Albert Einstein

“ An observer who is sitting eccentrically on the disc is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference-body . But the observer on the disc may regard his disc as a reference-body which is "at rest"; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. ”

“ Albrecht Einstein has now spread far beyond the narrow pale of scientific investigators owing to the brilliant confirmation of his predicted deflection of light-rays by the gravitational field of the sun during the total solar eclipse of May 29, 1919. But to the serious student of science, he has been known from the beginning of the current century, and many dark problems in physics has been illuminated with the lustre of his genius, before, owing to the latest sensation just mentioned, he flashes out before public imagination as a scientific star of the first magnitude. ”

“ In Einstein's theory like in the older interpretation there is a guidance field that is followed by a body according to the Galilean principle, as long as no forces act on it. The catastrophe happens at the train and not at the church steeple, since the first is thrown out of its path by the molecular forces of the oncoming train, but the church steeple is not. This answer is also completely in agreement with "commons sense", which whole-heartedly agrees that the inertial-tendency of the guidance field (that opposes to the forces) can be seen as a physical reality. ”

“ The popular name for this is the Einstein theory, because in 1905 Albert Einstein, working on some theories developed by Lorentz and Fitzgerald, published his first principle of relativity which suggested that the velocity of light is constant, however the position of an observer may vary and that space and time are variable. In 1917 Einstein enlarged this idea in order to include all the laws of nature.
Space and time are treated as just mental concepts. They lack the concreteness of matter, but they compose the framing of the universe and give it form and continuity. ”

“ In proportion as a theory becomes complex it loses in usefulness—a theory which is obliged to requisition a whole array of arbitrary assumptions in order to explain special facts is practically worse than useless, as it serves to disjoin, rather than to unite, the several groups of facts. The optical experiments of the last quarter of the nineteenth century showed the impossibility of constructing a simple ether theory, which would be amenable to analytic treatment and would at the same time stimulate further progress. ”

“ As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the “truth” of the theory lies. ”

“ After leaving school at Munich, he accompanied his parents to Milan, whence he proceeded to Switzerland six months later to continue his studies.
From 1896 to 1900 Albert Einstein studied mathematics and physics at the Technical High School in Zurich, as he intended becoming a secondary school (Gymnasium) teacher. ”

“ A four-dimensional continuum described by the "co-ordinates" , , , , was called "world" by Minkowski, who also termed a point-event a "world-point." From a "happening" in three-dimensional space, physics becomes, as it were, an "existence" in the four-dimensional "world."
This four-dimensional "world" bears a close similarity to the three-dimensional "space" of (Euclidean) analytical geometry. If we introduce into the latter a new Cartesian co-ordinate system (', ', ') ”

“ We thus free ourselves from the distasteful conception that the material universe ought to possess something of the nature of a centre. Of course we purchase our emancipation from the fundamental difficulties mentioned, at the cost of a modification and complication of Newton’s law which has neither empirical nor theoretical foundation. We can imagine innumerable laws which would serve the same purpose, without our being able to state a reason why one of them is to be preferred to the others ”

“ The relativity principle states that all natural laws that hold in a reference frame moving uniformly relative to the ether are identical with those that hold in , a reference frame at rest relative to the ether. If that is so, we can just as well imagine the ether is at rest relative to , not . It is completely unnatural to distinguish the two reference frames and by introducing an ether that is at rest in one. A satisfying theory can only be reached if we dispense with the ether hypothesis. ”

“ This does not prove that there is no such thing as an ether but certainly does render the ether entirely superfluous. Universal compensation is due to a change in local units of length and time, or rather, being merely different descriptions of the same reality, there is no compensation at all.
There was another group of observed phenomena which could scarcely be fitted into a Newtonian scheme of dynamics without doing violence to it. The experimental work of Kaufmann, in 1901, made it abundantly clear that the “mass” of an electron depended on its velocity. ”

“ In the first place, we imagine an existence in two dimensional space. Flat beings with flat implements, and in particular flat rigid measuring-rods, are free to move in a plane. For them nothing exists outside of this plane: that which they observe to happen to themselves and to their flat “things” is the all-inclusive reality of their plane. In particular, the constructions of plane Euclidean geometry can be carried out by means of the rods e.g. the lattice construction, considered in Section XXIV. In contrast to ours, the universe of these beings is two-dimensional ”

“ Einstein’s theory connects up the law of gravitation with the laws of motion, and serves to establish a very intimate relationship between matter and physical space-*time. Space, time and matter (or energy) were considered to be the three ultimate elements in Physics. The restricted theory fused space-time into one indissoluble whole. The generalised theory has further synthesised space-time and matter into one fundamental physical reality. Space, time and matter taken separately are more abstractions. Physical reality consists of a synthesis of all three. ”

