Einstein (15 page)

How did it happen that something of this kind, in part exciting and in part absurd, was ascribed to Einstein’s theory? We saw above that it is actually a statement about concrete, observable events carried out with definite physical apparatuses. Why did people like to present Einstein’s clear deductions about physical experiments in a semi-mystical and incomprehensive language?

The reason is that Einstein not only asserted the existence of previously unknown physical occurrences, but also proposed to describe these new phenomena in a language by which they might be expressed most simply. The usual mode of expression in physics was intended to present as simply as possible phenomena that had already been known for a long time. To Einstein this traditional language of physics proved to be too inconvenient and complicated for the presentation of the newly discovered or predicted phenomena.

In ordinary physics the duration of an event was defined by the rotation of the hands of a clock or by the number of oscillations of a pendulum. This was a clear-cut definition as long as one believed that the functioning of such a mechanism was unaffected by its motion. But if Einstein’s deductions from his postulates are correct, then with moving clocks different durations of time will be obtained for the same physical event. As we saw above, the duration of the time taken for light to travel from the source (
S
) to a mirror (
M
) and back to S depends on whether the interval is measured by a clock at rest in the fundamental system (
F
) or by one in the laboratory (
L
) moving with velocity v with respect to
F
.

In order to express this situation most simply, Einstein proposed to speak no longer of the “duration of an event” without further qualification, but to speak of the “duration relative to a specific frame of reference.” By this he meant duration measured with the aid of a clock firmly attached to this specific frame of reference. The physical situation provides no basis for selecting one of these measurements in preference to others and describing it as the “actual duration” in contrast to others that are “apparent durations.” For, in accordance with the principle
of relativity, the duration of a specific occurrence in a laboratory should be independent of the velocity (
v
) of the laboratory, provided clocks are used that are at rest with respect to
L
. By no argument, however, one can be forced to accept Einstein’s proposal. One can also describe the above situation by saying: “The
true duration
of an event is the duration measured by means of the clock of a specific system of reference. Every other duration is only an illusion due to deliberate alteration in the rate of the clock.” This statement conveys exactly the same meaning about observable facts except that a specific reference frame is introduced, which on physical grounds is unnecessary.

Many authors have interpreted Einstein’s clear and unequivocal statement by the apparently profound but in reality meaningless statement: “Einstein said that sometimes time flows rapidly and sometimes slowly.” Indeed, to say that time
flows
is a figure of speech that is only partly appropriate to the description of the physical phenomena. To speak of “more rapid flow” is to take a simple metaphor seriously. If one differentiates between statements about new physical occurrences and the proposal for a new mode of expression, one can formulate what is exactly meant by claiming the “relativity of time.” It means to state: if we use the expression “time interval with respect to a specific system of reference,” we can describe the phenomena in a simpler way than by using the traditional expression “time interval without specification.” Einstein’s
relativity of time
is a reform in
semantics
, not in metaphysics.

If an investigation similar to the one on the duration of time as measured by clocks is carried out for “intervals in space” as measured by measuring rods, the length of a yardstick must also be affected by its motion. I shall not discuss this point in further detail, since we have already become acquainted with the method by which such results are obtained. I shall only state Einstein’s proposal that since moving measuring rods change their lengths relative to resting rods, one should speak only of “length relative to a specific system” and not of “length” as such.

Another consequence of Einstein’s basic hypotheses is that a statement like “two events at different places occur simultaneously” is better formulated with respect to a specific system of
reference. An observer in Chicago may receive simultaneously radio signals from two points at equal distances from Chicago. He would say that they were sent out at one and the same time, but an interceptor on a moving train receiving the same signals would not receive them simultaneously if they are sent out according to conventional clocks. Einstein therefore proposed that the word “simultaneous” should likewise be introduced only in the combination “simultaneous relative to a specific system of reference.” This would be again an improvement in
semantics
. “Simultaneity” without specification is an expression of little practical use.

Because of the continuity of laws, Newtonian mechanics must become invalid also for particles with velocities near to the velocity of light. Einstein soon found out that his hypotheses could be put to a very important task. They became an instrument for deriving from the laws of physics that are valid only for small velocities laws that are generally valid for all velocities. As we have learned already, it follows from Einstein’s two hypotheses that Newton’s law of mechanics cannot be valid for great velocities. For if it were, it would be possible, even by a small constant force, to accelerate a mass gradually until it attains the speed of light.

Einstein started from the assumption that for small velocities (i.e., much smaller than the speed of light,
c
) every mass moves according to Newton’s laws of motion. By applying the procedure mentioned above, Einstein succeeded in deriving from the Newtonian laws the laws of motion for high speed. The chief result obtained in this way is the rather startling fact that the mass of a body is not constant; like the duration of time and the length of a measuring rod, it is dependent on its velocity. The mass increase’s with velocity in such a way that as the velocity becomes very great, the mass also becomes very great. A given force will produce smaller and smaller change in the actual velocity the more it approaches the velocity of light. For this reason no particle can ever actually attain the velocity of light, no matter how great a force acts on it and for how long a time.

Proceeding to the domain of electromagnetic phenomena, Einstein was again led to the conclusion that electric and magnetic field strengths are also “relative quantities.” Every helpful description of electric or magnetic field strength must contain not only their magnitude but also the system with respect to which they are measured.

The necessity of this is easily seen. When an electric charge
is at rest in
L
, it possesses an electric field only “relative to
L
.” There is no magnetic field relative to
L
since an electric charge at rest exerts no magnetic force. However, when this same situation is described relative to
F
, the electric charge is moving with a velocity
v;
this means that there is an electric
current
. Since every electric current exerts a magnetic force, it is appropriate to say that there is magnetic field “relative to
F
.” The existence of these fields is, of course, a physical fact. But their descriptions “relative to
L
” and “relative to
F
” are different.

