Adapted from David Cassidy's book,
Einstein
and Our World.
Light and other electromagnetic
radiation, such as radio waves, are obviously waves—or so
everyone thought. Maxwell and Lorentz had firmly established the
wave nature of electromagnetic radiation in electromagnetic theory.
Numerous experiments on the interference, diffraction, and scattering
of light had confirmed it. We can well appreciate the shock and
disbelief when Einstein argued in 1905 that under certain circumstances
light behaves not as continuous waves but as discontinuous, individual
particles. These particles, or "light quanta," each carried
a "quantum," or fixed amount, of energy, much as automobiles
produced by an assembly plant arrive only as individual, identical
cars—never as fractions of a car. The total energy of the
light beam (or the total output of an assembly plant) is the sum
total of the individual energies of these discrete "light quanta"
(or automobiles), what are called today "photons." Theories
of matter and electromagnetic radiation in which the total energy
is treated as "quantized" are known as quantum theories.
Although Einstein was not the first to break the energy of light
into packets, he was the first to take this seriously and to realize
the full implications of doing so.^{1}
Like the special theory of relativity, Einstein's quantum hypothesis
arose from an experimental puzzle and an asymmetry or duality in
physical theories. The duality consisted of the wellknown distinction
between material atoms and continuous ether, or, as Einstein wrote
in the opening sentence of his light quantum paper, "between
the theoretical conceptions that physicists have formed about gases
and other ponderable bodies and the Maxwell theory of electromagnetic
processes in socalled empty space." ^{2}
As noted earlier, Boltzmann and others conceived of gases as consisting
of myriads of individual atoms, while Maxwell and Lorentz envisioned
electromagnetic processes as consisting of continuous waves. Einstein
sought a unification of these two viewpoints by removing the asymmetry
in favor of a discontinuous, "atomic," or quantum, theory
of light. Resolution of an experimental puzzle encouraged this approach.
The puzzle concerned socalled
blackbody radiation, that is, the electromagnetic radiation
given off by a hot, glowing coal in a fireplace, or the radiation
emerging from a small hole in a perfectly black box containing
electromagnetic radiation at a high temperature. Scientists
at the German bureau of standards in Berlin, who were interested
in setting standards for the emerging electric lighting industry
in Germany, had measured the distribution of the total electromagnetic
energy in a black box—which would also apply to a glowing
light bulb—among the different wavelengths of the light.
But no one until Max Planck, at the turn of the century, was
able to give a single mathematical formula for the observed
distribution of the energy among the emitted wavelengths. Starting
with the MaxwellLorentz theory of radiation and some natural
assumptions about energy, Planck hoped to derive this formula
from the second law of thermodynamics. Planck failed to attain
the observed formula on these assumptions. Even Lorentz had
to admit that his own electron theory could not account for
blackbody radiation.
Only by reluctantly introducing a radical new assumption into his
mathematics could Planck attain the correct formula. The assumption
was that the energy of the radiation does not act continuously,
as one would expect for waves, but exerts itself in equal discontinuous
parcels, or "quanta," of energy. In essence Planck had
discovered the quantum structure of electromagnetic radiation. But
Planck himself did not see it that way; he saw the new assumption
merely as a mathematical trick to obtain the right answer. Its significance
remained for him a mystery. Thomas Kuhn has argued that it is not
to Planck in 1900 but to Einstein in 1905 that we owe the origins
of quantum theory.^{3}
Encouraged by his brief but successful application of statistical
mechanics to radiation in 1904, in 1905 Einstein attempted to resolve
the duality of atoms and waves by demonstrating that part of Planck's
formula can arise only from the hypothesis that electromagnetic
radiation behaves as if it actually consists of individual "quanta"
of energy. The continuous waves of Maxwell's equations, which had
been confirmed experimentally, could be considered only averages
over myriads of tiny light quanta, essentially "atoms"
of light.^{4}
With his light quantum hypothesis Einstein could not only derive
part of Planck's formula but also account directly for certain hitherto
inexplicable phenomena. Foremost among them was the photoelectric
effect: the ejection of electrons from a metal when irradiated by
light. The wave theory of light could not yield a satisfactory account
of this, since the energy of a wave is spread over its entire surface.
Light quanta, on the other hand, acting like little particles, could
easily eject electrons, since the electron absorbs the entire quantum
of energy on impact.
At first Einstein believed
that the lightquantum hypothesis was merely "heuristic":
light behaved only as if it consisted of discontinuous quanta. But
in a brilliant series of subsequent papers in 1906 and 1907, Einstein
used his statistical mechanics to demonstrate that when light interacts
with matter, Planck's entire formula can arise only from the existence
of light quanta—not from waves. Einstein considered that light
quanta, together with the equivalence of mass and energy, might
result in a reduction of electrodynamics to an atombased mechanics.
But in 1907 he
discovered that atoms in matter are also subject to a quantum effect.^{5}
Here he made use of another galling experimental problem. Experimentalists
had found that when solid bodies were cooled, the amount of heat
they lost failed to fit a simple formula that followed from Newtonian
mechanics. Einstein showed that the experiments could be explained
only on the assumption that the oscillating atoms of the solid lattice
can have only certain, specific energies, and nothing in between.
In other words, even the motions of atoms—which are continuous
in Newtonian mechanics—exhibit a quantum structure. Mechanics
and electrodynamics both required radical revision, Einstein now
concluded: neither could yet account for the existence of electrons
or energy quanta.^{6}
You can EXIT
to an explanation and demonstration of the photoelectric effect.
Notes
1. Thomas S. Kuhn, BlackBody
Theory and the Quantum Discontinuity, 19841912 (1978). BACK
2. Kuhn, BlackBody Theory;
Martin J. Klein, "Einstein's First Paper on Quanta," Natural
Philosopher 2 (1963): 5986; Max Jammer, The
Conceptual Development of Quantum Mechanics (1966). Quote:
Albert Einstein, The Collected Papers of Albert Einstein,
ed. John Stachel et al. (1987), vol. 2, 150. BACK
3. Kuhn, BlackBody Theory;
Martin J. Klein, "Max Planck and the Beginnings of the Quantum
Theory," Archive for History of Exact Sciences 1
(1962): 45979. BACK
4. Klein, "Einstein's First
Paper"; Kuhn, BlackBody Theory. BACK
5. Kuhn, BlackBody Theory;
Einstein, Collected Papers, vol. 2, 13448. BACK
6. Martin J. Klein, "Einstein,
Specific Heats, and the Early Quantum Theory," Science
148 (1965): 17380. BACK
This text is adapted from David Cassidy, Einstein
and Our World (Humanities Press, 1995, reissued Amherst,
NY: Humanity Books, 1998). Copyright © 1995, 2004 by David Cassidy.
David Cassidy is Professor of Natural
Sciences at Hofstra University. He has served as an editor of the
Einstein Papers and is author of a number of works in history of
physics including Uncertainty: The Life and Science of Werner
Heisenberg (1991) and a related Web exhibit, Heisenberg/Uncertainty.