“ One is ordinarily accustomed to study geometry divorced from any relation between its concepts and experience. There are advantages in isolating that which is purely logical and independent of what is, in principle, incomplete empiricism. This is satisfactory to the pure mathematician. He is satisfied if he can deduce his theorems from axioms correctly, that is, without errors of logic. The question as to whether Euclidean geometry is true or not does not concern him. But for our purpose it is necessary to associate the fundamental concepts of geometry with natural objects ”

“ Nevertheless, there are two general facts which at the outset speak very much in favour of the validity of the principle of relativity. Even though classical mechanics does not supply us with a sufficiently broad basis for the theoretical presentation of all physical phenomena, still we must grant it a considerable measure of “truth,” since it supplies us with the actual motions of the heavenly bodies with a delicacy of detail little short of wonderful. The principle of relativity must therefore apply with great accuracy in the domain of mechanics. ”

“ The coincidence of the two has of late become a puzzle to science, and it was Albert Einstein who tried to solve it by establishing his General Theory of Relativity. The need to seek such solutions falls away in a science which extends scientific understanding to conditions of matter in which weight and inertia are no longer dominant characteristics. What becomes of inertia when matter is subject to magical causation can be brought to our immediate experience in the following way. ”

“ In Lorentzian electrodynamics it was transformed into a pure geometrical, i.e. a forever solid structure that won't be influenced by matter. In Einstein's special theory of relativity another one took its place, the affine geometric structure. In the general theory of relativity eventually the latter was, as an "affine connection" or "guidance field", transformed back into a state-field of physical reality, that is in effective connection with matter. And therefore Einstein considered it convenient, to reintroduce the old word aether for the completely changed concept ”

“ He considers time itself to be one of the co-ordinate axes, and in his four-dimensional world, that is in the space-time reality, relative motion is reduced to a rotation of the axes of reference. Thus, the diversity in the measurement of lengths and temporal rates is merely due to the static difference in the “frame-work” of the different observers.
The above theory of Relativity absorbed practically the whole of the electromagnetic theory based on the Maxwell-Lorentz system of field equations. It combined all the advantages of classic Maxwellian theory together with an electronic hypothesis. ”

“ Since the quantity that we have formed has a tensor character, its vanishing is proved for every other system of co-ordinates also, and naturally for every other four-dimensional point. The energy principle of matter (97) is thus a mathematical consequence of the field equations (96) .
In order to learn whether the equations (96) are consistent with experience, we must, above all else, find out whether they [Pg 90] lead to the Newtonian theory as a first approximation. ”

“ They take the place of the imaginary cause R1. Among all the conceivable spaces R1 and R2 moving in any manner relative to one another, there is a priori, no one set which can be regarded as affording greater advantages, against which the objection which was already raised from the standpoint of the theory of knowledge cannot be again revived. The laws of physics must be so constituted that they should remain valid for any system of co-ordinates moving in any manner. We thus arrive at an extension of the relativity postulate. ”

“ A special case in which the field-equations sought-for are evidently satisfied is that of the special relativity theory in which have certain constant values. This would be the case in a certain finite region with reference to a definite co-ordinate system . With reference to this system, all the components of the Riemann's Tensor [equation 43] vanish. These vanish then also in the region considered, with reference to every other co-ordinate system.
The equations of the gravitation-field free from matter must thus be in every case satisfied when all vanish. ”

“ We might imagine that, as regards geometry, our universe behaves analogously to a surface which is irregularly curved in its individual parts, but which nowhere departs appreciably from a plane: something like the rippled surface of a lake. Such a universe might fittingly be called a quasi-Euclidean universe. As regards its space it would be infinite. But calculation shows that in a quasi-Euclidean universe the average density of matter would necessarily be nil. Thus such a universe could not be inhabited by matter everywhere ”

“ It is true that Mach tried to avoid having to accept as real something which is not observable by endeavouring to substitute in mechanics a mean acceleration with reference to the totality of the masses in the universe in place of an acceleration with reference to absolute space. But inertial resistance opposed to relative acceleration of distant masses presupposes action at a distance; and as the modern physicist does not believe that he may accept this action at a distance, he comes back once more, if he follows Mach, to the ether, which has to serve as medium for the effects of inertia. ”

“ We already know from our previous discussion that the behaviour of measuring-rods and clocks is influenced by gravitational fields, i.e. by the distribution of matter. This in itself is sufficient to exclude the possibility of the exact validity of Euclidean geometry in our universe. But it is conceivable that our universe differs only slightly from a Euclidean one, and this notion seems all the more probable, since calculations show that the metrics of surrounding space is influenced only to an exceedingly small extent by masses even of the magnitude of our sun. ”

“ If the universe were quasi-Euclidean, then Mach was wholly wrong in his thought that inertia, as well as gravitation, depends upon a kind of mutual action between bodies. For in this case, with a suitably selected system of co-ordinates, the would be constant at infinity, as they are in the special theory of relativity, while within finite regions the would differ from these constant values by small amounts only, with a suitable choice of co-ordinates, as a result of the influence of the masses in finite regions. ”