Science in Christian Perspective



Speed Saves time: Scientifically Demonstrated
(Ecciesiastes 9:12)

Richard H. Bube

From: JASA 24 (December 1972): 158-159

Two brief papers in Science 177, 166-170, July 14, 1972 report experimental verification of the prediction of relativity theory that a clock in motion with respect to a reference clock runs slower than that reference clock through a "round trip." The authors are J. C. Hafele of the Department of Physics, Washington University, St. Louis, Missouri, and Richard E. Keating of the Time Service Division of the U.S. Naval Observatory, Washington, D.C. Their apparent decisive demonstration of the validity of this much debated aspect of relativity theory, and the reminder of their work to us that time itself is part of the warp and woof of our created universe, prompts this summary.

Among the predictions of relativity theory that shatter our common sense concepts of the universe around us, none seems harder to grasp than the prediction that the measurement of time itself depends on the relative velocity between two clocks. Given one reference clock at rest in an inertial reference system, the theory predicts that a clock in motion with a velocity x with respect to this system will record less time than the reference clock, such that

tmoving/treference = [1-(Y/c)2]1/2

where c is the velocity of light. 

Common sense objections (joined also by much more sophisticated technical arguments) to this apparent violation of experience attempt to make the moving clock "appear" slower without really being slower. There are many kinds of clocks however, and one kind is simply the biological clock of a human being; the prediction then is that the moving human being ages more slowly than the reference human being at rest. A twin moving in space flight while his twin brother remains on earth should then age more slowly than the twin on earth, and this age difference should be obvious when the moving twin returns to earth. Disagreements about this interpretation have given origin to the debate about the so-called "twin paradox."

The ideal way to solve theoretical dilemmas is to perform a suitable experiment, i.e., permit the universe to give its own answer. But physically realizable speeds are so much less than the velocity of light that the predicted rate differences are impossible to measure by most known means. The velocity of an airliner going
600 miles per hour, for example, corresponds to a speed of 1 6 of a mile per second compared to the speed of light of 186,000 miles per second, i.e., the velocity of light is over a million times larger than the velocity of a jet airplane. Experimentally the solution of the problem requires either faster speeds (by many orders of magnitude) or much more sensitive methods of measuring time. The former is not presently practical; the latter has in recent years become possible.

It is clear that standard clocks or biological clocks are not going to be anywhere near exact enough for the demands of the above experiment. In recent years, however, a standard of time has been developed in terms of the specific frequency of a well-defined electronic transition in the 133 Cs atom, which in the ideal case has exactly 9,192,631,770 periods in one second. By using this transition as the standard it has become possible to construct "cesium beam atomic clocks" with an ideal accuracy of almost 1 part in 1010, i.e., 1 part in 10 thousand million. Relativistically predicted differences in the rates of these clocks are large enough to be measurable and to check the prediction.

The experiment was carried out as follows. During October 1971, four (to eliminate random variations) cesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward. The eastward trip involved 41.2 hr of flight, and the westward trip 48.6 hr of flight. At the end of their flights around the world, the moving clocks were compared with reference clocks at the U.S. Naval Observatory, and predicted results of rate loss or gain compared to that actually measured. The theory, for reason noted below, predicted that the clocks would lose 40±23 nanoseconds during the eastward trip, and would gain 275±21 nanoseconds during the westward trip (a nanosecond is 10
second, i.e., one thousandth of a millionth of a second). The mean measured values were a loss of 59±10 nanoseconds for the eastward trip, and a gain of 273±7 nanoseconds for the westward trip, in apparent striking confirmation of the predicted results.

In carrying out the experimental measurements described above, several additional factors had to be taken into account, (1) The reference clock in this ease is on the surface of the earth, and hence not at rest. However its rate relative to a non-rotating frame of reference can he calculated in terms of the rate of rotation of the earth. Similarly the rate of the flying clock can be expressed with respect to this non-rotating reference system, and the time difference between the flying clock and the clock on the earth's surface can be calculated. (2) A rate difference for the flying clock exists independently of its motion, simply because of its height, and hence different gravitational potential from the reference clock. This rate difference is positive and represents a time gain for the moving clock. (3) When the flying clock travels eastward, its velocity is in the same direction as the rotational velocity of the earth, and a large time loss is predicted, which is counterbalanced by the time gain due to the gravitational term, producing finally a small time loss (i.e., the predicted 40±23 nanosec.) When the flying clock travels westward, its velocity is counter to that of the rotational velocity of the earth, and a time gain is predicted, which is accentuated by the time gain due to the gravitational term, producing the larger time gain (i.e., the predicted 275±21 nanosec.). (4) The jet plane does not of course travel around the earth at constant velocity; the total trip must therefore be broken down into short constant-velocity segments and the actual numbers calculated piecemeal rather than in one single calculation.

The authors close with a statement that is dear to an experimental scientist's heart.

There seems to be little basis for further arguments about whether clocks will indicate the same time after a round trip, for we find that they do not.

How important is the effect? Philosophically it is mind stretching. Practically it is small indeed. If a man started flying eastward on a jet-plane travelling its standard speed as in this experiment, while his twin brother flew westward for the same time, after one year of flight, their ages would differ by only 57 millionths of a second. Even after a hundred years of such flight, their ages would differ by only 6 thousandths of a second. The reason for the very small effect is, of course, the small velocity of the jetliner with respect to the velocity of light, and the dependence of the effect on the square of the ratio (v/c)2. If the flight speed were much larger, then of course the result would be quite different. If, for example, the flight speed were increased up to 10% of the velocity of light (i.e., one circumnavigation of the earth every 1.3 see!), a time loss would be experienced for either direction of flight, but still with a sufficiently small magnitude that it would take a flight of over 6 months to produce a 1 day difference in age between a flying twin and his brother remaining stationary on earth.

Still, it does make time a much less well defined quantity, doesn't it?