Einstein's Theories of Relativity and Gravitation by Albert Einstein, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. The World Geometry
The World Geometry
The fundamental creed of the new theory is that the space-time universe constitutes a true four-dimensional space of one negative dimension, this dimension being time. The variations from point to point of the direction-defining and length-defining magnitudes generate the geometrical properties of curvature, etc., and these are cognised by the human mind as physical phenomena: our sense-impressions are nothing more nor less than perceptions of the [268]geometry of a fourspace. So instead of inferring from our sense-impressions the existence of matter, motion and the like as we are accustomed to do, we should with equal justice infer the existence of a geometrical fourspace. Thus it becomes necessary to prepare a dictionary in which the familiar things of our world are identified with those geometrical properties of the four-space which really constitute them, and in so doing parts of our geometrical knowledge assume the guise of new physical knowledge.
Through the fourspace our consciousness travels, cognising a changing three-dimensional section of it as it goes and thus giving rise to time. It becomes aware that the fourspace is pleated or folded along lines all running roughly in the same direction, and possibly because this is the easiest direction to follow, it travels along the lines. The direction of this motion is the negative dimension. Thus consciousness is always aware of the nearly constant forms of the cross-sections of the pleats along which it travels. These unvarying forms constitute matter: matter is the form of a section through a uniform pleat of the fourspace—a three-dimensional aspect of a four-dimensional curvature; so that in strict accuracy we should say that a stone is the shape or form of a changing section of a four-dimensional object, the complete object being a long fold in the fourspace. The physical interpretation of this conservation of form of the cross-section is that matter is conserved. It is thus seen that the conscious mind, by following these pleats, has so determined time that the law of the conservation of matter must hold. The mathematical treatment of the [269]subject makes it clear that practically all other physical laws similarly follow as a direct result of this choice of time. The type of order prevailing in the physical universe, the laws of gravitation, heat, motion and the rest are not directly imposed by some external power, but are apparently chosen by mind itself.
In the neighborhood of these pleats the fourspace is still curved, but to a smaller degree. This we cognise as energy or as a field of force. Thus energy is seen to be the same kind of thing as matter and would therefore be expected to have weight. This was experimentally demonstrated in 1919 when light was in effect actually weighed. Conversely, matter consists of energy; and it is calculated that one liter of water contains sufficient energy to develop a million horsepower for about four years. It is now believed that the sun’s energy is derived from the disintegration of the matter of which it is made.
The method of establishing these identifications will be clear from the following: We already knew that matter is made up of electrons and that radiant energy is electromagnetic and before the advent of this theory it was regarded as certain that practically all observed physical phenomena except gravitation were manifestations of the electromagnetic field. The new theory has confirmed this belief. It is found that the gravitational and electromagnetic conditions of the universe are completely defined if to each point of space-time a gravitational and an electric potential are ascribed. These are magnitudes of the same nature as the direction-defining and length-defining magnitudes which must necessarily be [270]associated with every point of space-time if it is a true “space,” and they are therefore identified with these. By performing ordinary mathematical operations on these magnitudes statements of fact clothed in mathematical form are obtained, which are to be interpreted on the one hand as physical laws and on the other as geometrical properties of the fourspace. Nearly all our physical laws are derivable mathematically in this way, so that an extensive identification is effected which has been fruitful of results.
It has been mentioned that a slight curvature is sometimes cognised as force and as this identification appeared originally as a postulate its history is interesting.
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This book is part of the public domain. Albert Einstein (2020). Einstein's Theories of Relativity and Gravitation. Urbana, Illinois: Project Gutenberg. Retrieved October 2022.
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