Baggott J. The Quantum Story: A History in 40 Moments

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the quantum story

140

concluded that the theory provides an incomplete description of indi-

vidual quantum systems.

Bohr heard of Einstein’s further adaptation of the photon box experi-

ment in a letter from Austrian physicist Paul Ehrenfest dated 9 July 1931.

Einstein was due to visit Ehrenfest in Leiden towards the end of October

that year, and Ehrenfest was hopeful that Bohr could join them there for

a quiet exchange of views (RUHIG, he wrote, in capital letters). He set out

the details of Einstein’s latest challenge.

Bohr summarized his response in his contribution to a 1949 volume dedi-

cated to Einstein in celebration of his 70th birthday. Bohr had been unmoved:

Since, however, according to the quantum-mechanical formalism, the speci-

ﬁ cation of the state of an isolated particle cannot involve both a well- deﬁ ned

connection with the time scale and an accurate ﬁ xation of the energy, it

might thus appear as if this formalism did not offer the means of an ade-

quate description . . . In fact, we must realize that in the problem in question

we are not dealing with a single speciﬁ ed experimental arrangement, but are

referring to two different, mutually exclusive arrangements . . .

On the question of our ability to exercise a choice of measurement, he

had this to say:

It may also be added that it obviously can make no difference as regards

observable effects obtainable by a deﬁ nite experimental arrangement,

whether our plans of constructing or handling the instruments are ﬁ xed

beforehand or whether we prefer to postpone the completion of our plan-

ning until a later moment when the particle is already on its way from one

instrument to another.

Bohr had dismissed Einstein’s challenge, though he had been less than

clear regarding the reasons. For the physicists of the Copenhagen–

Göttingen schools, the debate had in any case already been won by

Bohr and there were more pressing problems to be dealt with.

But Einstein’s 1931 adaptation of the photon box experiment contained

the seeds of another, more powerful challenge to the authority of the

Copenhagen interpretation. Bohr would be quite unprepared for Ein-

stein’s next move.

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The early 1930s saw the dramatic rise of experimental nuclear physics. In February 1932,

Cambridge physicist James Chadwick obtained evidence for an electrically neutral parti-

cle—the neutron.

Although it was not immediately recognized as a fundamental nuclear

particle, the neutron would soon resolve many puzzles.

Later that year, Cambridge physi-

cists John Cockcroft and Ernest Walton used a linear particle accelerator to demonstrate

the ﬁ rst artiﬁ cially induced nuclear reactions.

Other types of particle accelerators were developed. In California, American physi-

cist Ernest Lawrence embarked on the construction of a series of ever-larger cyclotrons,

designed to accelerate particles around a circular path created by an electromagnet, prom-

ising greater efﬁ ciencies and higher particle energies. In 1932 Lawrence constructed a

cyclotron containing a magnet with an eleven-inch diameter pole face delivering proton

energies of over a million electron volts.

In the meantime, Dirac had given up on his hole-derived proton, ﬁ nally accepting

in 1931 that the hole would have to have the same mass as the electron. He introduced

A Bolt from the Blue

Princeton, May 1935

Chadwick’s letter to Nature, ‘Possible Existence of a Neutron’, Nature, 129, 1932, p. 312

is reproduced, together with a handwritten letter to Bohr outlining the discovery, in Brown,

pp. 365–367.

Physicists were still convinced that the nucleus contained electrons as well as protons and

for a time the neutron was believed to be a composite proton–electron particle. The neutron

was recognized to be a fundamental particle a year after its discovery.

The Cockcroft–Walton apparatus used a system of voltage multipliers to accelerate protons

to energies around 700,000 electron-volts.

the quantum story

142

the positive electron, ‘a new kind of particle, unknown to experimental physics, having

the same mass and opposite charge to an electron.’ American physicist Carl Anderson

found evidence for this particle, which he named the positron, in cosmic ray experiments

in 1932–33.

Dirac shared the 1933 Nobel Prize for physics with Schrödinger. The Nobel Committee

also announced the award of the 1932 Prize to Heisenberg. All three physicists went to

Stockholm in December 1933. In his Prize lecture, Dirac speculated on the possible exist-

ence of a negative proton, and of stars composed entirely of what would later become

known as anti-particles.

On 30 January 1933 Adolf Hitler became Chancellor of Germany. In April, the new

National Socialist government introduced laws forbidding Jews from holding positions in

the Civil Service, including academic positions in German universities. Max Planck, now

the venerated president of the Kaiser Wilhelm Gesellschaft, made a direct appeal to Hitler,

arguing that the forced emigration of Jewish scientists would destroy German science.

