Time dilation

“ Until machines for accurately measuring time were invented, apparent time—time, that is to say, given by the sun itself, as by a sun-dial—was the only time about which men knew or cared. But when reasonably good clocks and watches were made, it was very soon seen that at different times in the year there was a marked difference between sun-dial time and that shown by the clock, the reason being simply that the apparent rate of motion of the sun across the sky was not always quite the same, whilst the movement of the clock was, of course, as regular as it could be made. ”

“ It is well that modern clocks have no wise saws and [Pg 32] mottoes telling of the unalterable hand of Time; "Old Time, the clock-setter, that bald sexton, Time," as Shakespeare says in King John.
Early Mechanism.—The problem for the old clockmakers who wished to supplant the primitive measurement of time by candle, by the hour-glass, and later by the sundial, was to produce a piece of mechanism which would in twenty-four hours, the prescribed period of day and night, indicate the flight of time hour by hour. ”

“ The observation of the moon is often said to be the oldest form of time-reckoning. This statement involves a certain danger, viz. the overlooking of the fact that the time-indications from natural phases and from the stars—as I hope has been shewn above—are just as primitive and must be just as old. But if by time-reckoning the continuous principle and measure of time are implied the statement is in that sense true. The moon is indeed the first chronometer, and this fact is due to the nature of its concrete appearance, which draws attention to the duration, and not to the point, of time. ”

“ Complicated Watches are so called because besides the ordinary watch movement they possess other mechanism more or less complicated, by means of which they can indicate special portions of time,—as for instance the Chronograph, which marks on its dial the fifth of a second; the Quarter, and Half-Quarter, and Minute Repeaters, which furnish the time in the dark to within a minute, and are invaluable to invalids and blind persons; the Clock-Watch, which strikes the hours even in the pocket ”

“ But experience convinces us that in the limit, as the phenomenon to be measured gets closer to the clock, there is no measurable difference, whether communication with the clock is maintained by light, or acoustical or tactual signals, so that we have come in physical practice to accept measurement of the time of events in the immediate neighborhood of the clock (local time) as one of the ultimately simple things behind which we do not attempt to go. ”

“ Hence it is evident that if we indicate the exact interval of time between the culmination of the sun and that of one particular star, or name the star with which the sun precisely culminates, we can determine the day of the solar year. This is the principle of one method of computing time which was very common among ancient and primitive peoples, but has entirely dropped out of use in modern times owing to our paper calendar. The stars are so to speak the stationary ciphers on the clock-face and the sun is the hand. ”

“ Leaving, then, this constant error in time-appreciation, we will pass to the variable and more palpable errors in the retrospective measurement of time. Each person's experience will have told him that in estimating the distance of a past event by a mere retrospective sense of duration, he is liable to extraordinary fluctuations of judgment. Sometimes when the clock strikes we are surprised at the rapidity of the hour. At other times the timepiece seems rather to have lagged behind its usual pace. ”

“ The modern astronomer does not pretend to keep his clock correct within less than a minute; he determines by observation how far it is wrong, on each date of observation, and adds so much to the time given by the clock, or subtracts it, as the case may be, in order to get the correct moment of true time. In the case of the French astronomers, the clock would frequently be fifteen minutes or more in error, for the reason that they used apparent time, instead of mean time as we do. ”

“ But the moon alone moves with sufficient rapidity to act as a time indicator for terrestrial voyagers. It is hardly necessary to explain why rapidity of motion is important; but the following illustration may be given for the purpose. The hour-hand of a clock does in reality indicate the minute as well as the hour; yet, owing to the slowness of its motion, we regard the hour-hand as an unsatisfactory time-indicator, and only consider it as showing what hour is in progress. ”

“ A good clock is also a necessary adjunct for astronomical observations, and the astronomical clocks and chronometers now in use record the time with almost perfect accuracy. The improvement in telescopes, the use of micrometers, etc., have greatly facilitated observations. In the transit clock we have a most useful timekeeper, for the ordinary clocks are not sufficiently accurate for very close observations. The sidereal time differs from solar time, and the twenty-four hours’ period is calculated from the moment a star passes the meridian until it passes it again. ”

“ In order that a clock should be used as an indicator of time, it is not enough that its error at every instant should be known; its error must be continually corrected so that its face-reading shall always indicate true time. And, in order that a clock should be used as a distributor of time, it must be provided with apparatus, distinct from the mechanism which keeps the time and in no way interfering with it, which is capable of sending time to other clocks. ”

“ We are constantly correcting their errors and never entirely succeed in getting them to run accurately to periods of time which exist entirely outside of such little things as men and clocks. So a clock is better as it approximates or bears a regular relation to some motion in nature. The sidereal clock of the astronomer does run to a regular motion; but our 24-hour clocks do not, as we shall see later. Now consider the year, or the sun's apparent motion in the Zodiac, from any given star around to the same one again. ”

“ If with the naked eye or with a telescope you watch a clock moving away from you, you will find that its minute hand takes a longer time to cover its five-minute intervals than does the chronometer in your hand, and if the clock travelled with the velocity of light you would forever see the minute hand at precisely the same point. That which is true of the clock is, of course, also true of all time intervals which it measures, so that if you moved away from the earth with the velocity of light everything on it would appear as still as on a painted canvas. ”

