Adapted from David Cassidy's book, Einstein
and Our World.
The Challenge of Heat
At the turn of the century Einstein,
by holding to the nineteenthcentury ideal of unifying physics on
the foundation of mechanics, was in a dwindling minority. Most other
theoretical physicists sought unity in one of two nonmechanical
alternatives: the socalled energetic and electromagnetic points
of view. These alternatives arose from nineteenthcentury challenges
to the mechanical program in studies of heat and electromagnetism.
It was in an effort to reform mechanics and electrodynamics in the
wake of these developments that Einstein produced his 1905 works.
The study of the dynamics of heat flow, or thermodynamics, had
culminated in two fundamental laws regarding heat. The first law
related heat, energy, and useful work to each other in thermal processes.
This law could be understood in terms of the motions and collisions
of Newtonian atoms. The second law could not. According to the second
law, the flowing of heat in natural processes, such as the melting
of an ice cube, is always irreversible; that is, heat will not naturally
flow of its own accord in the opposite direction—the melted
cube at room temperature will not refreeze by itself. How to account
for this in mechanical terms?
If, as Newton and others had suggested, all matter consists of
atoms (or molecules), then heat is nothing but the energy of motion,
or kinetic energy, of the atoms. But, like so many bouncing marbles
or billiard balls, all atoms in their microscopic interactions must
obey Newtonian mechanics. Those interactions are reversible: a motion
picture of a collision between simple atoms will look perfectly
normal if it is run backwards in time. So how does the irreversibility
of macroscopic events, such as melting ice cubes, arise?
This and other paradoxes
encouraged those who, like Ernst Mach, chose to deny the very existence
of material atoms. One group, led by physical chemist Wilhelm Ostwald,
seeing their chance in paradox, rejected the entire mechanical program,
holding the laws of thermodynamics, not mechanics, as fundamental."^{1}
Mechanics required hypotheses about matter
and invisible atoms in motion, but thermodynamics referred only
to energy and its observed transformations in the everyday world.
Because thermodynamic laws were closer to laboratory observations,
universal, freed of paradox, and independent of matter, Ostwald
and his followers proclaimed the predominance of a new "energetic"
worldview: energy and the laws of thermodynamics are the bases for
understanding all processes within physical science, and even beyond.
Upholders of this view, known as "energeticists," though
unable to make much of their position, maintained it even into the
depths of World War 1, which they condemned as an enormous waste
of energy (to say little of human lives).
Others, of course, held tightly to material atoms. They found support
in the work of Maxwell, Rudolf Clausius, and Ludwig Boltzmann, who
managed to resolve the reversibility paradox in favor of atoms.
The second law of thermodynamics says that most natural processes
are irreversible, in contradiction to the Newtonian mechanics of
atoms. Boltzmann in particular resolved this contradiction by interpreting
the second law as a new type of law: a statistical, not an absolute,
law. Since there are so many atoms or molecules, even in a tiny
ice cube, it is extremely unlikely—but not impossible—for
the myriads of molecules in a melted cube to return in a finite
time from the disorder of a liquid to their original orderly, crystalline
arrangement. The macroscopic properties of heat and material objects,
such as irreversibility, arise from the statistical behavior of
numerous mechanical atoms, a behavior to be described by a new "statistical
mechanics."
Boltzmann and the American physicist J. Willard Gibbs provided
the first accounts of how exactly the second law of thermodynamics
arises from the statistical behavior of myriads of randomly moving
atoms, Unaware of these writings, Einstein devoted three brilliant
early papers during the years 1902 to 1904 to an independent derivation
of the second law in the course of developing his own "statistical
mechanics," based on atoms and mechanics. Continuing in this
work, Einstein used mechanics, atoms, and statistical arguments
to achieve what he called a "general molecular theory of heat,"
confirming that both laws of thermodynamics are, indeed, fully explicable
on mechanical grounds.^{2}
Brownian Motion Click
here to "see" Brownian Motion (Java applet)
In his doctoral dissertation,
submitted to the University of Zurich in 1905, Einstein developed
a statistical molecular theory of liquids. Then, in a separate
paper, he applied the molecular theory of heat to liquids in
obtaining an explanation of what had been, unknown to Einstein,
a decadesold puzzle. Observing microscopic bits of plant pollen
suspended in still water, English botanist Robert Brown had
noticed in 1828 that even tinier particles mixed in with the
pollen exhibited an incessant, irregular "swarming"
motion — since called "Brownian motion." Although
atoms and molecules were still open to objection in 1905, Einstein
predicted that the random motions of molecules in a liquid impacting
on larger suspended particles would result in irregular, random
motions of the particles, which could be directly observed under
a microscope. The predicted motion corresponded precisely with
the puzzling Brownian motion! From this motion Einstein accurately
determined the dimensions of the hypothetical molecules.^{3}
By 1908 the molecules could no longer be considered hypothetical.
The evidence gleaned from Brownian motion on the basis of Einstein's
work was so compelling that Mach, Ostwald, and their followers were
thrown into retreat, and material atoms soon became a permanent
fixture of our knowledge of the physical world. Today, with the
advent of scanning
tunneling microscopes, scientists are nearly able to see and
even to manipulate actual, individual atoms for the first time—a
circumstance that would satisfy even the most entrenched Machian
skeptic.
In the course of his fundamental work on applications of statistical
methods to the random motions of Newtonian atoms, Einstein discovered
a connection between his statistical theory of heat and the behavior
of electromagnetic radiation—the first step toward his hopedfor
unification of these two fields. Einstein obtained a mathematical
expression for the fluctuations, or oscillations, in the average
energy of any system, using his statistical theory of heat. He applied
this expression to the average energy of thermal radiation—the
electromagnetic waves given off by glowing bodies—in a perfectly
reflecting box (often called "blackbody radiation"). He
obtained results in close agreement with experimental observations.
This connection, he declared in obvious understatement, "ought
not to be ascribed to chance."^{4}
For a physicist like Einstein interested in uniting perspectives,
the connection provided an extraordinary opportunity. Einstein's
fundamental papers on relativity and quantum theory, also submitted
in 1905, may be seen as farreaching explorations of the connection.
Notes
1. John T. Merz, A History
of European Thought in the Nineteenth Century, 4 vols.
(19041912), vol. 3, 391; Christa Jungnickel and Russell McCormmach,
The Intellectual Mastery of Nature: Theoretical Physics
from Ohm to Einstein, 2 vols. (1986), vol. 2, 21720. BACK
2. Albert Einstein, The Collected
Papers of Albert Einstein, ed. John Stachel et al. (1987),
vol. 2, 4155; Martin J. Klein, "Fluctuations and Statistical
Physics in Einstein's Early Work," in Gerald Holton and Yehudi
Elkana, eds., Albert Einstein: Historical and Cultural Perspectives
(1982); Thomas S. Kuhn, BlackBody Theory and the Quantum Discontinuity,
19841912 (1978). .BACK
3.Albert Einstein, Investigations
on the Theory of Brownian Movement, ed. R. Fürth, translated
by A.D. Cowper (1926, reprinted 1956); Einstein, Collected Papers,
vol. 2, 17082, 20622. BACK
4. Einstein, Collected Papers,
vol. 2, 107. 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.
