Bohr v Einstein

By Rochelle Forrester

© *All Rights Reserved*

* *

*Published in 2002*

The
debate between Bohr and Einstein over the interpretation of quantum theory
began in 1927 at the fifth Solvay Conference of physicists and ended at
Einstein’s death in 1955. The most active phase of the debate ran from 1927 to
1936 when Bohr replied to the EPR paper written by Einstein and two colleagues.
The debate took the form of various thought experiments invented by Einstein in
which it would be theoretically possible to measure complementary properties
such as the position and momentum of a particle or its energy at a certain
point in time. If these measurements were possible it would show that Bohr’s
idea of complementarity and Heisenburg’s uncertainty principle were wrong and
that the quantum theory proposed by Bohr, called the Copenhagen Interpretation,
was wrong. Before addressing Einstein’s attack on Bohr’s theory, it is
necessary to examine the theory to see what Einstein was objecting to.

The best way to understand quantum
theory is in comparison with the classical theory of physics derived from
Newtonian laws of motion, Maxwell’s electro-magnetic theory and statistical
thermodynamics. Classical physics provides a description of the physical world
that assumes a continuity of motion and fields of force. This means that we are
able to use a series of observations to see the changes in a particular system.
We are able to given a continuity of description of the system as it under goes
particular changes. Classical physics also assumes causal interactions in space
and time between bodies which are considered to be independent objects. The
mathematics used to describe a physical system amounted to a theoretical model
in which the terms of the theory correspond to the elements in the physical
system. It was possible for example to make a series of measurements of the
positions and motions of the planets and using Newton’s laws to determine with
certainty the past and future behaviour of the planets. As long as the system
was closed and not subject to any external disturbances we could know the state
of the system at any time, past or future.

Observations
made of the system could confirm whether the predictions made under the theory
were correct or not, but would not disturb the system itself. The system could
be considered as being entirely independent of the observer and any
disturbances caused by the observation or measurement could be controlled or
allowed for by the observer.

Bohr’s
theory for the quantum world differed radically from the classical theory in a
number of respects. A key factor in Bohr’s theory was the discovery of Planck’s
constant. In 1900 Max Planck while working on a problem in physics concerning
blackbody radiation suggested that radiated energy should be seen as not being
continuous as is assumed by classical theory, but as being composed of discrete
indivisible bundles of energy. This unit of energy, also know as a quantum or
the quantum of action, was soon used to explain other problems in physics such
as the photo-electric effect where electrons are ejected from metals and the
orbits of electrons in atoms.

A
further important factor in Bohr’s theory was wave-particle duality.
Electro-magnetic energy had been assumed to consist of waves, but the discovery
of Planck’s constant, the photo-electric effect and eventually in the 1920’s
the Compton effect, where x-rays were found to knock electrons out of a gas, it
was concluded that electro-magnetic energy could also behave as particles.
Quantum entities such as electrons were normally regarded as particles but were
also found to behave as waves in certain experiments. This meant that both
energy and matter were capable of behaving as both waves and particles. This
was considered to be a problem as waves and particles had contradictory
qualities such as waves are inherently in motion, spread out in space and may
merge together to reinforce or cancel each other out, while particles may be
stationary and occupy a single point in space and rebound of each other like
billiard balls when they collide.

Bohr’s
theory also concerned the problem of how can we objectively describe the things
we can not directly experience. Bohr considered we have no choice but to use the
language of classical physics and our everyday macro-world experience when
describing the quantum world. This is because there is no other language we
could use. If we tried to use a purely theoretical language not related to our
experiences in the macro-world, we would not be able to objectively communicate
to each other what we thought was happening in the quantum world. Such a
language not being related to our common experiences in the macro-world would
be ambiguous and would be unable to be used objectively to describe the quantum
world. It is a necessary condition for the unambiguous communication of our
ideas of the quantum world that they be in a language that relates to the
everyday world we are all familiar with. The principle that we must use the
familiar classical concepts to describe the quantum world is known as the
correspondence principle. Bohr actually used the term correspondence principle
to refer to two separate ideas. The other use of the correspondence principle
is the situation where the macro-world and the quantum world merge and where
for the higher quantum numbers the classical and quantum theories produce the
same calculations.