It was to no avail. There followed an exodus of near biblical proportions. A quarter

of all the physicists in Germany were displaced, including many Nobel Prize winners.

Among them were Max Born and James Franck. Although he was not Jewish and there-

fore not subject to the new laws, Schrödinger was disgusted by the policies of the Nazi

regime. He left Berlin for exile in Oxford.

In October 1932 Einstein had accepted an appointment at the newly founded Institute

for Advanced Study in Princeton. He had intended to spend ﬁ ve months of each year in

Princeton and the balance of his time in Berlin. But in December 1932 he left Germany,

never to return. He settled into permanent residence in Princeton in October 1933. Look-

ing around for bright young mathematicians with whom to work, Einstein was drawn to

a Russian, Boris Podolsky, and an American, Nathan Rosen.

They worked together to reﬁ ne Einstein’s latest and most compelling challenge on the

completeness of quantum theory.

Einstein had needed to ﬁ nd a physical situation in which it is possible in

principle to acquire knowledge of the state of a quantum particle without

disturbing it in any way. Bohr would thereby be denied access to the argu-

ments he had used to escape Einstein’s earlier challenges. The modiﬁ ed

Anderson initially thought that the particle tracks he had observed in these experiments

were due to protons. In May 1933 he suggested that they were, in fact, due to positrons. These

particles were subsequently conﬁ rmed to be Dirac’s positive electrons by Patrick Blackett and

Guiseppe Ochialini.

a bolt from the blue

143

photon box experiment, in which the experimenter is allowed to choose

which of two complementary observables to measure exactly, was a ﬁ rst

step towards the solution.

The Einstein–Podolsky–Rosen (EPR) gedankenexperiment now took the

approach a stage further. The experiment involves measurements made

on one of two quantum particles that have interacted at some time in

their recent history and have subsequently moved apart. We will denote

these as particle A and particle B. The position and momentum of particle

A are complementary observables and we cannot measure one without

introducing an uncertainty in the other in accordance with Heisenberg’s

uncertainty principle. Similar arguments can be made for the position

and momentum of particle B.

However, if we now consider the difference between the positions of

particles A and B, q

− q

, and the sum of their momenta, p

+ p

, it is

possible to show that these are quantities whose operators do commute.

There is therefore no restriction in principle on the precision with which

we can measure these quantities simultaneously.

Einstein, Podolsky, and Rosen ﬁ rst established what seems to be a fairly

reasonable (though philosophically loaded) deﬁ nition of physical reality:

If, without in any way disturbing a system, we can predict with certainty

(i.e. with a probability equal to unity) the value of a physical quantity, then

there exists an element of physical reality corresponding to this physical

quantity.

The purpose of this statement is to make clear that for each particle

considered individually, the measurement of one physical quantity (the

position of B, say) with certainty implies an inﬁ nite uncertainty in its

momentum. Therefore, according to this deﬁ nition of reality, under these

circumstances the position of particle B is an element of physical reality

but the momentum is not. Obviously, by choosing to perform a different

measurement, we can (in the language of Einstein, Podolsky, and Rosen)

establish the reality of the momentum of particle B but not its position.

But we can show that the difference in the positions of particles A and

B and the sum of their momenta are not subject to this constraint. Sup-

pose we now allow the two particles to interact and move a long distance

the quantum story

144

apart. We perform an experiment on particle A to measure its position

with certainty. We know that the difference in position must be a physi-

cally real quantity and so we can deduce the position of particle B also

with certainty. We therefore conclude that the position of B must be an

element of physical reality according to the deﬁ nition given above.

However, suppose instead that we choose to measure the momentum

of particle A with certainty. We know that the sum of the momenta must

be physically real, and so it follows that we can deduce the momentum

of particle B with certainty. We conclude that it too must be an element

of physical reality. Thus, although we have not performed any measure-

ments on particle B following its separation from A, we can establish

the reality of either its position or its momentum from measurements we

choose to perform on A which, by deﬁ nition, do not disturb B.

The Copenhagen interpretation denies that we can do this. We are

forced to accept that if this interpretation of quantum theory is correct,

the physical reality of either the position or momentum of particle B is

determined by the nature of a measurement we choose to make on a

completely different particle an arbitrarily long distance away. Einstein,

Podolsky, and Rosen argued that: ‘No reasonable deﬁ nition of reality

could be expected to permit this.’

