Three Scientific Revolutions: How They Transformed Our Conceptions of Reality (21 page)

While working in close collaboration between 1900 and 1903, Rutherford and Soddy made a startling discovery regarding the
transmutation
of radioactive substances, though fearing they might be ridiculed as alchemists, they called the process a “transformation.” Their unexpected discovery was that radioactive emissions indicate a change in the
internal structure
of the radioactive substance creating two or more forms of the same element. Soddy introduced the term “isotope” in 1913 to refer to elements that were identical in their chemical properties and position on the Periodic table but differ in their mass and radioactive properties, such Ra
²²⁴
, Ra
²²⁶
, and Ra
²²⁸
. Moreover, when chemically separated from the original radioactive material but left in contact with it, the residue became similarly radioactive and the sum of the curves representing the loss or gain of radioactivity over a prior of time between the two substances remained constant.

Yet, having made these surprising discoveries, physicists were still as baffled by the radioactive process itself as by what produced it, since nothing was yet known about the internal structure of the atom. As Marie Curie described the situation in 1900: “Uranium exhibits no appreciable change of state, no visible chemical transformation; it remains, or so it seems, identical with itself, the source of energy which it emits remains undetectable—and therein lies the profound interest of the phenomenon.”
⁶⁶
Still, the fact that Rutherford and Soddy attributed the radiation to subatomic transmutations was a bold advance. As Pais states, they surmised that “radioactive bodies contain unstable atoms of which a fixed fraction decay per unit time. The rest of the decayed atom is a new radio-element which decays again, and so forth, till finally a stable element is reached” (p. 113). Thus Rutherford and Soddy realized that the emission of energy from the radioactive bodies is caused by the inherent modification of the atoms and therefore does not negate the important law of the conservation of energy.

Though Rutherford received the Nobel Prize in chemistry in 1908 for his outstanding research in radioactivity—such as the discovery of alpha and beta particles and the transmutation of radioactive substances—his major contribution to discovering the internal structure of the atom would not occur until after he had returned to England. In 1921 Soddy also received the Nobel Prize in chemistry for his assistance in discovering radioactive transmutations and the identification of isotopes.

Since what makes an individual a scientist is his or her curiosity and desire to explain ordinary phenomena rather than just accepting them or declaring them miracles, the next discovery marked the beginning of a new inquiry that would further revolutionize the physical sciences. It had been known since household coal furnaces were used that inserting a black poker into the burning coal causes it to change color as the heat increases from red, to violet, to white. It was called “blackbody radiation” because the spectroscopic analysis had established that the various colors corresponded to the different frequencies of the electromagnetic emissions, but without any conception of the internal composition of the atom it was unknown how this occurred.

Since metals are good conductors of electricity and Rutherford had identified the electron as the unit of electrical charge, it was believed that metals somehow contain electrons to explain the flow of electric current. Furthermore, it was hypothesized that the cause of the change in the emitted colors as the temperature increased could be explained if the added heat energy produced an increased oscillation (the still accepted Newtonian explanation) of the electrons thus explaining the increased frequencies. And if the equipartition principle—that any addition of heat was distributed equally among the gas particles increasing their velocities—were true also of blackbody radiation, then since a blackbody absorbs all the incident heat or energy, the distributed increase in energy could account for the increased frequencies of the metallic oscillators.

Thus the spectral distribution and frequency intensities would be indicative of the amount of electromagnetism per unit volume of the blackbody that also could account for the fact that a thermal equilibrium had been reached, as indicated by the specific color. But while there were a number of discovered mathematical laws that contributed to a somewhat more precise correlation between the energy or frequency of the spectral emission and the incident temperature, there still was no explanation as to what accounted for the correlation. Furthermore, the Rayleigh-Jeans Law, governing the path of electromagnetic waves, made the disturbing prediction that the equal distribution of the energy, along with the fact that the higher frequency oscillations radiate their energy more efficiently, would result over time in an increase in the high-frequency radiation tending to infinity. Thus it would be dangerous sitting before a fireplace because of the increasing radiation in the ultraviolet range.

It was called “the ultraviolet catastrophe” owing to the fatal implications and also because it conflicted with the experimentally corroborated fact that the spectral intensity corresponded to the thermal equilibrium as indicated by the specific color and thus did not continue to rise. It was one of “the two dark clouds” (the other being the null results of the Michelson-Morley experiment to be discussed shortly) mentioned by Lord Kelvin that threatened physics at the turn of the century.

This was the situation confronting Max Planck in 1900, who, con­­servative by nature, introduced his famous formula describing blackbody radiation that issued in a startlingly new turn in physics. Ironically, asserting that “I had always regarded the search for the absolute as the loftiest goal of all scientific activity,”
⁶⁷
he ended up introducing the greatest
indeterminateness
or
uncertainty
in physics of all time.

His explanation was revolutionary because it indicated that thermodynamic or radiational processes, rather than being continuous as previously assumed, were discrete or discontinuous. Flowing water is an example of a continuous process while a sprinkler or rain drops are examples of discontinuous processes. Planck's task was to find the correct mathematical and physical interpretation of the relation between the energy distribution of the emission density and the entropy distribution of the thermal equilibrium that would eliminate the ultraviolet catastrophe. Years later, when he was asked how he had solved the problem, he replied

It was an act of desperation. For six years I had struggled with the blackbody theory. I knew the problem was fundamental and I knew the answer. I had to find a theoretical explanation at any cost, except for the inviolability of the two laws of thermodynamics.
⁶⁸

The two laws of thermodynamics introduced by R. Clausius in 1885 were first that the energy of the universe is constant and second that the entropy of the universe tends to a maximum. Entropy is the maximum disorder or randomness of the components of a system that is in thermal equilibrium. As Planck admitted, while he was well schooled in thermodynamics he was weak in statistics, so it was Ludwig Boltzmann who first stated the mathematical ratio between entropy and probability as S =
k
log W, where S stands for entropy, W for the thermodynamic probability, and
k
is a universal constant. This proved so important that Planck called the k in the formula “Boltzmann's constant.”

