Discussions with Einstein on Epistemological Problems in Atomic Physics

Discussions with Einstein on Epistemological Problems in Atomic Physics
Niels Bohr (1949)
Discussions with Einstein
on Epistemological Problems in Atomic Physics
Source
: From
Albert Einstein: Philosopher-Scientist
(1949), publ. Cambridge University Press, 1949. Neils Bohr's report of conversations with Einstein and Einstein's reply.
WHEN invited by the Editor of the series,
Living Philosophers
to write an article for this volume in which contemporary scientists are
honouring the epoch-making contributions of Albert Einstein to the progress
of natural philosophy and are acknowledging the indebtedness of our whole
generation for the guidance his genius has given us, I thought much of
the best way of explaining how much I owe to him for inspiration. In this
connection, the many occasions through the years on which I had the privilege
to discuss with Einstein epistemological problems raised by the modern
development of atomic physics have come back vividly to my mind and I have
felt that I could hardly attempt anything better than to give an account
of these discussions which, even if no complete concord has so far been
obtained, have been of greatest value and stimulus to me. I hope also that the account may convey to wider circles an impression of how essential the open-minded exchange of ideas has been for the progress in a field where new experience has time after time demanded a reconsideration of our views.
From the very beginning the main point under debate has been the attitude to take to the departure from customary principles of natural philosophy characteristic of the novel development of physics which was initiated in the first year of this century by Planck's discovery of the universal quantum of action. This discovery, which revealed a feature of atomicity in the laws of nature going far beyond the old doctrine of the limited divisibility of matter, has indeed taught us that the classical theories of physics are idealisations which can be unambiguously applied only in the limit where all actions involved are large compared with the quantum. The question at issue has been whether the renunciation of a causal mode of description of atomic processes involved in the endeavours to cope with the situation should be regarded as a temporary departure from ideals to be ultimately revived or whether we are faced with an irrevocable step towards obtaining the proper harmony between analysis and synthesis of physical phenomena. To describe the background of our discussions and to bring out as clearly as possible the arguments for the contrasting viewpoints, I have felt it necessary to go to a certain length in recalling some main features of the development to which Einstein himself has contributed so decisively.
As is well known, it was the intimate relation, elucidated primarily
by Boltzmann, between the laws of thermodynamics and the statistical regularities
exhibited by mechanical systems with many degrees of freedom, which guided
Planck in his ingenious treatment of the problem of thermal radiation,
leading him to his fundamental discovery. While, in his work, Planck was
principally concerned with considerations of essentially statistical character
and with great caution refrained from definite conclusions as to the extent
to which the existence of the quantum implied a departure from the foundations
of mechanics and electrodynamics, Einstein's great original contribution
to quantum theory (1905) was just the recognition of how physical phenomena
like the photo-effect may depend directly on individual quantum effects.
In these very same years when, in developing his theory of relativity,
Einstein laid a new foundation for physical science, he explored with a
most daring spirit the novel features of atomicity which pointed beyond
the whole framework of classical physics.
With unfailing intuition Einstein thus was led step by step to the conclusion
that any radiation process involves the emission or absorption of individual
light quanta or "photons" with energy and momentum
hf
and
hs
(1)
respectively, where
is Planck's constant, while
and
are the number of vibrations per unit time and the number of waves
per unit length, respectively. Notwithstanding its fertility, the idea
of the photon implied a quite unforeseen dilemma, since any simple corpuscular
picture of radiation would obviously be irreconcilable with interference
effects, which present so essential an aspect of radiative phenomena, and
which can be described only in terms of a wave picture. The acuteness of
the dilemma is stressed by the fact that the interference effects offer
our only means of defining the concepts of frequency and wavelength entering
into the very expressions for the energy and momentum of the photon.
In this situation, there could be no question of attempting a causal
analysis of radiative phenomena, but only, by a combined use of the contrasting
pictures, to estimate probabilities for the occurrence of the individual
radiation processes. However, it is most important to realize that the
recourse to probability laws under such circumstances is essentially different
in aim from the familiar application of statistical considerations as practical
means of accounting for the properties of mechanical systems of great structural
complexity. In fact, in quantum physics we are presented not with intricacies
of this kind, but with the inability of the classical frame of concepts
to comprise the peculiar feature of indivisibility, or "individuality,"
characterising the elementary processes.
The failure of the theories of classical physics in accounting for atomic
phenomena was further accentuated by the progress of our knowledge of the
structure of atoms. Above all, Rutherford's discovery of the atomic nucleus
(1911) revealed at once the inadequacy of classical mechanical and electromagnetic
concepts to explain the inherent stability of the atom. Here again the
quantum theory offered a clue for the elucidation of the situation and
especially it was found possible to account for the atomic stability, as
well as for the empirical laws governing the spectra of the elements, by
assuming that any reaction of the atom resulting in a change of its energy
involved a complete transition between two so-called stationary quantum
states and that, in particular, the spectra were emitted by a step-like
process in which each transition is accompanied by the emission of a monochromatic
light quantum of an energy just equal to that of an Einstein photon.
These ideas, which were soon confirmed by the experiments of Franck
and Hertz (1914) on the excitation of spectra by impact of electrons on
atoms, involved a further renunciation of the causal mode of description,
since evidently the interpretation of the spectral laws implies that an
atom in an excited state in general will have the possibility of transitions
with photon emission to one or another of its lower energy states. In fact,
the very idea of stationary states is incompatible with any directive for
the choice between such transitions and leaves room only for the notion
of the relative probabilities of the individual transition processes. The
only guide in estimating such probabilities was the so-called correspondence
principle which originated in the search for the closest possible connection
between the statistical account of atomic processes and the consequences
to be expected from classical theory, which should be valid in the limit
where the actions involved in all stages of the analysis of the phenomena
are large compared with the universal quantum.
At that time, no general self-consistent quantum theory was yet in sight,
but the prevailing attitude may perhaps be illustrated by the following
passage from a lecture by the writer from 1913:
I hope that I have expressed myself sufficiently clearly so that you
may appreciate the extent to which these considerations conflict with the
admirably consistent scheme of conceptions which has been rightly termed
the classical theory of electrodynamics. On the other hand, I have tried
to convey to you the impression that just by emphasising so strongly this
conflict it may also be possible in course of time to establish a certain
coherence in the new ideas.
Important progress in the development of quantum theory was made by
Einstein himself in his famous article on radiative equilibrium in 1917,
where he showed that Planck's law for thermal radiation could be simply
deduced from assumptions conforming with the basic ideas of the quantum
theory of atomic constitution. To this purpose, Einstein formulated general
statistical rules regarding the occurrence of radiative transitions between
stationary states, assuming not only that, when the atom is exposed to
a radiation field, absorption as well as emission processes will occur
with a probability per unit time proportional to the intensity of the irradiation,
but that even in the absence of external disturbances spontaneous emission
processes will take place with a rate corresponding to a certain
a priori
probability. Regarding the latter point, Einstein emphasised the fundamental
character of the statistical description in a most suggestive way by drawing
attention to the analogy between the assumptions regarding the occurrence
of the spontaneous radiative transitions and the well-known laws governing
transformations of radioactive substances.
In connection with a thorough examination of the exigencies of thermodynamics
as regards radiation problems, Einstein stressed the dilemma still further
by pointing out that the argumentation implied that any radiation process
was "unidirected" in the sense that not only is a momentum corresponding
to a photon with the direction of propagation transferred to an atom in
the absorption process, but that also the emitting atom will receive an
equivalent impulse in the opposite direction, although there can on the
wave picture be no question of a preference for a single direction in an
emission process. Einstein's own attitude to such startling conclusions
is expressed in a passage at the end of the article, which may be translated
as follows:
These features of the elementary processes would seem to make the development
of a proper quantum treatment of radiation almost unavoidable. The weakness
of the theory lies in the fact that, on the one hand, no closer connection
with the wave concepts is obtainable and that, on the other hand, it leaves
to chance (
Zufall
) the time and the direction of the elementary
processes; nevertheless, I have full confidence in the reliability of the
way entered upon.
