Einstein (13 page)

Besides this “principle of relativity,” Einstein needed a second principle dealing with the interaction of light and motion. He investigated the influence of the motion of the source of light on
the velocity of the light emitted by it. From the standpoint of the ether theory, it is self-evident that it makes no difference whether or not the source of light moves; light considered as mechanical vibration in the ether is propagated with a constant velocity with respect to the ether. This velocity depends only on the elasticity and density of the ether.

Dropping the ether theory of light, Einstein had to reformulate this law into a statement about observable facts. There is one system of reference,
F
(the fundamental system), with respect to which light is propagated with a specific speed,
c
. No matter with what velocity the light source moves with respect to the fundamental system (
F
), the light emitted is propagated with the same specific velocity (
c
) relative to
F
. This statement is usually called the “principal of the constancy of the speed of light.”

The constancy of the speed of light has been confirmed empirically from the observation in double stars. They are stars of approximately equal masses, which are close together and revolve about each other, and are well known to astronomers. If the velocity of light depended on the velocity of the source, then as the stars revolve, the time taken for light to reach the earth from the member of the pair that is approaching the earth will be shorter than the corresponding time of the light from the receding member. Analysis of the two beams of light has shown that there is no observable effect from the velocity of the source.

It was a characteristic feature of Einstein’s mode of work to deduce from his fundamental principles all the logical consequences to the limit. He showed that from these hypotheses, which appeared quite harmless and plausible, a rigorous deduction led to results that seemed very novel and in part even “incredible.” From these results he went on to others, which not only seemed incredible but were even pronounced “paradoxical,” “absurd,” and “incompatible with sound logic and psychology.”

There are at present thousands of papers in which attempts are made to explain Einstein’s theory to the lay public. It is not the purpose of this book to go into all the details of his theories, but to give a description of Einstein’s personality and his relation
to his environment. It is necessary, however, to go into his scientific work to a certain extent in order to give the reader some idea of the manner in which he attacked scientific problems in comparison with that of other scientists. In particular we should try to understand how it happened that his theories not only were of interest to physicists, but also stimulated and excited philosophers, thus indirectly stirring up a public that had only slight interest in scientific questions but that participated in the general intellectual life of our period.

From the two basic assumptions Einstein was able to conclude not only that the mechanistic theory of light was erroneous, but that even the Newtonian mechanics of material objects could not be generally valid. This result can be fairly easily understood if we trace it back to the way Einstein speculated on the properties of light as early as at the age of sixteen.

While still a student, Einstein had pictured to himself the remarkable things that would occur if a body could travel with the speed of light — at the rate of 186,000 miles per second. Let us consider the fundamental system (
F
) and a laboratory (
L
) for optical experiments which moves with constant velocity (
v
) with respect to
F
. Let there be a source of light (
R
) at rest in
F
, from which a beam of light is propagated with velocity
c
in the same direction as the laboratory (
L
) is moving. Now, if the velocity (
v
) of the laboratory (
L
) is equal to the velocity of light (
c
) then, according to Newtonian mechanics, the ray of light will be stationary with respect to the laboratory. No vibration is registered in
L
. Since light does not move with respect to
L
, there are no rays in
L
, and the usual experiments of reflection and refraction cannot be performed (
fig. 1
).

It is, of course, imaginable that in such a rapidly moving system (
L
) there would no longer be any optical phenomena in the ordinary sense. This occurrence, however, would be inconsistent with Einstein’s principle of relativity in optics. For according to this principle, all optical experiments should give the same result whatever the speed (
v
) of the laboratory may be.

The same difficulty appears if we compare directly the results of Einstein’s two principles (relativity and constancy) within the ether theory of light. We consider again a laboratory that is moving with the speed of light (
c
) relative to the fundamental system (
F
). Suppose a mirror is set up in
L
to reflect the beam of light emitted by a source that is at rest in
L
. With respect to
L
this reflection is just the ordinary occurrence of light reflected by a mirror at rest. According to the principle of constancy, however, nothing is changed if we assume the source of light at rest in
F
. Then, however, the beam of light can never be reflected, since both the light and the mirror are traveling in the same direction with the same velocity (
c
). The light can never catch up to the mirror. Thus there would be again an influence of the speed of the laboratory on the optical phenomena within, and therefore a violation of Einstein’s principle of relativity.

