Arthur Eddington

“ The distinction between horizontal and vertical is not an illusion; and the man who thinks it can be disregarded is likely to come to an untimely end. Yet we cannot arrive at a comprehensive view of nature unless we combine horizontal and vertical dimensions into a three-dimensional space. ”

“ Consequently for an observer travelling with the speed of light all ordinary objects become two-dimensional, preserving their lateral dimensions, but infinitely thin longitudinally. The fact that events take place "in no time" is usually explained by saying that the inertia of any particle moving with the velocity of light becomes infinite so that all molecular processes in the observer must stop; many things may happen in 's world in a twinkling of an eye—of 's eye. ”

“ Fortunately it will be sufficient for us to consider only the one dimension of space and deal with the phenomena of "line-land," i.e. we limit ourselves to motion to and fro in one straight line in space. ”

“ Hence it appears that mass (inertia) and energy are essentially the same thing, or, at the most, two aspects of the same thing. It must be remembered that on this view the greater part of the mass of matter is due to concealed energy, which is not as yet releasable.
The question whether electrical energy not bound to electric charges has mass, is answered in the affirmative in the case of light. Light has mass. Presumably also gravitational energy has mass; or, if not, mass will be created when, as often happens, gravitational energy is converted into kinetic energy. ”

“ A natural body extends in time as well as in space, and is therefore four-dimensional; but for the analogy to hold, the object must have one dimension less than the world, like the square seen from the third dimension. ”

“ We cannot use a scale at all; some kind of clock is needed. The most natural connection between the measure of time and length is given by the fact that light travels 300,000 kilometres in 1 second. For the four-dimensional world we shall accordingly regard 1 second as the equivalent of 300,000 kilometres, and measure lengths and times in seconds or kilometres indiscriminately; in other words we make the velocity of light the unit of velocity. ”

“ When the calculations are extended to charges moving with high velocities, it is found that the electrical inertia is not strictly constant but depends on the speed; in all cases the variation is summed up in the statement that the inertia is simply proportional to the total energy of the electromagnetic field. We can say if we like that the mass of a charged particle at rest belongs to its electrostatic energy; when the charge is set in motion, kinetic energy is added, and this kinetic energy also has mass. ”

“ Hence, even if the discovery of a new ray led us to modify the reckoning of time and space, it would still be necessary in the study of material systems to preserve the present absolute distinction of time-like and space-like intervals, under a new name if necessary.
It may be asked whether it is possible for anything to have a speed greater than the velocity of light. Certainly matter cannot attain a greater speed ”

“ Although there is an absolute past and future, there is between them an extended neutral zone; and simultaneity of events at different places has no absolute meaning. For our selected observer all events along are simultaneous with one another; for another observer the line of events simultaneous with would lie in a different direction. The denial of absolute simultaneity is a natural complement to the denial of absolute motion. ”

“ Later on we shall reach in a more general way the identification of mass with energy and the variation of mass with speed; but, since the experimental measurement of inertia involves the study of a body in non-uniform motion, it is not possible to enter on a satisfactory discussion of mass until the more general theory of relativity for non-uniform motion has been developed. ”

“ According to the time-reckoning of our chosen observer , is after , because it lies above the line ; but there is nothing absolute about this. The track corresponds to a velocity greater than that of light, so that we know of no particle or physical impulse which could follow the track. An observer experiencing the event could not get news of the event by any known means until after had happened. The order of the two events can therefore only be inferred by estimating the delay of the message and this estimate will depend on the observer's mode of reckoning space and time. ”

“ Any entity with a speed greater than light would have the peculiarity of Sir Boyle Roche's bird. It can scarcely be said to be a self-contradictory property to be in two places at the same time any more than for an object to be at two times in the same place. ”

“ These differences are summed up in the statement that the geometry of space is Euclidean, but the geometry of space-time is semi-Euclidean or "hyperbolic." The association of a geometry with any continuum always implies the existence of some uniquely measurable quantity like interval or distance; in ordinary space, geometry without the idea of distance would be meaningless. ”

“ The section gives three-dimensional space at some moment, and the perpendicular dimension is (imaginary) time. Clearly the slice may be taken in any direction; there is no question of a true separation and a fictitious separation. There is no conspiracy of the forces of nature to conceal our absolute motion—because, looked at from this broader point of view, there is nothing to conceal. The observer is at liberty to orient his rectangular axes of , , and arbitrarily, just as in three-dimensions he can orient his axes of , , arbitrarily. ”

“ The fact that the velocity of light is the same for all observers is a consequence rather than a cause of its pre-eminent character. Our first introduction of it, for the purpose of coordinating units of length and time, was merely conventional with a view to simplifying the algebraic expressions. ”

“ The two velocities and their resultant are not all reckoned with respect to the same partitions of space and time. When measures 's velocity relative to him he uses his own space and time, and it must be corrected to reduce to 's space and time units, before it can be added on to a velocity measured by .
If we continue the chain, introducing whose velocity relative to , and measured by , is 100 km. per sec., and so on ad infinitum, we never obtain an infinite velocity with respect to , but gradually approach the limiting velocity of 300,000 km. per sec., the speed of light. ”

“ If quantity of matter is to be identified with its mass, the second phenomenon does not happen. It could easily be conceived of as happening, but it is provided against by a special law of nature—the conservation of mass. ”

“ The case for the electrical theory of matter is actually weakened, because many experimental effects formerly thought to depend on the peculiar properties of electrical forces are now found to be perfectly general consequences of the relativity of observational knowledge. ”

“ It should be possible for a body to enter a completely closed room, by travelling into it in the direction of the fourth dimension, just as we can bring our pencil down on to any point within a square without crossing its sides. ”

“ It can be shown that the different space and time used by the aviator in Chapter i correspond to an orientation of the time-axis along his own course in the four-dimensional world, whereas the ordinary time and space are given when the time-axis is oriented along the course of a terrestrial observer. The FitzGerald contraction and the change of time-measurement are given exactly by the usual formulae for rotation of rectangular axes [2] . ”

“ It is the relation of order which is intrinsic in nature, and is the same both for the squares and diamonds; shape is put into nature by the observer when he has chosen his partitions.
We can now deduce the FitzGerald contraction. Consider a rod of unit length at rest relatively to the observer . The two extremities are at rest in his space, and consequently remain on the same space-partitions; hence their tracks in four dimensions , (Fig. 7) are entirely in the time-direction. The real rod in nature is the four-dimensional object shown in section as . ”