“ For if we suppose the time marked to be an hour, the space passed over by the minute hand, that is, the circumference of the dial, has no relation with the hour except what the artificer gave it by so constructing the watch that the minute hand would make one revolution every hour. ”

“ Similar considerations apply to the slowing down of time. Duration, and time are mere relatives, mere expressions of relationships, and have no absolute significance per se. This does not mean that the duration we sense is a myth; for as our consciousness always accompanies our human body wherever we go, we always experience the same flow of time. All that is implied is that this rate of time-flow cannot be credited with any unique significance in nature, and a comparison of time-flows characteristic of various Galilean frames will reveal differences in the rate of flow. ”

“ To discover, therefore, whether our clock is right on any given night, it is merely necessary to watch a star with the telescope, and note the exact instant by the clock when it reaches the little cross in the field of view. Knowing from the astronomical tables the time when the star ought to have been on the meridian, and having observed the clock time when it is actually there, the difference is, of course, the error of the clock. ”

“ Moreover, by being transported from place to place, chronometers are liable to change their rate. By the rate of any timepiece is meant its deviation from perfect accuracy. Thus, if a clock should gain one second per day, one day with another, and we should find it impossible to bring it nearer to the truth, we may reckon this as its rate, and allow for it in our estimate of the time of any particular observation. ”

“ Since it must now be regarded as the natural course of development that the systematic has gradually arisen out of the unsystematic, and that the indication of concrete phenomena following one another in the regular succession of Nature has preceded the abstract numerical indication of time offered by our calendars, the origin of the time-reckoning must be sought not in any one system, however simple, but in the discontinuous or pars pro toto time-indications which are related to concrete phenomena. ”

“ Now, the exact time of the day at the place where we are, can be ascertained by well known and easy observations of the Sun if visible for a few minutes at any time from his being ten degrees high until within an hour of noon, or from an hour after noon until he is only 10 degrees high in the afternoon; if therefore, at any time when such observation is made, a Timekeeper tells us at the same moment what o'clock it is at the place we sailed from, our Longitude is clearly discovered. ”

“ The days are joined into months and the months into years; only more rarely are the seasons interposed as regular units of time. The system is like a chain the links of which run into one another without gaps: each link is equivalent, or as nearly as possible equivalent, to every other link of the same class, and therefore need only be given a name and counted, not necessarily conceived in the concrete, although this is not excluded. This is the only genuine system, a system of continuous time-reckoning, which excludes all gaps in the chain and all links of indeterminate length. ”

“ The examples just given are not numerous, and this corresponds to the actual state of affairs, since we have here to do with the treatment of a genuine calendarial science by certain peoples,—only at a quite undeveloped stage can questions of the time-reckoning be dealt with in a deliberative assembly—and our researches are concerned with primitive peoples. The end which the calendar-maker has in view is the establishing of an ordered series of days marked out into divisions, the series being kept in place by certain fixed points, and recurring cyclically. ”

“ A simple contrivance, connected with the tubes and the clock, lets off a puff of air every minute or half-minute, and the fingers of all the clocks in the system are in that manner pushed forward with unerring accuracy, in accordance with the time indicated by the standard timepieces in the observatory, so that exact uniformity can be maintained without difficulty in the time shown on any number of dials. ”

“ I saw his famous clock last winter at Mr. George Graham’s: the sweetness of its motion, the contrivances to take off friction, to defeat the lengthening and shortening of the pendulum through heat and cold, and to prevent the disturbance of motion by that of the ship, cannot be sufficiently admired.”—Ms. Journal. [18]
An exact measure of time is of the utmost importance to many of the sciences. Horology is indispensable to astronomy, in which the variation even of two or three seconds is of the greatest consequence. ”

“ The astronomer’s clock, for instance, is no standard of the efflux of time; it serves but to subdivide, with approximate accuracy, the interval of successive passages of a star across the meridian, which it may effect perhaps to the tenth part of a second, or 1/864000 part of the whole. The moving globe itself is the real standard clock, and the transit instrument the finger of the clock, while the stars are the hour, minute, and second marks, none the less accurate because they are disposed at unequal intervals. ”

“ In spatial rhythms the point of division is almost always easily perceived; hence the greater difficulty of analyzing the simplest time-rhythms as compared with the most complex space-rhythms. Moreover, the basis of measurement, that by which the 'distance' between any point of division and that which follows it is determined, must, by definition, be duration of time. Suppose, however, that the time-distance between successive points of emphasis or division is equal, is the rhythm therefore necessarily regular? No, because the points of emphasis themselves may vary in force or energy. ”

“ But since then many improvements have been made in it, so that makers are now enabled to produce a pocket watch, with the short angle lever escapement, which marks time at a steady rate of within four or five seconds weekly,—a rate which approaches so near to the time-keeping of a pocket chronometer, that unless the minutest exactness for some specific purpose is required, the last-named watch is all that can be wished for. ”

“ The clock is constructed to mark uniform time in such wise that the length of the clock day shall be the average of all the solar days in the year. Four times a year the clock and the sun-dial agree exactly; but the sun-dial, now going a little slower, now a little faster, will be sometimes behind, sometimes before the clock—the greatest accumulated difference being about sixteen minutes for a few days in November, but on the average much less. ”