Baggott J. The Quantum Story: A History in 40 Moments
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the quantum story
100
Bohr believed that Heisenberg was missing the point. He had by now
realized that the position–momentum and energy–time uncertainty
relations actually manifest the complementarity between the classical
wave and particle concepts. Wave behaviour and particle behaviour are
inherent in all quantum systems exposed to experiment and by choosing
an experiment—choosing the wave mirror or the particle mirror—we
introduce an inevitable uncertainty in the properties to be measured.
This is not an uncertainty introduced through the ‘clumsiness’ of our
measurements, as Heisenberg had argued, but arises because our choice
of apparatus forces the quantum system to reveal one kind of behaviour
rather than another.
This can be extended to a second level of complementarity, between
an essentially causal description of phenomena in terms of momentum
and energy, and a space–time description in terms of position and time.
For as long as we do not interfere with it, an electron in a stationary state
or stable orbit around a nucleus will behave according to causal laws,
with predictable momentum and energy. But a space–time description,
in which we fi x the electron’s position and time, requires some form of
interaction which implies a discontinuity, precludes causality, and leaves
us to deal with quantum probabilities.
According to Bohr, the uncertainty relations place a fundamental limit
not on what is measureable, but on what is in principle knowable.
Bohr was insistent. Heisenberg’s paper contained fundamental errors,
it was premature, and considered only a special case for which a general
rule in terms of complementarity could now be formulated. Heisenberg’s
paper—by now in press—should be withdrawn.
Heisenberg stubbornly refused to yield. As far as he was concerned,
the error in the gamma-ray microscope gedankenexperiment did not under-
mine the basic argument of his uncertainty paper and he saw no reason
to withdraw it. Young Swedish physicist Oskar Klein, recently arrived in
Copenhagen on a visiting fellowship, was drawn into the argument. He
took Bohr’s side and, as can often happen in such super-heated circum-
stances, the argument became bitter and personal.
Their confl ict was ‘very disagreeable’, Heisenberg later admitted.
‘I remember that it ended with my breaking out in tears because I just
couldn’t stand this pressure from Bohr.’ Heisenberg in his turn uttered
the ‘kopenhagener geist’
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regrettable statements, meant only to wound. Bohr sent a plea for help
to Pauli and even offered to pay his travel expenses to Copenhagen. But
Pauli was unavailable.
The debate wore on, relentlessly, through the spring of 1927. Bohr argued
in favour of making the complementarity of waves and particles the cen-
trepiece of uncertainty. Heisenberg saw no value in sticking to classical
concepts with no demonstrable validity in the quantum domain. ‘Well,’
he argued, ‘we have a consistent mathematical scheme and this consistent
mathematical scheme tells us everything which can be observed. Nothing
is in nature which cannot be described by this mathematical scheme.’
Bohr rejected the notion that nature follows a mathematical scheme.
Heisenberg countered:
Well, waves and [particles] are, certainly, a way in which we talk and we do
come to these concepts from classical physics. Classical physics has taught
us to talk about particles and waves, but since classical physics is not true
there [at the quantum level], why should we stick so much to these con-
cepts? Why should we not simply say that we cannot use these concepts
with a very high precision, therefore the uncertainty relations, and there-
fore we have to abandon these concepts to a certain extent. When we get
beyond this range of the classical theory, we must realise that our words
don’t fi t. They don’t really get a hold in the physical reality and therefore
a new mathematical scheme is just as good as anything because the new
mathematical scheme then tells what may be there and what may not be
there. Nature just in some way follows the scheme.
But this wouldn’t do. As far as Bohr was concerned our words have to
fi t, because understanding comes from the words we use in our descrip-
tions, not from mathematical schemes. And our words are all we have.
‘Naturally,’ Heisenberg complained to Pauli in a letter dated 16 May, ‘if
one starts with [wave–particle duality], one can do everything without
fear of contradiction.’ But by now Heisenberg’s resolve had been eroded
by the force of Bohr’s personality and conviction. He was now at least
ready to accept that Bohr was right about the origin of uncertainty in
the gamma-ray microscope experiment. In the same letter, he conceded
to Pauli that: ‘. . . the [position–momentum uncertainty relation] indeed
comes out naturally, but not entirely as I had thought.’
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At Klein’s suggestion, Heisenberg agreed to add a note in the proof of
his soon-to-be published paper on uncertainty:
In this connection Bohr has brought to my attention that I have overlooked
essential points in the course of several discussions in this paper. Above
all, the uncertainty in our observation does not arise exclusively from the
occurrence of discontinuities, but is tied directly to the demand that we
ascribe equal validity to the quite different experiments which show up
in the [particulate] theory on one hand, and in the wave theory on the
other hand.