When I had the great experience of meeting Einstein for the first time
during a visit to Berlin in 1920, these fundamental questions formed the
theme of our conversations. The discussions, to which I have often reverted
in my thoughts, added to all my admiration for Einstein a deep impression
of his detached attitude. Certainly, his favoured use of such picturesque
phrases as "ghost waves (
Gespensterfelder
) guiding the photons"
implied no tendency to mysticism, but illuminated rather a profound humour
behind his piercing remarks. Yet, a certain difference in attitude and
outlook remained, since, with his mastery for co-ordinating apparently
contrasting experience without abandoning continuity and causality, Einstein
was perhaps more reluctant to renounce such ideals than someone for whom
renunciation in this respect appeared to be the only way open to proceed
with the immediate task of co-ordinating the multifarious evidence regarding
atomic phenomena, which accumulated from day to day in the exploration
of this new field of knowledge.
In the following years, during which the atomic problems attracted the
attention of rapidly increasing circles of physicists, the apparent contradictions
inherent in quantum theory were felt ever more acutely. Illustrative of
this situation is the discussion raised by the discovery of the Stern-Gerlach
effect in 1922. On the one hand, this effect gave striking support to the
idea of stationary states and in particular to the quantum theory of the
Zeeman effect developed by Sommerfeld, on the other hand, as exposed so
clearly by Einstein and Ehrenfest, it presented with unsurmountable difficulties
any attempt at forming a picture of the behaviour of atoms in a magnetic
field. Similar paradoxes were raised by the discovery by Compton (1924)
of the change in wave-length accompanying the scattering of X-rays by electrons.
This phenomenon afforded, as is well known, a most direct proof of the
adequacy of Einstein's view regarding the transfer of energy and momentum
in radiative processes; at the same time, it was equally clear that no
simple picture of a corpuscular collision could offer an exhaustive description
of the phenomenon. Under the impact of such difficulties, doubts were for
a time entertained even regarding the conservation of energy and momentum
in the individual radiation processes; a view, however, which very soon
had to be abandoned in face of more refined experiments bringing out the
correlation between the deflection of the photon and the corresponding
electron recoil.
The way to the clarification of the situation was, indeed, first to
be paved by the development of a more comprehensive quantum theory. A first
step towards this goal was the recognition by de Broglie in 1925 that the
wave-corpuscle duality was not confined to the properties of radiation,
but was equally unavoidable in accounting for the behaviour of material
particles. This idea, which was soon convincingly confirmed by experiments
on electron interference phenomena, was at once greeted by Einstein, who
had already envisaged the deep-going analogy between the properties of
thermal radiation and of gases in the so-called degenerate state. The new
line was pursued with the greatest success by Schrödinger (1926) who,
in particular, showed how the stationary states of atomic systems could
be represented by the proper solutions of a wave-equation to the establishment
of which he was led by the formal analogy, originally traced by Hamilton,
between mechanical and optical problems. Still, the paradoxical aspects
of quantum theory were in no way ameliorated, but even emphasised, by the
apparent contradiction between the exigencies of the general superposition
principle of the wave description and the feature of individuality of the
elementary atomic processes.
At the same time, Heisenberg (1925) had laid the foundation of a rational
quantum mechanics, which was rapidly developed through important contributions
by Born and Jordan as well as by Dirac. In this theory, a formalism is
introduced, in which the kinematical and dynamical variables of classical
mechanics are replaced by symbols subjected to a non-commutative algebra.
Notwithstanding the renunciation of orbital pictures, Hamilton's canonical
equations of mechanics are kept unaltered and Planck's constant enters
only in the rules of commutation h
qp
pq
= -(
/2
) ,
(2)
holding for any set of conjugate variables
and
. Through
a representation of the symbols by matrices with elements referring to
transitions between stationary states, a quantitative formulation of the
correspondence principle became for the first time possible. It may here
be recalled that an important preliminary step towards this goal was reached
through the establishment, especially by contributions of Kramers, of a
quantum theory of dispersion making basic use of Einstein's general rules
for the probability of the occurrence of absorption and emission processes.
This formalism of quantum mechanics was soon proved by Schrödinger
to give results identical with those obtainable by the mathematically often
more convenient methods of wave theory, and in the following years general
methods were gradually established for an essentially statistical description
of atomic processes combining the features of individuality and the requirements
of the superposition principle, equally characteristic of quantum theory.
Among the many advances in this period, it may especially be mentioned
that the formalism proved capable of incorporating the exclusion principle
which governs the states of systems with several electrons, and which already
before the advent of quantum mechanics had been derived by Pauli from an
analysis of atomic spectra. The quantitative comprehension of a vast amount
of empirical evidence could leave no doubt as to the fertility and adequacy
of the quantum-mechanical formalism, but its abstract character gave rise
to a widespread feeling of uneasiness. An elucidation of the situation
should, indeed, demand a thorough examination of the very observational
problem in atomic physics.
This phase of the development was, as is well known, initiated in 1927
by Heisenberg, who pointed out that the knowledge obtainable of the state
of an atomic system will always involve a peculiar "indeterminacy."
Thus, any measurement of the position of an electron by means of some device,
like a microscope, making use of high frequency radiation, will, according
to the fundamental relations (1), be connected with a momentum exchange
between the electron and the measuring agency, which is the greater the
more accurate a position measurement is attempted. In comparing such considerations
with the exigencies of the quantum-mechanical formalism, Heisenberg called
attention to the fact that the commutation rule (2) imposes a reciprocal
limitation on the fixation of two conjugate variables,
and
expressed by the relation
approx=
(3)
where
and
are suitably defined latitudes in the determination of these variables.
In pointing to the intimate connection between the statistical
description in quantum mechanics and the actual possibilities of measurement,
this so-called indeterminacy relation is, as Heisenberg showed, most important
for the elucidation of the paradoxes involved in the attempts of analysing
quantum effects with reference to customary physical pictures.
The new progress in atomic physics was commented upon from various sides
at the International Physical Congress held in September 1927, at Como
in commemoration of Volta. In a lecture on that occasion, I advocated a
point of view conveniently termed "complementarity," suited to
embrace the characteristic features of individuality of quantum phenomena,
and at the same time to clarify the peculiar aspects of the observational
problem in this field of experience. For this purpose, it is decisive to
recognise that,
however far the phenomena transcend the scope of classical
physical explanation, the account of all evidence must be expressed in
classical terms
. The argument is simply that by the word "experiment"
we refer to a situation where we can tell others what we have done and
what we have learned and that, therefore, the account of the experimental
arrangement and of the results of the observations must be expressed in
unambiguous language with suitable application of the terminology of classical
physics.
This crucial point, which was to become a main theme of the discussions
reported in the following, implies the impossibility of any sharp separation
between the behaviour of atomic objects and the interaction with the measuring
instruments which serve to define the conditions under which the phenomena
appear. In fact, the individuality of the typical quantum effects finds
its proper expression in the circumstance that any attempt of subdividing
the phenomena will demand a change in the experimental arrangement introducing
new possibilities of interaction between objects and measuring instruments
which in principle cannot be controlled. Consequently, evidence obtained
under different experimental conditions cannot be comprehended within a
single picture, but must be regarded as complementary in the sense that
only the totality of the phenomena exhausts the possible information about
the objects.
