Einstein (16 page)

It had long been known that small but microscopically visible particles, when suspended in a fluid with approximately the same density, exhibit a constant, apparently irregular zigzag motion. It had been discovered by the Scottish botanist Robert Brown for pollen dust suspended in water, and for this reason it is known as
Brownian motion
. It is not caused by any external influence jarring the vessel or by currents of water in the vessel, and the agitation increases in intensity when the temperature of the water is raised. For this reason it had been conjectured that the motion is connected with the heat motion of the molecules. According to this view, the kinetic energy of the water molecules in constant collision with the microscopic particles produces irregular forces in random directions, which give rise to the observed motions.

In 1902 Einstein had restated Boltzmann’s theory of random motion in a simplified form. He now treated the Brownian motion with this method and arrived at a surprisingly simple result. He showed that the results of the kinetic theory of molecules should also hold for particles visible by microscope — for instance, that the average kinetic energy of the particles in the Brownian motion should have the same value as that for the molecules. Hence, by observing the motion of the microscopically visible particles, much valuable information could be obtained about the invisible molecules. In this way Einstein was able to derive a formula which stated that the average displacement of the particles in any direction increases as the square root of the time. He showed (1905) how one can determine the number of molecules in a unit volume by measuring the distances traveled by the visible particles.

The actual observations were later made by the French physicist Jean Perrin, who completely verified Einstein’s theory. The phenomenon of Brownian motion has subsequently always been included among the best “direct” proofs of the existence of the molecule.

To Einstein it was always clear that his theory of relativity could not claim (and, indeed, it never did claim) to solve all the mysteries of the behavior of light. The properties of light investigated by Einstein concerned only a certain group of phenomena dealing with the relation between the propagation of light and moving bodies. For all these problems light could be conceived along the lines of traditional physics as undulatory electromagnetic processes which filled space as a continuum. By the theory of relativity it was assumed that some objects can emit light of this nature, and no attempt was made to analyze the exact process by which light is emitted or to investigate whether it sufficed for a derivation of all the laws for the interaction of light with matter.

The investigations on the nature of light and its interaction with matter, however, were to lead to the rise of the “quantum theory,” a revolution in physical thought even more radical than the theory of relativity. And in this field, too, Einstein’s genius had a profound influence on its early development. In order to make understandable the nature of Einstein’s contributions, I shall describe briefly the situation prior to his researches.

The simplest way of producing light is by heating a solid body. As the temperature rises, it begins to glow from a dull cherry red to a brighter orange, and then to blinding white light. The reason for this is that visible light consists of radiations of different frequencies ranging from red at the low end through the colors of the spectrum up to violet at the high end. The quality of light emitted by a solid body depends solely on its temperature; at low temperatures the low-frequency waves predominate and hence it looks red; at higher temperatures the shorter wave lengths appear and mingle with the red to give the white color.

Attempts to explain this change in quality of light with temperature on the basis of nineteenth-century physics had ended in failure, and this was one of the most important problems facing physicists at the beginning of the twentieth century. At that time the emission of light was thought to be produced by the oscillations of charged particles (electrons), the frequency of light emitted being equal to the frequency of the vibration. According to Boltzmann’s statistical law, already mentioned,
the average energy of oscillation of an electron should be exactly equal to the average kinetic energy of gas molecules, and hence simply proportional to the absolute temperature. But this led to the conclusion that the energy of vibrations is independent of the frequency of oscillation, and hence light of different frequencies will be emitted with the same energy. This conclusion obviously was contradicted by the observations on light emitted by heated bodies. In particular, we know that light of very short wave lengths is not emitted to any great extent by hot bodies. As the temperature increases, rays of increasingly higher frequencies appear, but yet at a given temperature there is no perceptible radiation above a certain definite frequency. Consequently it appeared that somehow it must be difficult to emit light of very high frequencies.

Since all arguments based on the mechanistic theory of matter and electricity led to results conflicting with experience, the German physicist Max Planck in the year 1900 introduced a new assumption into the theory of light emission. At first it appeared to be rather inconsequential, but in the course of time it has led to results of an increasingly revolutionary character. The turn in physics coincided exactly with the turn of the century. I shall sketch Planck’s idea in a somewhat simplified and perhaps superficial form.

According to Boltzmann’s statistical law, the average energy of oscillation of an electron in a body is equal to the average kinetic energy of the molecules. The actual energies of the individual atoms or molecules can, of course, have very different values; the statistical law only relates the
average
energy with the temperature. Boltzmann, however, had been able to derive a second result which determined the distribution of the energy of the particles around the average value. It stated that the number of particles with a certain energy depends on the percentage by which this energy differs from the average value. The greater a deviation, the less frequent will be its occurrence.

As Planck realized, the experimental results indicated that the oscillating electrons in a body cannot emit radiation with an arbitrary frequency. The lack of high-frequency radiation shows that the mechanism of radiation must be such that it is somehow difficult to emit light of high frequency. Since no explanation of such a mechanism existed at that time, Planck was led to make the new assumption that, for some reason as yet unknown, the energy of oscillation of the atoms cannot have just any value, but can only have values that are integral
multiples of a certain minimum value. Thus, if this value is called
, then the energy of the oscillations can only have the discrete values
0
,
, 2
 … or
n
, whose
n
is zero or an integer. Consequently the radiation emitted or absorbed must take place in portions of amount
. Smaller amounts cannot be radiated or absorbed since the oscillation cannot change its energy by less than this amount. Planck then showed that if one wants to account for the well-known fact that a shift to higher temperatures means a shift to higher frequencies, one has to take values for
that vary for different values of the frequencies of the oscillations, and in fact
has to be proportional to the frequency.