The note corrected the misinterpretation of the gamma-ray microscope
gedankenexperiment, and acknowledged the debt of gratitude to Bohr:
‘I owe great thanks to Professor Bohr for sharing with me at an early
stage the results of these more recent investigations of his—to appear
soon in a paper on the conceptual structure of quantum theory—and for
discussing them with me.’
Pauli fi nally found time to make the journey to Copenhagen in early
June 1927. Wounds were healed, though the scars they left behind would
be visible to the protagonists for some time to come. With Pauli’s sup-
port, Bohr and Heisenberg achieved something of a rapprochement. This
was not so much a united front, more a rather uneasy alliance between
the very different interpretational views of the three physicists.
The pillars of this common-ground interpretation were the comple-
mentarity of waves and particles, the uncertainty principle, the inter-
pretation of the wavefunction in terms of quantum probabilities, the
correspondence between the eigenvalues of the wave theory and the
measured values of observable quantities, such as momentum and
energy, and the correspondence principle—the transition from quantum
to classical behaviour in the limit of very large quantum numbers.
What was remarkable was the zeal with which the disciples of this new
quantum orthodoxy embraced and spread the new gospel. Heisenberg
spoke and wrote of the ‘Kopenhagener Geist der Quantentheorie’, the
‘Copenhagen spirit’ of quantum theory.
It became known as the Copenhagen interpretation.
103
By June 1927 Heisenberg had received word that he was once again to be called to a
professorship in Leipzig. There followed a number of further job opportunities, in Halle,
Munich, America, and Zurich. He would have greatly preferred Munich but this was
an offer of an associate professorship under his former thesis advisor Sommerfeld,
on the understanding that he would succeed Sommerfeld on the latter’s retirement in
about seven years’ time. The opportunities in Leipzig and Halle were full professorships,
however, and in German universities. As he had already turned down an associate
professorship, protocol demanded that he now accept one of these offers. He agreed to
take the Leipzig chair.
It was Debye, recently arrived in Leipzig from the ETH in Zurich, who had called him
back to Germany. Pauli succeeded Debye at the ETH. Jordan succeeded Pauli in Ham-
burg. Klein took the position vacated by Heisenberg in Copenhagen. Within a matter of
a few months, the disciples of the ‘Kopenhagener Geist’ had risen to tenured positions in
prestigious universities, from where they could preach the Copenhagen doctrine to a new
generation of quantum physicists.
There were still some voices of dissent, however. Schrödinger succeeded Planck at the
University of Berlin. He arrived in Berlin, where he now joined fellow dissenter Einstein,
shortly before his fortieth birthday in August 1927.
Bohr had won the argument with Heisenberg which put complementarity at the
heart of the new interpretation of quantum theory. But his principle had yet to be
articulated outside of the small group of physicists that had been involved in the debate.
12
There is no Quantum World
Lake Como, September 1927
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An opportunity to present his ideas arrived in the form of an invitation to an interna-
tional congress convened to commemorate the centenary of the death of Alessandro Volta,
to be held in September 1927 at the Istituto Carducci on the shore of Lake Como in Italy.
He had begun work on his lecture in April, assisted by Klein. The process was tortu-
ous. Bohr was driven by an insatiable desire for clarity in what was, he believed, to be a
fundamentally important contribution to the philosophy of physics. He would establish
the very basis on which we would attempt to make sense of physical reality at the quantum
level. ‘Bohr dictated and the next day all he had dictated was discarded and we began
anew,’ Klein explained. There were endless drafts.
As the Como meeting approached, Niels’ brother Harald insisted that he get some-
thing properly written down.
It was an illustrious international group of physicists that assembled
that September in the city of Como. Among the group arriving in Como
were Born, de Broglie, Compton, Debye, the Italian physicist Enrico
Fermi, Franck, Heisenberg, Max von Laue, Lorentz, Millikan, Paschen,
Pauli, Planck, Rutherford, Sommerfeld, Stern, and Zeeman. There were
some notable absences, however. Einstein had been invited, but could
not attend. Schrödinger, too, was absent. As was Dirac.
Bohr stood to deliver his lecture on 16 September. The text of this
lecture has not survived, although many earlier drafts have been pre-
served. It was subsequently published in a set of conference proceedings
and reprinted in the British scientifi c journal Nature in 1928. He opened
thus:
. . . I shall try, by making use only of simple considerations and without
going into any details of technical mathematical character, to describe to
you a certain general point of view which I believe is suited to give an
impression of the general trend of the development of the theory from its
very beginning and which I hope will be helpful in order to harmonise the
apparently confl icting views taken by different scientists.
