Four-Dimensional Vistas

by Claude Fayette Bragdon

Let us then, in this predicament, consider time not from the standpoint of experiment, but of conscious experience—what Bergson calls "real duration."

Every point along the line of memory, of conscious experience, has been traced out by that unresting stylus we call "the present moment." The question of its rate of motion we will not raise, as it is one with which we have found ourselves impotent to deal. We believe on the best of evidence that the conscious experience of others is conditioned like our own. For better understanding let us have recourse to a homely analogy: let us think of these more or less parallel lines of individual experience in the semblance of the strands of a skein of flax. Now if, at the present moment, this skein were cut with a straight knife at right angles to its length, the cut end would represent the time plane—that is, the present moment of all—and it would be the same for all providing that the time plane were flat But is it really flat? Isn't the straightness of the knife a mere poverty of human imagination? Existence is always richer and more dramatic than any diagram.

"Line in nature is not found;
Unit and universe are round.
In vain produced, all rays return;
Evil will bless and ice will burn."

Undoubtedly the flat time-plane represents with fair accuracy the temporal conditions that obtain in the human aggregate in this world under normal conditions of consciousness, but if we consider our relation to intelligent beings upon distant worlds of the visible universe the conditions might be widely different The time section corresponding to what our straight knife made flat in the case of the flax may be—nay, probably is—strongly curved.

RELATIVITY

This crude analogy haltingly conveys what is meant by curved time. It is an idea which is implicit in the Theory of Relativity. This theory has profoundly modified many of our basic conceptions about the universe in which we are immersed. It is outside the province of this book and beyond the power of its author even so much as to sketch the main outlines of this theory, but certain of its conclusions are indispensable, since they baldly set forth our dilemma in regard to the measurement of space and time. We can measure neither except relatively, because they must be measured one by the other, and no matter how they vary, these variations always compensate one another, leaving us in the same state of ignorance that we were in before.

Suppose that two intelligent beings, one on Mars, let us say, and the other on the earth, should attempt to establish the same moment of time, by the interchange of light signals, or by any other method which the most rigorous science could devise. Assume that they have for this purpose two identically similar and mechanically perfect chronometers, and that every difficulty of manipulation were successfully overcome. Their experiment could end only in failure, and the measure of this failure neither one, in his own place, could possibly know. If, after the experiment, the Martian, chronometer in hand, could be instantly and miraculously transported to the earth, and the two settings compared, they would be found to be different: how different, we do not know.

The reason for the failure of any such experiment anywhere conducted can best be made plain by a crude paraphrase of a classic proposition from Relativity. Suppose it is required to determine the same moment of time at two different places on the earth's surface, as must be attempted in finding their difference in longitude. Take the Observatory at Greenwich for one place, and the observatory at Washington for the other. At the moment the sun is on the meridian of Greenwich, the exact time of crossing is noted and cabled to Washington. The chronometer at Washington is set accordingly, and the time checked back to Greenwich. This message arrives two seconds, say, after the original message was sent. Washington is at once notified of this double transmission interval. On the assumption that HALF of it represents the time the message took to travel from east to west, and the other half the time from west to east again, the Washington chronometer is set one second ahead of the signalled time, to compensate for its part of the loss. When the sun has reached the meridian of Washington, the whole process is repeated, and again as before, half of the time the message has taken to cross and recross the Atlantic is added to the Greenwich record of noon at Washington. The number of hours, minutes, seconds, and fractions of a second between these two corrected records represents the difference in solar time between the two places, and incidentally the same moment of time has been established for both—at least, so it would appear.

But is it established? That each message took an equal time to travel each way is pure assumption, and happens to be a false one. The accuracy of the result is vitiated by a condition of things to which the Relativists have called attention. Our determination might be defended if Washington and Greenwich could be assumed to remain at rest during the experiments, and some argument might even be made in its favor if we could secure any cosmic assurance that the resultant motion of the earth should be the same when Greenwich signalled its noon to Washington and Washington its noon to Greenwich.

Our present discussion is merely illustrative, or diagrammatic; so we will neglect the velocity of the earth in its orbit round the sun, some forty times greater than that of a cannon ball, and the more uncertain and more vertiginous speed of the whole solar system towards its unknown goal. Let us consider only the rotation of the earth on its axis, the tide-speed of day and night. To fix our idea, this may be taken, in our latitudes, at eighteen thousand miles per day, or perhaps half the speed of a Mauser rifle bullet.