaccelerated." ”

“ This problem of rotation affords a hint as to the cause of the incomplete relativity of Newtonian mechanics. The laws of motion are formulated with respect to an unaccelerated observer, and do not apply to a frame of reference rotating with the earth. Yet mathematicians frequently do use a rotating frame. ”