Albert Einstein

On gravitational waves

The rigorous solution for cylindrical gravitational waves is given. For the convenience of the reader the theory of gravitational waves and their production, already known in principle, is given in the first part of this paper.After encountering relationships which cast doubt on the existence of rigorous solutions for undulatory gravitational fields, we investigate rigorously the case of cylindrical gravitational waves. It turns out that rigorous solutions exist and that the problem reduces to the usual cylindrical waves in euclidean space.

Physics and reality

Abstract Physics constitutes a logical system of thought which is in a state of evolution, and whose basis cannot be obtained through distillation by any inductive method from the experiences lived through, but which can only be attained by free invention. The justification (truth content) of the system rests in the proof of usefulness of the resulting theorems on the basis of sense experiences, where the relations of the latter to the former can only be comprehended intuitively. Evolution is going on in the direction of increasing simplicity of the logical basis. In order further to approach this goal, we must make up our mind to accept the fact that the logical basis departs more and more from the facts of experience, and that the path of our thought from the fundamental basis to these resulting theorems, which correlate with sense experiences, becomes continually harder and longer. Our aim has been to sketch, as briefly as possible, the development of the fundamental concepts in their dependence upon the facts of experience and upon the strife towards the goal of internal perfection of the system. Todays state of affairs had to be illuminated by these considerations, as they appear to me. (It is unavoidable that historic schematic representation is of a personal color.) I try to demonstrate how the concepts of bodily objects, space, subjective and objective time, are connected with one another and with the nature of the experience. In classical mechanics the concepts of space and time become independent. The concept of the bodily object is replaced in the foundations by the concept of the material point, by which means mechanics becomes fundamentally atomistic. Light and electricity produce insurmountable difficulties when one attempts to make mechanics the basis of all physics. We are thus led to the field theory of electricity, and, later on to the attempt to base physics entirely upon the concept of the field (after an attempted compromise with classical mechanics). This attempt leads to the theory of relativity (evolution of the notion of space and time into that of the continuum with metric structure). I try to demonstrate, furthermore, why in my opinion the quantum theory does not seem likely to be able to produce a usable foundation for physics: one becomes involved in contradictions if one tries to consider the theoretical quantum description as a complete description of the individual physical system or happening. On the other hand, up to the present time, the field theory is unable to give an explanation of the molecular structure of matter and of quantum phenomena. It is shown, however, that the conviction to the effect that the field theory is unable to give, by its methods, a solution of these problems rests upon prejudice.

Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie

Es ist wohlbekannt, das die Poissonsche Differentialgleichung

On the Quantum Theory of Radiation

\Delta \phi = 4\pi K\varrho

Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle

(1) in Verbindung mit der Bewegungsgleichung des materiellen Punktes die Newtonsche Fernwirkungstheorie noch nicht vollstandig ersetzt. Es mus noch die Bedingung hinzutreten, das im raumlich Unendlichen das Potential φ einem festen Grenzwerte zustrebt. Analog verhalt es sich bei der Gravitationstheorie der allgemeinen Relativitat; auch hier mussen zu den Differentialgleichungen Grenzbedingungen hinzutreten fur das raumlich Unendliche, falls man die Welt wirklich als raumlich unendlich ausgedehnt anzusehen hat.

Hamiltonsches Prinzip und allgemeine Relativitätstheorie

In a previous paper (Ann. of Math., Vol. 46, No. 4) one of us developed a generally relativistic theory, which is characterized as follows: (1) Group of real transformations of the four coordinates (xi, ,X4) (2) As only dependent variable to which everything is reduced we have the tensor gik, which is taken there to be complex and of Hermitian symmetry. W. Pauli noted, that the theory developed on this basis is such that the limitation to the case of the Hermitian tensor is not needed for the formalism. (3) It was added in proof that it seems natural to assume that the field satisfy the equations

Elementary derivation of the equivalence of mass and energy

on the assumption of discrete portions of energy, from which quantum theory developed rapidly. It was then only natural that Wien’s argument, which had led to eq. (2), should have become forgotten. Not long ago I discovered a derivation of Planck’s formula which was closely related to Wien’s original argument 1 and which was based on the fundamental assumption of quantum theory. This derivation displays the relationship between Maxwell’s curve and the chromatic distribution curve and deserves attention not only because of its simplicity, but especially because it seems to throw some light on the mechanism of emission and absorption of radiation by matter, a process which is still obscure to us. By postulating some hypotheses on the emission and absorption of radiation by molecules, which suggested themselves from quantum theory, I was able to show that molecules with a quantum-theoretical distribution of states in thermal equilibrium, were in dynamical equilibrium with the Planck radiation; in this way, Planck’s formula (4) could be derived in an astonishingly simple and general way. It was obtained from the condition that the internal energy distribution of the molecules demanded by quantum theory, should follow purely from an emission and absorption of radiation. But if these hypotheses on the interaction between radiation and matter turn out to be justified, they must produce rather more than just the correct statistical distribution of the internal energy of the molecules: for

A Brief Outline of the Development of the Theory of Relativity

How does it come about that alongside of the idea of ponderable matter, which is derived by abstraction from everyday life, the physicists set the idea of the existence of another kind of matter, the ether? The explanation is probably to be sought in those phenomena which have given rise to the theory of action at a distance, and in the properties of light which have led to the undulatory theory. Let us devote a little while to the consideration of these two subjects. Outside of physics we know nothing of action at a distance. When we try to connect cause and effect in the experiences which natural objects afford us, it seems at first as if there were no other | mutual actions than those of immediate contact, e.g. the communication of motion by impact, push and pull, heating or inducing combustion by means of a flame, etc. It is true that even in everyday experience weight, which is in a sense action at a distance, plays a very important part. But since in daily experience the weight of bodies meets us as something constant, something not linked to any cause which is variable in time or place, we do not in everyday life speculate as to the cause of gravity, and therefore do not become conscious of its character as action at a distance. It was Newton’s theory of gravitation that first assigned a cause for gravity by interpreting it as action at a distance, proceeding from masses. Newton’s theory is probably the greatest stride ever made in the effort towards the causal nexus of natural phenomena. And yet this theory evoked a lively sense of discomfort among Newton’s contemporaries, because it seemed to be in conflict with the principle springing from the rest of experience, that there can be reciprocal | action only through contact, and not through immediate action at a distance. It is only with reluctance that man’s desire for knowledge endures a dualism of this kind. How was unity to be preserved in his comprehension of the forces of nature? Either by trying to look upon contact forces as being themselves distant forces which admittedly are observable only at a very small distance—and this was the road which Newton’s followers, who were entirely under the spell of his doctrine, [3]