The EPR thought experiment strikes right at the heart of the Copenhagen

interpretation of quantum theory. If the uncertainty principle applies

to an individual quantum particle, then it appears that we must invoke

some kind of ‘spooky’ action at a distance if the reality of the position

or momentum of particle B is to be determined by measurements we

choose to perform on A.

Whether it involves a change in the physical state of the system or merely

some kind of communication, the fact that this action at a distance must be

exerted instantaneously on a particle an arbitrarily long distance away from

our measuring device suggests that it violates the postulates of special rela-

tivity, which restrict any signal to be communicated no faster than the speed

of light. Einstein, Podolsky, and Rosen did not believe that it is necessary to

invoke such action at a distance. The position and momentum of particle B

are deﬁ ned all along and, as there is nothing in the wavefunction which tells

us how these quantities are deﬁ ned, quantum theory is incomplete.

a bolt from the blue

145

They concluded:

While we have thus shown that the wave function does not provide a com-

plete description of physical reality, we left open the question of whether

or not such a description exists. We believe, however, that such a theory

is possible.

The Einstein, Podolsky, Rosen paper, entitled ‘Can the Quantum-

mechanical Description of Physical Reality be Considered Complete?’ was

published in the journal Physical Review in May 1935. The paper appears to

have been written largely by Podolsky, and there is much in the language

and nature of the argumentation employed that Einstein appears later to

have regretted. In particular, the criterion of physical reality as described

above unnecessarily exposed the EPR argument to a powerful counter-

argument. All the more disappointing, perhaps, as the main challenge

presented by Einstein, Podolsky, and Rosen does not require this (or any)

criterion of physical reality, though it does rest on the assumption that,

however reality is deﬁ ned, it is deﬁ ned to be local.

The EPR challenge was reported in the popular press before it was

published in Physical Review. On Saturday, 4 May 1935 The New York Times

carried an article entitled ‘Einstein Attacks Quantum Theory’ which pro-

vided a non-technical summary of the main arguments, with extensive

quotations from Podolsky. He concluded that whilst quantum mechan-

ics could be regarded as technically correct, it ‘is not a complete theory.’

Einstein deplored the article and the publicity surrounding it. The arti-

cle was followed in the same edition by a report by American physicist

Edward Condon who noted that the arguments raised a ‘point of doubt’

but who went on to identify the reality criterion as the argument’s most

signiﬁ cant weakness.

Bohr ﬁ rst heard of the EPR argument from Rosenfeld, who was at that

time working with Bohr in Copenhagen. Rosenfeld later reported that:

This onslaught came down upon us as a bolt from the blue. Its effect on

Bohr was remarkable . . . as soon as Bohr had heard my report of Einstein’s

argument, everything else was abandoned: we have to clear up such a mis-

understanding at once. We should reply by taking up the same example

and showing the right way to speak about it. In great excitement, Bohr

the quantum story

146

immediately started dictating to me the outline of such a reply. Very soon,

however, he became hesitant. ‘No, this won’t do, we must try all over

again . . . we must make it quite clear . . .

’ So it went on for a while, with

growing wonder at the unexpected subtlety of the argument.

Others were devastated by the EPR challenge. Pauli was furious. Dirac

exclaimed: ‘Now we have to start all over again, because Einstein proved

that it does not work.

Bohr and his colleagues worked on their defence day after day, week

after week. They took the EPR thought experiment to pieces and reas-

sembled it. A solution began to emerge. ‘They do it “smartly”,’ Bohr

remarked, ‘but what counts is to do it right.’

Bohr’s reply to the EPR argument was published in outline in Nature in

June 1935 and subsequently in more detail in Physical Review in October. In

the latter paper he chose to use the same title that Einstein, Podolsky, and

Rosen had used in May and the abstract reads as follows:

It is shown that a certain ‘criterion of physical reality’ formulated in a recent

article with the above title by A. Einstein, B. Podolsky and N. Rosen con-

tains an essential ambiguity when it is applied to quantum phenomena. In

this connection a viewpoint termed ‘complementarity’ is explained from

which quantum-mechanical description of physical phenomena would

seem to fulﬁ ll, within its scope, all rational demands of completeness.

