Download Sidelights on Relativity djvu

Other books that Einstein wrote that address relativity are The Meaning of Relativity,The Principle of Relativity, and Relativity: The Special and the General Theory.

This short book contains two essays: "Ether and the Theory of Relativity" (1920), and "Geometry and Experience" (1921); both essays were based on lectures Einstein gave.

He begins the first essay by asking, "How does it come about that alongside of the idea of ponderable matter, which is derived by abstraction from everyday life, that 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." (Pg. 3)

He states, "we can assert by reason of the relativistic equations of gravitation that there must be a departure from Euclidean relations, with spaces of cosmic order of magnitude, if there exists a positive mean density, no matter how small, of the matter in the universe. In this case the universe must of necessity be spatially unbounded and of finite magnitude, its magnitude being determined by the value of that mean density." (Pg. 20-21)

He suggests, "Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation." (Pg. 22-23)

In the second essay, he says, "the question whether the universe is spatially finite or not seems to me to be a decidedly pregnant question in the sense of practical geometry... Let us call to mind what the general theory of relativity teaches in this respect. It offers two possibilities: 1. The universe is spatially infinite. This can be so only if the average spatial density of the matter in universal space, concentrated in the stars, vanishes... 2. The universe is spatially finite. This must be so, if there is a mean density of the ponderable matter in universal space differing from zero... Experience alone can finally decide which of the two possibilities is realised in nature." (Pg. 41-42)

He gives an illustration of non-Euclidean space: "Place a paper disc on [a] spherical surface, and around it in a circle place six more discs, each of which is to be surrounded in turn by six discs, and so on... we have an uninterrupted disposition in which there are six discs touching every disc except those which lie on the outside... In this way creatures which cannot leave the spherical surface... into three-dimensional space, might discover, merely by experimenting with discs, that their two-dimensional 'space' is not Euclidean, but spherical space. From the latest results of the theory of relativity it is probable that our three-dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry, if only we consider parts of space which are sufficiently great." (Pg. 49-50)

He concludes, "In this way, by using as stepping-stones the practice in thinking and visualization which Euclidean geometry gives us, we have acquired a mental picture of spherical geometry. We may without difficulty impart more depth and vigour to these ideas by carrying out special imaginary constructions... My only aim today has been to show that the human faculty of visualization is by no means bound to capitulate to non-Euclidean geometry." (Pg. 55-56)

These short essays will be of considerable interest to anyone studying modern physics.

Other books that Einstein wrote that address relativity are The Meaning of Relativity,The Principle of Relativity, and Relativity: The Special and the General Theory.

This short book contains two essays: "Ether and the Theory of Relativity" (1920), and "Geometry and Experience" (1921); both essays were based on lectures Einstein gave.

He begins the first essay by asking, "How does it come about that alongside of the idea of ponderable matter, which is derived by abstraction from everyday life, that 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." (Pg. 3)

He states, "we can assert by reason of the relativistic equations of gravitation that there must be a departure from Euclidean relations, with spaces of cosmic order of magnitude, if there exists a positive mean density, no matter how small, of the matter in the universe. In this case the universe must of necessity be spatially unbounded and of finite magnitude, its magnitude being determined by the value of that mean density." (Pg. 20-21)

He suggests, "Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation." (Pg. 22-23)

In the second essay, he says, "the question whether the universe is spatially finite or not seems to me to be a decidedly pregnant question in the sense of practical geometry... Let us call to mind what the general theory of relativity teaches in this respect. It offers two possibilities: 1. The universe is spatially infinite. This can be so only if the average spatial density of the matter in universal space, concentrated in the stars, vanishes... 2. The universe is spatially finite. This must be so, if there is a mean density of the ponderable matter in universal space differing from zero... Experience alone can finally decide which of the two possibilities is realised in nature." (Pg. 41-42)

He gives an illustration of non-Euclidean space: "Place a paper disc on [a] spherical surface, and around it in a circle place six more discs, each of which is to be surrounded in turn by six discs, and so on... we have an uninterrupted disposition in which there are six discs touching every disc except those which lie on the outside... In this way creatures which cannot leave the spherical surface... into three-dimensional space, might discover, merely by experimenting with discs, that their two-dimensional 'space' is not Euclidean, but spherical space. From the latest results of the theory of relativity it is probable that our three-dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry, if only we consider parts of space which are sufficiently great." (Pg. 49-50)

He concludes, "In this way, by using as stepping-stones the practice in thinking and visualization which Euclidean geometry gives us, we have acquired a mental picture of spherical geometry. We may without difficulty impart more depth and vigour to these ideas by carrying out special imaginary constructions... My only aim today has been to show that the human faculty of visualization is by no means bound to capitulate to non-Euclidean geometry." (Pg. 55-56)

These short essays will be of considerable interest to anyone studying modern physics.