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 New World
THE NEW WORLD
A Universe in Which Geometry Takes the Place of Physics, and Curvature That of Force
BY GEORGE FREDERICK HEMENS, M.C., B.SC., LONDON
It is familiar knowledge that the line, the surface and ordinary Euclidean space are to be regarded as spaces of one, two and three dimensions respectively and readers of this journal are aware that a hypothetical space of four dimensions has been closely investigated. The most convenient space to study is the surface or two-space, since we can regard it as embedded in a three-space. If a surface is curved it is generally impossible to draw a straight line on it, for as we see clearly, the “straightest” line is changing its direction at every point. To describe this property accurately it is necessary to ascribe to each point a magnitude which expresses what happens to the direction of a short line in the region when displaced a short distance parallel to itself. This is called the direction-defining magnitude. Different sets of values of this magnitude relate to surfaces of different curvatures.
A second fundamental property has recently been pointed out. There is inherent in every part of a space a measure of length peculiar to that particular [266]region and which in general varies from region to region. To describe this variation accurately it is necessary to ascribe to each point another magnitude called the length-defining magnitude, which expresses the change from each point to the next of the unit of length. These two magnitudes define the surface completely.
Similarly, a space of any number of dimensions is defined completely by a similar pair of magnitudes. A space is the “field” of such a magnitude-pair and the nature of these magnitudes defines the dimensions of the space. The four-space usually described is the Euclidean member of an infinity of four-spaces.
In considering what at first sight may appear to be fantastic statements made by this theory, it must be borne in mind that all our knowledge of the external universe comes through our sense-impressions, and our most confident statements about external things are really of the nature of inferences from these sense-impressions and, being inferences, liable to be wrong. So that if the theory says that a stone lying on the ground is not a simple three-dimensional object, and that its substance is not the same as its substance a moment before, the matter is one for due consideration and not immediate disbelief.
The idea that the universe extends in time as well as in space is not new, and fiction-writers have familiarized us with wonderful machines in which travellers journey in time and are present at various stages of the world’s history. This conception of the universe, to which the name “space-time” is usually applied, is adopted by the new theory and assigned the status of a physical reality.
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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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