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 Four-Dimensional World of Events

The Four-Dimensional World of Events

We too have created a distinction in our minds corresponding to no sufficient reality. Our minds seize on time as inherently separable from space. We see the world made up of things in a continuum of three space dimensions; to make this dead world [186]live there runs through it a one-dimensional time continuum, imposed from without, unrelated.

But did you ever observe anything suggesting the presence of time in the absence of space, or vice versa? No; these vessels of the universe always occur together. Association of the space dimensions into a manifold from which time is excluded is purely a phenomenon of the mind. The space continuum cannot begin to exist until the time dimension is supplied, nor can time exist without a place to exist in.

The external world that we observe is composed, not of points, but of events. If a point lacks position in time it does not exist; give it this position and it becomes an event. This world of events is four-dimensional—which means nothing more terrifying than that you must make four measures to locate an event. It does not mean, at all, that you must visualize four mutually perpendicular lines in your accustomed three-space or in a four-space analogous to it. If this world of four dimensions seems to lack reality you will be able to exhibit no better reality for your old ideas. Time belongs, without question; and not as an afterthought, but as part of the world of events.

To locate an event we use four measures: X, Y and Z for space, T for time. Using the same reference frame for time and space, we locate a second event by the measures x, y, z, t. Minkowski showed that the quantity

is the same for all observers, no matter how different their x’s and y’s.

Such a quantity, having the same value for all observers, is absolute. In the plane it represents the true, absolute distance between the points—their intrinsic property. In dealing with events it represents the true, absolute “interval,” in time and space together between the events. It is not space, nor time, but a combination of the two. We have always broken it down into separate space and time components. In this we are as naive as the plane observer who could not visualize the distance PQ until it was split into separate horizontals and verticals. He understood with difficulty that another observer, employing a different reference frame because in different position, would make the decomposition differently. We understand with difficulty that another observer, employing a different reference frame because in uniform motion relative to us, will decompose the “interval” between events into time and space components different from ours. Time and space are relative to the observer; only the interval representing space-time is absolute. So common sense stands reconciled to the Special Theory of Relativity.

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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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The Four-Dimensional World of Events

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