A B C D E F
F. Progress in science
Aside from what it tells us about the thermodynamics
of solids, this analysis by Einstein illustrates some important things
about the way scientific progress is made.
For one, it serves as a typical example of how discoveries
about one phenomenon often help us understand others that had no obvious
relation to it earlier. In this case, newly discovered properties
of light suggested significant facts about solids-and about whether or
not solids were made of atoms. Einstein thus found another significant
relation between thermodynamics and optics besides the ones already known
earlier.
Another point this work illustrates is that progress
doesn't always require understanding everything at once. It turned
out that solids do act like they're made of atoms, but atoms whose own
behavior defied expectations for reasons that were yet to be learned. There
was already reason to believe atoms really did absorb energy in quanta
instead of continuously, since that kind of behavior was consistent with
what Max Planck had discovered about light. Einstein didn't know why atoms
wouldn't absorb energy in continuous streams, but he did know that they
apparently don't, and that turned out to be enough to explain the discrepancy
between 19th-century atomic theory and actual observations.
This work also illustrates one aspect of how advances
in basic science and practical application often depend on each other. Knowing
how much heat different materials absorb or shed for a given change of
temperature has practical value in the design of things whose temperatures
change during use. But Einstein's analysis didn't start with practical
considerations. He was mostly trying to understand certain basic
things about how nature worked. By figuring out what Planck's discoveries
about light's energy quanta implied about the behavior of matter that emits
and absorbs energy quanta, he learned some things that turned out to have
practical importance.
Einstein's work led not just to raw data but to a more
complete understanding of why the data is what it is. Without analyses
like those of Einstein, practical interests alone might have eventually
led people to make more low-temperature measurements of many different
substances, resulting in figures not unlike Figure 1 from which a general
law for all substances might have been worked out. But a practical
enough reason to undertake such extensive measurements might have been
a long time in coming on its own. Indeed, in the absence of knowledge
that solids' heat-absorption rates were very different at low and high
temperatures, investigating these rates might not have seemed useful.
Practical benefits are advanced by practical motivations,
but also by the desire to understand things, which motivates people to
advance basic science. If we focused entirely on taking the most
obvious, straightforward path to the solution of every practical problem,
many fewer practical problems would be solved as soon as they are. People
taking that narrow a focus would be like someone trying to reach the top
of a cliff by going straight up the cliff face, even though there is a
trail, slightly beyond his range of vision, that provides an easier, if
roundabout, way to the top. If he doesn't see the trail right away
and doesn't consider looking for one, it will probably be found first by
someone else, who may not even be looking for a way to the top of the cliff. But
if the trail's discoverer tells what he's found, the climber can use the
trail. Similarly, if we attend to basic science, which is motivated
at least partly by other than practical considerations, we gain, in addition
to the basic knowledge itself, information of practical value that its
discoverers may not have set out to find.
But basic science is also advanced by practical motivations
as well as by the desire to understand nature. One example: the
science of thermodynamics began with attempts to make the steam engine
more efficient. Heat flow occurs throughout nature, but mostly in
such complex ways that the simple laws governing it weren't obvious. The
steam engine was simple enough that it made the laws governing the relation
of heat to useful work much easier to figure out. Other attempts
to solve practical problems have also brought numerous new phenomena to
our attention, thus giving us many more clues to nature's universal laws
than we might have had otherwise.
Next article: Einstein
and the Daytime Sky
Links, References, and Comments:
"Die Plancksche Theorie der Strahlung und die Theorie
der spezifischen Wärme" ("Planck's Theory of Radiation and the Theory of
Specific Heat") by Albert Einstein.
The term specific heat is the usual English name
for the rate at which the energy of a unit mass of material increases
with temperature; this is directly proportional to the rate for one atom
illustrated in the figures above.
This paper, written in 1906 and originally published
in 1907 in Annalen der Physik (volume 22, pp. 180-190), is currently
available in the original German, with annotations in English, in The
Collected Papers of Albert Einstein, Volume 2: The Swiss Years: Writings,
1901-1909, edited by John Stachel, David C. Cassidy, Jürgen Renn, and
Robert Schulmann. A translation is available in this volume's English
translation supplement by Anna Beck (translator) and Peter Havas (consultant).
Hyperphysics [exit federal site] by
C. R. Nave:
"Specific
Heat", [exit federal site] "Law
of Dulong and Petit", [exit federal site] "Einstein-Debye
Specific Heats". [exit federal site]
Peter Debye's theory of specific heat, published in
1912, takes account of the different frequencies of sound waves in a solid
as discussed above. Its implications are similar to those of Einstein's
first-step, one-frequency theory, but represent solids' low-temperature
behavior more accurately.
"Joseph
Black, M.D." [exit federal site]
Brief biography of the chemist who first studied the
heating rates of different substances experimentally, and formulated the
concept of specific heat. From the "Historical
Background" [exit federal site] website of the University
of Glasgow 's Chemistry Department.
The Rise of the New Physics (in two volumes)
by Abraham D'Abro
Chapter 22 ("The Classical Kinetic Theory of Gases")
and Chapter 24 ("Planck's Original Quantum Theory") describe historical
background of Einstein's analysis. The energy-temperature problem
is a focus of pp. 421-423 (classical theory) and pp. 463-464 (quantum theory).
"The
Theory of the Specific Heat of Solids" [exit federal site] by M. Blackman, in Reports
on Progress in Physics, volume 8 (1941), issue 1, pp. 11-30.
A more detailed review of the subject's history, from
classical analysis, through Einstein's early quantum-physical approach,
to further refinement by Debye and other researchers and comparison of
theory with experiment.
Fundamentals of Statistical and Thermal Physics by
Frederick Reif
Thermal Physics, second edition by Charles Kittel
and Herbert Kroemer
Advanced undergraduate textbooks. In Reif's book,
sections 7.5 through 7.7 treat much the same concepts as Einstein did in
his 1906 paper, while sections 10.1 and 10.2 treat Debye's more refined
theory. Kittel and Kroemer review Debye's theory on pages 102-109
of their book; they don't deal with Einstein's preliminary theory, except
for outlining the analysis of a single vibrating particle that can absorb
and emit energy quanta on pages 82-84.
A B C D E F
Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information