Although the arguments between Bohr and Heisenberg had hinged on
the inclusion of a complementary wave description, in his lecture Bohr
concentrated his attention on the complementarity of the causal and
space–time perspectives. He said:
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On one hand, the defi nition of the state of a physical system, as ordinarily
understood, claims the elimination of all external disturbances. But in that
case, according to the quantum postulate [the essential discontinuity of quan-
tum change], any observation will be impossible, and, above all, the concepts
of space and time lose their immediate sense. On the other hand, if in order to
make observation possible we permit certain interactions with suitable agen-
cies of measurement, not belonging to the system, an unambiguous defi ni-
tion of the state of the system is naturally no longer possible, and there can
be no question of causality in the ordinary sense of the word. The very nature
of quantum theory thus forces us to regard the space–time co-ordination and
the claim of causality, the union of which characterises the classical theories,
as complementary but exclusive features of the description, symbolising the
idealisation of observation and defi nition respectively.
Despite Bohr’s efforts to achieve clarity in the endless redrafts he had
worked on with Klein, his soft-spoken words remained vague and con-
fusing. A highlight was his elegant derivation of the uncertainty relations
from equations of classical wave optics, but the often obscure terminol-
ogy he employed in his long and wordy lecture left his audience broadly
unimpressed.
Hungarian physicist Eugene Wigner remarked to Belgian Léon Rosen-
feld, one of Bohr’s close associates: ‘This lecture will not induce any one
of us to change his own [opinion] about quantum mechanics.’
But the confusion of the moment could not mask the simple fact that
complementarity—however Bohr chose to defi ne it—represented a
marked break with the past.
For the fi rst time in its history, science was confronting what Bohr
believed to be a profound limitation on our ability to acquire scientifi c
knowledge. Classical physics had known no such limitation. The means
by which we determine the magnitudes of physical quantities in our
classical world has no bearing on the nature or the magnitudes of the
quantities themselves. We quite happily assume that a classical object
possesses these properties, with whatever magnitudes, whether we per-
form a measurement or not.
But now Bohr was claiming that it is not meaningful to regard a
quantum wave–particle as having any intrinsic properties independent
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of some measuring device or means of observation. Although we may
speak of the position of an electron, or its velocity, momentum, etc., as
though these are independently existing properties, they are nevertheless
properties that can only become ‘real’ when the electron interacts with
an instrument specifi cally designed to reveal them. These concepts help
us to correlate and describe our observations, but they have no meaning
beyond their use as a means of connecting the object of our study with
the instrument we use to study it.
‘The quantum theory is characterised by the acknowledgement of a
fundamental limitation in the classical physical ideas when applied to
atomic phenomena,’ Bohr said. ‘The situation thus created is of a peculiar
nature, since our interpretation of the experimental material rests essen-
tially upon the classical concepts.’
Summarizing the situation many years later, Heisenberg put it this way:
The Copenhagen interpretation of quantum theory starts from a paradox.
Any experiment in physics, whether it refers to the phenomena of daily
life or to atomic events, is to be described in the terms of classical physics.
The concepts of classical physics form the language by which we describe
the arrangement of our experiments and state the results. We cannot and
should not replace these concepts by any others. Still the application of
these concepts is limited by the relations of uncertainty. We must keep
in mind this limited range of applicability of the classical concepts while
using them, but we cannot and should not try to improve them.
The mathematical formalism of quantum theory then becomes an
attempt to repackage complementary wave and particle descriptions in
a single structure. This, Bohr insisted, does not imply that the theory is
wrong or somehow incomplete.
It is, perhaps, diffi cult to resist the temptation to conjure up a mental
picture of an individual electron existing in some kind of predetermined
state independently of our measurements. But according to the Copen-
hagen interpretation, such a mental picture would be at best unhelpful
and at worst positively misleading.
Those with some understanding of contemporary philosophy could
detect a strong empiricist or even positivist fl avour in the Copenhagen
interpretation.
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The empiricist tradition can be traced loosely from Scottish philoso-
pher David Hume, through French philosopher Auguste Comte to the
physicist Ernst Mach. Mach was professor of physics at the Universities
of Prague and Vienna from 1867 to 1901. He argued that scientifi c activity
involves the study of facts about nature revealed to us through our sen-
sory perceptions and the attempt to understand their interrelationship
through observation and experiment. According to Mach, this attempt
should be made in the most economical way possible.
Mach rejected as non-scientifi c any statements that could be made
about the world that cannot be verifi ed by experiment or observation.
He argued that there is no purpose to be served by seeking to describe a
reality beyond our immediate senses. Instead, our judgement should be
guided by the criteria of verifi ability (does the theory agree with experi-
ment or observation?) and simplicity (is it the simplest theory that will
agree with experiment or observation?).
In constructing a physical theory we should seek the most economi-
cal way of organizing facts and making connections between them. We
should not attach a deeper signifi cance to the concepts used in a theory
or the conceptual entities they describe if these are not in themselves
observable. According to Mach, only those elements that we can perceive
actually exist, and there is no point in searching for a physical reality
that we cannot perceive: we can only know what we experience. Seeing
is believing.
