Hans Kramers: a master thinker Physics World - Institute of Physics

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Hans Kramers: a master thinker
Hans van Leeuwen
From
Physics World
August 1998
© IOP Publishing Ltd 2012
ISSN: 0953-8585
Institute of Physics Publishing
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REVIEWS
Han* vdii
Hans Kramers: a master thinker
Master of Modern Physics: The Scientific
Contributions of H A Kramers
1998 Princeton University Press 296pp
£27.50/$39.50hb
With the approach of the new millennium,
the physics community is more than usually
inclined to look back in amazement at the
marvellous developments in physics during
the first half of this century. Unfortunately,
the heroes of that great period did not really
bother to record the history of their painful
struggle to come to terms with new realities
such as relativity and quantum physics.
However, the next generation of physicists,
who were still able to witness the giants, were
more reliable at keeping historical records.
Thanks to their efforts, we now have a
host of (auto)biographies about such scientists,
which explain the ins and outs of the
personal relationships and the atmosphere
in which the research took place. Aimed at
the general public, the scientific content of
these books is, however, usually restricted to
a few elementary formulae. Not so in this
new book by Dirk ter Haar on the scientific
achievements of the great Dutch physicist
Hendrik Kramers.
Kramers, who was known to his friends as
Hans, is a most intriguing personality—both
for his contributions to physics and for his
style and character. He began his career in
1916 as a student of Niels Bohr, and pretty
soon he became his main assistant. He
stayed at Bohr's institute in Copenhagen
until 1926, when he went back to the
Netherlands to become a professor, first in
Utrecht and later in Leiden, where he
remained until his death in 1952, aged 57.
In 1987 the late Max Dresden wrote an
extensive biography of Kramers, which
includes an exciting record of the development
of the old quantum theory to its
Dutch master - Kramers shone throughout physics
chosen 12 of Kramers' papers, all of which
appear here translated into English. The
author comments on each paper in detail,
before putting them in the context of
Kramers' overall work. The choice of
papers was difficult - and personal, as the
author admits. For example, he has included
a short paper on band structure at the instigation
of another Dutch physicist, Hendrik
Casimir. While it does not contain any
particularly important results, it reveals
the characteristic elegance of so much of
Kramers' work.
Naturally, Kramers' papers from 1924 on
dispersion relations get ample attention, as
they were central to his pre-occupation with
the interaction between radiation and
matter. They were the last great step in the
"old" quantum theory, being the immediate
forerunners of Heisenberg's formulation of
matrix mechanics. Unavoidably, the relationship
between dispersion relations and
the paper by Bohr, Kramers and Slater
(BKS) on radiation processes is discussed,
present form {HA Kramers: Between Traditionwhich
for a while Kramers considered to be
and Revolution, Springer, 1987). One mighthis
major achievement.
wonder what motivated ter Haar to devote This ill-fated attempt to create a theory of
another book to Kramers so soon after the interaction of radiation and matter in
Dresden's elaborate study. Ter Haar's the context of the old quantum theory is
answer is that Dresden pictured Kramers now almost forgotten. It abandoned the
as a giant who narrowly missed a number idea that energy and momentum are con-
of important discoveries, which portrayed served in every quantum jump and restored
Kramers as a somewhat tragic figure. Ter the conservation only on a statistical level.
Haar wants instead to highlight Kramers' However, soon after the BKS theory was
great scientific achievements, through introduced, it was refuted by the measure-
which he will be remembered in physics. ments of the Compton effect, which showed
So ter Haar does not repeat or quarrel that the conservation laws were indeed
with Dresden, but gives a careful account of obeyed in each quantum process.
Kramers' ideas, analysing his discoveries Bohr took the setback light-heartedly, but
step by step. Rather than trying to cover for Kramers it was a much more serious
every aspect of his work, ter Haar has blow. However, history has shown us that
the BKS theory was pivotal in the development
of quantum mechanics, in particular
by associating a probability field with quantum
processes. This was a seminal step in
the interpretation of the wavefunction, as
shown by the fact that Schrodinger, its
inventor, found it hard to come to terms
with the probabalistic interpretation of the
wavefunction. In fact, Max Born, who ultimately
formulated the probability interpretation,
gave much credit to the BKS theory.
Ter Haar also takes great pleasure in
describing Kramers' derivation of the
Wentzel-Kramers-Brillouin (WKB) approximation
to the wavefunction. This
paper typifies the way in which Kramers
excelled through his unsurpassed knowledge
of mathematical physics and the old
quantum theory. Anomer paper, which is
described like a novel by ter Haar, is the
so-called "Kramers problem" of how a
Brownian particle tunnels through a potential
barrier. Ter Haar goes as far as to say
that reading this paper is like listening to a
Mozart string quartet. This and other
papers on charge conjugation, the Kramers'
degeneracy and the introduction of the
transfer-matrix method all show the broad
scope of Kramers' work.
One can forgive anybody who spent 10
years in Copenhagen — as Niels Bohr's first
lieutenant during the crucial time in the
development of quantum mechanics - to be
obsessed exclusively with the deeper aspects
of physics. But even in his Copenhagen
years, surrounded by the almost oppressive
influence of Bohr, Kramers found time to
divert his interest to other fields, such as general
relativity and statistical physics.
Famous old papers can be hard to appreciate
in their proper context, and Kramers'
are no exception. Indeed, he had such great
powers that his papers need — to use the
words of his student Nico van Kampen - a
"careful perusal" to properly digest their
lines of argument. Ter Haar's book therefore
comes as a very welcome service to the
physics community.
However, the reader should follow ter
Haar's advice and also consult Dresden's
biography of Kramers; indeed, the two
books together provide an ideal way of
understanding Kramers and his work.
Whereas Dresden is mainly concerned with
Kramers' role in the development of quantum
mechanics and quantum field theory,
and in Kramers as a person, ter Haar balances
this by highlighting the broad impact
of Kramers in other areas of physics. Ter
Haar's method of including a selected set of
Kramers' papers in one half of the book
PHYSICS WORLD AUOUST 1998 55

» r it i mm c
and discussing them in the other is a happy
combination that greatly simplifies the study
of his work. In doing so, the author not
only straightens the historical record on
Kramers, but also highlights his virtuosity at
handling the most subtle problems.
Future generations of physicists and his-
torians will therefore benefit greatly from
this "careful perusal" of the scientific contributions
of Kramers - probably more so
than the personal tales of this century's
other giants of physics. The ability of ter
Haar to explain and comment on the papers
physics is truly admirable. It makes him,
without doubt, a true student of this great
master of modern physics.
Hans van Leeuwe, is an emeritus professor of
physics at the Instituut-Lorentz, Leiden University,
of Kramers across such a broad spectrum of the Netherlands
Philip Anderson
Panoramic view picks out physics
Tlie Ascent of Science
1998 Oxford University Press 552pp
£25.00/$35.00hb
Brian Silver's book is an enormously ambitious
project, and might well be subtitled
"Everything you always wanted to know
about science". Silver proposes to explain to
an idealized layreader (whom he calls
"HMS" for "l'homme moyen sensuel") the
"great breakthroughs of science" achieved
in the "major battles". He does indeed
demonstrate that he is a fine writer and a
very knowledgeable scientist.
Silver's method is basically historical, so
that the reader acquires a lot of insight into
the process of science and the philosophical
attitudes from which modern science arose.
He emphasizes again and again the remarkable
inertia of the scientific establishment in
the face of new ideas. He does so by telling
stories, which, as he points out, make a second
point - that the correct idea eventually
won through, often against the odds. In this,
as elsewhere, he follows the ideas of the
philosopher Karl Popper.
The Ascent of Science would seem to be recognizably
a physicists' book. Almost my
first thought on reading it was "What a wonderful
text for a physics course for nonmajors"
- what is often called "physics for
poets". Silver, in fact, makes a serious
attempt to bring HMS through the kinetic
theory of gases, Newton's laws, entropy, elementary
thermodynamics, the concept of a
field, the basic laws of electromagnetism,
chaos and - finally - quantum mechanics,
the theory of the atom and the Standard
Model of particle physics. All this is topped
off with a dash of astrophysics, relativistic
cosmology, and even inflation.
There is, however, comparatively little
coverage of the historical sciences, such as
geology, palaeontology, linguistics, archaeology
and anthropology, even though there
have surely been "great breakthroughs" and
"major battles" in these fields. Of the 552
pages, a few more than 100 are devoted to
biology, 40-50 to chemistry, 20 to applied
science, while true astronomy (as opposed to
cosmology) is covered in 10. The author
takes, one feels, the physicists' somewhat
arrogant view that all other sciences are ba-
Field trip - this journey through science for the layreader focuses on physics
sically applied physics. In the end he seems to
take the extreme reductionist position, emphasizing
Steven Weinberg's "little white
arrows" that lead everything back to the presumably
fundamental laws of physics.
Clearly, as he covers all of physics in about
300 pages of small, dense print, the book is
quite a heavy read — even for one who can
be presumed to be familiar with most of the
contents. I have no experience to tell me
how much the layreader (HMS) can absorb,
although he is probably given a much better
chance than by books such as Stephen
Hawking's A Brief History Of Time, Weinberg's
Dreams of a Final Theory or Murray
Gell-Mann's The Quark and the Jaguar.
However, one particular — and hopefully
intelligent - layreader who I used as a testbed
balked. Nonetheless, for the rather large
scientifically literate (or even semi-literate)
public, this book is a wonderful refresher
course; it is full of unexpected bits of history
and is remarkably readable. I, for instance,
was intrigued to discover who Carl Linnaeus
was and how he arrived at his classification
scheme for biological species.
The only real error I noted was on page
199 in the discussion of black-body radiation.
"If the temperature goes up," says
Silver, "...the light at the lowest frequencies
will decrease in intensity...". This is illustrated
by figure 15-8a, in which the distribution
is normalized to fit on the same scale
for different temperatures. Of course, the
opposite is true: the light increases in intensity
at the lowest frequencies.
There are a few conversations I would like
to have had with the author, who unfortunately
died shortly before the book was published.
First, need the 21 st-century reader be
bewildered by dogmatic 19th-century statements
such as "the entropy of the universe is
increasing", when it will later become clear
that in an expanding, quantum universe this
is a meaningless claim? Secondly, and letting
myself in for more controversy, should not
readers be told - now that decoherence has
become an experimental fact - that the
Copenhagen interpretation of quantum
mechanics and mysterious statements like
Feynman's facetious "Nobody understands
quantum mechanics" do not belong in the
21st century either? These ideas were a
crutch suitable for the first half of the 20th
century, which we were able to discard as we
came to understand the quantum theory of
macroscopic systems.
Finally, I find the book's reductionist slant a
bit excessive; I would have liked to have had
included, for instance, concepts of emergence
(at least in its simplest manifestation) as well
as phase transitions and broken symmetry.
Indeed, the concept of thermodynamic
phase, which is important for understanding
modern theories of the universe - much less
daily life — is missing entirely.
As I write, I can't but wonder if perhaps I
am not the appropriate reviewer for this
worthy tome. Nevertheless, it is a fine book,
explaining what it covers with care, thoughtfulness
and wit.
Ptiilip Anderson is in the Department of Physics,
Princeton University, US
56 PHYSICS WORLD GUST 1998