Relativity: The Special and General Theory by Albert Einstein is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here . CHAPTER XXVII. THE SPACE-TIME CONTINUUM OF THE GENERAL THEORY OF RELATIVITY IS NOT EUCLIDEAN CONTINUUM In the first part of this book we were able to make use of space-time co-ordinates which allowed of a simple and direct physical interpretation, and which, according to Section , can be regarded as four-dimensional Cartesian co-ordinates. This was possible on the basis of the law of the constancy of the velocity of light. But according to Section the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. In connection with a specific illustration in Section , we found that the presence of a gravitational field invalidates the definition of the coordinates and the time, which led us to our objective in the special theory of relativity. XXVI XXI XXIII In view of the results of these considerations we are led to the conviction that, according to the general principle of relativity, the space-time continuum cannot be regarded as a Euclidean one, but that here we have the general case, corresponding to the marble slab with local variations of temperature, and with which we made acquaintance as an example of a two-dimensional continuum. Just as it was there impossible to construct a Cartesian co-ordinate system from equal rods, so here it is impossible to build up a system (reference-body) from rigid bodies and clocks, which shall be of such a nature that measuring-rods and clocks, arranged rigidly with respect to one another, shall indicate position and time directly. Such was the essence of the difficulty with which we were confronted in Section . XXIII When we were describing the motion of a material point relative to a body of reference, we stated nothing more than the encounters of this point with particular points of the reference-body. We can also determine the corresponding values of the time by the observation of encounters of the body with clocks, in conjunction with the observation of the encounter of the hands of clocks with particular points on the dials. It is just the same in the case of space-measurements by means of measuring-rods, as a little consideration will show. About HackerNoon Book Series: We bring you the most important technical, scientific, and insightful public domain books. This book is part of the public domain. Einstein, Albert, 2004. Relativity: The Special and General Theory. Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from https://www.gutenberg.org/files/5001/5001-h/5001-h.htm#ch27 This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org, located at https://www.gutenberg.org/policy/license.html. Photo by Andrew George on Unsplash

The Space-Time Continuum of Relativity Is Not Euclidean Continuum

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

A Few Inferences From the General Principle of Relativity

A Few Inferences From the General Principle of Relativity

A Short Biographical Note on Albrecht Einstein

Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference

Community in 12 Quotes

Cosmological Difficulties of Newton's Theory

A Few Inferences From the General Principle of Relativity

A Few Inferences From the General Principle of Relativity

A Short Biographical Note on Albrecht Einstein

Behaviour of Clocks and Measuring-Rods on a Rotating Body of Reference

Community in 12 Quotes

Cosmological Difficulties of Newton's Theory

Light-Mode

Classic

Newspaper

Minty

Dark-Mode

Neon Noir

Minty

HN StartUps