FIGURE 1

This diagram represents light waves propagated in a horizontal direction through the ether. If T is a half-period of the light, the first line represents the state of the wave at the time T after the emission from the source R. The other lines represent the states of the same wave after the times 2T, 3T, and 4T respectively. If a device is placed at a fixed spot in the ether it will record the state of the wave (along the line OA) at the consequent instances of time T, 2T, 3T, and 4T. These states are represented by the interrupted lines. They indicate a vibration. But if the device of registration is moving with the speed of light in the direction of the wave propagation, it is recording the states of waves along OB. They are represented by a thick line. It is clear that
no
vibration is recorded by the moving instrument. Briefly, there is no light for a recording instrument moving with the speed of light.

If we accept Einstein’s two basic hypotheses, then the above considerations lead us to the conclusion: it is
not
possible for a laboratory (
L
) to move with velocity of light (
c
) with respect to the fundamental system (
F
); for if that were possible, the relativity principle could not be valid. Or, since the laboratory is a material body like any other,
no material body can move with the velocity of light
(
c
).

This conclusion may at first seem absurd. It is reasonable to think that any velocity can be attained by the continual addition of even a certain small increment of velocity. For, according to Newton’s law of force, every force imparts to a body upon which it acts an additional velocity that is smaller the greater its mass is. One need only to let a force, no matter how small, act long enough on a body, and its velocity can be increased beyond any magnitude whatever. This circumstance shows the incompatibility of Einstein’s principles with Newtonian mechanics; the former demand the impossibility of the velocity of light for material bodies, while the latter affords the possibility.

In Einstein’s mechanics, therefore, the velocity of light in empty space plays a very special role. It is a velocity that cannot be attained or exceeded by any material body. We thus find an intimate connection created between mechanical and optical phenomena. Furthermore, owing to this circumstance, it becomes meaningful to speak of “small” or “great” velocity without further qualification. It means that the velocity is “small” or “great” in comparison with the velocity of light.

Not only did Einstein’s fundamental principles give rise to results conflicting with Newtonian mechanics; they also led to drastic changes in our use of the words “space” and “time.” The laws of physics contain statements about phenomena whose effects can be observed in terms of measuring rods and clocks,
and much can be deduced about their behavior from Einstein’s postulates.

Let us consider a situation similar to the one in the previous section. A laboratory system (
L
) moves with constant velocity (
v
, smaller than
c
) with respect to a fundamental system (
F
). There is a source of light (
S
) and a mirror (
M
) at a distance (
d
) from
S
in the laboratory (
L
) such that the light from
S
travels to
M
, is reflected, and returns to
S
, and such that the direction of the ray
SM
is perpendicular to the direction of the velocity
v
of
L
in respect to
F
. In going from the source (
S
) to the mirror (
M
) and back, the light has to travel a distance 2
d
measured by yardsticks attached to
L
, but by yardsticks attached to
F
the path is longer because the mirror (
M
) is moving with respect to
F
. Let the length of this path be 2
d
^*
. The ratio
, which will be designated by
k
for the sake of conciseness, is easily calculated. It requires no greater mathematical knowledge than the Pythagorean theorem, and its expression is
, As
v
is smaller than
c, k
is greater than 1.
k
is not much greater than 1 if
v
is very small compared to
c
, but becomes very large as
v
approaches
c
.

In order to determine the dependence of (
k
) upon (
v
) we have to consider the time required for light to travel from the source
S
to mirror
M
and back to
S
. Some sort of a time-measuring device, such as a clock on the wall, a pocket watch on the table, a pendulum hanging from the ceiling, or an hour-glass, is needed in the laboratory (
L
). The time interval between the starting out of the light ray from
S
and its return is measured in terms of the time that the hand of a clock or watch takes to move through a certain angle, the pendulum to make a certain number of oscillations, or a certain amount of sand to flow through the hour-glass. The unit of time is a certain arbitrary angle of the clock or watch, an arbitrary number of pendulum oscillations, or an arbitrary quantity of sand.