Under these circumstances an essential element of ambiguity isinvolved
in ascribing conventional physical attributes to atomic objects, as is
at once evident in the dilemma regarding the corpuscular and wave properties
of electrons and photons, where we have to do with contrasting pictures,
each referring to an essential aspect of empirical evidence. An illustrative
example, of how the apparent paradoxes are removed by an examination of
the experimental conditions under which the complementary phenomena appear,
is also given by the Compton effect, the consistent description of which
at first had presented us with such acute difficulties. Thus, any arrangement
suited to study the exchange of energy and momentum between the electron
and the photon must involve a latitude in the space-time description of
the interaction sufficient for the definition of wave-number and frequency
which enter into the relation (1). Conversely, any attempt of locating
the collision between the photon and the electron more accurately would,
on account of the unavoidable interaction with the fixed scales and clocks
defining the space-time reference frame, exclude all closer account as
regards the balance of momentum and energy.
As stressed in the lecture, an adequate tool for a complementary way
of description is offered precisely by the quantum-mechanical formalism
which represents a purely symbolic scheme permitting only predictions,
on lines of the correspondence principle, as to results obtainable under
conditions specified by means of classical concepts. It must here be remembered
that even in the indeterminacy relation (3) we are dealing with an implication
of the formalism which defies unambiguous expression in words suited to
describe classical physical pictures. Thus, a sentence like "we cannot
know both the momentum and the position of an atomic object" raises
at once questions as to the physical reality of two such attributes of
the object, which can be answered only by referring to the conditions for
the unambiguous use of space-time concepts, on the one hand, and dynamical
conservation laws, on the other hand. While the combination of these concepts
into a single picture of a causal chain of events is the essence of classical
mechanics, room for regularities beyond the grasp of such a description
is just afforded by the circumstance that the study of the complementary
phenomena demands mutually exclusive experimental arrangements.
The necessity, in atomic physics, of a renewed examination of the foundation
for the unambiguous use of elementary physical ideas recalls in some way
the situation that led Einstein to his original revision on the basis of
all application of space-time concepts which, by its emphasis on the primordial
importance of the observational problem, has lent such unity to our world
picture. Notwithstanding all novelty of approach, causal description is
upheld in relativity theory within any given frame of reference, but in
quantum theory the uncontrollable interaction between the objects and the
measuring instruments forces us to a renunciation even in such respect.
This recognition, however, in no way points to any limitation of the scope
of the quantum-mechanical description, and the trend of the whole argumentation
presented in the Como lecture was to show that the viewpoint of complementarity
may be regarded as a rational generalisation of the very ideal of causality.
At the general discussion in Como, we all missed the presence of Einstein,
but soon after, in October 1927, I had the opportunity to meet him in Brussels
at the Fifth Physical Conference of the Solvay Institute, which was devoted
to the theme "Electrons and Photons." At the Solvay meetings,
Einstein had from their beginning been a most prominent figure, and several
of us came to the conference with great anticipations to learn his reaction
to the latest stage of the development which, to our view, went far in
clarifying the problems which he had himself from the outset elicited so
ingeniously. During the discussions, where the whole subject was reviewed
by contributions from many sides and where also the arguments mentioned
in the preceding pages were again presented, Einstein expressed, however,
a deep concern over the extent to which causal account in space and time
was abandoned in quantum mechanics.
To illustrate his attitude, Einstein referred at one of the sessions
to the simple example, illustrated by Fig. 1, of a particle (electron or
photon) penetrating through a hole or a narrow slit in a diaphragm placed
at some distance before a photographic plate.
On account of the diffraction of the wave connected with the motion
of the particle and indicated in the figure by the thin lines, it is under
such conditions not possible to predict with certainty at what point the
electron will arrive at the photographic plate, but only to calculate the
probability that, in an experiment, the electron will be found within any
given region of the plate. The apparent difficulty, in this description,
which Einstein felt so acutely, is the fact that, if in the experiment
the electron is recorded at one point A of the plate, then it is out of
the question of ever observing an effect of this electron at another point
(B), although the laws of ordinary wave propagation offer no room for a
correlation between two such events.
Einstein's attitude gave rise to ardent discussions within a small circle,
in which Ehrenfest, who through the years had been a close friend of us
both, took part in a most active and helpful way. Surely, we all recognised
that, in the above example, the situation presents no analogue to the application
of statistics in dealing with complicated mechanical systems, but rather
recalled the background for Einstein's own early conclusions about the
unidirection of individual radiation effects which contrasts so strongly
with a simple wave picture. The discussions, however, centred on the question
of whether the quantum-mechanical description exhausted the possibilities
of accounting for observable phenomena or, as Einstein maintained, the
analysis could be carried further and, especially, of whether a fuller
description of the phenomena could be obtained by bringing into consideration
the detailed balance of energy and momentum in individual processes.
To explain the trend of Einstein's arguments, it may be illustrative
here to consider some simple features of the momentum and energy balance
in connection with the location of a particle in space and time. For this
purpose, we shall examine the simple case of a particle penetrating through
a hole in a diaphragm without or with a shutter to open and close the hole,
as indicated in Figs. 2a and 2b, respectively. The equidistant parallel
lines to the left in the figures indicate the train of plane waves corresponding
to the state of motion of a particle which, before reaching the diaphragm,
has a momentum P related to the wave-number
by the second of equations
(1). In accordance with the diffraction of the waves when passing through
the hole, the state of motion of the particle to the right of the diaphragm
is represented by a spherical wave train with a suitably defined angular
aperture
and, in case of Fig. 2b, also with a limited radial extension.
Consequently, the description of this state involves a certain latitude
in the momentum component of the particle parallel to the diaphragm
and, in the case of a diaphragm with a shutter, an additional latitude
of the kinetic energy.
Since a measure for the latitude
in location of the particle
in the plane of the diaphragm is given by the radius
of the hole,
and since
approx= (1/
sa
), we get, using (1), just
approx=
uP
approx= (
), in accordance with the
indeterminacy relation (3). This result could, of course, also be obtained
directly by noticing that, due to the limited extension of the wave-field
at the place of the slit, the component of the wave-number parallel to
the plane of the diaphragm will involve a latitude
approx= (1/
) approx= (1/
).
Similarly, the spread of the frequencies of the harmonic components
in the limited wave-train in Fig. 2b is evidently
approx= (1/
),
where
is the time interval during which the shutter leaves the
hole open and, thus, represents the latitude in time of the passage of
the particle through the diaphragm. From (1), we therefore get
approx=
(4)
again in accordance with the relation (3) for the two conjugated variables
and
From the point of view of the laws of conservation, the origin of such
latitudes entering into the description of the state of the particle after
passing through the hole may be traced to the possibilities of momentum
and energy exchange with the diaphragm or the shutter. In the reference
system considered in Figs. 2a and 2b, the velocity of the diaphragm may
be disregarded and only a change of momentum
between the particle
and the diaphragm needs to be taken into consideration. The shutter, however,
which leaves the hole opened during the time t, moves with a considerable
velocity
approx= (
), and a momentum transfer
involves therefore an energy exchange with the particle, amounting
to
approx= (1/
) .
approx=
), being just of the same order of magnitude as the
latitude
given by (4) and, thus, allowing for momentum and energy
balance.
The problem raised by Einstein was now to what extent a control of the
momentum and energy transfer, involved in a location of the particle in
space and time, can be used for a further specification of the state of
the particle after passing through the hole. Here, it must be taken into
consideration that the position and the motion of the diaphragm and the
shutter have so far been assumed to be accurately co-ordinated with the
space-time reference frame. This assumption implies, in the description
of the state of these bodies, an essential latitude as to their momentum
and energy which need not, of course, noticeably affect the velocities,
if the diaphragm and the shutter are sufficiently heavy. However, as soon
as we want to know the momentum and energy of these parts of the measuring
arrangement with an accuracy sufficient to control the momentum and energy
exchange with the particle under investigation, we shall, in accordance
with the general indeterminacy relations, lose the possibility of their
accurate location in space and time. We have, therefore, to examine how
far this circumstance will affect the intended use of the whole arrangement
and, as we shall see, this crucial point clearly brings out the complementary
character of the phenomena.
Returning for a moment to the case of the simple arrangement indicated
in Fig. 1, it has so far not been specified to what use it is intended.
In fact, it is only on the assumption that the diaphragm and the plate
have well-defined positions in space that it is impossible, within the
frame of the quantum-mechanical formalism, to make more detailed predictions
as to the point
of the photographic plate where the particle will be recorded. If, however,
we admit a sufficiently large latitude in the knowledge of the position
of the diaphragm it should, in principle, be possible to control the momentum
transfer to the diaphragm and, thus, to make more detailed predictions
as to the direction of the electron path from the hole to the recording
point. As regards the quantum-mechanical description, we have to deal here
with a two-body system consisting of the diaphragm as well as of the particle,
and it is just with an explicit application of conservation laws to such
a system that we are concerned in the Compton effect where, for instance,
the observation of the recoil of the electron by means of a cloud chamber
allows us to predict in what direction the scattered photon will eventually
be observed.
The importance of considerations of this kind was, in the course of
the discussions, most interestingly illuminated by the examination of an
arrangement where between the diaphragm with the slit and the photographic
plate is inserted another diaphragm with two parallel slits, as is shown
in Fig. 3. If a parallel beam of electrons (or photons) falls from the
left on the first diaphragm, we shall, under usual conditions, observe
on the plate an interference pattern indicated by the shading of the photographic
plate shown in front view to the right of the figure. With intense beams,
this pattern is built up by the accumulation of a large number of individual
processes, each giving rise to a small spot on the photographic plate,
and the distribution of these spots follows a simple law derivable from
the wave analysis. The same distribution should also be found in the statistical
account of many experiments performed with beams so faint that in a single
exposure only one electron (or photon) will arrive at the photographic
plate at some spot shown in the figure as a small star. Since, now, as
indicated by the broken arrows, the momentum transferred to the first diaphragm
ought to be different if the electron was assumed to pass through the upper
or the lower slit in the second diaphragm, Einstein suggested that a control
of the momentum transfer would permit a closer analysis of the phenomenon
and, in particular, to decide through which of the two slits the electron
had passed before arriving at the plate.
A closer examination showed, however, that the suggested control of
the momentum transfer would involve a latitude in the knowledge of the
position of the diaphragm which would exclude the appearance of the interference
phenomena in question. In fact, if
is the small angle between
the conjectured paths of a particle passing through the upper or the lower
slit, the difference of momentum transfer in these two cases will, according
to (1), be equal to
hsw
and any control of the momentum of the diaphragm
with an accuracy sufficient to measure this difference will, due to the
indeterminacy relation, involve a minimum latitude of the position of the
diaphragm, comparable with 1/
sw
. If, as in the figure, the diaphragm
with the two slits is placed in the middle between the first diaphragm
and the photographic plate, it will be seen that the number of fringes
per unit length will be just equal to
hsw
and, since an uncertainty
in the position of the first diaphragm of the amount of 1/
sw
will
cause an equal uncertainty in the positions of the fringes, it follows
that no interference effect can appear. The same result is easily shown
to hold for any other placing of the second diaphragm between the first
diaphragm and the plate, and would also be obtained if, instead of the
first diaphragm, another of these three bodies were used for the control,
for the purpose suggested, of the momentum transfer.
This point is of great logical consequence, since it is only the circumstance
that we are presented with a choice of
either
tracing the path of
a particle or observing interference effects, which allows us to escape
from the paradoxical necessity of concluding that the behaviour of an electron
or a photon should depend on the presence of a slit in the diaphragm through
which it could be proved not to pass. We have here to do with a typical
example of how the complementary phenomena appear under mutually exclusive
experimental arrangements and are just faced with the impossibility, in
the analysis of quantum effects, of drawing any sharp separation between
an independent behaviour of atomic objects and their interaction with the
measuring instruments which serve to define the conditions under which
the phenomena occur.
Our talks about the attitude to be taken in face of a novel situation
as regards analysis and synthesis of experience touched naturally on many
aspects of philosophical thinking, but, in spite of all divergencies of
approach and opinion, a most humorous spirit animated the discussions.
On his side, Einstein mockingly asked us whether we could really believe
that the providential authorities took recourse to dice-playing (".
. .
ob der liebe Gott würfelt
"), to which I replied by
pointing at the great caution, already called for by ancient thinkers,
in ascribing attributes to Providence in every-day language. I remember
also how at the peak of the discussion Ehrenfest, in his affectionate manner
of teasing his friends, jokingly hinted at the apparent similarity between
Einstein's attitude and that of the opponents of relativity theory; but
instantly Ehrenfest added that he would not be able to find relief in his
own mind before concord with Einstein was reached.
Einstein's concern and criticism provided a most valuable incentive
for us all to re-examine the various aspects of the situation as regards
the description of atomic phenomena. To me it was a welcome stimulus to
clarify still further the role played by the measuring instruments and,
in order to bring into strong relief the mutually exclusive character of
the experimental conditions under which the complementary phenomena appear,
I tried in those days to sketch various apparatus in a pseudo-realistic
style of which the following figures are examples. Thus, for the study
of an interference phenomenon of the type indicated in Fig. 3, it suggests
itself to use an experimental arrangement like that shown in Fig. 4, where
the solid parts of the apparatus, serving as diaphragms and plateholder,
are firmly bolted to a common support.
In such an arrangement, where the knowledge of the relative positions
of the diaphragms and the photographic plate is secured by a rigid connection,
it is obviously impossible to control the momentum exchanged between the
particle and the separate parts of the apparatus. The only way in which,
in such an arrangement, we could insure that the particle passed through
one of the slits in the second diaphragm is to cover the other slit by
a lid, as indicated in the figure; but if the slit is covered, there is
of course no question of any interference phenomenon, and on the plate
we shall simply observe a continuous distribution as in the case of the
single fixed diaphragm in Fig. 1.
In the study of phenomena in the account of which we are dealing with
detailed momentum balance, certain parts of the whole device must naturally
be given the freedom to move independently of others. Such an apparatus
is sketched in Fig. 5, where a diaphragm with a slit is suspended by weak
springs from a solid yoke bolted to the support on which also other immobile
parts of the arrangement are to be fastened. The scale on the diaphragm
together with the pointer on the bearings of the yoke refer to such study
of the motion of the diaphragm, as may be required for an estimate of the
momentum transferred to it, permitting one to draw conclusions as to the
deflection suffered by the particle in passing through the slit. Since,
however, any reading of the scale, in whatever way performed, will involve
an uncontrollable change in the momentum of the diaphragm, there will always
be, in conformity with the indeterminacy principle, a reciprocal relationship
between our knowledge of the position of the slit and the accuracy of the
momentum control.
In the same semi-serious style, Fig. 6 represents a part of an arrangement
suited for the study of phenomena which, in contrast to those just discussed,
involve time coordination explicitly. It consists of a shutter rigidly
connected with a robust clock resting on the support which carries a diaphragm
and on which further parts of similar character, regulated by the same
clock-work or by other clocks standardised relatively to it, are also to
be fixed. The special aim of the figure is to underline that a clock is
a piece of machinery, the working of which can completely be accounted
for by ordinary mechanics and will be affected neither by reading of the
position of its hands nor by the interaction between its accessories and
an atomic particle. In securing the opening of the hole at a definite moment,
an apparatus of this type might, for instance, be used for an accurate
measurement of the time an electron or a photon takes to come from the
diaphragm to some other place, but evidently, it would leave no possibility
of controlling the energy transfer to the shutter with the aim of drawing
conclusions as to the energy of the particle which has passed through the
diaphragm.
If we are interested in such conclusions we must, of course, use an
arrangement where the shutter devices can no longer serve as accurate clocks,
but where the knowledge of the moment when the hole in the diaphragm is
open involves a latitude connected with the accuracy of the energy measurement
by the general relation (4).
The contemplation of such more or less practical arrangements and their
more or less fictitious use proved most instructive in directing attention
to essential features of the problems. The main point here is the distinction
between the
objects
under investigation and the
measuring instruments
which serve to define, in classical terms the conditions under which the
phenomena appear. Incidentally, we may remark that, for the illustration
of the preceding considerations, it is not relevant that experiments involving
an accurate control of the momentum or energy transfer from atomic particles
to heavy bodies like diaphragms and shutters would be very difficult to
perform, if practicable at all. It is only decisive that, in contrast to
the proper measuring instruments, these bodies together with the particles
would in such a case constitute the system to which the quantum-mechanical
formalism has to be applied. As regards the specification of the conditions
for any well-defined application of the formalism, it is moreover essential
that the
whole experimental arrangement
be taken into account. In
fact, the introduction of any further piece of apparatus, like a mirror,
in the way of a particle might imply new interference effects essentially
influencing the predictions as regards the results to be eventually recorded.
The extent to which renunciation of the visualisation of atomic phenomena
is imposed upon us by the impossibility of their subdivision is strikingly
illustrated by the following example to which Einstein very early called
attention and often has reverted. If a semi-reflecting mirror is placed
in the way of a photon, leaving two possibilities for its direction of
propagation, the photon may either be recorded on one, and only one, of
two photographic plates situated at great distances in the two directions
in question, or else we may, by replacing the plates by mirrors, observe
effects exhibiting an interference between the two reflected wave-trains.
In any attempt of a pictorial representation of the behaviour of the photon
we would, thus, meet with the difficulty: to be obliged to say, on the
one hand, that the photon always chooses
one
of the two ways and,
on the other hand, that it behaves as if it had passed
both
ways.
It is just arguments of this kind which recall the impossibility of
subdividing quantum phenomena and reveal the ambiguity in ascribing customary
physical attributes to atomic objects. In particular, it must be realised
that besides in the account of the placing and timing of the instruments
forming the experimental arrangement all unambiguous use of space-time
concepts in the description of atomic phenomena is confined to the recording
of observations which refer to marks on a photographic plate or to similar
practically irreversible amplification effects like the building of a water
drop around an ion in a cloud-chamber. Although, of course, the existence
of the quantum of action is ultimately responsible for the properties of
the materials of which the measuring instruments are built and on which
the functioning of the recording devices depends, this circumstance is
not relevant for the problems of the adequacy and completeness of the quantum-mechanical
description in its aspects here discussed.
These problems were instructively commented upon from different sides
at the Solvay meeting, in the same session where Einstein raised his general
objections. On that occasion an interesting discussion arose also about
how to speak of the appearance of phenomena for which only predictions
of statistical character can be made. The question was whether, as to the
occurrence of individual effects, we should adopt a terminology proposed
by Dirac, that we were concerned with a choice on the part of "nature"
or, as suggested by Heisenberg, we should say that we have to do with a
choice on the part of the "observer" constructing the measuring
instruments and reading their recording. Any such terminology would, however,
appear dubious since, on the one hand, it is hardly reasonable to endow
nature with volition in the ordinary sense, while, on the other hand, it
is certainly not possible for the observer to influence the events which
may appear under the conditions he has arranged. To my mind, there is no
other alternative than to admit that, in this field of experience, we are
dealing with individual phenomena and that our possibilities of handling
the measuring instruments allow us only to make a choice between the different
complementary types of phenomena we want to study.
The epistemological problems touched upon here were more explicitly
dealt with in my contribution to the issue of
Naturunssenschaften
in celebration of Planck's 70th birthday in 1929. In this article, a comparison
was also made between the lesson derived from the discovery of the universal
quantum of action and the development which has followed the discovery
of the finite velocity of light and which, through Einstein's pioneer work,
has so greatly clarified basic principles of natural philosophy. In relativity
theory, the emphasis on the dependence of all phenomena on the reference
frame opened quite new ways of tracing general physical laws of unparalleled
scope. In quantum theory, it was argued, the logical comprehension of hitherto
unsuspected fundamental regularities governing atomic phenomena has demanded
the recognition that no sharp separation can be made between an independent
behaviour of the objects and their interaction with the measuring instruments
which define the reference frame.
In this respect, quantum theory presents us with a novel situation in
physical science, but attention was called to the very close analogy with
the situation as regards analysis and synthesis of experience, which we
meet in many other fields of human knowledge and interest. As is well known,
many of the difficulties in psychology originate in the different placing
of the separation lines between object and subject in the analysis of various
aspects of psychical experience. Actually, words like "thoughts"
and "sentiments," equally indispensable to illustrate the variety
and scope of conscious life, are used in a similar complementary way as
are space-time co-ordination and dynamical conservation laws in atomic
physics. A precise formulation of such analogies involves, of course, intricacies
of terminology, and the writer's position is perhaps best indicated in
a passage in the article, hinting at the mutually exclusive relationship
which will always exist between the practical use of any word and attempts
at its strict definition. The principal aim, however, of these considerations,
which were not least inspired by the hope of influencing Einstein's attitude,
was to point to perspectives of bringing general epistemological problems
into relief by means of a lesson derived from the study of new, but fundamentally
simple physical experience.
At the next meeting with Einstein at the Solvay Conference in 1930,
our discussions took quite a dramatic turn. As an objection to the view
that a control of the interchange of momentum and energy between the objects
and the measuring instruments was excluded if these instruments should
serve their purpose of defining the space-time frame of the phenomena Einstein
brought forward the argument that such control should be possible when
the exigencies of relativity theory were taken into consideration. In particular,
the general relationship between energy and mass, expressed in Einstein's
famous formula
E = mc
(5)
should allow, by means of simple weighing, to measure the total energy
of any system and, thus, in principle to control the energy transferred
to it when it interacts with an atomic object.
As an arrangement suited for such purpose, Einstein proposed the device
indicated in Fig. 7, consisting of a box with a hole in its side, which
could be opened or closed by a shutter moved by means of a clock-work within
the box.
If, in the beginning, the box contained a certain amount of radiation
and the clock was set to open the shutter for a very short interval at
a chosen time, it could be achieved that a single photon was released through
the hole at a moment known with as great accuracy as desired. Moreover,
it would apparently also be possible, by weighing the whole box before
and after this event, to measure the energy of the photon with any accuracy
wanted, in definite contradiction to the reciprocal indeterminacy of time
and energy quantities in quantum mechanics.
This argument amounted to a serious challenge and gave rise to a thorough
examination of the whole problem. At the outcome of the discussion, to
which Einstein himself contributed effectively, it became clear, however,
that this argument could not be upheld. In fact, in the consideration of
the problem, it was found necessary to look closer into the consequences
of the identification of inertial and gravitational mass implied in the
application of relation (5). Especially, it was essential to take into
account the relationship between the rate of a clock and its position in
a gravitational field well known from the red-shift of the lines in the
sun's spectrum following from Einstein's principle of equivalence between
gravity effects and the phenomena observed in accelerated reference frames.
Our discussion concentrated on the possible application of an apparatus
incorporating Einstein's device and drawn in Fig. 8 in the same pseudo-realistic
style as some of the preceding figures. The box, of which a section is
shown in order to exhibit its interior, is suspended in a spring-balance
and is furnished with a pointer to read its position on a scale fixed to
the balance support. The weighing of the box may thus be performed with
any given accuracy
by adjusting the balance to its zero position by means of suitable loads. The essential point is now that any determination
of this position with a given accuracy
will involve a minimum
latitude
in the control of the momentum of the box connected
with
by the relation (3). This latitude must obviously again
be smaller than the total impulse which, during the whole interval
of the balancing procedure, can be given by the gravitational field to
a body with a mass
, or
approx=
q T . g .
(6)
where
is the gravity constant. The greater the accuracy of
the reading
of the pointer, the longer must, consequently, be
the balancing interval
, if a given accuracy
of the weighing of the box with its content shall be obtained.
Now, according to general relativity theory, a clock, when displaced
in the direction of the gravitational force by an amount of
will change its rate in such a way that its reading
in the course of a time interval
will differ by an amount
given by the relation
= (1/c
q,
(7)
By comparing (6) and (7) we see, therefore, that after the weighing
procedure there will in our knowledge of the adjustment of the clock be
a latitude
/ (
) ,
Together with the formula (5), this relation again leads to
> h,
in accordance with the indeterminacy principle. Consequently,
a use of the apparatus as a means of accurately measuring the
energy of the photon will prevent us from controlling the moment
of its escape.
The discussion, so illustrative of the power and consistency of
relativistic arguments, thus emphasised once more the necessity
of distinguishing, in the study of atomic phenomena, between the
proper measuring instruments which serve to define the reference
frame and those parts which are to be regarded as objects under
investigation and in the account of which quantum effects cannot
be disregarded. Notwithstanding the most suggestive confirmation
of the soundness and wide scope of the quantum-mechanical way
of description, Einstein nevertheless, in a following conversation
with me, expressed a feeling of disquietude as regards the apparent
lack of firmly laid down principles for the explanation of nature,
in which all could agree. From my viewpoint, however, I could
only answer that, in dealing with the task of bringing order into
an entirely new field of experience, we could hardly trust in
any accustomed principles, however broad, apart from the demand
of avoiding logical inconsistencies and, in this respect, the
mathematical formalism of quantum mechanics should surely meet
all requirements.
The Solvay meeting in 1930 was the last occasion where, in common
discussions with Einstein, we could benefit from the stimulating
and mediating influence of Ehrenfest, but shortly before his deeply
deplored death in 1933 he told me that Einstein was far from satisfied
and with his usual acuteness had discerned new aspects of the
situation which strengthened his critical attitude. In fact, by
further examining the possibilities for the application of a balance
arrangement, Einstein had perceived alternative procedures which,
even if they did not allow the use he originally intended, might
seem to enhance the paradoxes beyond the possibilities of logical
solution. Thus, Einstein had pointed out that, after a preliminary
weighing of the box with the clock and the subsequent escape of
the photon, one was still left with the choice of either repeating
the weighing or opening the box and comparing the reading of the
clock with the standard time scale. Consequently, we are at this
stage still free to choose whether we want to draw conclusions
either about the energy of the photon or about the moment when
it left the box. Without in any way interfering with the photon
between its escape and its later interaction with other suitable
measuring instruments, we are, thus, able to make accurate predictions
pertaining
either
to the moment of its arrival
or
to
the amount of energy liberated by its absorption. Since, however,
according to the quantum-mechanical formalism, the specification
of the state of an isolated particle cannot involve both a well-defined
connection with the time scale and an accurate fixation of the
energy, it might thus appear as if this formalism did not offer
the means of an adequate description.
Once more Einstein's searching spirit had elicited a peculiar
aspect of the situation in quantum theory, which in a most striking
manner illustrated how far we have here transcended customary
explanation of natural phenomena. Still, I could not agree with
the trend of his remarks as reported by Ehrenfest. In my opinion,
there could be no other way to deem a logically consistent mathematical
formalism as inadequate than by demonstrating the departure of
its consequences from experience or by proving that its predictions
did not exhaust the possibilities of observation, and Einstein's
argumentation could be directed to neither of these ends. In fact,
we must realize that in the problem in question we are not dealing
with a
single
specified experimental arrangement, but are
referring to
two
different, mutually exclusive arrangements.
In the one, the balance together with another piece of apparatus
like a spectrometer is used for the study of the energy transfer
by a photon; in the other, a shutter regulated by a standardised
clock together with another apparatus of similar kind, accurately
timed relatively to the clock, is used for the study of the time
of propagation of a photon over a given distance. In both these
cases, as also assumed by Einstein, the observable effects are
expected to be in complete conformity with the predictions of
the theory.
The problem again emphasises the necessity of considering the
whole experimental arrangement, the specification of which is
imperative for any well-defined application of the quantum-mechanical
formalism. Incidentally, it may be added that paradoxes of the
kind contemplated by Einstein are encountered also in such simple
arrangements as sketched in Fig. 5. In fact, after a preliminary
measurement of the momentum of the diaphragm, we are in principle
offered the choice, when an electron or photon has passed through
the slit, either to repeat the momentum measurement or to control
the position of the diaphragm and, thus, to make predictions pertaining
to alternative subsequent observations. It may also be added that
it obviously can make no difference as regards observable effects
obtainable by a definite experimental arrangement, whether our
plans of constructing or handling the instruments are fixed beforehand
or whether we prefer to postpone the completion of our planning
until a later moment when the particle is already on its way from
one instrument to another.
In the quantum-mechanical description our freedom of constructing
and handling the experimental arrangement finds its proper expression
in the possibility of choosing the classically defined parameters
entering in any proper application of the formalism. Indeed, in
all such respects quantum mechanics exhibits a correspondence
with the state of affairs familiar from classical physics, which
is as close as possible when considering the individuality inherent
in the quantum phenomena. Just in helping to bring out this point
so clearly, Einstein's concern had therefore again been a most
welcome incitement to explore the essential aspects of the situation.
The next Solvay meeting in 1933 was devoted to the problems of
the structure and properties of atomic nuclei, in which field
such great advances were made just in that period due to the experimental
discoveries as well as to new fruitful applications of quantum
mechanics. It need in this connection hardly be recalled that
just the evidence obtained by the study of artificial nuclear
transformations gave a most direct test of Einstein's fundamental
law regarding the equivalence of mass and energy, which was to
prove an evermore important guide for researches in nuclear physics.
It may also be mentioned how Einstein's intuitive recognition
of the intimate relationship between the law of radioactive transformations
and the probability rules governing individual radiation effects
was confirmed by the quantum-mechanical explanation of spontaneous
nuclear disintegrations. In fact, we are here dealing with a typical
example of the statistical mode of description, and the complementary
relationship between energy-momentum conservation and time-space
co-ordination is most strikingly exhibited in the well-known paradox
of particle penetration through potential barriers.
Einstein himself did not attend this meeting, which took place
at a time darkened by the tragic developments in the political
world which were to influence his fate so deeply and add so greatly
to his burdens in the service of humanity. A few months earlier,
on a visit to Princeton where Einstein was then guest of the newly
founded Institute for Advanced Study to which he soon after became
permanently attached, I had, however, opportunity to talk with
him again about the epistemological aspects of atomic physics,
but the difference between our ways of approach and expression
still presented obstacles to mutual understanding. While, so far,
relatively few persons had taken part in the discussions reported
in this article, Einstein's critical attitude towards the views
on quantum theory adhered to by many physicists was soon after
brought to public attention through a paper with the title
Can
Quantum-Mechanical Description of Physical Reality Be Considered
Complete?
, published in 1935 by Einstein, Podolsky and Rosen.
The argumentation in this paper is based on a criterion which
the authors express in the following sentence: "If, without
in any way disturbing a system, we can predict with certainty
(i.e., with probability equal to unity) the value of a physical
quantity, then there exists an element of physical reality corresponding
to this physical quantity." By an elegant exposition of the
consequences of the quantum-mechanical formalism as regards the
representation of a state of a system, consisting of two parts
which have been in interaction for a limited time interval, it
is next shown that different quantities, the fixation of which
cannot be combined in the representation of one of the partial
systems, can nevertheless be predicted by measurements pertaining
to the other partial system. According to their criterion, the
authors therefore conclude that quantum mechanics does not "provide
a complete description of the physical reality," and they
express their belief that it should be possible to develop a more
adequate account of the phenomena.
Due to the lucidity and apparently incontestable character of
the argument, the paper of Einstein, Podolsky and Rosen created
a stir among physicists and has played a large role in general
philosophical discussion. Certainly the issue is of a very subtle
character and suited to emphasise how far, in quantum theory,
we are beyond the reach of pictorial visualisation. It will be
seen, however, that we are here dealing with problems of just
the same kind as those raised by Einstein in previous discussions,
and, in an article which appeared a few months later, I tried
to show that from the point of view of complementarity the apparent
inconsistencies were completely removed. The trend of the argumentation
was in substance the same as that exposed in the foregoing pages,
but the aim of recalling the way in which the situation was discussed
at that time may be an apology for citing certain passages from
my article.
Thus, after referring to the conclusions derived by Einstein,
Podolsky and Rosen on the basis of their criterion, I wrote:
Such an argumentation, how ever, would hardly seem suited to affect
the soundness of quantum-mechanical description, which is based
on a coherent mathematical formalism covering automatically any
procedure of measurement like that indicated. The apparent contradiction
in fact discloses only an essential inadequacy of the customary
viewpoint of natural philosophy for a rational account of physical
phenomena of the type with which we are concerned in quantum mechanics.
Indeed the
finite interaction between object and measuring
agencies
conditioned by the very existence of the quantum
of action entails - because of the impossibility of controlling
the reaction of the object on the measuring instruments, if these
are to serve their purpose - the necessity of a final renunciation
of the classical ideal of causality and a radical revision of
our attitude towards the problem of physical reality. In fact,
as we shall see, a criterion of reality like that proposed by
the named authors contains - however cautious its formulation
may appear - an essential ambiguity when it is applied to the
actual problems with which we are here concerned.
As regards the special problem treated by Einstein, Podolsky and
Rosen, it was next shown that the consequences of the formalism
as regards the representation of the state of a system consisting
of two interacting atomic objects correspond to the simple arguments
mentioned in the preceding in connection with the discussion of
the experimental arrangements suited for the study of complementary
phenomena. In fact, although any pair
and
, of
conjugate space and momentum variables obeys the rule of non-commutative
multiplication expressed by (2), and can thus only be fixed with
reciprocal latitudes given by (3), the difference q
- q
between
two space-co-ordinates referring to the constituents of the system
will commute with the sum
of the corresponding
momentum components, as follows directly from the commutability
of
with
and
with
. Both
and
can, therefore,
be accurately fixed in a state of the complex system and, consequently,
we can predict the values of either
or
if either
or
respectively, are determined by
direct measurements. If, for the two parts of the system, we take
a particle and a diaphragm, like that sketched in Fig. 5, we see
that the possibilities of specifying the state of the particle
by measurements on the diaphragm just correspond to the situation
described above, where it was mentioned that, after the particle
has passed through the diaphragm, we have in principle the choice
of measuring either the position of the diaphragm or its momentum
and, in each case, to make predictions as to subsequent observations
pertaining to the particle. As repeatedly stressed, the principal
point is here that such measurements demand mutually exclusive
experimental arrangements.
The argumentation of the article was summarised. in the following
passage:
From our point of new we now see that the wording of the above-mentioned
criterion of physical reality proposed by Einstein, Podolsky,
and Rosen contains an ambiguity as regards the meaning of the
expression ' without in any way disturbing a system.' Of course
there is in a case like that just considered no question of a
mechanical disturbance of the system under investigation during
the last critical stage of the measuring procedure. But even at
this stage there is essentially the question of
an influence
on the very conditions which define the possible types of predictions
regarding the future behaviour of the system
. Since these
conditions constitute an inherent element of the description of
any phenomenon to which the term "physical reality"
can be properly attached, we see that the argumentation of the
mentioned authors does not justify their conclusion that quantum-mechanical
description is essentially incomplete. On the contrary, this description,
as appears from the preceding discussion, may be characterised
as a rational utilisation of all possibilities of unambiguous
interpretation of measurements, compatible with the finite and
uncontrollable interaction between the objects and the measuring
instruments in the field of quantum theory. In fact, it is only
the mutual exclusion of any two experimental procedures, permitting
the unambiguous definition of complementary physical quantities,
which provides room for new physical laws, the coexistence of
which might at first sight appear irreconcilable with the basic
principles of science. It is just this entirely new situation
as regards the description of physical phenomena that the notion
of
complementarity
aims at characterising.
Rereading these passages, I am deeply aware of the inefficiency
of expression which must have made it very difficult to appreciate
the trend of the argumentation aiming to bring out the essential
ambiguity involved in a reference to physical attributes of objects
when dealing with phenomena where no sharp distinction can be
made between the behaviour of the objects themselves and their
interaction with the measuring instruments. I hope, however, that
the present account of the discussions with Einstein in the foregoing
years, which contributed so greatly to make us familiar with the
situation in quantum physics, may give a clearer impression of
the necessity of a radical revision of basic principles for physical
explanation in order to restore logical order in this field of
experience.
Einstein's own views at that time are presented in an article
Physics and Reality
, published in 1936 in the
Journal
of the Franklin Institute
. Starting from a most illuminating
exposition of the gradual development of the fundamental principles
in the theories of classical physics and their relation to the
problem of physical reality, Einstein here argues that the quantum-mechanical
description is to be considered merely as a means of accounting
for the average behaviour of a large number of atomic systems
and his attitude to the belief that it should offer an exhaustive
description of the individual phenomena is expressed in the following
words: "To believe this is logically possible without contradiction;
but it is so very contrary to my scientific instinct that I cannot
forego the search for a more complete conception."
Even if such an attitude might seem well-balanced in itself, it
nevertheless implies a rejection of the whole argumentation exposed
in the preceding, aiming to show that, in quantum mechanics, we
are not dealing with an arbitrary renunciation of a more detailed
analysis of atomic phenomena, but with a recognition that such
an analysis is
in principle
excluded. The peculiar individuality
of the quantum effects presents us, as regards the comprehension
of well-defined evidence, with a novel situation unforeseen in
classical physics and irreconcilable with conventional ideas suited
for our orientation and adjustment to ordinary experience. It
is in this respect that quantum theory has called for a renewed
revision of the foundation for the unambiguous use of elementary
concepts, as a further step in the development which, since the
advent of relativity theory, has been so characteristic of modern
science.
In the following years, the more philosophical aspects of the
situation in atomic physics aroused the interest of even larger
circles and were, in particular, discussed at the Second International
Congress for the Unity of Science in Copenhagen in July 1936.
In a lecture on this occasion, I tried especially to stress the
analogy in epistemological respects between the limitation imposed
on the causal description in atomic physics and situations met
with in other fields of knowledge. A principal purpose of such
parallels was to call attention to the necessity in many domains
of general human interest to face problems of a similar kind as
those which had arisen in quantum theory and thereby to give a
more familiar background for the apparently extravagant way of
expression which physicists have developed to cope with their
acute difficulties.
Besides the complementary features conspicuous in psychology and
already touched upon, examples of such relationships can also
be traced in biology, especially as regards the comparison between
mechanistic and vitalistic viewpoints. Just with respect to the
observational problem, this last question had previously been
the subject of an address to the International Congress on Light
Therapy held in Copenhagen in 1932, where it was incidentally
pointed out that even the psycho-physical parallelism as envisaged
by Leibniz and Spinoza has obtained a wider scope through the
development of atomic physics, which forces us to an attitude
towards the problem of explanation recalling ancient wisdom, that
when searching for harmony in life one must never forget that
in the drama of existence we are ourselves both actors and spectators.
Utterances of this kind would naturally in many minds evoke the
impression of an underlying mysticism foreign to the spirit of
science at the above mentioned Congress in 1936 I therefore tried
to clear up such misunderstandings and to explain that the only
question was an endeavour to clarify the conditions, in each field
of knowledge, for the analysis and synthesis of experience. Yet,
I am afraid that I had in this respect only little success in
convincing my listeners, for whom the dissent among the physicists
themselves was naturally a cause of scepticism as to the necessity
of going so far in renouncing customary demands as regards the
explanation of natural phenomena. Not least through a new discussion
with Einstein in Princeton in 1937, where we did not get beyond
a humorous contest concerning which side Spinoza would have taken
if he had lived to see the development of our days, I was strongly
reminded of the importance of utmost caution in all questions
of terminology and dialectics.
