Arthur Eddington

“ To express this unmanageable mass of detail in a unified way, a world-geometry is found in which the tracks of greatest length are the actual tracks of the particles. It only remains to express the laws of this geometry in a concise form. The change from a mechanical to a geometrical theory of fields of force is not so fundamental a change as might be supposed. If we are now reducing mechanics to a branch of natural geometry, we have to remember that natural geometry is equally a branch of mechanics, since it is concerned with the behaviour of material measuring-appliances. ”

“ When we choose the non-rotating observer the centrifugal force disappears completely and everywhere. When we choose the occupant of the falling projectile, gravitation disappears in his immediate neighbourhood; but he would notice that, although unsupported objects round him experienced no acceleration relative to him, objects on the other side of the earth would fall towards him. So far from getting rid of the field of force, he has merely removed it from his own surroundings, and piled it up elsewhere. Thus gravitation is removable locally, but centrifugal force can be removed everywhere. ”

“ The centrifugal force is made to disappear if we choose a suitable standard observer not rotating with the earth; the gravitational force was made to disappear when we chose as standard observer an occupant of Jules Verne's falling projectile. If the possibility of annulling a field of force by choosing a suitable standard observer is a test of unreality, then gravitation is equally unreal with centrifugal force. ”

“ The field of force is not only perceived by the observer in his sensations, but reveals itself in his physical measures. It should be understood, however, that the curvature of track must not have been otherwise allowed for. Naturally if the observer in the lift recognises that his measures are affected by his own acceleration and applies the appropriate corrections, the artificial force will be removed by the process. It only exists if he is unaware of, or does not choose to consider, his acceleration. ”

“ Those who seek for an explanation of gravitation naturally aim to find a model which will reproduce its effects; but no one before Einstein seems to have thought of finding the clue in these artificial fields, familiar as they are.
When a lift starts to move upwards the occupants feel a characteristic sensation, which is actually identical with a sensation of increased weight. The feeling disappears as soon as the motion becomes uniform; it is associated only with the change of motion of the lift, that is to say, the acceleration. Increased weight is not only a matter of sensation ”

“ The projectile was responding freely to the pull of gravity, and so were its occupants. When an occupant let go of a plate, the plate could not "fall" any more than it was doing already, and so it must remain poised.
It will be seen that the sensation of weight is not felt when we are free to respond to the force of gravitation; it is only felt when something interferes to prevent our falling. It is primarily the floor or the chair which causes the sensation of weight by checking the fall. It seems literally true to say that we never feel the force of the earth's gravitation ”

“ Although it has become necessary to throw our formula into the melting-pot, that does not create any difficulty in measuring the interval. Without going into technical details, it may be pointed out that the innovations arise solely from the introduction of gravitational fields of force into our scheme. When there is no force, the tracks of all particles are straight lines as our previous geometry requires. In any small region we can choose an observer (falling freely) for whom the force vanishes, and accordingly the original formula holds good. ”

“ But even in elementary mechanics an important natural force appears, which does not seem to operate in this manner. Gravitation is not resolvable into a succession of molecular blows. A massive body, such as the earth, seems to be surrounded by a field of latent force, ready, if another body enters the field, to become active, and transmit motion. ”

“ Newtonian mechanics proceeds on the supposition that there is some super-observer. If he feels a field of force, then that force really exists. Lesser beings, such as the occupants of the falling projectile, have other ideas, but they are the victims of illusion. It is to this super-observer that the mathematician appeals when he starts a dynamical investigation with the words "Take unaccelerated rectangular axes, , , ...." Unaccelerated rectangular axes are the measuring-appliances of the super-observer. ”

“ Clearly the artificial field of force is associated with curvature of track, and we can lay down the following rule:—
Whenever the observer's track through the four-dimensional world is curved he perceives an artificial field of force. ”

“ Now, if the worst came to the worst, and we could not reconcile a geometry based on measures with clocks and scales and a geometry based on the natural tracks of moving particles—if we had to select one or the other and keep to it—I think we ought to prefer to use the geometry based on the tracks of moving particles. The free motion of a particle is an example of the simplest possible kind of phenomenon ”

“ FIELDS OF FORCE
For whenever bodies fall through water and thin air, they must quicken their descents in proportion to their weights, because the body of water and subtle nature of air cannot retard everything in equal degree, but more readily give way overpowered by the heavier; on the other hand empty void cannot offer resistance to anything in any direction at any time, but must, as its nature craves, continually give way ”

“ It is quite possible that there might be a super-observer, whose views have a natural right to be regarded as the truest, or at least the simplest. A society of learned fishes would probably agree that phenomena were best described from the point of view of a fish at rest in the ocean. ”

“ Similar artificial fields are produced when an aeroplane changes its course or speed; and one of the difficulties of navigation is the impossibility of discriminating between these and the true gravitation of the earth with which they combine. ”

“ To sum up—the interval between two (near) events is something quantitative which has an absolute significance in nature. The track between two (distant) events which has the longest interval-length must therefore have an absolute significance. Such tracks are called geodesics. Geodesics can be traced practically, because they are the tracks of particles undisturbed by material impacts. By the practical tracing of these geodesics we have the best means of studying the character of the natural geometry of the world. ”

“ There is no help for it, if the longest track can be a spiral like that known to be described by the earth. Non-Euclidean geometry is necessary. In Euclidean geometry the shortest track is always a straight line; and the slight modification of Euclidean geometry described in Chapter iii is found to give a straight line as the longest track. ”

“ Primarily it is an acceleration relative to the earth ; but then that can equally well be described as an acceleration of the earth relative to , and it is not fair to regard it as something located with . Its importance in Newtonian philosophy is that it is an acceleration relative to what we have called the super-observer. ”

“ One usually thinks of this influence as existing in the space round the earth even when there is no test-body to be affected, and in a rather vague way it is suspected to be some state of strain or other condition of an unperceived medium. ”

“ Each portion of the circumference is moving in the direction of its length, and might be expected to undergo the FitzGerald contraction due to its velocity; each portion of a radius is moving transversely and would therefore have no longitudinal contraction. ”