Einstein (14 page)

Now, the
constancy of the velocity of light
means that the quotient of the distance traveled by the light ray divided by the time taken is equal to a constant (
c
), whatever the speed (
v
) of the source may be. The value of the distance is
d
if we measure it with the yardstick attached to
L
, and
d
^*
if we use the yardstick attached to
F
. Thus if we designate the time interval for
the light to go from
S
to
M
and back by
t
if we use the
L
-yardstick and by
t
^*
if we use the
F
-yardstick, we have
c
= 2
d
/
t
and
c
= 2
d
^*
/
t
^*
, and hence
(
fig. 2
). This means, however, that the result of the measurement depends on
k
, and consequently on
v
. The greater the velocity of the laboratory (
L
) with respect to the system (
F
), the greater is the angle through which the hand of the clock turns while the light travels to the mirror and back. Similarly with a pendulum and an hour-glass, the greater is the number of oscillations and the quantity of sand. Therefore, by measuring this time interval, the observer in
L
should be able to determine the velocity (
v
) by observations conducted solely in his laboratory
L
. This, however, conflicts with Einstein’s
principle of relativity
.

FIGURE 2

The source of light S and the mirror M are moving with one and the same speed v with respect to the ether, while light itself travels at speed c. The left diagram shows a light ray emitted from S and reflected by M back to S. The line SM is the trace of the ray on a screen that participates in the motion of S and M. The time t of the relection is t = 2d/c, according to the principle of relativity. The right diagram shows the trace of the same light ray on a screen that is at rest in the ether and that does not participate in the motion of S and M. According to the principle of constancy we obtain
. If we consider the rectangular triangle SM
₁
S
₁
, it follows from the Pythagorean theorem that (d
^*
)
²
= d
²
+ (vt
^*
/2)
²
. If we substitute the results of the principles of relativity, d = ct/2, and of constancy, d
^*
= ct
^*
/2, we obtain

The contradiction arises from a traditional assumption that is based on Newton’s idea of absolute time. According to Newton, all clocks, watches, hour-glasses, and any other time-measuring devices function at exactly the same rate, no matter what their velocities are. In particular, a clock in the laboratory system (
L
) runs at exactly the same rate as a clock firmly attached to the
fundamental system (
F
). If this is so,
t
cannot differ from
t
^*
. On the other hand, we have derived from Einstein’s two hypotheses that
t
^*
=
kt
. This means that the time
t
^*
is different from
t
, and that the difference depends upon
k
. As
k
depends upon
v
, the rate of a time-keeper depends upon the velocity (
v
) of its motion. Hence if Einstein’s hypotheses are accepted, the traditional assumption must be dropped, that the rate of a time-keeper is independent of its speed. In order to build up a theory of light and motion that is consistent with Einstein’s hypotheses, we have to assume that the clock in the laboratory (
L
) runs slower than that in the fundamental system (
F
), the rate depending upon the speed (
v
) of
L
relative to
F
. Then, while the hands of the clock in
F
rotate through an angle (
a
), that of the clock in
L
rotate through the smaller angle
a
/
k;
while the pendulum in
F
makes
n
oscillations, that in
L
makes only
n
/
k;
while
q
ounces of sand run through the hour-glass in
F
, only
q
/
k
ounces run in
L;
hence the time interval for light to travel from
S
to
M
and back as measured by any time-measuring device attached to
L
will depend only on the velocity (
v
) of
L
and not on the special kind of device that we use.

Thus an entirely new property of time-keepers, which is not consistent with the traditional view, has been deduced from Einstein’s two fundamental hypotheses. A moving clock, no matter what its construction, runs slower than an identical clock that is at rest. This is a physical fact that may be true or false, but there is nothing “paradoxical” about it.

Einstein even indicated a method whereby this assertion could be subjected to direct experimental verification. He pointed out that atoms could be used as natural clocks since they emit electromagnetic waves of certain definite frequencies. These frequencies of oscillation can be taken as natural time units for the atom, and frequencies of one group of atoms at rest in the laboratory can be compared with those of another group moving at a great velocity. The comparison of the frequencies can be made by means of a spectograph. The radiation of definite frequencies emitted by atoms form distinct spectral lines on photograph plates, with the position of the lines arranged according to the magnitude of the frequency. Einstein’s result would be verified if the spectral lines of the moving atoms were shifted slightly to the low-frequency side as compared with the spectral lines of the stationary atoms. Actually this experiment was carried out in 1936 by H. Ives, of the Bell Telephone Laboratories, New York City, with positive result.

This effect must, of course, be distinguished from the so-called Doppler effect, which is also an alteration of the frequencies of radiation due to the motion of the atoms. The Einstein effect, however, is independent of the direction of motion of the atoms, while the Doppler effect depends critically on the direction. The shift has the greatest value if the motion of the atoms has a direction opposite to the velocity of the mirror or screen by which the light is intercepted.

There was something of a sensation when Einstein pointed out that the beat of the human heart is also a sort of clock and the rate of its beating must also be affected by its motion. Consider a person at rest in
F
whose heart beats at the rate of 70 per minute. If this same person moves with velocity
v
relative to
F
, then his heart will only beat
times a minute. But it must be remembered that it is
as measured by a clock fixed in
F;
if measured by a clock that travels with the person, this clock itself will move slower and the heart-beat will then be just 70. Since the same retardation likewise affects all the metabolic processes in the body, it can be said that the person moving with the system
L
“ages” less than a person remaining in
F
. Such a circumstance may sound novel, but it cannot account sufficiently for the impression that this new physical theory made upon the masses of the public. For there was an impression that all our thinking about the universe had suffered a severe shock.

In the fall of 1912 I first realized that Einstein’s theory of the “relativity of time” was about to become a world sensation. At that time, in Zurich, I saw in a Viennese daily newspaper the headline: “The Minute in Danger, a Sensation of Mathematical Science.” In the article a professor of physics explained to an amazed public that by means of an unprecedented mathematical trick a physicist named Einstein had succeeded in proving that under certain conditions time itself could contract or expand, that it could sometimes pass more rapidly and at other times more slowly. This idea changed our entire conception of the relation of man to the universe. Men came and went, generations passed, but the flow of time remained unchanged. Since Einstein this is all ended. The flow of time itself can be changed, and at that by a “mathematical” trick. To most people this appeared incomprehensible. Some rejoiced that anything so absurd could happen and that traditional science, which is always unpopular with some people, had suffered such a defeat. Others
were vexed that something should happen which ran counter to all common sense. People were inclined to regard it as a phantasm of the mathematicians, or as an exaggeration by an author desirous of creating a sensation. At any rate, it was exciting that something of the sort could happen and that our generation was chosen to witness the overthrow of the foundations of the universe.