A
further factor in Bohr’s thought was that if one wished to provide an objective
description of the world, it is necessary to have external points of reference
available. Such external points of reference available in the macro-world are
the concepts of space and time and of causality, yet these points of reference
are not available in the quantum world. The only external points of reference
available when investigating the quantum world are re-identifiable macroscopic
particulars and measuring apparatus. It is the existence of such apparatus that
allows quantum theory to be objective. (Horner,1987,149.) The example is given
of two identical pens which in the macro-world one can distinguish by virtue of
their different spacial locations. If they were both put in a box which is then
closed and shaken about, it will then no longer be possible to re-identify which
pen is which. Observations of the quantum world are like opening the box; in
both situations we have lost the continuity which exists in the macro-world.
This leaves the macro-scopic measuring apparatus as the only frame of reference
available for creating objective descriptions of the quantum world. (Horner,
1987, 204-205). This situation is forced on us by the quantum of action (or
Planck’s constant) which causes the discontinuity which exists in the quantum
world. A later measurement will render information gained by an earlier
measurement to be of dubious value due to the interaction between the quantum
entity being observed and the measuring apparatus. With no continuity in space
and time available as a frame of reference and given the effect that observations
have on the quantum entities being observed, the interaction between the
quantum entity and measuring apparatus is the only frame of reference
available. (Horner, 1987, 67). Due to this Bohr considered the quantum theory
could not describe the unobserved state of quantum entities, but only the
interaction between the entity and the measuring apparatus. The quantum world
is observer dependant.

A
further important element in Bohr’s thought is the concept of complementarity.
Complementarity provides a general framework to put together various aspects of
nature which cannot be understood within a more restricted framework. It allows
phenomena which might otherwise be considered contradictory, like wave-particle
duality, to be put together. The contradiction is avoided as matter and energy
do not behave as wave and particle at the same time in the same experiment.
Complementarity allows the complete description of quantum phenomena; without
it descriptions would be incomplete. Bohr considered complementarity replaced
but also embraced the classical concept of causality, when dealing with the
quantum world. It is not possible to consider observations as being in a
series, as one does in classical physics, in the quantum world. In the quantum
world you have to go back and forth between sets of observations which may be
put together under the framework of complementarity.

The
uncertainty principle established by Heisenberg was also part of the Copenhagen
Interpretation championed by Bohr. The uncertainty principle states that it is
not possible to obtain completely accurate measurements of certain pairs of
properties of quantum systems, such as position and momentum or time and
energy, at the same time. The more accurately one property such as position was
measured, the less accurately momentum could be simultaneously measured. This
is caused by the quantum of action which is of sufficient size to disturb
quantum systems when we observe them and because the quantum of action is
indivisible we cannot reduce the disturbance by reducing the amount of energy
used to observe the quantum system. The other problem is that the disturbance
is uncontrollable and unpredictable and so cannot be allowed for when observing
quantum systems. The uncertainty principle meant that determinism, the ability
to assess both the past and future behaviour of a physical system was no longer
possible. The initial information required, for example both the position and
momentum of a body is impossible to establish with certainty and any changes
are unpredictable.

The
final element making up the Copenhagen Interpretation is the wave function
invented by Schrodinger, but which was interpreted by Max Born as being
probability waves. It is not possible according to quantum theory to predict
the behaviour of individual quantum systems; rather we can only predict the
probable behaviour of the individual system. This is caused by the
discontinuity in the quantum world and because each measurement involves an
interaction with the system being measured. This interaction, which disturbs
the system, is uncontrollable and unpredictable.

When
a measurement is made the probability waves are considered to have collapsed to
a specific state giving the actual position (or whatever else is being
measured) of the quantum system. Prior to the measurement the quantum system is
considered not to have any real position at all. It is the actual act of
measurement which brings the quantum system into existence or whatever property
of the system that is being measured. This is because the focus of the
Copenhagen Interpretation is on what can be known. It is not possible *in
principle* to know what a quantum system is doing prior to measurement. The
determinism that enables the behavior of bodies in the macro-world to be
calculated simply does not exist in the quantum world. The indivisibility of
the quantum of action and the fact that measurements disturb quantum systems in
an uncontrollable and unpredictable way eliminates the possibility of
determinism in the quantum world.

Bohr’s argument has
been summarized by Max Jammer in “The Philosophy of Quantum Mechanics” as

“1. Indivisibility of the quantum of
action. (quantum postulate”).

2. Discontinuity (or indivisibility)
of elementary processes.

3. Uncontrollability of interaction
between object and instrument.

4. Impossibility of a (strict)
spatio-temporal and at the same time causal description.

5. Renunciation of the classical
mode of description.”

(as
quoted in Horner, 1987, 106)

A
more detailed summary of Bohr’s though is provided by Horner. It is

“(0)
All knowledge presents itself within a conceptual framework adapted to account
for previous experience, and any such frame may prove to narrow to comprehend
new experiences.

(i)
The quantum of action is a discovery which is universal and elementary.

(ii)
The quantum of action denotes a feature of indivisibility in atomic processes.

(iii)
Ordinary or classical descriptions are only valid for macroscopic processes,
where reference can be unambiguous.

(iv)
Any attempt to define an atomic process more sharply than the quantum allows
must entail the impossible, dividing the indivisible.

(v)
Because of the limit of indivisibility a new and more general account of
description and definition must be devised.

