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 Question of Visualization

The Question of Visualization

To the layman there is a great temptation to say that while, mathematically speaking, the space-time continuum may be a great simplification, it does not really represent the external world. To be sure, you can’t see the space-time continuum in precisely the same way that you can the three-dimensional space continuum, but this is only because Einstein finds the time dimension to be not quite freely interchangeable with the space dimension. Yet you do perceive this space-time continuum, in the manner appropriate for its perception; and it would be just as sensible to throw out the space continuum itself on the ground that perception of the two is not of exactly the same sort, as to throw out the space-time continuum on this ground. With appropriate conventions, either may stand as the mental picture of the external world; it is for us to choose which is the more convenient and useful image. Einstein tells us that his image is the better, and tells us why.

Before we look into this, we must let him tell us something more about the geometry of his continuum. What he tells us is, in its essentials, just [163]this. The observer in a pure space continuum of three dimensions finds that as he changes his position, his right-and-left, his backward-and-forward, and his up-and-down are not fixed directions inherent in nature, but are fully interchangeable. The observers, in the adjoined sketch, whose verticals are as indicated by the arrows, find very different vertical and horizontal components for the distance between the points O and P; a similar situation would prevail if we used all three space directions. The statement analogous to this for Einstein’s four-dimensional continuum of space and time combined

is that, as observers change their relative motion, their time axes take slightly different directions, so that what is purely space or purely time for the one becomes space with a small component in the time direction, or time with a small component in the space direction, for the other. This it will be seen explains fully why observers in relative motion can [164]differ about space and time measurements. We should not be at all surprised if the two observers of the figure reported different values for horizontals and verticals; we should realize that what was vertical for one had become partly horizontal for the other. It is just so, says Einstein, with his observers of time and space who are in relative motion to one another; what one sees as space the other sees as partly time, because their time axes do not run quite parallel.

The natural question here, of course, is “Well, where are their time axes?” If you know what to look for, of course, you ought to be able to perceive them in just the way you perceive ordinary time intervals—with the reservation that they are imaginary, after all, just like your space axes, and that you must only expect to see them in imagination. If you look for a fourth axis in Euclidean three-space to represent your time axis, you will of course not find it. But you will by all means agree with me that your time runs in a definite direction; and this it is that defines your time axis. Einstein adds that if you and I are in relative motion, my time does not run in quite the same direction as yours.

How shall we prove it? Well, how would we prove it if he told us that our space axes did not run in precisely the same direction? Of course we could not proceed through direct measures upon the axes themselves; we know these are imaginary. What we should do would be to strike out, each of us, a very long line indeed in what seemed the true horizontal direction; and we should hope that if we made them long enough, and measured them [165]accurately enough, we should be able to detect any divergence that might exist. This is precisely what we must do with our time axes if we wish to verify Einstein’s statement that they are not precisely parallel; and what better evidence could we demand of the truth of this statement than the evidence already presented—that when we measure our respective time components between two events, we get different results?

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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 Question of Visualization

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