Celebrating Einstein

"Solid Cold" (continued)


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.


Prepared by Dr. William Watson, Physicist
DOE Office of Scientific and Technical Information
Date Modified: 09/01/2005
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