Mach’s criterion of what constituted a verifi able statement was par-
ticularly stringent. It led him to reject the concepts of absolute space and
absolute time, and to side with Ludwig Boltzmann’s opponents in reject-
ing the reality of atoms and molecules.
Speculations that are intrinsically not verifi able, that involve some kind
of appeal to the emotions or to faith, are not scientifi c. However, these
speculations, which belong in a branch of philosophy called metaphysics
(literally, ‘beyond physics’), are not rejected outright. They are recognized
as a legitimate part of the process of developing an attitude towards life,
but they are perceived to have no place in science. This emphasis on veri-
fi ability and an unmerciful attitude to the elimination of metaphysics is a
philosophical position generally known as positivism, a name fi rst coined
by Comte.
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Mach’s views were enormously infl uential in the development of a
new school of philosophical thought that emerged in Vienna in the early
1920s. Centred around Moritz Schlick, professor of philosophy at the Uni-
versity of Vienna, German-born philosopher Rudolf Carnap, Austrian
philosopher Otto Neurath, and others, the ‘Vienna Circle’ extended the
positivist outlook through the use of formal logical analysis. They drew
their inspiration from a wide variety of sources, particularly the work of
the physicists Mach,
1
Boltzmann, and Einstein. Philosophically, their par-
ticular brand of positivism was foreshadowed in the work of Hume and
Comte, and they were greatly infl uenced by the analytical approaches of
their contemporaries Bertrand Russell in Cambridge and Ludwig Witt-
genstein (a former student of Russell’s) in Vienna.
The Vienna Circle began with the contention that the only true
knowledge is scientifi c knowledge and that, in order to be meaningful,
a scientifi c statement has to be both formally logical and verifi able. The
foundations of their philosophy, which is sometimes known as logical
positivism, was logical analysis, the criterion of verifi ability and a strict
demarcation between science and metaphysics.
Most importantly, the use of logical analysis leads to the elimination
of all metaphysical statements as meaningless. With one stroke, the
logical positivists eliminated from philosophy centuries of ‘pseudo-
statements’ about mind, being, reality, and God. The views of the Vienna
Circle came to dominate the philosophy of science in the middle of the
twentieth century.
The implications for the development of physical theories are clear.
Theories are merely instruments for making connections between obser-
vations or the results of experiments in the most economical way pos-
sible. If they describe the behaviour of entities that we cannot directly
perceive, then the entities themselves are merely convenient theoretical
devices and should not be misinterpreted as elements of an independent
reality.
This does not necessarily mean that there is no such thing as reality.
Scientifi c theories describe elements of an empirical reality—the reality
manifested as effects that we can directly perceive and hence verify—but
1
They called themselves the ‘Ernst Mach Society’.
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don’t expect to be able to go beyond this empirical level. To do so is to
engage in meaningless speculation.
Of the physicists of the Copenhagen school, Heisenberg was the positiv-
ist. It had been Heisenberg who in his paper on matrix mechanics had
insisted on a new language, insisted on a rejection of classical concepts
and their replacement with a consistent mathematical scheme. Many
years later he wrote:
Our actual situation in research work in atomic physics is usually this: we
wish to understand a certain phenomenon, we wish to recognise how this
phenomenon follows from the general laws of nature. Therefore, that part of
matter or radiation which takes part in the phenomenon is the natural ‘object’
in the theoretical treatment and should be separated in this respect from the
tools used to study the phenomenon. This again emphasises a subjective ele-
ment in the description of atomic events, since the measuring device has been
constructed by the observer, and we have to remember that what we observe
is not nature in itself but nature exposed to our method of questioning.
Although they were not particularly concerned to devote much time to
the elaboration of their philosophy, the physicists of the Copenhagen
school were nevertheless aware that their interpretation created consid-
erable problems for the understanding of what constitutes knowledge at
the quantum level and the methods of its acquisition. Heisenberg in par-
ticular made it his business to raise awareness of these issues in his many
public addresses on the subject.
2
The Copenhagen interpretation essentially states that in quantum the-
ory we have reached the limit of what we can know. To try to go beyond
this limit is pointless: how can we ever hope to know something that is
unknowable? The argument is that any attempt to introduce a new con-
cept to describe an underlying independent reality inevitably involves a
reworking of familiar classical concepts and a descent into metaphysics.
2
Eventually, the philosophers began to take note and, in correspondence spanning the years
1930–32, Schlick of the Vienna school sought advice and direction from Heisenberg on quantum
theory’s implications for causality and the philosophy of knowledge. Clearly, the positivists
of the Vienna Circle found much resonance with what the Copenhagen physicists were now
saying.