(vi)
It is a necessary condition for the possibility of unambiguous communication,
that suitably refined everyday concepts be used no matter how far the processes
concerned transcend the range of ordinary experience.

(vii)
Our position as observers in a domain of experience where unambiguous
application of concepts depends essentially on conditions of observation
demands the use of complementary descriptions if description is to exhaustive.”

(Horner,1987,104).

Unlike Jammer’s description this introduces
both the Correspondence Principle as (vi) and complementarity as (vii). However
both descriptions of Bohr’s thought emphasize that it is the indivisibility of
the quantum of action that is the cause of the need for a new non-classical
theory for the quantum world. However Bohr’s view of the situation was not
accepted by Einstein.

Einstein
did not like Bohr’s interpretation of quantum theory. He did not like the
uncertainty principle and the probability inherent in Bohr’s theory. He
considered “God did not play dice.” He also did not like the discontinuity and
the loss of causality involved in the theory. Most of all he did not like the
loss of a world that existed independently of our observations. Einstein wanted
a more complete view of the universe than Bohr’s theory provided and he wanted
a single view to cover both the quantum world and the macro-world. The view he
considered ought to apply to both worlds was the view of classical physics with
its independent reality, causality, determinism, continuity and space-time
framework. Einstein’s view was essentially ontological. He wanted to know what
was going on “out there”.

Bohr’s
view on the other hand was more epistemological. He was interested in what we
can know and the conditions for the unambiguous communication of our
observations of the quantum world. Bohr accepts the existence of an indivisible
quantum of action and the discontinuity of quantum processes that follow from
the indivisible quantum of action. Einstein on the other hand regarded the
quantum of action as merely provisional or as a heuristic device rather than as
the fundamental fact of nature Bohr considered it to be.

Einstein’s
criticism of Bohr’s view of quantum theory began at the fifth Solvay conference
in Brussels in 1927. Einstein would invent thought experiments to show that the
uncertainty principle or complementarity did not always apply. One such
experiment involved the double slit experiment which Einstein modified so it
would be possible to tell which slit a particle passed through while still
allowing the interference pattern to exist. If this was possible it would show
a quantum entity acting as a particle (i.e. when you can tell which slit it
passed through) and a wave (due to the evidence of the interference pattern) at
the same time. This would contradict Bohr’s idea of complementarity.

Einstein’s
idea is shown on the diagram below:

Particles First Screen Second Screen

on
Rollers

Einstein’s modification of the double slit
experiment is that the screen containing the two slits should rest on rollers
and be able to move. A particle arriving at point P on the detecting screen
would receive an upward kick as it went through the slit. This would mean the
screen would receive a downward kick and the size of the kick would be greater
if the particle had passed through slit 1 than if it had passed through slit 2.
By measuring the motion of the screen it would be possible to tell which slit
the quantum entity had passed through which involves the entity acting as a
particle while at the same time retaining the interference pattern.

Bohr
soon came up with a problem for Einstein’s experiment. Bohr considered that in
order to see which slit the quantum entity had passed through it was necessary
to measure the movement of the screen to a particular accuracy. Any lesser
degree of accuracy in the measurement will not provide us with the information
required to tell us through which slit the entity went through. However due to the
uncertainty principle there will be a degree of uncertainty as to the position
of the slits. The uncertainty as to the position of the slits is sufficient to
eliminate the interference pattern. This is because interference requires a
certain relationship between the wavelength of the entity and the distance the
two slits are apart and the distance between the two screens being

__distance between the two screens x wavelength__

distance between the two slits

Uncertainty
in the position of the two slits in the experiment will eliminate the
interference pattern. Placing the first screen on rollers in order to observe
the movement of the slits so it is possible to tell which slit the entity went
through causes uncertainty in the position of the slits of a sufficient amount
to eliminate the interference pattern. (Greenstein & Zajonc,1997,86-88).

A
further thought experiment invented by Einstein at the fifth Solvay Conference
involved a stream of electrons hitting a screen with a single slit in it. The
electrons that pass through the slit would form a diffraction pattern on the
second screen. A diagram is below:

Electrons First Screen Second Screen

Einstein considered the experiment showed
Bohr’s theory could not describe the behaviour of individual electrons. If an
electron arrived at A on the diagram above then we immediately know it has not
arrived at B. However quantum theory does not explain why the electron arrived
at A rather than B. It only predicted the probability that a particular
electron would hit a particular point on the second screen. Einstein suggested
we should be looking for a better theory.

Bohr’s
reply was that there was a change in momentum of the electron as it passed
through the slit due to interaction between the electron and the screen. The
width of the slit which effects the position of the electron and the wave cone
brings a degree of uncertainty into the position of the electron as its
momentum changes. This uncertainty was consistent with Heisenberg’s uncertainty
principle and the only way to predict with certainty where an individual
electron would land would be to have a slit of zero width (e.g. no slit at all)
or an infinite number of diffraction rings which is no diffraction at all.
(Horner,1987,119-121).