With Boltzmann's formula Planck was able to calculate the probability of the entropy at its maximum in thermal equilibrium. Then, as Segrè states, he

divided the energy of an oscillator into small but finite quantities, so that the energy of the oscillators could be written as E = Pε where P is an integral number. With this hypothesis Planck could calculate the average energy of an oscillator and thus find the blackbody formula. Planck expected that ε could become arbitarily small and that the decomposition of E in finite amounts would only be a calculational device. However, for the results to agree with Wien's thermodynamic law, ε had to be finite and proportional to the frequency of the oscillatore ε =
hv
, where
h
is a new universal constant, appropriately called
Planck's constant
. (p. 73)

His equation demonstrated and conformed to the experimental evidence that the energy distributed among the oscillators did not tend to infinitely high frequencies, but to the frequency corresponding to the incident energy, thus eliminating the ultraviolet catastrophe. The physical significance of his discovery is that the electronic oscillators, contrary to classical electrodynamics where the energy could acquire any value in a continuum, according to his formula the energy is restricted to discrete values that are integral multiples of
nhv
, where
n
equals 1, 2, 3, etc. He calculated the value of the constant
h
, known as Planck's constant, to be “6.55 × 10
^-27
[
erg. sec.
] which today is calculated as
h
= 6.6262 × 10
^-27
[
erg. sec
]” (p. 73)
.

Proving its significance, he derived a number of constants and empirical values from it, one of the strongest indications of a theory's truth. As Segrè further states, even in his first paper “Planck pointed out that from Stefan's law and from Wien's thermodynamical law it is possible to infer the two universal constants
h
[his] and
k
, and from these the charge of the electron, Avogadro's number and more” (p. 73). But despite his success in resolving the problem and receiving the Nobel Prize in physics in 1920 for his achievement, Planck never was reconciled to the conclusion. As he stated:

I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate. . . . My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.
⁶⁹

Nor was he the only one to be disconcerted by his discovery. Even Einstein had his misgivings about the introduction of quantum mechanics despite his own similar interpretation of the photoelectric effect in terms of
particles of light
called “photons.” As he declared in his “Autobiographical Notes,” where he discusses the theoretical and experimental background and significance of Planck's discovery:

Planck got his radiation-formula if he chose his energy-elements ε of the magnitude ε =
hv.
. . . All of this was quite clear to me shortly after the appearance of Planck's fundamental work; so that, without having a substitute for classical mechanics, I could nevertheless see to what kind of consequences this law of ­temperature-radiation leads. . . . All my attempts, however, to adapt the theoretical foundation of physics to this [new type of knowledge] failed completely. It was as if the ground had been pulled out from under one, with no firm foundation to be seen anywhere, upon which one could have built.
⁷⁰

This last quotation points to the year 1905, Einstein's famous
annus mirabilis
, when at age twenty-six he sent six articles to the
Annalen der Physik
(Annals of Physics) between March and December that were promptly published heralding a new era in physics. The first contained his explanation, just described, of the photoelectric effect positing the existence of discrete light quanta or photons, analogous to Planck's explanation of blackbody radiation, that contributed to the emerging revolutionary and contentious science of quantum mechanics. The second, his doctoral thesis, presented his original method for calculating molecular dimensions. The third and sixth pertained to Brownian motion presenting the most convincing evidence then of the existence of molecules. The fourth and fifth introduced his special theory of relativity that dealt with E the electrodynamics of moving bodies from which he derived his famous formula
E
=
m
c
²
, a rival to Newton's F = ma, undoubtedly the two most famous scientific formulas known to humanity.

Although like Planck he was adamantly opposed to the quantum theory throughout his life, his first paper paradoxically was a major contribution to its acceptance, along with explicitly raising the question, perhaps for the first time, of the dual nature of light since photons, as light quanta, complemented the wave theory then accepted. It also was the main reason for awarding him the Nobel Prize in 1921, since his major achievements, the theories of relativity, were unconfirmed at the time.

This is not to imply that his introduction of a strange new particle was universally accepted since it met with considerable skepticism. It was not until Arthur Compton demonstrated in 1923 the scattering of X-rays by electrons, indicating that they followed the same laws of deflection and momentum as colliding particles with the energy
hv
predicted by Planck and Einstein, that the reality of photons was generally accepted. As usual scientists are generally skeptical of new discoveries until they are confirmed by additional evidence.

It was his third article on Brownian motion, cited more frequently than the others, that was the most successful. Ever since Robert Brown had suspended pollen grains in water in 1827, attributing their observed motion to the impact of the underlying molecules, this had provided the most convincing evidence of their existence. Assuming that the motion of the molecules was due to their size and density, as well as the viscosity and temperature of the water, utilizing the kinetic theory of gases Einstein was able to provide additional evidence of their reality, along with deriving new values for Avogadro's number and for Boltzmann's constant
k
. When these values were confirmed the uncertainty of the existence of molecules was resolved. As French physicist Jean Perrin stated in 1909: