The
Impact of the Neutron:
Bohr and Heisenberg
BY JOAN BROMBERG*
INTRODUCTION
1.
Niels
Bohr
and Werner
of
the neutron
received word of Chadwick's
Heisenberg
in
of March
the middle
1932. In this
discovery
I examine
the impact of the neutron on their ideas about
paper,
I cover is the three years before
the atomic nucleus. The
period
announcement
after it. I have
Chadwick's
and
the six months
to bring my examination
to bear on two problems. First,
attempted
suc
of hearing
within
three months
of the neutron, Heisenberg
of
in using it as the basis of a semiquantitative
ceeded
explanation
the composition
and
and
Bohr
makes
berg
of Heisen
stability of nuclei. A comparison
to elucidate and, in part, to explain
it possible
of
achievement.
Second, I have taken up the question
Heisenberg's
a
as
the place of nuclear
whole.
theoretical physics
theory within
This problem has not yet been dealt with by historians of science;
I treat only a part of it here?the
state of affairs as Bohr
and
saw it. This
is, however, a significant part, for because
Heisenberg
of their abilities,
and
all,
and, above
situation, Heisenberg
age,
a
com
an
Bohr were in
to
in
have
1929-1932
position
unusually
prehensive view of the whole of their subject.
The
I have
conclusions
been
the second
led to may be best summarized
by
first. At the end of the twenties,
answering
question
nuclear physics was a part of relativistic quantum mechanics.
To put
the situation too simply for the moment,
the reason for it was this.
two
were
fundamental
known:
the proton and the
Only
particles
electron.
*
To
Department
account
of
for
the History
nuclear
and
masses
Philosophy
and
charges,
of Science,
as
therefore,
Hebrew
University,
Jerusalem.
307
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
well
STUDIES
IN THE
PHYSICAL
as for the emission
of beta-rays (electrons),
to protons. The
in addition
SCIENCES
electrons were assumed
to be in nuclei
relations,
uncertainty
as light as electrons are retained
that
if
however,
require
particles
in volumes as small as nuclei,
they must have kinetic energies that
are so large that relativistic
effects become
important. Therefore,
nuclear
electrons and, hence, nuclei must be treated by a relativis
tic theory.
It is thus necessary to look at the situation in relativistic quantum
at
and in the related field of quantum
mechanics
electrodynamics
was created in 1925 and 1926
this time. When
quantum mechanics
physicists expected
the electromagnetic
that it would
field. These
be
capable
to
of being extended
too
optimistic.
proved
early hopes
a
the theory was not relativistic, and attempts to make
met with difficulties. By 1929
theory of charged particles
the state of this part of physics was widely felt to be unsatisfactory.
results of experiments
This
feeling was strengthened by the puzzling
on nuclei, which were seen as part of the same problem-complex.
on beta-ray energies and on nuclear
Above
all, the experiments
to the sense of mystery.
statistics contributed
in
transformation
to
feel that another major
began
Physicists
to
with
these
deal
be
would
necessary
problems,
thought
physical
as radical with respect to the ordinary quantum
a transformation
as the latter had been with respect to the physics of the
mechanics
Moreover,
relativistic
a consequence,
among the concerns of Bohr and
were
the
search for a new physics and
this
in
Heisenberg
period
of
its domain
between
a
the
of
for
boundary
precise definition
and that of ordinary quantum mechanics.
applicability
is that statements
this has for the historian
The
implication
terms
not
be
about nuclear
may
interpreted solely in
phenomena
internal to nuclear physics. A case in
of the ideas and experiments
well-known
Bohr's
to this paper?is
that is central
point?one
fails for beta-ray
of energy conservation
suggestion that the principle
as giving a
It is usually?and
incorrectly?regarded
disintegrations.
the difficulties
measure
of the gravity with which physicists viewed
on the nucleus
for nuclear
created by experiments
theory alone.1
early
twenties. As
in his pioneer
M. Purcell
of Edward
this is the interpretation
example,
and Contradictions,"
Clues
the Neutron;
without
"Nuclear
Physics
ing study,
Xth
International
of Science,
1962),
of the History
Proceedings
(Ithaca,
Congress
Forces
Brink, Nuclear
1965), p. 8.
1, 128. See also D. M.
(Oxford,
1. For
308
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON!
BOHR
AND
HEISENBERG
the context of the
Instead, Bohr's hypothesis must be seen within
a
new
search for
theory. It was part of the overarching
attempt he
was making
to judge which parts of the old physics were likely to be
retained
in such a theory and which were not.
a more
state of affairs also produced
complicated
towards nuclear
than I suggested above. For if
electrons
same
This
attitude
to put electrons
in the nucleus was a chief reason
for
nuclear
with
the
relativistic
connecting
quantum
theory,
physics
itself facilitated proposals
for eliminating
connection
electrons from
the nucleus. That
such proposals were made will be demonstrated
the need
use of bold
a time
they had to make
hypotheses?at
were
and
electrons
known?is
from
clear
the
only
protons
fact that the mass of nuclei, measured
in units of the proton's mass,
below.
That
when
is roughly
twice the nuclear
in units of the proton's
an
in which
charge.2 Strange
encouraged
by
atmosphere
a new
was
a
not
correct
to
As
it
is
result,
say that
physics
expected.
to contain electrons in this
nuclei were universally
assumed
period.
were more
Attitudes
the hypothesis
that electrons were
in
open;
were
were
and
the intuition
nuclei
that they
held
excluded
ideas were
charge, measured
simultaneously.3
It is now
to see the character of Heisenberg's
achievement.
neutron
to change
the
of
the
it
made
Broadly put,
discovery
possible
the relation between nuclear
and
of
the
domain
unsolved
physics
now became
problems.4 A substantial number of nuclear problems
solvable
by
easier
mechanics.
quantum
ordinary
was
to see this
and
possibility
Heisenberg
formal expression.
The
of
achievement
to give it
find a way
same
a way
2. The
to get
One must
devise
thing is also clear from beta-decay.
out of nuclei
electrons
without
them
inside. This
having
part of the problem
was not affected
of the neutron
and
bold
ideas.
It is
by the discovery
required
not
that in the ideas of Bohr
before
1932 we shall also find elements
surprising
of the solution
in his beta-decay
Fermi
of 1933 and
1934.
gave
papers
I differ from Purcell,
also
3. Here
who wrote
that with
the exception
of an
to be loaded with
article written
model
had
those
by J. Dorfman,
"every nuclear
the discussion
electrons
before
and
it seemed
that every other
could
begin
prin
be sacrificed
before
their presence
be
would
ciple would
("Nuclear
questioned."
the Neutron,"
is, above
all,
my
p. 131.) However,
Physics without
interpretation
on
the
while
his
Purcell
based
sources,
suggested
by
unpublished
published
papers.
4. Compare
to the paper
S. Devon's
in the Xth
"Comments"
of Emilio
Segre
. . .
International
1, 155-158.
Congress
Proceedings,
309
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
2 and 3 below deal with Bohr and Heisenberg,
discovery. They
tively, in the three years before Chadwick's
evidence for the picture I have given of the state of nuclear
Sections
The
documents
examined
also
illustrate
the contrast between
respec
present
theory.
Bohr's
fourth section begins with
intellectual
and Heisenberg's
styles. The
a description of Bohr's reactions to the neutron, placing Heisenberg's
to an analysis of Heisenberg's
work in sharper relief, and proceeds
articles. I have
tried, among other things, to trace the effect of
to
own contribution
style in these articles. Bohr's
Heisenberg's
not
model?did
nucleus
structure
nuclear
compound
theory?the
come until the end of 1935. It is interesting that although Bohr's
and others,
model
essentially on the work of Heisenberg
depended
itwas
work that placed nuclear structure under quantum mechanics,
a profound difference between
same
of
the
conviction
inspired by
in such a different
and atomic
nuclear
systems that is expressed
form in the documents
studied here.5
BEFORE THE NEUTRON:
2.
BOHR
on 1 July 1929, "has truly been
to
of the various small
the
completion
very ungracious
respect
to send. ...
So that you may see that the
notes I had promised
two fragments.
I enclose
was not a complete
falsehood,
promise
on
. . .The
the beta-ray spectra, that has
second is a little piece
in the last days,
on my mind, and that I have had recopied
long been
to
send it off, as
to
able
without, however, being
persuade myself
so
executed."6
is
and
so
little positive,
it gives
roughly
of
nuclei
of
radioactive
The
by the emission
disintegration
from the disintegration
showed a significant difference
beta-rays
the latter case, all the
In
of
emission
alpha-rays (helium nuclei).
by
In
velocities.
a
well-defined
have one
emitted particles
few)
(or
on.
zero
The
from
all
velocities
have
the
the former case,
particles
as to whether
the
C. D. Ellis and L. Meitner
between
early dispute
a
continuous
with
from the nuclei
electrons
emerged
actually
"Fate,"
Bohr
wrote W.
Pauli
with
137
and Nuclear
Constitution,"
"Neutron
Nature,
5. See Bohr's
Capture
to the Fara
reference
its explicit
6, with
344-348,
paragraph
particularly
(1936),
4.
and paragraph
day Lecture,
abbre
Scientific
to Pauli,
1 July 1929, Bohr
6. Bohr
(hereafter
Correspondence
are mine.
in this article
All
translations
Danish
viated
original.
BSC),
310
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON:
AND
BOHR
HEISENBERG
as Ellis maintained,
or only
in their energy values,
as
a
this
distribution
of
result
energy
acquired
secondary processes,
as Meitner
held, had been settled to Ellis' satisfaction in 1927 with
the calorimeter
with W. A. Wooster.
he conducted
experiments
distribution
Meitner
and W.
Orthmann
confirmed
these results
in an article
they
the same time, they disposed of the
that part of the energy released by the decaying nuclei
suggestion
was carried off by gamma-rays.7 This
of why
left the question
into
nuclei
could
seemingly identi
seemingly identical parent
decay
in December
submitted
1929. At
nuclei with
daughter
Bohr's
letter and
energy.
the
cal
written
at a time when
almost attained
The
itsmost
immediate
to have
emission
of
of differing amounts
note on beta-rays were
accompanying
the data on energy
puzzling form.8
occasion
been
loss in beta
decay
had
of the note seems
for the composition
two articles by G. P. Thomson
in 1928
by
provided
for the results of
the most plausible
interpretation
that "energy is not conserved
advocated
Thomson
Ellis and Wooster,
that this
act of emission." He
further maintained
in the individual
wave
a "natural
was
of the
theory of matter."10
consequence
and
1929.9 As
a nuclear
electron could be
argued that the emission of
as "sudden."
the
emerging electron should
Consequently,
regarded
wave
wave
a
well-localized
be described
packet
packet. This
by
be
so
the
of
that
the
front
would
packet would
spread,
quickly
the
rear. Thomson
implicitly associated
increasingly ahead of the
front of the wave group with fast electrons and the rear with slow
ones. Some electrons would
therefore speed up after emission, and
slow down.11
others would
Thomson
of
"The
Ellis
and W. A. Wooster,
128. C. D.
7. Purcell,
Average
Energy
p.
and
Proc. Roy.
117
of RaE,"
109-132; L. Meitner
Soc,
(1927),
(A)
Disintegration
der
der Energie
eine
"?ber
absolute
W.
Orthmann,
prim?ren
Bestimmung
60
von Radium
143-155.
E," Zeits.
f. Phys.,
jS-Strahlen
(1930),
is equal
limit of the beta-ray
that the upper
result
8. The
spectrum
important
and daughter
of the parent
nuclei was not estab
to the difference
in the energies
"The
of Radioactive
lished until
1933. See C. D. Ellis,
Disintegra
/3-Ray Type
. . .
and
on
London
1934
International
tion,"
Conference
Papers
Physics,
46.
Discussions
England,
1935), 1,
(Cambridge,
E from the Point
of View
of Radium
"The
9. G. P. Thomson,
Disintegration
the Waves
Associated
"On
121
of Wave
615-616;
Nature,
Mechanics,"
(1928),
Phil.
Free Electrons
and Their
between
and
the Relation
Waves,"
with
?-Rays
Mag.,
7 (1929), 405-417 (dated 7 Jan. 1929).
10. Thomson,
11. Thomson,
"On
"The
the Waves
Disintegration
with
Associated
of Radium
?-Rays,"
E," p.
p.
615.
406.
311
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
STUDIES
HISTORICAL
IN THE
PHYSICAL
SCIENCES
In his second long article, Thomson
the ideas underlying
made
a
his argument
"The
in motion
is
of
conception
explicit:
particle
to have a definite
almost meaningless
unless
it can be supposed
. . .We
a
at
time.
definite
can,
however,
velocity
keep both the
of
and
the
whole
moving
analytical machinery
conception
particles
of the wave mechanics
to allow
the possibility
(at least for free electrons)
of an electron changing
characteristic
of Bohr
space."12
It was
neous
his
could
Bohr
that an argument
and start him
on which
in
led
prepared
in force-free
he
on
thought erro
a multisided
the argument
touched.
the emergence
of
1924, before
conservation
that energy
mechanics,
events
effect. Subsequent
quantum
are
speed
attention
engage
of the problem
himself had
suggested
consideration
ifwe
him
Compton
however, and at least by the time of the Como
he had satisfied himself that energy conservation
is violated
in
the
to reconsider
Conference
this,
in 1927,
is valid in quantum
note, entitled, "/3-Decay Spectra and Energy Con
idea
therefore by arguing against Thomson's
servation,"14 began
of the energy law can be derived
from wave
that a violation
From this, however, Bohr did not conclude
that energy
mechanics.
mechanics.13
must
be
outside
wrote,
His
in beta-decay,
of wave
competence
conserved
the
that
there
on
based
?-spectra
Bohr next
theoretical
principles
took
but
rather
mechanics:
that beta-decay
is unlikely,
It
is
he
of the continuous
is "any simple explanation
wave
of
mechanics."
the ordinary ideas
of whether
there were
the question
any
up
on which one could "defend a violation
of the
grounds
of conservation
in radioactive
processes."
He
suggested
"On
the Waves
12. Thomson,
Associated
with ?-Rays,"
p. 413.
and J. C. Slater,
"The Quantum
13. N. Bohr, H. A. Kramers
of Radia
Theory
See Martin
47 (1924),
"The
First Phase
785-802.
of
tion," Phil. Mag.,
J. Klein,
the Bohr-Einstein
in the Physical
Historical
Studies
2
Sciences,
Dialogue,"
on Bohr's
of any historical
1-39. I do not know
reconsideration
of
study
(1970),
the Compton
effect in the years when
matrix
and wave
and
their
mechanics
as "The
took shape. The
address was published
Como
interpretation
Quantum
and
the Recent
Mechanics
121
of Atomic
Nature,
Development
Theory,"
(1928), 579-590.
14. Bohr
are
manu
Collection
abbreviated
The
Manuscript
(hereafter
BMC).
title. The
is in English
and
catalogued
by year and
manuscript
and
from the reply of Pauli's
from its contents
to be a
cited below
sent Pauli.
version
It consists
of what
Bohr
of five pages:
slightly different
a second
three pages
consecutive
of undated,
"3" dated
21 June
narrative,
page
the dated
"3."
1929, and a "3a" page
correcting
scripts
appears
312
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
that such grounds might
in which
the "problem
BOHR
NEUTRON.*
exist within
of
the
AND
HEISENBERG
the context
constitution
of
of physical
ideas
the elementary
out "has so
is treated. The
latter, he pointed
particles"
a proper
treatment on the basis of classical
far escaped
electro
one
reasons
in
the
last
of
Bohr
remark
is
the
dynamics."
Implicit
was willing
to entertain solutions like nonconservation
in this circle
electric
In the proper
of problems.
mechanics
limit, ordinary
quantum
no
the
of
is
results
classical
there
However,
satisfactory
gives
physics.
result in classical physics for the problem of the electron's
structure,
and where we do not know the limiting, classical behavior we are
one of the
then mentioned
liable to surprises. Bohr
particularly
and
its possible
results of recent work in quantum
electrodynamics
a violation
in
the
nucleus.
for
of
conservation
energy
implications
only the emitted betas, Bohr wrote, but the nuclear electrons
also "seem to fall entirely outside the field of consistent application
even
in their quantum
of the ordinary mechanical
concepts,
reference is partly to the high kinetic
theoretical modification."
The
to nuclear
that must be attributed
electrons, but more
energies
measurements
of nuclear
to the growing puzzle of the "anomalous"
Not
this point of view," Bohr
continued,
spins and statistics. "From
should rather be regarded as the
"the disintegration
of the nucleus
of the electron
creation of the dynamical
individuality
expelled.
should
evidence
If, therefore, experimental
really corroborate
[that
. . . we can
this
the conservation
sug
hardly
reject
fail]
principles
violation
of
on purely
The
theoretical
energy
grounds."
gestion
the production
also explain
Bohr
conservation,
suggested, might
of energy
in stars. Under
the right initial conditions,
of betas and their subsequent
involving both the capture
might result in a net gain of energy.
to this was
immediate
reaction
Pauli's
and
a process
reemission
unfavorable.
After
Bohr had
for the first of the manuscripts
expressing
"It is otherwise with the note on beta-rays.
sent him, he continued,
1 must
say that I am little satisfied by it." Pauli went on to give
his enthusiasm
and
specific objections,
note aside for a good
more
peace!"15 A little
15. Pauli
to Bohr,
17 July
"In any case, therefore, lay this
concluded,
in
let the stars radiate
And
while.
long
than one year later, Pauli was to offer his
1929
(BSC),
German
original.
313
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
own
of beta-decay,
hypothesis
as
thirties
rival
the principal
momentum
and
energy
theory,
PHYSICAL
which
was
SCIENCES
to stand
in the
early
In Pauli's
to Bohr's
interpretation.
are conserved, but the unobserved
are carried off by one
very light, neutral par
portions
(or more)
to
name
Fermi
which
later
of
the
"neutrino."16
ticles,
gave
on
Other
in this period
aspects of Bohr's
thoughts
beta-decay
can be seen from an exchange
at the end of
of letters with Dirac
the first letter began, "From Gamow
I hear
1929.17 "Dear Dirac,"
that you are now back in England
and
that
made
have
you
again,
with
of the hitherto unsolved
the mastering
difficulties
progress
in your theory of the electron. As we have not yet heard about any
and I should be very thankful if you would
be so
details, Klein
kind to tell us something of your present views." The
principal
difficulties Bohr had in mind, as the letter later makes
clear, were
those associated with the so-called "Klein paradox"
that Oskar Klein,
then in Copenhagen,
to Dirac's
According
electrostatic
had
wave
field where
rest mass,
electron
It may be stated as follows:
just discovered.
an
an electron is
if
equation,
subject to
more
than the
the potential
increases by
in a distance
of less than the Compton
mc2,
it has a considerable
of passing
h/mc,
wavelength,
probability
a
a negative
the
barrier
into
has
where
it
through
region
potential
kinetic energy, that is, where
it behaves
like a particle of negative
mass. After
on a
Bohr went on to speculate
posing his question,
connection
the Klein
the beta-ray spectrum, and
paradox,
a
new
that
kind of complementary
suggested
energies.
come into effect, one between
relation might
the validity of the
on
momentum
conservation
laws
the one hand and the
energy and
on the other.
as the
concept of particle permanence
Just
complemen
momentum
between
and
is
tarity
governed
by Planck's
position
between
He
stellar
constant, the classical
the universal constant
16. See
Pauli,
gang Pauli:
"Zur
radius of the electron may play
in this new complementarity.18
?lteren
und
neueren
Collected Scientific Papers
Geschichte
the role
des Neutrinos,"
of
in Wolf
(New York, 1964), 2, 1313-1337, and the
to Fermi's
on
introduction
in Enrico
Fermi,
by F. Rassetti
papers
beta-decay,
Collected
Papers
(Chicago,
1962), 1, 538-540.
to Dirac,
to Bohr,
17. Bohr
24 Nov.
to Dirac,
26 Nov.
1929; Dirac
1929; Bohr
to Bohr,
5 Dec.
9 Dec.
to Dirac,
23 Dec.
1929; Dirac
1929 (BSC).
1929; Bohr
These
letters are in English.
18. "My view was
that the difficulties
in your theory might
be said to reveal
a contrast
the claims of conservation
between
on one
of energy and momentum
314
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
It should be noticed
between
he did
THE
OF
Bohr
is drawing
BOHR
AND
HEISENBERG
a
quite different connection
than
of particles and energy conservation
In the latter the possibility
that the elec
in the nucleus with mechanical
individuality
the permanence
in the manuscript.
tron does
NEUTRON:
not persist
that conservation
the
instead of sug
fails. Here,
opens
possibility
conservation
and the mechanical
individuality
gesting mechanical
laws becoming
invalid together, Bohr poses the validity of the first
as excluding
the validity of the second; that is, if one can follow a
in its transition from a positive to a negative kinetic
electron
given
energy state, then one cannot at the same time have energy con
that Bohr brings a fundamental
servation. It is noteworthy
length,
electron radius, into the theory, typically introducing
relation. Bohr did not pursue
of a complementarity
He
however.
this idea for long,
gave it up in favor of the attempt
con
to resolve
the paradox
by the analysis of the experimental
ditions, which we shall find in his second letter to Dirac.
the classical
it by means
on Bohr's
Gamow
speak
replied that he had already heard
own
he
of
this
at Kapitza's
Club.
"My
question,"
opinion
to
conservation
of
wrote, "is that I should prefer
keep rigorous
even the concept of
rather abandon
energy at all costs and would
Dirac
views
than the con
of separate atoms and electrons
consisting
the difficulty
is a simple way of avoiding
of energy. There
to
kinetic energy." Dirac
of electrons having negative
proceeded
in which
transitions
sketch the solution Bohr had inquired about,
matter
servation
these states are almost
energy states are barred because
an
and in which
of
"sea"
filled
infinite
electrons,
by
completely
themselves as positively
holes in this sea exhibit
charged protons.
a fundamental
with
answered
Bohr
against Dirac's
objection
an infinite
infinite sea of electrons should produce
suggestion. An
It was
his own position.
then explained
electric charge density. He
from
of
the
transitions
not simply Dirac's
positive
interpretation
to negative
on
side. The
the other
of the individual
side and of the conservation
particles
treatment
in the usual
both
these claims
of fulfilling
correspondence
possibility
of the constitu
on the
the problem
of neglecting
would
thus depend
possibility
to me
It
in non-relativistic
mechanics.
classical
tion of the electron
appeared
on classical
be
to the electron
that the finite size ascribed
might
electrodynamics
a hint as to the limit for the
the claims mentioned."
of reconciling
possibility
(Bohr to Dirac, 24 Nov.
1929 [BSC].)
315
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
to negative
but the whole
of
energy that he opposed,
program
to
terms
in
them
of
"In
the
interpret
attempting
ordinary concepts.
difficulties of your old theory I still feel inclined to see a limit of
the fundamental
rests
atomic
concepts on which
theory hitherto
rather than a problem of interpreting the
in
evidence
experimental
a proper way by means
of these concepts." As he pointed out later
in the letter, Bohr's hope was
that those parts of Dirac's
theory
which had been so successful in explaining
could be
experiments
separated from those which involved the transitions between positive
and negative energy states. Bohr then suggested that the key to the
revealed by Klein might be a more
critical inquiry into
problem
the experimental
the transitions
conditions
under which
show
the field strength that is necessary a number
of electrons would need to be massed
together; the massing would
a situation outside
be so great that one would
the
have
already
reach of classical concepts.
themselves. To
achieve
then restated his ideas on beta-decay and added, "In the fact
can be measured
that the total charge of the nucleus
before and
and that the results are in conformity
after the /3-raydisintegration
Bohr
of electricity I see a support for upholding
the
of the elementary charges even at the risk of abandon
to the Rome
of energy." In his contributions
ing the conservation
on nuclear
1931 and to the Solvay Con
meetings
physics in October
with
conservation
conservation
It was his willing
1933 similar comments appear.
gress of October
ness to allow charge conservation
a
preferred position over energy
conservation
other
that, among
things, separated Bohr from Pauli
over
the interpretation of beta-decay.19
their controversy
throughout
interest in Dirac's
Of particular
is the first para
reply to Bohr
am afraid," Dirac wrote, "I do not
"I
graph.
completely agree with
...
see
reason
cannot
I
views.
for
your
any
thinking that quantum
limit
mechanics
of its development.
has already reached the
I think
. . . and
it will undergo a number of small changes
means
these
by
most of the difficulties now confronting the theory will be removed.
. . . are found to be
If any of the concepts now used
of
incapable
et Proprietes
19. See Structure
des Noyaux
et Discus
Atomiques;
Rapports
. . .
sions du Septieme
de Physique
Conseil
Solvay
(Paris,
1934), p. 324
(Pauli),
and Bohr,
"Sur
la methode
de correspondance
dans
la theorie de l'electron,"
pp.
see also Bohr,
"Atomic
and Conservation
di
227-228;
Laws,"
Stability
Convegno
Fisica Nucleare,
1931
Ottobre
(Rome,
1932), p. 119.
316
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
one will have to replace
them by some
an exact meaning,
some drastic altera
a little more general, rather than make
thing
did not agree
Dirac
in
late
tion in the whole
1929,
Thus,
theory."
in physics.
of
crisis
the
of
the
with Bohr's
severity
appreciation
on
situation
the
their
outlooks
in
the difference
general
Clearly,
con
of Dirac's
turned in part on the difference in their evaluation
having
was optimistic. Bohr, in
cept of an "infinite sea of electrons." Dirac
his final letter, indicated again that he found the infinite electron
the
optimism proved justified by
density a "fatal" objection. Dirac's
six years later their positions
discovery of the positron. Nevertheless,
were to be dramatically
reversed. It was then to be Dirac?in
despair
over the difficulties of relativistic quantum
theory?who was willing
in beta-decay.
of experiment
on Pauli's
based
to countenance
Bohr,
with
on
the idea of energy nonconservation
the contrary, encouraged
by the agreement
that Fermi had
theory of beta-decay
was to consciously
letter of 1929: "I under
Dirac's
echo
hypothesis20
the present
stand of course the weight of your arguments regarding
was
to write to
Bohr
difficulties of relativistic quantum mechanics,"
to
"but I am inclined to think that the only way
Dirac,
progress is
in
as far as possible
to trace the consequences
of the present methods
the same spirit as your positron
theory."21
the
alone
are sufficiently supported by these documents
points
that
that they may be asserted here. First, there is Bohr's expectation
not be
electrons would
of nuclear
and the behavior
beta-emission
unam
is
failure
This
quantum
physics.
by existing
explained
Bohr
adduced
where
the
in
stated
fragment,
manuscript
biguously
the fact of the continuous
important
beta-ray spectrum. Another
Certain
dei Raggi
di una
teoria dell' Emissione
"Tentativo
'Beta',"
20. Enrico
Fermi,
der
einer Theorie
"Versuch
2
I,"
Ric.
491-495;
/3-Strahlen.
Scientifica,
(1933),
88 (1934),
161-171.
Zeits.
f. Phys.,
of Energy
"Does
Conservation
See Dirac,
to Dirac,
2 July 1936 (BSC).
21. Bohr
"Conserva
and Bohr,
137 (1936),
Processes?"
in Atomic
298-299,
Hold
Nature,
article
Dirac's
138 (1936),
25. Although
in Quantum
tion Laws
Nature,
Theory,"
on the
on Shankland's
was
based
effect, a care
Compton
experiments
ostensibly
him.
that troubled
that it wTas the more
shows
ful reading
general
problems
nature
"The
non-relativistic
1936 to Bohr
See also his letter of 9 June
(BSC):
I was writing
to me most
of the present
strongly when
theory appeared
quantum
from a relativ
I tried to build
where
In the first edition
up everything
my book.
were
I found
state
and
of
istic definition
observable,
many
things which
one makes
when
all vanish
to
But
these difficulties
awkward
extremely
explain.
be something
fundamental
I think there must
ideas.
free use of non-relativistic
underlying
this."
317
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
reason
for the failure of quantum
of
physics is that the dimensions
are
same
in
of the
order as the classical size of the electron;
nuclei
his later Rome
that nonrelativistic
address, Bohr argued
quantum
mechanics
can only be
to systems so large with respect to
applied
electrons that the latter can be treated as points.
as only
there is Bohr's vision of these nuclear phenomena
their constituent
Second,
part of the group for which a new physics would have to be found;
the group included the structure of elementary electric particles and
the Klein paradox. That Bohr foresaw that this new physics would
have some new and surprising features is evident throughout
these
Not least, it is reflected in the last of Dirac's
documents.
letters to
in seeking the new theory Bohr proceeded
in a
Finally,
over the concepts and laws of the
acteristic way. He pondered
ing theory, trying to distinguish which were likely to remain
in the coming theory and which were likely to fail. It was not
Bohr.
the mechanical
conservation
of conservation
of charge,
the conservation
have
seen, Bohr
mechanical
char
exist
valid
only
laws Bohr weighed;
it was also the law
and the concept, closely connected with
of the permanence
of particles. As we
principles,
to
retain charge conservation
and relinquish
opted
conservation.
in which Bohr presented his thoughts on the nucleus
were the Faraday
for publication
and Rome Lectures,
at
composed
same
on
was
time.
The
the
based
roughly
published Faraday Lecture
on
in
London
the talk Bohr gave at the Chemical
8 May
Society
1930, and on three lectures given at Cambridge
University
during
Bohr did some preliminary
the same visit to England.
Although
writing on the article as early as the summer of 1930, the work only
the section on the nucleus
to
began in earnest in 1931. He mailed
The
works
England
extensive
in the fall of 1931, and he gave
revision in December
1931. The
an
the entire manuscript
lecture deals with all of
quantum
theory, and is organized historically. The
form the subject of the final section.22
nucleus
problems
of the
. . .
Lecture
and
the
22. Bohr,
of
"Faraday
Chemistry
Quantum
Theory
Soc.
Atomic
For
Constitution,"
Journ.
1, pp. 349-384.
of the Chem.
(1932), Part
the origins
of the published
the publications
with
the manu
paper,
compare
see Leon
the dating
of the writing,
om
Minder
Rosenfeld,
scripts. For
"Nogle
Et Mindeskrift
Niels
Bohr:
Bohr," Niels
(Copenhagen,
1963), pp. 69-70, and also
to S. E. Carr,
to Bohr,
Bohr
15 Sept.
to Carr,
30 Oct.
1931; Carr
1931; Bohr
4
I am indebted
1932
to Mrs.
S.
(Bohr Administrative
Jan.
Correspondence).
the latter
for bringing
to my attention.
Hellmann
correspondence
318
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON!
BOHR
AND
HEISENBERG
was based on the informal remarks Bohr gave
on nuclear
in October
1931. He
physics in Rome
on
the
train
back
from
the fin
Rome,
began writing
mailing
trip
on 12 March
ished paper to Fermi for inclusion
in the proceedings
The
Rome
Lecture
at the meeting
title of the article
1932. The
Laws,"
and Bohr's
recently
is "Atomic
Stability and Conservation
doubt has
that, "Serious
explains
the concept of energy can find an unam
introduction
arisen, whether
to radioactive
application
in which electrons
biguous
disintegrations
. . .The
are
from
nuclei.
atomic
expelled
following remarks may
serve as an introduction
to a discussion
It is the
of this problem."23
Lecture,
therefore, which was specifically directed to the ques
tion of the validity of energy conservation
for beta-decay.
Since, in
it gives Bohr's views at a moment
learned
of
he
before
addition,
just
Rome
the discovery of the neutron,
I shall
it with
supplement
outlining here. In doing
from
the section on the nucleus
it deserves
this is legitimate because
Faraday Lecture;
same time and is consistent with the Rome
Bohr's
Rome
it was written
Lecture
about
so,
the
the
in content.
of the
the position
in succession
in
rela
laws in ordinary quantum
theory,
ordinary quan
theory, and in nuclear physics. The
foundations:
Bohr began, rests on two independent
article
discussed
conservation
mechanical
tivistic quantum
tum mechanics,
that it
"is so constructed
the classical
theory of particles, which
and the
of energy and momentum,"
satisfies the laws of conservation
of action (p. 120). Ordinary
quantum
theory has certain
quantum
a limitation belonging
to the classical
limits. First, it incorporates
on
a
contradiction:
contains
of
The
classical
theory
theory
particles.
the one hand, it treats the electron as a point mass; on the other, it
to the electron to avoid an infinite
diameter
attributes a minimum
interaction with its own field. This
self-energy from the electron's
the theory to the
is circumvented
by restricting
of
of
diameter
with
systems
respect to the electron
large
description
is that it is not
diameter. A second limitation of quantum mechanics
reasons
and
The
that quan
invariant (pp. 120
122).
relativistically
in describing
tum mechanics
successful
the
has nevertheless
been
contradiction
behavior
and
"Atomic
Bohr,
Stability
to this paper
will
be made
see Bohr
to Fermi,
the writing,
23.
ences
of
of atoms are twofold: first, the dimensions
Conservation
Laws,"
in the text by page
13 Nov.
1931, and
of atoms are very
refer
p. 119. Hereafter,
For
the dating
number.
12 March
1932
(BSC).
319
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
of the electron;
second,
large compared with the classical diameter
are
small (pp. 121-123).
the relativistic effects
relativistic
Bohr next took up Dirac's
theory of the electron and
theories of quantum
the contemporary
Both, Bohr
electrodynamics.
come up against fundamental
difficulties. For the Dirac
explained,
was still the existence of the transitions to states of negative
theory, it
it was
mass that Bohr saw as critical; for quantum
electrodynamics,
of infinite energy. Bohr envisioned a final solution in
the appearance
a theory where, in contrast to quantum mechanics,
"the elementary
as
features"
action
of
appear
inseparable
particles and the quantum
to go beyond
Bohr
this general appraisal,
(p. 123). It is necessary
to some extent, "the
of whether,
and pose the question
continued,
for the analysis of the
guidance
present
theory offers a reliable
follows a rich and complex analysis of
phenomena"
(p. 123). There
of these two parts of theory to a series of cases (pp.
the application
result is that the theory is not sufficient to yield a
123-126). The
about the conservation
conclusion
laws, and, therefore, we can reason
Bohr implied that it is necessary to separate
only from experiment.
"As far as the extra-nuclear
elec
atomic from nuclear phenomena:
trons in atoms are concerned,"
"there is no experi
Bohr concluded,
laws" (p. 127).
mental
indication of a failure of the conservation
Bohr
energy
for the validity of the
the experimental
evidence
in
in
in
final
law
the nucleus
the
detail
section. He gave first
treated
place to the argument from nuclear
tion. The
information on nuclear
statistics to energy nonconserva
spins and statistics, which had
to 193 2,24 posed
the following
from 1929
considerably
can
tell
how many protons and elec
One
problem.
unequivocally
trons each nucleus
from its charge and mass, and since
possesses
increased
protons and electrons each have spin
ber of spin i/2 particles each nucleus
gives the rule that a system composed
particles
obeys
one can tell the total num
contains.
Quantum
of an odd number
mechanics
of spin i/2
was
This
in
conflict with the
statistics.
information on statistics of nuclei. As Purcell
Fermi-Dirac
evolving experimental
pointed out, the reaction of physicists to this problem was to say that
was suppressed when
In
the electron's
it entered the nucleus.
spin
not
to
"the
of
Bohr's
is
found
idea
be
formulation,
spin
applicable
to
intra-nuclear
electrons."25
24. See Purcell,
126-127,
pp.
25. Bohr,
Lecture,"
"Faraday
and
p.
Brink,
380.
pp.
5-6.
320
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
Bohr
OF
IMPACT
THE
BOHR
NEUTRON:
AND
HEISENBERG
'passivity' of the intra-nuclear
electrons in the determination
of the statistics is a very direct indica
of the idea of separate
limitation
tion, indeed, of the essential
we
to
entities
when
electrons.
dynamical
Strictly speaking,
applied
a definite
a nucleus
are not even
contains
in
that
saying
justified
continued:
"This
remarkable
is
of electrons, but only that its negative
electrification
a
equal to whole number of elementary units, and, in this sense, the
of a /3-ray from a nucleus may be regarded as the creation
expulsion
number
of an electron
as a mechanical
entity."26 "We cannot therefore be
to
should
the last thought, "if these processes
surprised," he added
as the conservation
laws of
be found not to obey such principles
which
and
formulation
of
the
is
momentum,
energy
essentially based
on
the idea of material
of the argument
version
particles"
is an elaborated
(p. 128).27 This
sketched in the 1929 fragment, and
use of a
form
is making
particular
already
it is extremely important. Bohr
of the concept of the creation of material
them
particles in regarding
to
This
mechanical
their
respect
provides
properties.
a model
of the nucleus which, in a partial sense, is free of electrons.
Electrons are in the nucleus with respect to their existence as discrete
as created with
units of charge, but not with
respect
to their existence
as mechanical
entities.
At
in the beta-ray spectrum.
and
conservation
energy
applies,
of the product of a radioactive
disintegration
amounts of energy and are hence different, or
the end of the section Bohr
two alternatives.
He
poses
the individual
nuclei
Either
brings
are left with differing
does
energy conservation
are released
energies
the first alternative,
showing
the existence
so that, although
not apply,
differing
in their formation, the nuclei are identical. In
for experiments
it becomes difficult to account
of definite
rates of decay
for radioactive
ele
in the Rome
the same phrases
127-128.
article,
pp.
appear
the
out
that the laws of quantum
mechanics?in
particular
pointed
in sharp
rules
for nuclear
for statistics?do
hold
mechanical
protons
quantum
an
to electrons
In seeking
contrast
of the dif
understanding
128-129).
(pp.
the mass
he made
the suggestion
that the ratio m/M,
of the electron
ference,
a fundamental
in the
over
of the
the mass
of the proton,
part
"plays
question
the problem
constitution
In this respect
nuclei.
of nuclear
of atomic
stability
a characteristic
from
that of the constitution
of the extra
difference
exhibits
is essen
the stability
since
of this configuration
nuclear
electron
configuration,
of the mass-ratio."
Lecture,
p. 379.) The
significance
(Faraday
tially independent
Bohr made
is that it is one of a series of attempts
of this suggestion
throughout
to exhibit
fix the essential
between
atomic
and
and
the thirties
difference
26.
27.
nuclear
Ibid.
Bohr
Almost
systems.
321
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
merits
with
IN THE
STUDIES
PHYSICAL
as well
SCIENCES
as for facts
to the essential
pointing
the same numbers of protons and electrons
identity of nuclei
among nonradio
that of
elements;
thus, evidence favors the second alternative,
was
a
law
There
third
alterna
the
energy
renouncing
(pp. 129-130).
to speak for it.28
tive, however, and Pauli was at the Rome meeting
to Bohr, Heisenberg
In an article written for a memorial
volume
active
"His insight into
Bohr's
style of work in these words:
the structure of the theory was not a result of a mathematical
analysis
with
but rather of an intense occupation
of the basic assumptions,
characterized
the actual phenomena."
structure would obscure
Bohr
"feared
that the formal mathematical
the physical core of the problem, and in any
that a complete physical explanation
should
case, he was convinced
was
formulation."29
It
the
mathematical
the
absolutely
precede
to the phenomena
that lay behind his reluctance
a neutrino. Bohr felt that experi
of
hypothesis
were
ment
should decide whether
energy and momentum
truly
or whether
some hitherto unknown
in beta-emission
indefinite
priority Bohr gave
to entertain Pauli's
was
carrying the missing portions away. A theory could only
after the facts; this is the sense of his remark in the 1929
no
non
fragment that we shall have
grounds in theory for rejecting
in case "experimental
conservation
evidence
should really corrobo
rate the suggestion."
It is also behind his remarks on the neutrino
in
particle
be built
In his Solvay paper,
of the 1933 Solvay Congress.
the proceedings
more
than a month after he had received one of Fermi's
completed
the opinion
that "before
articles on beta-decay, Bohr still expressed
...
seems
one has new
me
to
to be
in
it
this
area,
experiments
difficult
to take
a
position
on
the
subject
of Pauli's
suggestion."30
interesting
In the event, theory preceded
experiment. Most physicists came
before
the neutrino was detected
Pauli's
accept
long
hypothesis
to
in
to favor it over his
suggestion of non
in 1936. In
conservation
by the time of his controversy with Dirac
new view, however, he again stressed the
his
justifying
priority of
1956. Bohr
himself had
come
note
cited above,
28. Rassetti,
16, p. 538.
and
Its Interpretation,"
Niels
ed.
29. Heisenberg,
Bohr,
Theory
"Quantum
S. Rozenthal
1967), pp. 95 and 98.
(Amsterdam,
dans
la theorie
de
Conseil
30. Bohr,
l'electron,"
Septieme
"Correspondance
. . .
on which
the dates
Bohr
de Physique
received
Fermi's
p. 228. For
Solvay,
see Bohr
his Solvay manuscript,
to Fermi,
and
31 Jan.
1934,
paper
completed
to Pauli,
1934 (BSC).
and Bohr
3 March
322
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
OF
IMPACT
phenomena,
grounding
between
the rapidly
THE
NEUTRON!
his position
BOHR
AND
HEISENBERG
in "the
suggestive agreement
evidence
experimental
regard
increasing
and
the consequences
of the neutrino
phenomena
so
of
Pauli
in
Fermi's
hypothesis
remarkably developed
theory."31
the problematic
character of nuclear physics in the years
Despite
reflection on it.
1929-1932, Bohr had not held back from continuous
are a number
There
of reasons
for this. First, Bohr was always
a view of the whole
interested in obtaining
of physics and of the
relations of its parts. No clearer indication
of this side of Bohr's
ing ?-ray
than the Rome Lecture
itself. This preoccupation
thought is needed
would
have led him to wrestle with physics' more puzzling
aspects
whether or not he saw them as ripe for solution. Second, although
he was certainly in the camp of the radicals, he was more
sanguine
than the others about the possibility of progress. "I do not share the
that you and
pessimistic attitude
[about the fundamental problems]
Pauli
like to express so humorously,"
to Heisenberg
in
he wrote
a fresh attack
December
that he was preparing
1930, explaining
these problems.32
this optimism
is connected
with
upon
Finally,
Bohr's
intellectual
the phenomena
confronted
style. He
directly
with
to first possess a mathematical
access to
than
problems
Pauli's
and Heisenberg's
on
one
was
the
it
For,
hand,
approaches.
not necessary for Bohr to take a
initial
in
the
formulation
large step
of a theory, while, on the other, he could
more
smaller,
employ
subtle adjustments
in altering the theory. As a consequence
of his
he was, by the end of this period,
in possession
of an
procedure,
the concepts,
formulation. This
without
having
of an
admitted
easier
elaborate
analysis of the situation in nuclear theory within the frame
the totality of physics. As it
this analysis was
happened,
a
form on the eve of the discovery of the neutron.
completed
work
of
given
BEFORE THE NEUTRON:
3.
had been
"Conservation
to Heisenberg,
to Heisenberg
in
cited
Feb.
1931.
31.
32.
on a
States and to
trip through the United
first letter to Bohr after his
during most of 1929. His
was a Christmas
to Leipzig
greeting and comment on the
Heisenberg
the Far East
return
HEISENBERG
Bohr,
Bohr
in Quantum
Laws
p. 25.
Theory,"
8 Dec.
letter and all the others
1930. This
from Bohr
are
in Danish.
this paper
See
also
the letter of
18
323
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
wrote that despite some
scientific problems of the day.33 Heisenberg
"remains
his and Pauli's quantum
electrodynamics34
improvements,
a very grey theory" so long as the difficulty of transitions in Dirac's
is "quite
theory is unsolved. About Dirac's own solution, Heisenberg
seems
but
misfortune
also
"a
great,
interesting
sceptical." Moreover,
as
if the electrons do not
to enter with nuclear
spins." It appears
contribute
to the
at all, and this, along with the continuous
spin
no longer really are electrons
spectrum, suggests that "there
beta-ray
in the nucleus
'Electronen' mehr im Kern gibt)."
(es nicht eigentlich
launched a new and radical attack on the
Shortly after, Heisenberg
this work is recorded
in letters he
difficulties he had enumerated;
on 26 February and 10 March
1930.35 The most com
was
attack
for
the desire to solve the
motivation
Heisenberg's
pelling
to
In analogy
of the infinite self-energy of the electron.
problem
the
classical
electron
radius
introduced
classical
theory, Heisenberg
wrote
to Bohr
as a fundamental
tude as nuclear
mass
length is of the same order of magni
length. This
diameters and as the quantity h/Mc, where M
is the
of the proton.
Since
the proton was
the heaviest
known,
particle then
the smallest
wavelength?was
h/Mc?the
proton's Compton
to
relations allowed a particle
the uncertainty
length within which
as
seen
the
be localized. This
be
theorist
indeterminacy may
giving
a freedom to alter physical
laws for dimensions
less than h/Mc.
construction
the
of a "lattice
Heisenberg
Accordingly,
proposed
world"
relations
of cells of volume
("Gitterwelt")
the cells. He
would
hold within
in which new
(h/Mc)3,
characterized
this as the
by which a fundamental
length could be intro
duced. A theory of this kind must be constructed so that systems that
are large with respect to the cells obey quantum mechanics,
while
same
new
of
the
of
order
laws.
In
systems
magnitude
obey
particular,
the nucleus was a system which would
be governed
by any new
"crudest method"
33. Heisenberg
are
in this paper
34. Heisenberg
to Bohr,
20 Dec.
1929 (BSC).
in German.
and Pauli,
"Quantentheorie
56 (1929), 1-61, and 59 (1929), 168-190.
All
letters
from Heisenberg
der Wellenfelder,"
Zeits.
cited
f. Phys.,
a
of close
35. Following
communication
Heisenberg's
began
trip,
period
and Heisen
Bohr
the two physicists.
between
fifty letters between
Approximately
are
to
start
the
end
in
1930
the
of
of April
from the
Bohr
1932
preserved
berg
at least
In addition,
the two met
times:
in
Scientific
eight
Correspondence.
and October
of 1930, in March
in
of 1931, and
April,
January,
June, September,
are deduced
and April
dates
from the letters.
of 1932. The
March,
meeting
324
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
results
OF
IMPACT
THE
BOHR
NEUTRON:
AND
HEISENBERG
that might
of the results
follow from the theory. One
was
"a
for
kind
of
in force'
'reconnaissance
hoped
. . .,which allows one to
every
[gewaltsame Erkunding]
anticipate
thing that can occur in nuclear physics."36
Heisenberg
a
for a mathematical
formulation, Heisen
point of departure
the Klein-Gordon
which
differential
berg wrote down
equation,
a
relativistic
of
the
electron.
gives
quantum-mechanical
description
As
the
confined himself to the one-dimensional
case, introducing
cell length, a ? h/Mc, by converting the differentials with respect to
is similar
length into differences.37 The resulting difference equation
to one in the theory of metal
lattices.38 Possibly with the aid of this
He
sketched out
analogy, Heisenberg
tion of wave number. The crucial
the curve of the energy as a func
feature of the energy dependence
as
to the differential
opposed
that
is
it
is
equation,
interpreted the difference
periodic. Heisenberg
as
a
that
behaves
like an electron in the
equation
describing
particle
a
of
minima
like
and
energy
proton near the maxima.
neighborhood
derived
from the difference
equation,
it represents a
for light quanta;
the wave packet
situation where
for light has a vanishing
group
in
the
maxima.
of
the
energy
velocity
region
smaller than
found that within systems of dimensions
Heisenberg
A
similar
curve
can
be
derived
nor charge was con
energy, momentum,
as
in ordinary
is, these laws all hold
approximations
further
A
atomic physics, but fail in nuclear
interesting
physics.
consist only of
result would
be this: that atomic nuclei would
protons and (slow) light quanta of mass M, not of electrons. For in
one can only use
order to build wave packets of nuclear dimensions,
neither
cell-dimensions,
served. "That
He
of the ?-curve."
in the neighborhood
of the maximum
"I don't know whether you regard this radical attempt
as completely
crazy. But I have the feeling that nuclear
physics is
waves
concluded:
to Bohr,
1930 (BSC).
23 March
36. Heisenberg
?
is C]0 +
37. The
Klein-Gordon
O
0, where
m2c2<f>
equation
to ?E2/c2
that <f>?
ential
+
operator
p2. Assuming
corresponding
case and
time in the ordinary
the one-dimensional
manner,
treating
gets ?(E/c)2un +
approximates
the proton's
38. I am
elucidation
(h/2wia)2 [un+i
?
2un+
un-\ +
\
rest energy?near
electron's
mc2?the
maxima.
rest energy?near
to Dr.
Franco
indebted
in these
the physics
of
Iachello
letters.
m2c2un?
minima
for pointing
and
is the differ
T(t)u
(x) for
Heisenberg
0. The
this out,
energy
~
Mc2?
and
for
he/lira
an
325
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
not
to be had much
was willing
even ready
IN THE
STUDIES
more
to abandon
PHYSICAL
SCIENCES
like Bohr,
cheaply."39 Thus Heisenberg,
laws. He was
conservation
the mechanical
to jettison conservation
of charge. It was here
on grounds of
He
considerations.
correspondence
that Bohr
explained
charge did not relate
In addi
electrodynamics.
objected
that he felt Heisenberg^
to the charge
properly
treatment of electric
concept in classical
is
severely the classical
theory's area of application
can be marked
felt "doubtful
that these boundaries
out in as simple a manner
as you seem to hope."
"I have been
Bohr informed Heisenberg,
occupied with precisely this question,"
and he enclosed a copy of his beta-ray manuscript
and one of his
to give Heisenberg
letters to Dirac
"the direction my thoughts have
tion, however
limited, Bohr
taken."40
in possession
of each
this point, with Bohr and Heisenberg
was
due
the
breaks.
Heisenberg
correspondence
hypotheses,
in Copenhagen
the occasion being one of
the second week in April,
At
other's
on current problems
in physics held at the
the informal meetings
Institute for Theoretical
Physics in these years. Pauli was also there,
and Gamow
had come from Cambridge
where he had been occupied
with the problem
of nuclear
electrons. Among
the others present
were L. Landau, R. Peierls, W. Heitler,
and, from Sweden, I.Waller.
as well as the
From the list of participants,
correspondence
preceding
it can be inferred that both Heisenberg's
the meeting,
lattice-world
and Bohr's
ideas were
After Heisenberg
lattice-world model.
discussions
were
discussed.41
returned
Whether
decisive
to Leipzig,
he stopped work on the
or not the
conference
Copenhagen
is unclear.
had already raised
Heisenberg
his own model
in his letter of 10 March,
weighty objections
against
where, above all, he had pointed out that it did not satisfy the cri
terion of relativistic
invariance. Whatever
the cause, his first letter
to Bohr on his return from the conference sketches an
entirely new
to Bohr,
39. Heisenberg
10 March
1930 (BSC).
to Heisenberg,
40. Bohr
18 March
1930 (BSC).
41. For
wrote
to Bohr
on 23 March
1930 (BSC),
example
Heisenberg
"[Ich]
m?chte
die Diskussion
auf unser Beisammensein
in Kopenhagen
Ich
verschieben.
m?chte
auch
dann
ausf?hrlich
Deinen
kennen
lernen."
See
gern
Standpunkt
to Bohr,
also Gamow
and 23 March
25 Feb.
names
1930 (BSC). The
of partici
are taken
from the "Udenlandske
Gaester
Institut
for
pants
paa Universitetets
teoretisk
This
of foreign
in the Niels
Bohr
Fysik."
register
guests,
preserved
contains
arrival
entries
from 1919 to 1956.
Archive,
326
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
to the
approach
problem of the electron's self-energy, one based on
the study of very fast particles.42 In an article embodying
this pro
a
in
included
1930,
gram, completed
passage
August
Heisenberg
to introduce
is probably a history of his shift. If one decides
which
the classical
electron
radius, r0, into quantum
theory, Heisenberg
to introduce
first of all seem plausible
it in such a
wrote, "it would
r03, and
way that one divides
space into cells of finite magnitude
the previous
with difference
differential
equa
replaces
equations
tions. . . .Although
such a lattice-world has . . . interesting proper
from the present
ties, one must also observe that it leads to deviations
not
seem
from the point of view of
plausible
the
that a minimum
length
experiment.
assumption
one
can see no way to
and
exists is not relativistically
invariant,
for relativistic
invariance
into conformity with
bring the demand
theory which
do
In particular,
therefore seem
of a fundamental
length. It would
the length r0 in the
for the present not to introduce
invariance.
foundations of the theory, but to hold fast to relativistic
an essential
If one takes this second viewpoint,
simplification of the
of electrons
is achieved
by considering
only the motions
problem
that of light."43
and protons whose velocity approaches
the introduction
more
correct
related to cosmic
changed program of investigation
Heisenberg's
as
had
to
his
model
lattice-world
nuclear
rather
than
rays,
physics,
on
a
to
I
attack
indicate
is nothing
have found
done. There
parallel
in the succeeding
Years
nuclear
constitution
eighteen months.44
42. Heisenberg
to Bohr, 26 April 1930 (BSC).
"Die
Zeits.
des Elektrons,"
43. Heisenberg,
f. Phys., 65 (1930), 4-5.
Selbstenergie
new
The
of locating
the source of the difficulties more
approach
proved
capable
them.
rather than of solving
accurately
on Heisenberg^
and his letters to Bohr. The
this conclusion
44. I base
papers
on the self-energy
of the
ten papers
between
the article
Heisenberg
published
are on
field
Two
fall into four groups.
and
the first nuclear
electron
paper
on the mathematics
of his and Pauli's
electrodynamics
("Bemerkun
theory: one
zur
the other on
Ann.
and
d. Phys.,
9
gen
338-346);
Strahlungstheorie,"
[1931],
in
einem
fluctuations
energy
Strahlungsfeld,"
Energieschwankungen
("?ber
83
deal with
Berichte
S?chs.
Akad.
Wiss.
applied
Leipzig,
3-9). Three
[1931],
on
one
der
the
quantum
theory of ferromagnetism
("Zur Theorie
problems:
Zeits.
69 [1931], 287
und der Magnetisierungskurve,"
f. Phys.,
Magnetostriktion
one on the treatment
shell structure
Ausschlies
of atomic
("Zum Paulischen
297);
10
and
the third
is a short
Ann.
d. Phys.,
888-904);
sungsprinzip,"
[1931],
out at the
of
from atoms,
carried
of X-rays
of the scattering
calculation
request
von
32
die
inkoh?rente
Phys. Zeits.,
Streuung
R?ntgenstrahlen,"
Debye
("?ber
a lecture on uncer
or
are
articles:
Three
737-740).
philosophic
popular
[1931],
in der modernen
der Unbestimmtheitsrelationen
Rolle
Physik,"
tainty
("Die
327
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
that at this time no ground was felt to
recalled
later, Heisenberg
exist for doing nuclear physics. "There was one exception. That was
But one had the feeling that
for alpha-decay.
the theory of Gamow
this was a very lucky case where one could do something without
the nucleus. There was just no basis, however,
really understanding
for coming to a real theory of the nucleus."45
There
was
thus a break
into nuclear
a year and a half in Heisenberg's
structure between the winter of 1930 and
of about
investigations
the months after the discovery of the neutron. This gap is related to
his way of doing physics. In his article in the Bohr memorial
volume,
in his and in Bohr's
contrasted the role of mathematics
Heisenberg
work
was being
in the years 1924-1927 when quantum mechanics
It came more naturally to him than to Bohr to use "a formal
created.
a
he placed
Unlike
Bohr, moreover,
standpoint."
on
from the initial
certain confidence
logical deductions
purely
an
as a means
at
of
arriving
interpretation of them.46
propositions
wrote
letter Heisenberg
after
the
A
paper
"Self-Energy"
shortly
mathematical
his work as some
implies the same work style. Here he described
am
on
"I
what
relativistic
"grey
grey."
trying to think about
to
I
found
but
have
now,
theory,
up
absolutely no formal
quantum
of
attack
point
(formale Angriffspunckt).
Perhaps one must indeed
first see the entire development
of nuclear
physics,
before
one
can
a short review
u.
38
article on fer
f. Math.
Phys.,
[1931], 365-372);
in der Theorie
Metallwirt
des Ferromagnetismus,"
romagnetism
("Fortschritte
an
on
and
9
article
und
schaft,
causality
843-844);
("Kausalgesetz
[1930],
2
two are on cosmic
Erkenntnis,
Finally,
Quantenmechanik,"
[1931],
172-182).
treatment
of the interaction
of fast particles
first is a detailed
and
rays. The
with matter;
the nucleus
is considered
insofar as the contri
radiation
energetic
to the
of gamma
and
bution
rays from the nuclear
scattering
alpha
particles
zur H?hen
is taken up ("Theoretische
"free" electrons
respectively
?berlegungen
is a related
note
d. Phys.,
The
Ann.
13 [1932], 430-452).
other
strahlung,"
("?ber
die durch Ultrastrahlung
Naturwiss.,
hervorgerufenen
Zertr?mmerungsprozesse,"
Monatshefte
20 [1932], 365-366).
on nuclear
45. Interview
with Heisenberg
theory in the thirties, by the author,
16 June
interview
is on deposit
in the Niels
at the
1970. The
Bohr Archive,
Niels
Bohr
Institute
in Copenhagen,
and
in the Center
for the History
and
at the American
of Physics
Institute
to
of Physics.
I am grateful
Philosophy
to reproduce
for permission
Professor
Heisenberg
parts of it here.
46. Heisenberg,
and
Its
104.
Theory
pp. 98 and
"Quantum
Interpretation,"
328
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
get farther here."47 The phrases "formal mathematical
standpoint"
and "formal point of attack" refer to a method
in which
the initial
are
a
in
set
of
embodied
mathematical
physical insights
propositions
as the first
next step,
of the theory. The
step in the construction
to
use
is
new
to reveal
mathematical
deduction
then,
physical results.
an
lattice-world
is
illustration
of
this
The
Heisenberg's
procedure.
a
difference
which
the
embodies
idea
of
fundamental
equation,
length, serves as the theory's formal point of departure.
By mathe
matical deduction,
a
new
the equation
reveals
picture of the behavior
of matter
and photons
and a new nuclear model.
the time,
At
the lattice-world and, hence,
the model
of the
Heisenberg
judged
nucleus which
followed from it to be unsatisfactory. The
discovery
of the neutron was to provide him with the clue to a new mathema
tical starting point in the spring of 1932. In the intervening years,
to proceed
could not see a way
and did not occupy himself
further with the problem.
he
THE RESPONSE
4.
TO THE NEUTRON
Bohr
It was
that
in Heisenberg's
of Bavaria
ski hut in the mountains
of his Rome
address in March
finished the manuscript
1932.
one of the tasks awaiting him was
When
he returned to Copenhagen,
on cur
that of organizing
informal
the year's
Institute Conference
Bohr
rent problems
in physics. It was to take place at Easter, and Bohr
see Heisenberg
for Bohr was
again at that time. Also waiting
a letter from
a
of
Chadwick's
containing
James Chadwick,
page-proof
note in Nature
neutron.
will
the
"As
see," Chad
you
announcing
would
wick
think
told Bohr, "I have put this forward rather cautiously,
but I
the evidence
is really rather strong."48 Bohr's
interest was
to Bohr,
In a sense, Heisenberg
18 Sept.
1930 (BSC).
followed
47. Heisenberg
he
here.
In
the program
in 1936, he used
suggests
investigations
beginning
as a
treatment
to solve prob
Fermi's
of beta-decay
for an attempt
starting point
lems in relativistic
the
mechanics
introduction
of a fundamental
by
quantum
in a more
in particular,
the review
See,
article,
way.
length
sophisticated
der Elementarteilchen
und
universellen
Ann.
d. Phys.,
"Theorie
32
L?nge,"
(1938), 20-33.
to Bohr,
48. Chadwick
a Neutron,"
129
Nature,
24
Feb.
(1932),
1932
312.
(BSC).
Chadwick,
"Possible
Existence
of
329
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
IN THE
STUDIES
HISTORICAL
PHYSICAL
SCIENCES
Their
strong and immediate, as was Heisenberg's.49
responses, how
were
ever,
sharply different. Bohr immediately grasped that the new
neutral particle could illuminate
the treatment of collision problems
in quantum
surprisingly
was a reason
for the
sought an explanation
of neutron-electron
collisions,50 which
sooner.
had not been detected
Heisenberg,
he
mechanics;
low frequency
the neutron
in contrast, took up
problems of nuclear
therefore
of the neutron
the implications
structure.
for the unsolved
as a nuclear
to the neutron
appear in
component
on
some
the introduction
and concluding
remarks of
manuscripts
It is worth sketching them, chiefly as an aid to
collision problems.
Let me recall first the well-known
fact
understanding
Heisenberg.
in
first suggested the possibility of a neutron
that when Rutherford
reactions
Bohr's
lecture of 1920, he had in mind a compound
system of
He
that
he
had
electron.
believed,
mistakenly,
proton plus
just dis
of three protons and one electron. By
covered helium-3, composed
he suggested the existence of hydrogen-2
analogy and extrapolation,
we
are
correct in this assumption,"
neutron.
"If
he wrote,
and of the
one
referring to the structure of helium-3, "it seems very likely that
can also bind
two H
electron
nuclei
and possibly
also one H
his Bakerian
nucleus."51
When
in the winter of
his discovery
was
the
neutral
thought
particle
probably
atom Rutherford
had
suggested.52 Not
Chadwick
1932, he and Rutherford
the collapsed
hydrogen
it was
unnaturally,
of
point
departure.
neutron
The
is
this model
therefore
49.
Bohr
1932 (BSC).
Bohr wrote,
to Heisenberg,
the neutron
of
an
Bohr
took as his
of
the alpha-particle,
"From a formal point
original proposal.
as a nucleus
"the neutron may be considered
as in Rutherford's
exactly
of view,"
made
22 March
analogue
1932,
and
Heisenberg
to Bohr,
24 March
did not publish
his solution.
It is in manuscript:
of the
50. Bohr
"Properties
i Fysisk Forening,"
9 May
1932; and "Atomic
Neutron,"
1932; "Foredrag
April
1932.
Collision
Problems,"
probably
of Atoms:
The
Col
Bakerian
51. Rutherford,
Constitution
"Nuclear
Lecture,"
ed. Sir J. Chadwick
lected Papers
of Lord
Rutherford
of Nelson,
(London,
not use
the word
"neutron."
does
1965), 3, 34. Rutherford
129 (132), 458. Chad
of the Gamma
52. Rutherford,
Nature,
Rays,"
"Origin
Foundations
ed. R. T.
of a Neutron,"
"The
Existence
wick,
of Nuclear
Physics,
Beyer (New York, 1949), p. 19.
330
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
IMPACT
THE
of an element
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
of atomic number zero."53 The
significance of its dis
our
all . . . that we have augmented
[the range of]
is "above
covery
to the
the neutron
of nuclei."54 Bohr
thus assimilated
knowledge
at
Easter
the
In
talk
of
he
had
his
nuclei
analysis
just completed.
in
conference, he reminded his listeners of his treatment of nuclei
He
indicated
the Faraday
lecture, which had just been published.
on nuclear
that the considerations
statistics may be carried over to
thus expect that it will obey the exclusion
as the electron or the
statistics] just
principle
[that is, Fermi-Dirac
some external agency,
proton, and that if it could be broken up by
find no
we may expect that the idea of energy conservation would
constitu
"as
Further,
regards
[the neutron's]
simple application."
to offer
tion, it is at the present stage of atomic theory not possible
mass
and charge suggest that
Of course, its
any detailed explanation.
of a proton and an electron,
is formed by a combination
the neutron
in this way, as
but we can not explain why these particles combine
little as we can explain why four protons and two electrons should
to form a helium nucleus."55
combine
con
of nuclear
"with regard to the question
conclusion
Bohr's
struction itself" was that "we stand without any aids to understand
. . .These
is an area where one is collecting data.
it.This
investiga
the neutron.
"We
shall
. . . have
the unusually
interest, that they relate
great physical
one
and
of experience,
to an accumulation
may thereby hope to be
of the
for a further expansion
able to find a point of departure
Bohr's analysis left the difficulties of
theoretical methods."56 Thus,
nuclear structure almost exactly where they were before.
Bohr's response to the neutron was surely conditioned
by his life
seems
that it
But it
probable
long concern with collision problems.
was also affected by the fact he had just thought his way through to
the
a detailed
and comprehensive
reducing
analysis of the nucleus,
a
to
as
nuclear
structure;
see
neutron
clue
the
chance that he would
as concerns its relation to the nucleus, he was ready with a concep
tions
"Extract
from
. . .
Copenhagen,
problems
cited in note
the Neutron,"
53.
54.
Bohr,
Bohr,
55. Bohr,
56. Bohr,
"Foredrag,"
"Extract,"
"Foredrag,"
an
address
7-13 April
50.
p. 5.
1-2.
pp.
p. 17.
at
delivered
1932,"
p.
. . . atomic
on
the conference
of
in "Properties
1, contained
331
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
STUDIES
HISTORICAL
IN THE
PHYSICAL
SCIENCES
tual pigeon hole for it. Of course, he saw very quickly that one need
no longer have "free" electrons in the nucleus, but that one could
neutrons. But at the initial moment,
pack all nuclear electrons into
a
a mystery, and the neutron became
structure remained
nuclear
case
of this mystery.
new, special
Heisenberg
structure was carried out at the
work on nuclear
Heisenberg's
same time that Bohr
published his
expressed these views. Heisenberg
of
December
and
in
submitted
in
three
June, July,
parts,
theory
the period of this
these, the third does not fall within
and will be considered only in so far as it elucidates
the ideas
1932.57 Of
paper,
of the first two.58
saw very soon after hearing
of the
Undoubtedly
Heisenberg
in
neutron
the charge and mass of nuclei
that one could explain
terms of numbers of neutrons and protons without having to use the
hypothesis of nuclear electrons. He must also have realized from the
start that one could also explain beta-decay without electrons, if one
the assumption
that a neutron
could disintegrate
into a
accepted
proton and an electron. He surely also saw right away that one could
account
for nuclear
the neutron a
spins and statistics by assigning
statistics. These
spin of i/2 and the property of obeying Fermi-Dirac
that Bohr
Heisenberg
sent Heisenberg
Bohr's
to a number
of physicists independently.59
It seems
of
them
the
time
he met
by
thought
at the Easter meeting;
this is implied in comments he
ideas occurred
certain
had
also
in acknowledgment
of the June paper. Moreover,
is entirely consonant with these insights.
Easter
lecture
57. Heisenberg,
"?ber
den
Bau
der
Atomkerne,"
Zeits.
f. Phys.,
77
(1932),
1-11; 78 (1932), 156-164; 80 (1933), 587-596. Hereafter, thesewill be cited in the
text
and page
The
number.
first paper
and part of the third are
by volume
on pp.
The
errors and omis
144-160
of Brink.
translation
translated
contains
sions, however.
the objections
reflects
third paper
of the theory's critics.
It also con
58. The
to a new stage of theory. Of
that belong
is the
tains concepts
interest
particular
new
to the
of the nature
formulation
of the neutron.
Heisenberg
gives
problem
or my
on
See
article,
80, 595, penultimate
"Heisenberg's
paragraph,
Papers
on
International
the
Nuclear
Structure,"
of the Xllth
Proceedings
Congress
1968
Paris,
of Science,
History
August,
(in press).
were
first by D.
"The
Neutron
59. They
Ivanenko,
published
Hypothesis,"
129 (1932),
798.
Nature,
332
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
BOHR
NEUTRON:
AND
HEISENBERG
was a difference between Bohr's and Heisenberg's
view of
There
cata
in
Bohr's
concurred
the neutron, however. While
Heisenberg
a
he
in
the
of
neutron,
recog
logue
inhering
compound
problems
nized an additional
difficulty: the neutron seemed to be elementary
as well as
I do not believe Bohr shared this view in the
complex.
as a result of his
to Heisenberg
of
It
1932.
may have occurred
spring
have
concern with nuclear
arisen after the
and
hence
structure,
may
as having been
it
In 1970, Heisenberg
Easter conference.
portrayed
on
and
of neutrons
the numbers
facts
linked with the empirical
"At that time we had an unclear
feeling that the
protons in nuclei.
as consisting of proton and
can be considered
neutron
somehow
seemed
electron, but also somehow not, because after all the neutron
the
to be very similar to the proton. I had from the very beginning
.
.
.
from
idea that the neutron was a kind of brother to the proton
neu
and
of
number
the fact that an approximately
protons
equal
. . .And, on account of this
trons were in the nucleus.
symmetry, it
con
was not so nice to say that the neutron
is a compound
particle
the proton
is an elementary
sisting of proton and electron, while
particle."60
Heisenberg's
paper
throughout. He
June
of
expressions
in his introduction
contains
wrote
this
state
of
that "if one
uncertainty
of proton and electron,
the neutron as composed
wishes to picture
one must ascribe Bose statistics and zero
to the electron. It does
spin
a picture
not seem purposeful,
to
in more
into
such
however,
go
neutron
shall be
detail
solches
Bild
n?her
The
auszuf?hren).
(ein
fundamental
constituent, which
regarded rather as an independent,
can
a proton and an electron,
under proper circumstances
split into
in a process where the conservation
laws for energy and momentum
no longer
probably
applicable"
(77, 1-2). In this statement,
as an elementary
neutron
favors
the
view
of
the
Heisenberg
particle.
are
In the concluding
the compound
however, he recognizes
paragraph,
as indispensable
for understanding
like scatter
phenomena
from
nuclei
ing
(77, 10-11).61
neutron
The
double
view of the neutron
with Heisenberg,
60. Interview
61. See also 78, 160-163. This
See
months
April.
just before
cited
in note
H?henstrahlung,"
16 June
is connected
was
incorporated
1970, p. 2.
with Heisenberg's
"Theoretische
Heisenberg,
440-442.
44, pp.
in the mathe
researches
?berlegungen
in the
zur
333
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
a "formal
formulation Heisenberg's
achieved
theory. He
use
of
two
of
the
first of
point
by making
departure"
analogies,
which
is based on the idea of the neutron as elementary,
the second
on the idea of the neutron as
compound. He added to the customary
four coordinates which give the position and the
spin of each of the
which
takes the value
heavy nuclear particles a fifth coordinate,
+ 1 for the neutron and ?1 for the proton. This
coordinate, which
matical
called the "p-spin," later came to be called the "isotopic
Heisenberg
It
represents the neutron and proton in a formal sense as two
spin."
to make an
different states of the same system. It was now possible
two
states
the
the
of the
between
and
analogy
isotopic spin
spin
electron,
describes
thereby
electron
carrying over the mathematical
spin. It is clear that with respect
that
apparatus
to this aspect of
the theory, the neutron and proton are entirely symmetrical.
drew an analogy between a system
At the same time, Heisenberg
a proton and a neutron
and a hydrogen molecule
of
composed
an analogy between a system of two neutrons and a hydro
This
enabled him to use the physics and mathematics
gen molecule.
the neutron
of the quantum
theory of chemical binding. Between
a charge-exchange
force similar to that
and proton he postulated
the two neutrons
he
ion together. Between
which
holds
the H2
a
to
the
force
introduced
weaker
interaction, corresponding
binding
a neutral hydrogen molecule.
Finally, using the same comparison, he
no force between
assumed
the bare protons except the Coulomb
ion and
part of the theory, therefore, rests on a conception
as
and the proton as elementary. More
compound
of neutron and proton leads to
the asymmetry in the models
repulsion. This
of the neutron
over,
asymmetry
themselves.
in the forces
than
the neutron-neutron
stronger
nuclear force is nonexistent.
force is
neutron-proton
and
the
force,
proton-proton
The
arrived at in this way was
expression Heisenberg
as
of the nucleus
conceived
the energy operator, or Hamiltonian,
neutrons
most
of
and
The
heavy
protons.62
entirely
composed
The
mathematical
62. The
Hamiltonian
H =
?
+
is:
1/2M S pk2
k
1/4
2
k>
1/4 2
k>
1/2 2
k>
J (m) (p^ pz*+
i
K (rti) (1+ piO (1+ p*0
i
,2/r*z (1
piO (1
pfcO
i k
pjbfpz")
1/2D 2 (1+
334
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
pkt).
THE
extended
OF
IMPACT
THE
BOHR
NEUTRON!
AND
HEISENBERG
use he made
of this operator was to deduce criteria predict
of the radio
exist in nature and which members
ing which isotopes
active decay series emit beta- and which alpha-rays.63 To determine
whether a given nucleus will be stable or not, he used the Hamil
tonian to estimate the binding energies of the lowest states of various
nuclei. For example, at the start of the second paper, he takes up the
of light nuclei. He considers all nuclei with a fixed n = rix
question
+ n2, where rix is the number of neutrons
in a given nucleus and n2
is the number of protons. The
short-range character of the neutron
forces is expressed by the assumption
proton and neutron-neutron
on the
that the binding of a given neutron or proton is dependent
uses the Hamiltonian
to derive a
ratio nx/n2 (77, 7). Heisenberg
curve
curve of the binding
energy as a function of nx/n2. The
to a minimum
for some rix/n2 = a and then rises again. He
descends
in beta-decay
concludes
that nuclei for which rix/n2 > a are unstable
used sta
nonexistent
(78, 156-157).64 Thus Heisenberg
even in
on the
of
conservation
criteria
based
energy
bility
principle
since he
is remarkable,
those cases where he treated beta-decay. This
and
hence
conjectured
probably
attention
at the start of the paper that the process of beta-decay
is
not governed by energy conservation. He explicitly called
to this discrepancy
at the place where he first introduced
considerations
the application
"Although
a
to
laws
the
conservation
decay of neutron
in
fraglich erschient)
(durchaus
questionable
like that described
above.
of energy and momentum
appears
completely
on the continuous
nevertheless,
beta-spectrum,
light of the findings
. . . use will be made here of an
for
beta-radiation"
energy-balance
(77,
6).
In his December
"this attempt
principle,
even outside
conservation
paper,
to retain
he
certain
the boundaries
to
in
this point:
of energy
consequences
of its applicability
is,
returned
so that the first term is the kinetic
of the kth particle,
is the momentum
pk
to spin matrices.
in analogy
constructed
energy, p^,
pkv, and p^ are 2x2 matrices
on a neutron-proton
their charges
term in H, operating
The
second
pair, exchanges
on their separation.
The
third term gives
force dependent
and gives an attractive
term is the Coulomb
fourth
force. The
an attractive
neutron-neutron
repulsion
in the neutrons.
and the fifth the binding
between
energy of the electrons
protons,
is the mass
Here D
defect of the neutron
(77, 3).
Here
are
in 77, 6-11 and 78, 156-160,
these
which
63. Besides
developed
applications,
sta
to give brief explanations
of the special
used
his Hamiltonian
Heisenberg
forces (77, 5).
and of interatomic
the
of
4-5)
bility
particle
alpha
(77,
to
to estimate
no attempt
makes
64. Heisenberg
a; he immediately
proceeds
are
a more
treatment
in
which
odd and even nuclei
detailed
separated.
335
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
he continued,
it left
Nevertheless,
logically, completely
possible."
not sooner or later reveal
that present
theories would
little hope
the
inner difficulties. Therefore
"these stability criteria represent
least secure part of the considerations
carried out here" (80, 596).
to outline
It is worthwhile
series
the discussion
of radioactive
us
forms the major
part of the first paper, for it acquaints
with the first results of the theory as his contemporaries
received
a member
starts by considering
them. Heisenberg
of a decay series
which
with
even
The
ratio n1/n2 will increase with
a certain critical value. At
atomic
number
and which
reaches
energy which
would
be occasioned
decays
successive
with
alpha
emission.
alpha decays until it
this value,
the loss in binding
n-n
a neutron?the
loss
of
the
by
mass defect?would
than compen
be more
energy plus
a
sated by the gain occasioned
p-n energy
by the gain of
proton?the
term. Beta-decay now occurs and, consequently,
minus
the Coulomb
results from this
n1/n2 decreases. An odd atomic number nucleus
the neutron
that there is at least one proton which
an
cannot be bound
into
stable) alpha particle. Hence
(exceptionally
can now occur at a lesser value of the critical
another beta-decay
resumes until the ratio again
ratio n1/n2t after which alpha-decay
first beta-decay,
which means
sufficiently large so as to exceed the first critical value (77,
to extract from his analysis a
In
this
way Heisenberg
9).
managed
cor
each successive beta-decay must
quasi-numerical
prediction:
becomes
to the ratio's exceeding
one of two values. He
then com
this
with
for
natural
calculated
the
three
n1/n2
pared
prediction
not the
it
the
thorium
radioactive
and
actinium
but
fit
series;
series,
radium series (77, 9-10).
respond
Bohr's reaction to the first of Heisenberg's
papers is recorded in a
letter of 27 June. "In the hope that this letter can still reach you in
I am hurrying to write how much we all have liked your
Leipzig,
fine paper. As you may imagine, it was not completely
wonderfully
that all difficulties can be shoved over onto
the
strange to me
but that such a simple systematics with regard to the
neutrons;
can be achieved
connection between a- and ?-radiation
by this was a
and
great
happy surprise."65
The
insights that the neutron
is compound
and also analogous
65. Bohr to Heisenberg, 27 June 1932 (BSC).
336
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
to
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
in Heisenberg^
into a consistent model
the proton were not united
have
reconcile
them at that date would
1932 papers. To
probably
to foresee
a heroic creative act. Heisenberg
would
had
have
required
both the existence of the positron, announced
1932,
only in August
the decay of the proton
Joliots only at the beginning
and
that
addition,
the nuclear
by the
by positron emission, announced
of 1934. He would have had to guess, in
is
neutron
and proton
force between
neutron and neutron and
equal to the forces between
approximately
of charge indepen
between proton and proton;
this phenomenon
dence was not discovered until 1936.66
found even more
troublesome
that Heisenberg
An inconsistency
neutron and the experi
at the time was that between the compound
mental
evidence
on
the neutron's
mass.
Insofar
as Heisenberg
pic
as a
it
pictured
compound
particle,
it
In this respect,
combination
stability.
exceptional
possessing
the alpha particle. But the alpha particle has a binding
resembled
electron volts, while the measure
28 million
energy of approximately
a
to
ments of Chadwick
energy of only 1 to 2
binding
pointed
million
electron volts for the neutron.67 That
such a slightly bound
the neutron
tured
system
should
show
as
a
extraordinary
he
stability
presented
a
paradox
(78, 163).
was aware of both these inconsistencies.
It is perhaps
Heisenberg
the greatest strength of his papers that he did not allow himself to be
on two grounds. First, he
justified his theory
stopped by them. He
out
that
the
connected
with his neutron model
difficulties
pointed
rested on
But
to it of the laws of quantum mechanics.
the application
4'the very existence of the neutron contradicts
the laws of quan
tum mechanics
in their present
form. Both the validity of Fermi
to be sure?and
statistics for neutrons?hypothetical,
the negation of
the energy conservation
law in beta-decay show the inapplicability
of
to the structure of the neutron"
the current quantum mechanics
(78,
is precisely
the view of the neutron Bohr gave at the
163). This
Easter conference, and it is based on the view of nuclei which Bohr
to before 1932.
and Heisenberg
both adhered
"The
76 (1932),
I. Curie
66. C. D.
and
238.
Anderson,
Positron,"
Science,
nouveau
"Un
F. Joliot,
198
Rendus,
type de radioactivite,"
Comptes
(1934),
For
the researches
see Brink,
254-256.
establishing
charge
independence,
p. 61.
"The
of a Neutron,"
Existence
67. Chadwick,
p. 702.
337
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
STUDIES
IN THE
PHYSICAL
SCIENCES
his theory on the ground of its con
of the problem
of explaining
the neutron's
one
to
chose
the
idea
that
the neutron
stability,
particular
relinquish
can disintegrate with the emission of an electron, one could
picture
it as an elementary,
indestructible
particle
("einen unzerst?rbaren
Second, Heisenberg
If, because
sequences.
defended
Elementarbaustein"
[80, 594]). In that case, electrons must exist in
radioactive
beta emitters on the same footing as protons, neutrons,
or
alpha particles. This
picture entails an overwhelming
difficulty:
if electrons exist in nuclei
this way, they must be coupled
to the
to
for
the alpha particles, by strong
heavy components,
example,
forces. But this led one back again to the mystery of why
alpha
are emitted with definite
particles
energies and electrons are not.
More
it then is impossible
to comprehend
generally,
why heavy
nuclear
particles obey quantum mechanics,
electrons "whose behavior
in the nucleus
to
they are bound
lies entirely outside
the
since
of quantum mechanics."
the
By contrast, if one postulates
one
a
"makes
of
the
clean
neutron,
stability
separation of
possible
to quantum mechanics
the region accessible
from that which
is not
domain
since by virtue of this stability a purely quantum mechan
accessible,
can be built up in which
ical system of protons and neutrons
the
new features
not
to
of
because
do
rise
diffi
beta-decay
entering
give
culties. This
of a sharp division between
the quantum
possibility
mechanical
features and
for the nucleus
seems
nuclear
those new
to be
constituents"
independent
of a seemingly
inconsistent model
on
the basis that physical
defensible
any neutron model,
physics at all.
but
features which
lost when
it was
are characteristic
the electrons
(80, 595). Thus,
of the neutron
are regarded as
the acceptance
was
not
only
impotent to evaluate
a precondition
for doing nuclear
theory was
CONCLUSIONS
5.
the years before
1932, Bohr regarded nuclear physics as one
area
no satisfactory theory. His
of
part
larger
physics having
reasons
the continuous
included
the size of the nucleus,
beta-ray
In
of a
behavior
of nuclear
electrons. He
spectrum, and the anomalous
interested in the hypothesis of energy nonconservation
became
first
as an
for
the
beta-emission
it
Nevertheless,
spectrum.
explanation
338
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
was
for Bohr to make use of such an
possible
explanation
precisely
because nuclear physics belonged
to the domain which stood outside
the known
laws. Furthermore,
his interest in the validity of the
conservation
laws for beta-decay was a
special case of his interest in
out
which
of
mechanics
could
finding
concepts
ordinary quantum
to this domain
be applied
and which could not. This way of pro
the limits of validity of
ceeding?by
probing
existing
theory?was
characteristic of Bohr. In applying it to the nucleus, he arrived at the
idea that not only the mechanical
conservation
laws but the related
concept
proposed
mechanical
of mechanical
failed for nuclear
permanence
that was free of electrons with
a nucleus
its electrical
properties,
included
properties.
and beta-decay,
mentally new theory.
had a similar outlook.
Heisenberg
the existence
He
to its
respect
electrons with respect to
This
satisfied the data on nuclear
picture
but it rested on the anticipation
of a funda
but which
charges
electrons.
of nuclear
electrons
On
made
the one hand, he felt that
to solve the
it impossible
of the nucleus
on the
mechanics;
problems
by ordinary quantum
to picture an electron-free nucleus
other hand, he attempted
that
can yet emit betas.
was
constructed
of
model
Heisenberg's
protons
and equally massive
it was based
light quanta. No less than Bohr's,
on the
that the nucleus demanded
assumption
radically new laws.
a
as a starting
mathematical
formal,
Heisenberg
sought
expression
from Bohr. Perhaps
the most
point, and in this he differed markedly
striking
electron
illustration
radius,
of their difference
r0. Bohr
relation.
sought
is in the use of the classical
to make
it the keystone of a new
it into his theory as
brought
In Heisenberg's
lattice-world.
complementarity
Heisenberg
a dimension
fixing the cell-size of a
between
the domain
of ordinary quan
lattice-world, the boundary
tum mechanics
and the domain of the new physics is defined by the
of his theory of nuclear
structure
length r0. It was a concomitant
to redefine this boundary
that it was possible
in a more subtle way.
It ceased to be marked
out in terms of a length and became
instead
a division
the nucleus
as a collection
conceived
of heavy
the
constituent
themselves.
particles
particles
It was not a surprise to Bohr and Heisenberg
that this boundary
had to be characterized
in some new way; both had felt from the
start that Heisenberg's
use of r0was crude. It was a
surprise to them,
between
and
339
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
HISTORICAL
IN THE
STUDIES
PHYSICAL
SCIENCES
that the boundary
be drawn down
could (metaphorically)
however,
of the nucleus,
the middle
and this was the novelty that resulted
from the experimental
the anticipa
discovery of the neutron. While
tion had been that the solution to nuclear structure would be a part
of the solution
of relativistic
quantum
theory, the solution
(partial,
to be sure) was in fact a shift of nuclear physics out of the realm of
relativistic quantum
mechanics.
put the new situation
Heisenberg
with particular
in
review
of
nuclear
his
clarity
theory at the 1933
the experimental
the
facts concerning
have not carried us, up to now, to new
of quantum mechanics,
notions
it is necessary
outside
going
physical
or wave
to examine
to what
at the start ...
extent quantum
can be used in this new domain. As
as
a
mechanics
precise
possible
of the application
of quantum mechan
limitation of the possibilities
"Because
Solvay Congress.
structure of atomic nuclei
ics is one of the first tasks of nuclear
theory."68
that remained outside ordinary quantum
part of the nucleus
was the neutron. Here both Heisenberg
and Bohr inclined
mechanics
to the view they had held before; i.e., they expected the energy and
momentum
in the beta-disintegration
of neu
laws to be violated
The
the discovery of the neutron
together with Heisenberg's
neutron
to
make
their
view
less tenable. The
tended
theory
trons. Yet
1932
of Pauli's neutrino;
the plausibility
furthermore, Heisen
in his treatment of
fruitful use of energy conservation
use of the energy
his
At
the
time, Heisenberg
beta-decay.
regarded
law as an especially dubious
of
his
theory. In the event, the
part
increased
berg made
argument
was
treating beta
It remains
law in
reversed, and the success of the conservation
emission became a strong reason for retaining it.69
to discuss the factors that helped Heisenberg
arrive at
to build
the nucleus out of
attempted
neutral particles as early as the winter
his 1932 theory.
of 1930, I do not think that this attempt motivated
to try to find ways of con
that he continued
is no evidence
There
his
theory. Although
protons and equally
sructing
particles.
a nucleus
His
he had
massive
from a
combination
1930 attempt was
based
of positive
and neutral
on a desire to find a way of
sur
68. Heisenberg,
"Considerations
generates
th^oriques
. . .
de Physique
Conseil
p. 289.
Solvay,
noyau,"
Septieme
de M. Heisenberg,"
in the "Discussion
du Rapport
69. Pauli,
. . .
seil de Physique
324-325.
pp.
Solvay,
structure
la
Septieme
340
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions
du
Con
THE
IMPACT
OF
THE
NEUTRON:
BOHR
AND
HEISENBERG
an electron-free nucleus. That
this program
he held
constructing
meant
that he was particularly
sensitive to new clues for structuring
that he was sensitive to the
nuclei without
electrons and, hence,
efforts of 1930
A year and a half fell between Heisenberg's
break may well have
The
nuclear model.
his neutron-proton
of new ideas.
the emergence
given him a freshness that facilitated
neutron.
and
I have
connected
of using mathema
the time lapse with his method
of theories. By contrast, Bohr's opposite method
the neutron
place him in the position of confronting
tics in the creation
of work
helped
at a moment when
of
a detailed
consideration
just finished
initial
nuclear problems. This may have been one reason why Bohr's
was
so
neutron
to
from
the
different
Heisenberg's.
response
I have argued
that the view of the nucleus Heisenberg
Finally,
he had
for
1932 must also be counted among the preconditions
to
sustain an
It was necessary
that he should be able
so was the view
neutron model.
basis for doing
The
He
shared this
the nucleus outside quantum mechanics.
held before
his
theory.
inconsistent
that placed
view with Bohr,
and
indeed
it had
been
Bohr
who
had
it to the neutron.
given it
Heisen
public expression and who had extended
use of its extension
to the neutron precisely to show that
berg made
the analysis was no longer necessary for the rest of the nucleus.
ACKNOWLEDGMENTS
me with this paper.
Many people have extended themselves to help
for
I should like first of all to thank Professor Werner
Heisenberg
Gerald
to
Professor
and
the
with
time
discuss
me,
taking
subject
at the inception of my
for his support and encouragement
at
Institute who gave
the Niels Bohr
researches. Among
the many
me assistance,
I should like to single out Professor Leon Rosenfeld
Holton
for his informative
Niels
Bohr Archive
discussions, Professor Aage Bohr for access to the
to quote documents,
and Mrs.
and permission
Franco
Drs.
formoral as well as practical
support.
me.
the physics with
Siemens discussed
Finally,
Sophie Hellmann
Iachello and Philip
I thank Professor Brookes
fessor Paul
as history.
The
Science
Forman
work
was
Foundation.
Spencer, Dr. Peter Heimann,
for the important service of criticizing
supported
in part by a grant
and
Pro
the paper
from the National
341
This content downloaded from 128.112.86.85 on Wed, 24 Jul 2013 23:29:36 PM
All use subject to JSTOR Terms and Conditions