These aspects of the situation were especially discussed at a
meeting in Warsaw in 1938, arranged by the International Institute
of Intellectual Co-operation of the League of Nations. The preceding
years had seen great progress in quantum physics due to a number
of fundamental discoveries regarding the constitution and properties
of atomic nuclei as well as due to important developments of the
mathematical formalism taking the requirements of relativity theory
into account. In the last respect, Dirac's ingenious quantum theory
of the electron offered a most striking illustration of the power
and fertility of the general quantum-mechanical way of description.
In the phenomena of creation and annihilation of electron pairs
we have in fact to do with new fundamental features of atomicity,
which are intimately connected with the non-classical aspects
of quantum statistics expressed in the exclusion principle, and
which have demanded a still more far-reaching renunciation of
explanation in terms of a pictorial representation.
Meanwhile, the discussion of the epistemological problems in atomic
physics attracted as much attention as ever and, in commenting
on Einstein's views as regards the incompleteness of the quantum-mechanical
mode of description, I entered more directly on questions of terminology.
In this connection I warned especially against phrases, often
found in the physical literature, such as "disturbing of
phenomena by observation" or "creating physical attributes
to atomic objects by measurements." Such phrases, which may
serve to remind of the apparent paradoxes in quantum theory, are
at the same time apt to cause confusion, since words like "phenomena"
and "observations," just as "attributes" and
"measurements," are used in a way hardly compatible
with common language and practical definition.
As a more appropriate way of expression, I advocated the application
of the word
phenomenon
exclusively to refer to the observations
obtained under specified circumstances, including an account of
the whole experimental arrangement. In such terminology, the observational
problem is free of any special intricacy since, in actual experiments,
all observations are expressed by unambiguous statements referring,
for instance, to the registration of the point at which an electron
arrives at a photographic plate. Moreover, speaking in such a
way is just suited to emphasise that the appropriate physical
interpretation of the symbolic quantum-mechanical formalism amounts
only to predictions, of determinate or statistical character,
pertaining to individual phenomena appearing under conditions
defined by classical physical concepts.
Notwithstanding all differences between the physical problems
which have given rise to the development of relativity theory
and quantum theory, respectively, a comparison of purely logical
aspects of relativistic and complementary argumentation reveals
striking similarities as regards the renunciation of the absolute
significance of conventional physical attributes of objects. Also,
the neglect of the atomic constitution of the measuring instruments
themselves, in the account of actual experience, is equally characteristic
of the applications of relativity and quantum theory. Thus, the
smallness of the quantum of action compared with the actions involved
in usual experience, including the arranging and handling of physical
apparatus, is as essential in atomic physics as is the enormous
number of atoms composing the world in the general theory of relativity
which, as often pointed out, demands that dimensions of apparatus
for measuring angles can be made small compared with the radius
of curvature of space.
In the Warsaw lecture, I commented upon the use of not directly
visualisable symbolism in relativity and quantum theory in the
following way:
Even the formalisms, which in both theories within their scope
offer adequate means of comprehending all conceivable experience,
exhibit deep-going analogies. In fact, the astounding simplicity
of the generalisation of classical physical theories, which are
obtained by the use of multidimensional geometry and non-commutative
algebra, respectively, rests in both cases essentially on the
introduction of the conventional symbol sqrt(-1). The abstract
character of the formalisms concerned is indeed, on closer examination,
as typical of relativity theory as it is of quantum mechanics,
and it is in this-respect purely a matter of tradition if the
former theory is considered as a completion of classical physics
rather than as a first fundamental step in the thoroughgoing revision
of our conceptual means of comparing observations, which the modern
development of physics has forced upon us.
It is, of course, true that in atomic physics we are confronted
with a number of unsolved fundamental problems, especially as
regards the intimate relationship between the elementary unit
of electric charge and the universal quantum of action; but these
problems are no more connected with the epistemological points
here discussed than is the adequacy of relativistic argumentation
with the issue of thus far unsolved problems of cosmology. Both
in relativity and in quantum theory we are concerned with new
aspects of scientific analysis and synthesis and, in this connection,
it is interesting to note that, even in the great epoch of critical
philosophy in the former century, there was only question to what
extent
a priori
arguments could be given for the adequacy
of space-time co-ordination and causal connection of experience,
but never question of rational generalisations or inherent limitations
of such categories of human thinking.
Although in more recent years I have had several occasions of
meeting Einstein, the continued discussions, from which I always
have received new impulses, have so far not led to a common view
about the epistemological problems in atomic physics, and our
opposing views are perhaps most clearly stated in a recent issue
of
Dialectica
bringing a general discussion of these problems.
Realising, however, the many obstacles for mutual understanding
as regards a matter where approach and background must influence
everyone's attitude, I have welcomed this opportunity of a broader
exposition of the development by which, to my mind, a veritable
crisis in physical science has been overcome. The lesson we have
hereby received would seem to have brought us a decisive step
further in the never-ending struggle for harmony between content
and form, and taught us once again that no content can be grasped
without a formal frame and that any form, however useful it has
hitherto proved, may be found to be too narrow to comprehend new
experience.
Surely, in a situation like this, where it has been difficult
to reach mutual understanding not only between philosophers and
physicists but even between physicists of different schools, the
difficulties have their root not seldom in the preference for
a certain use of language suggesting itself from the different
lines of approach. In the Institute in Copenhagen, where through
those years a number of young physicists from various countries
came together for discussions, we used, when in trouble, often
to comfort ourselves with jokes, among them the old saying of
the two kinds of truth. To the one kind belong statements so simple
and clear that the opposite assertion obviously could not be defended.
The other kind, the so-called "deep truths," are statements
in which the opposite also contains deep truth. Now, the development
in a new field will usually pass through stages in which chaos
becomes gradually replaced by order; but it is not least in the
intermediate stage where deep truth prevails that the work is
really exciting and inspires the imagination to search for a firmer
hold. For such endeavours of seeking the proper balance between
seriousness and humour, Einstein's own personality stands as a
great example and, when expressing my belief that through a singularly
fruitful co-operation of a whole generation of physicists we are
nearing the goal where logical order to a large extent allows
us to avoid deep truth, I hope that it will be taken in his spirit
and may serve as an apology for several utterances in the preceding
pages.
The discussions with Einstein which have formed the theme of this
article have extended over many years which have witnessed great
progress in the field of atomic physics. Whether our actual meetings
have been of short or long duration, they have always left a deep
and lasting impression on my mind, and when writing this report
I have, so-to-say, been arguing with Einstein all the time even
when entering on topics apparently far removed from the special
problems under debate at our meetings. As regards the account
of the conversations I am, of course, aware that I am relying
only on my own memory, just as I am prepared for the possibility
that many features of the development of quantum theory, in which
Einstein has played so large a part, may appear to himself in
a different light. I trust, however, that I have not failed in
conveying a proper impression of how much it has meant to me to
be able to benefit from the inspiration which we all derive from
every contact with Einstein.
Further Reading:
Einstein's Reply
Einstein Archive
Biography of Niels Bohr
Biographies of various physicists
Werner Heisenberg
on History of Quantum Theory |
Percy Bridgman
on Operationalism |
Lenin
on Revolution in Natural Science |
The Structure of Scientific Revolutions
, Thomas Kuhn |
The Ethic of Knowledge and the Socialist Ideal
, Jacques Monod |
Against Method
, Paul Feyerabend
Hegel
references on Science
The Crisis in Modern Physics
Crisis in Modern Physics
Positivism
Science
Theory & Practice
Matter
Contradiction
Nature
Philosophy Archive @ marxists.org