From the same hypotheses Einstein was able to draw still another conclusion that at first one can hardly believe is contained in them. If an agglomeration of masses is formed or falls apart under production of kinetic energy or radiation the sum of the masses after the agglomeration or disintegration is smaller than before. The produced energy is given by
E
=
mc
²
, where
m
is the loss of mass. This statement may be considered as a law about the “transformation of mass into energy.” In a process where there is such a transformation from mass to energy or vice versa, the energy of the system will not be conserved unless account is taken for the gain or loss due to the change in mass.

This law has proved to be of immense significance in the development of our knowledge of the interior of the atom. According to our modern conception of the atom, it consists of a massive central core with positive charge, which is called the nucleus, and around it a number of negatively charged particles, called electrons, circulating at great speed. The nucleus itself is a complex structure built up of two kinds of particles, the positively charged protons, which are the nuclei of the simplest atom, hydrogen, and neutrons that are exactly like protons except for the lack of any electric charge. The various atoms found in nature differ only by the difference in the number of protons and neutrons they possess in the nucleus, the heavier atoms containing more particles and hence being of more complex structure. As stated already, hydrogen, the lightest atom, has a nucleus that is simply a proton. The next lightest atom is helium, whose nucleus contains two protons and two neutrons. These four particles are bound very tightly together in the nucleus by certain nuclear forces. It is one of the most important problems
of modern physics to investigate the strength, character, and quality of these nuclear forces which bind the atomic nuclei together.

A measure of the strength with which particles in the nucleus are packed together can be obtained by considering how much energy is necessary to pry the particles loose and separate them so they are all a large distance apart from one another. This energy is known as the binding energy of a nucleus. Now, according to Einstein’s theory, this energy (
E
) which is produced by the formation of the nucleus must appear as loss of mass due to the agglomeration. This means that the masses of the individual protons and neutrons added together are by
E
/
c
²
greater than the mass of the nucleus where these particles are bound together. Thus by measuring the masses of the protons and neutrons while they are free and the mass of the nucleus, it is possible to obtain the binding energy of the nucleus. Such measurements have been carried out for many of the atoms found in nature, and we are now able to classify according to how strongly the particles in the nuclei are bound together. These results have been of immense value in the planning and interpretation of recent researches on the artificial transmutation of atoms, where by bombarding various atomic nuclei with protons, neutrons, and other similar particles, new atoms have been produced.

Einstein’s mass-energy relation has also for the first time in history made possible the solution of the problem of the source of the sun’s energy. The sun has been radiating heat and light at the same rate as it is now doing for billions of years. If that energy had come from ordinary combustion, such as the burning of coal, the sun would have cooled off by now. The problem had the scientists completely baffled until
Einstein’s equation E
=
mc
²
appeared. The velocity of light (
c
) is a very large number, and with this squared, the formula states that a small quantity of mass can transform into a very large amount of energy. For this reason, by losing only an immeasurable amount of mass, the sun has been able to continue radiating for so long, and will continue to do so for billions of years to come. The actual mechanism of the transformation of mass to energy occurs in nuclear reactions that are going on in the interior of the sun. It is believed now that they ultimately boil down to the formation of helium nuclei from hydrogen. In this
“packing effect,”
as we have learned already, mass is lost and radiation emitted.

This possibility of using mass as a source of energy has aroused very optimistic hopes that methods of liberating the energy
stored in the atom as mass for practical use might be found. There has also been, on the other hand, a very frightening prospect that such a process might be used to produce an explosive so devastating that a pound of it would completely annihilate everything within a radius of many miles. This foreboding was fulfilled forty years later when the first atomic bomb destroyed Hiroshima.

To Einstein, however, the main value of his result was not in the applications, no matter how numerous or important. To himself his principal achievement was to have deduced the law
E
=
mc
²
from the relativity principle. It was in accord with Einstein’s conception of the universe to strive continually for the discovery of simple, logical bridges between the laws of nature. The wealth of conclusions derived from his two hypotheses constitutes what has been known since as the “theory of relativity.” Einstein had struck a rich well of information about nature, which would yield knowledge for many decades to come.

In the same year (1905) Einstein discovered new fundamental laws in two fields outside the theory of relativity. At the time when Einstein came to Bern, he was intensely occupied with the problem of light and motion, But he saw that the final goal could be attained only by attacking the problems from various angles. One of the paths to the goal, he realized, was to investigate the relations between light and heat, and those between heat and motion.

It had been known for some time that heat is connected with the irregular motion of molecules. The higher the temperature, the more violent is this motion. The statistical behavior of particles in such irregular motion had been investigated chiefly by the Scottish physicist James Clerk Maxwell (1831–79) and the Austrian Ludwig Boltzmann (1844–1906). It had been assumed even before, that the kinetic energy of the molecules is proportional to the absolute temperature. At the time of Maxwell and Boltzmann, however, the molecular constitution of matter was still a hypothesis which could be doubted. It enabled many different phenomena to be explained very simply, but there was as yet no very direct proof of the existence of the molecule. Furthermore, it had not yet been possible to obtain an accurate value of
such a significant quantity as the number of molecules in a unit volume of matter. Estimates of this number had been made by such men as the Austrian physicist Loschmidt (1865), but they were based on involved and rather indirect methods. Einstein strongly felt the necessity of investigating this matter more thoroughly and obtaining a more direct proof of molecular motion.