Erwin Freundlich

“ Gravitation, as a force acting at a distance, is, on the contrary, introduced only as a special force for a limited range of phenomena: and the surprising fact of the equality of inertial and gravitational mass, valid at all times and in all places, receives no further attention. One must, therefore, substitute for the law of inertia a fundamental law which comprises inertial and gravitational phenomena. This can be brought about by a consistent application of the principle of the relativity of all motions, as Einstein has recognized. ”

“ Newtonian mechanics attributes to every body a certain inertial mass, as a property that is in no wise influenced by the physical conditions to which the body is subject. Consequently, the Principle of the Conservation of Mass also appears in classical mechanics as independent from the Principle of the Conservation of Energy. The special principle of relativity shed an entirely new light on these circumstances when it led to the discovery that energy also manifests inertial mass, and it hereby fused together the two laws of conservation, that of mass and that of energy, to a single principle. ”

“ So long as we restrict ourselves to those systems of reference among all others that emerge out of each other as a result of transformations of the above type, there is no sense in [Pg 6] talking of absolute rest or absolute motion. For we may freely decide to regard either of two systems moving in such a way as the one that is at rest or in motion. According to classical mechanics it was, indeed, believed that only the Galilei-transformations could come into question when we were concerned with referring equivalent systems of reference to each other according to the principle of relativity. ”

“ From these remarks one inevitably gains the impression that a construction of mechanics upon an entirely new basis is an absolute necessity. There is no hope of a satisfactory formulation of the law of inertia without taking into account the relativity of all motions, and hence just as little hope of banishing the unwelcome conception of absolute motion out of mechanics; moreover, the discovery of the inertia of energy has taught us facts which refuse to fit into the existing system, and necessitate a revision of the foundations of mechanics. ”

“ Einstein arrives at these conclusions by critically examining our notions of space and time or of distance and simultaneity.
We know what simultaneity (time-coincidence of two events) means for our consciousness, but in making use of the idea of simultaneity in physics, we must be able to prove by actual experiment or observation that two events are simultaneous according to some definition of simultaneity. A conception only has meaning for the physicist if the possibility of verifying that it agrees with actual experience is given. ”

“ For the unsuccessful attempts that have been made during the last centuries to fit the doctrine of gravitation satisfactorily into the scheme of natural science necessarily lead to the conclusion that this would not be possible without giving up many deeply-rooted ideas. As a matter of fact, Einstein reverted to the foundation pillars of mechanics as starting-points on which to build his theory, and he did not satisfy himself by merely reforming the Newtonian law in order to establish a link with the more recent views. ”

“ TWO FUNDAMENTAL POSTULATES IN THE MATHEMATICAL FORMULATION OF PHYSICAL LAWS NEWTON had established the simple and fruitful law that two bodies, even when they are not visibly connected with one another, as in the case of the heavenly bodies, exert a mutual influence, attracting one another with a force directly proportional to the product of their masses, and inversely proportional to the square of the distance between them. ”

“ Any change, which an observer perceives in the passing of any event to be due to a gravitational field, would be perceived by him in exactly the same way, if the gravitational field were not present, provided that he—the observer—makes his system of reference move with the acceleration which was characteristic of the gravitation at his point of observation. ”

“ Every description in space of the scene of an event or of the position of a body consists in designating a point or points on a rigid body imagined for the purpose, which coincides with the spot at which the event takes place or the object is situated. We ordinarily choose as our rigid body a portion of the earth or a set of axes attached to it. ”

“ This meant that either there was a unique inertial system enabling us to define absolute motion and rest in nature, or that we would have to build up a theory of relativity, not on the inertial law and inertial systems, but on some new foundation which would definitely ensure that the form of all physical laws would be preserved in passing from one system of reference to another. ”

“ Again, "what we call measuring time is nothing but counting simultaneities; owing to the fact that our consciousness has organized the oscillations of a pendulum as a whole in memory, they are first preserved and afterwards disposed in a series: in a word, we create for them a fourth dimension of space, which we call homogeneous time, and which enables the movement of the pendulum, although taking place at one spot, to be continually set in juxtaposition to itself. ”

“ For in cosmic space such commands are continually resounding, proceeding from each of the heavenly bodies—from the sun, planets, moons, and comets. Every single body in space hearkens to the orders which the other bodies give it, always striving to carry them out punctiliously. Our earth would dash through space in a straight line, if she were not controlled and guided by the voice of command, issuing from moment to moment, from the sun, in which the instructions of the remaining cosmic bodies are less audibly mingled. ”

“ Their presence in a body alone, without any other visible body being present, enables one to demonstrate the fact that it is in rotation. Even if the earth were perpetually enveloped in an opaque sheet of cloud, one would be able to establish its daily rotation about its axis by means of Foucault's pendulum-experiment. This peculiarity of rotations led Newton to conclude that absolute motions exist. From the purely kinematical point of view, however, the rotation of the earth is not to be distinguished in any way from a translation ”

“ It is thus natural that we should start building up the new theory from this point. The new law of motion must be a differential law, which, in the first place, describes the motion of a point-mass under the influence of both inertia and gravity, and which, secondly, always preserves the same form, irrespective of the system of co-ordinates to which it be referred, so that no system of co-ordinates [Pg 45] enjoys a preference to any other. ”

“ As a matter of actual fact, we only observe the motions of bodies relatively to one another, and these are never absolutely rectilinear nor uniform. Pure inertial motion is thus a conception deduced by abstraction from a mental experiment—a mere fiction. ”

“ The third test, the results of which are still in abeyance, is perhaps the most important of the three, inasmuch as it depends upon a very simple calculation from Einstein's Principle of Equivalence, which [Pg 131] asserts that an observer cannot discriminate how much of his motion is due to a gravitational field and how much is due to an acceleration of his body of reference. Einstein illustrates his argument by supposing an observer situated in a closed box in free space. The observer has at first no sensation of weight, and need not support himself upon his feet. ”

“ If we demand that bodies are to be freely movable in space without suffering a change of dimensions, the "curvature" of the space must be the same at every point. The conception of curvature, as applied to any manifold of more than two dimensions, allows of strict mathematical formulation; the term itself only hints at its analogous meaning, as compared with the conception of curvature of a surface. In three-dimensional space, too, various cases can be distinguished, similarly to plane- and spherical-geometry in two-dimensional space. ”

“ The equations of motion of Newtonian mechanics do not preserve their form when new co-ordinates have been introduced with the help of the Lorentz-Einstein transformations. Consequently, the fundamental equation of mechanics had to be remodelled accordingly. It was then found that Newton's Second Law of Motion: force = mass x accel. cannot be retained, and that the expression for the kinetic energy of a body may no longer be furnished by the simple expression , which involves the mass and the velocity. ”