**Science
in Christian Perspective**

**
Speed Saves time: Scientifically Demonstrated**

"MAN DOES NOT KNOW HIS TIME"

(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.

**A**mong 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

**t**_{moving}/**t**_{reference} = [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?