Einstein
also attempted to disprove quantum theory at the sixth Solvay Conference in
1930 with the “Clock in the Box Experiment”. This involved a box with a hole in
one wall covered by a shutter which could be opened and closed by a clock
mechanism inside the box. The box also contained radiation which would add to
the weight of the box. The box would be weighed and then at a given moment the
clock would open the shutter allowing a single photon of radiation to escape.
The box could then be re-weighed, the difference between the two weights
telling us the amount of energy that escaped using the formula e=mc^{2}.
Under the uncertainty principle it is not possible to obtain an exact
measurement of the energy of the released photon and the time at which it was
released. Einstein’s experiment was designed to show such exact measurements
were possible, the clock measuring the time of release of the energy and the
weighing of the box disclosing the amount of energy involved. A diagram showing
Einstein’s idea is below.

Bohr’s
reply involved looking at the practicalities involved in making the required
measurements. The box had to be weighed so it had to be suspended by a spring
in a gravitational field. To weigh the box it is necessary to compare a pointer
attached to the box against a scale. After the photon had left the box weights
can be added to the box to restore the pointer to the same position against the
scale as it had been before the photon escaped. The weight added to the box
gives the weight of the escaped photon. However this involves a measurement of
the box to ensure the pointer is back at its original position. This
measurement is subject to the uncertainty principle concerning the position and
momentum of the box which brings uncertainty into the measurement of the weight
of the box. If there is uncertainty in the weight of the box, then there will
be an uncertainty in the energy of the released photon. There will also be
uncertainty in the time of the released energy as the speed of time depends
upon the position of a clock in a gravitational field. This position is
uncertain then the time of the release of the photon will also be uncertain.
This means both the time and the amount of energy released will be uncertain so
Einstein’s thought experiment did not contradict the uncertainty principle.
(Greenstein & Zajonc, 1997,89-92).

Einstein’s
thought experiments had previously tried to show quantum theory was wrong, but
in 1935 he presented a paper arguing quantum theory was incomplete. In this
paper Einstein and two colleagues proposed a thought experiment which involved
two co-related particles emitted from a source and moving away from the source
in opposite directions at the speed of light. Measuring the position of
particle1 can give an exact idea of its position, while measuring the exact
momentum of particle 2 allows us to know the exact momentum of particle1 due to
the co-relation of the two particles. Einstein also argued that the measurement
of particle1 could not disturb particle 2 due to the impossibility of faster
than light signaling. This means we can know the exact position and momentum of
particle 1 contrary to the uncertainty principle.

Bohr’s
reply was that if you make a measurement of particle 1 then this involves the
complete measuring system so that it is not possible to claim a relevant and
precise measurement of the conjugate
property of particle 2. Bohr considered both particles existed within the same
frame of reference so that a measurement of particle 1 will disturb particle 2
as it disturbs the whole frame of reference. If they are not considered to be
in the same frame of reference, then the measurements would be considered to be
successive experiments which does not establish simultaneous measurements of
motion and position.

Subsequent
developments on the EPR experiment involved a theorem invented by John Bell and
experiments carried out by Alain Aspect and others have tended to support
Bohr’s position. They are usually interpreted as requiring the abandonment of
either the idea of locality or the idea that quantum systems have their
properties independently of the act of measurement.

Conclusion

Einstein’s
attacks upon the Copenhagen Interpretation are widely regarded as having failed
to show the theory is either wrong or incomplete. His criticisms of the theory
and especially the eventual results of the practical application of the EPR
idea have greatly strengthened the theory, so that it became the orthodox
interpretation of the quantum world. The debate between Einstein and Bohr was conducted
with the two talking past each other, Einstein arguing how the quantum world
ought to be, while Bohr argued how the quantum world can be known to us. Bohr
accepted that there were some fundamental limits on our knowledge of the
quantum world, (such as the quantum of action) which as a matter of principle
we are unable to overcome. Einstein never accepted those limits, but was never
able to show to get around them. That does not mean that Einstein’s view that
the quantum world is like the macro-world is wrong, but it does mean that we
are unable to know in principle any more about the quantum world than Bohr and
the Copenhagen Interpretation suggest.

Bibliography:

Greenstein, G & Zajonc, A (1997) *The
Quantum Challenge* Jones & Bartlett Publishers: Sudbury Massachusetts

Horner, J (1987) *The Description of Nature*,
Clarendon Press: Oxford

Hooker, C A (1972) The Nature of Quantum
Mechanical Reality: Einstein v Bohr in *Paradigms and Paradoxes* (ed)
Colodny, R University of Pittsburgh Press