Abstract
II. WE have to admit, then, that a world-line can be bent by the proximity of other world-lines. It can also be bent, as you see, by the proximity of my thumb. The suggestion arises, May not the two modes of bending be essentially the same? The bending by my thumb (a mathematical transformation of space and time) is in a sense spurious; the world-line is pursuing a course which is straight relative to the original material. Or we may perhaps best put it this way—the world-line still continues to take the shortest path between two points, only it reckons distance according to the length that would be occupied in the unstretched state of the bladder. It is suggested that the deflection of a world-line by gravitation is of the same nature; from each world-line a state of distortion radiates, as if from a badly puckered seam, and any other world-line takes the shortest course through this distorted region, which would immediately become straight if the strain could be undone. The same rule—of shortest distance as measured in the undistorted state—is to hold in all cases. This is a mode of reasoning which has often been fruitful in scientific generalisations. A magnetic needle turns towards the end of a bar-magnet; it also turns towards a spot near the pole of the earth; hence the suggestion that the 'earth is a magnet. We assume the essential identity of the two modes of deflecting the needle. It is a daring step to apply the analogy and assume the essential identity of the two ways of deflecting world-lines; but at any rate we shall make this assumption and see what comes of it.
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Gravitation and the Principle of Relativity 1 . Nature 101, 34–36 (1918). https://doi.org/10.1038/101034a0
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DOI: https://doi.org/10.1038/101034a0