Bohr’s paper is essentially a summary of complementarity and its appli-

cation to quantum theory. He rejected the argument that the EPR thought

experiment creates serious difﬁ culties for the Copenhagen interpretation

and stresses once again the importance of taking into account the neces-

sary interactions between the objects of study and the measuring devices

used to study them. He wrote:

From our point of view 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 inﬂ uence on the very

a bolt from the blue

147

conditions which deﬁ ne 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.

In essence, Bohr argued that it does not matter that the position and

momentum of particle B can be inferred from measurements we make

on A. The simple fact is that we cannot conceive an experimental arrange-

ment that will allow us to exercise the choice demanded by Einstein,

Podolsky, and Rosen. By setting up an experiment to measure the posi-

tion of A with certainty, we deny ourselves the possibility of measur-

ing its momentum, and vice versa. And if we cannot actually exercise the

choice to measure either the position or momentum of particle A, then

the actual properties and behaviour of B are really rather moot. Even if

there is no mechanical disturbance of particle B (as EPR assumed and

Bohr accepted), its elements of physical reality are nevertheless deﬁ ned

by the nature of the measuring device we have selected for use with par-

ticle A.

The EPR argument pushed Bohr from his previous, perhaps rather

ambiguous philosophy to a ﬁ xed anti-realist position. It was at this point

that Bohr dropped the use of ‘disturbance’ as a counter-argument and

focused instead on the nature of the experimental arrangement itself pre-

cluding the type of reality that could be exposed. Mechanical disturbance

could no longer serve Bohr’s purpose, just as Einstein had intended.

Many in the physics community seemed to accept that Bohr’s paper

put the record straight. But Bohr’s wording is rather vague and uncon-

vincing. In emphasizing the fundamental role of the measuring instru-

ment in deﬁ ning the elements of reality that can be observed, he offered

no new insight as to how such a deﬁ nition is physically established.

However, Bohr failed to respond to the real challenge posed by Ein-

stein, Podolsky, and Rosen. What these physicists had created in their

thought experiment was a two-particle wavefunction that allows for cor-

relations to be established between quantum particles over potentially

vast distances. Making a measurement then involves a notional collapse

of this wavefunction, now formally enshrined in the theory of quantum

the quantum story

148

measurement as Hungarian mathematician John von Neumann’s ‘pro-

jection postulate’.

The collapse implies a spooky action at a distance that appears to vio-

late the basic postulates of special relativity.

Does such a measurement necessarily imply an action at a distance?

Certainly, if we could somehow delay our choice of measuring instru-

ment (position versus momentum) until almost the last moment, then

in principle the information potentially available to us about a particle

some considerable distance away appears to change instantaneously. We

are left to wonder how particle B is supposed to ‘know’ what physical

property—position or momentum—it is supposed to reveal as a result

of measurements we choose to make on A. An action at a distance will

be required if the measurement performed on A changes the physical

state of B or results in some kind of communication to B of particle A’s

changed circumstances.

Now if the two-particle wavefunction reﬂ ects only our state of knowl-

edge of the quantum system, then its collapse would not necessarily seem

to affect the system’s physical properties. However, the problem remains

that the collapse of the wavefunction requires that those physical proper-

ties become clearly deﬁ ned and manifested in the quantum system where

before they were vague and undeﬁ ned. The physical properties of particle

B suddenly become ‘real’ (or measurable), where before they were not.

There is simply no mechanism to account for this in the Copenhagen

interpretation of quantum theory.

In his book Mathematical Foundations of Quantum Theory, von Neumann distinguished

between continuous, causal dynamics described by the time-dependent Schrödinger wave

equation and the discontinuous, acausal measurement process. The book was ﬁ rst published

in Berlin in 1932.

149

Schrödinger was elected to a fellowship at Magdalen College, Oxford, in October 1933.

With support in the form of a two-year grant from Britain’s Imperial Chemical Indus-

tries (ICI), he and Anny moved to Oxford the following month. The Berlin Deutsche

Zeitung lamented his loss to German science: ‘[Schrödinger’s departure] is all the more

to be regretted, as only a short time ago Professor Hermann Weyl, Ordinarius for Math-

ematics at the University of Göttingen, also in the ﬁ eld of theoretical physics, accepted the

call to the American university of Princeton.’

It was at his formal welcome by other fellows of Magdalen College that Schrödinger

learned that he had won the 1933 Nobel Prize for physics. As he later recalled, the president

of the college, George Gordon, called him to his ofﬁ ce and advised him that: ‘ The Times

had said I would be among that year’s prize winners. And in his chevalieresque and witty

manner he added, “I think you may believe it. The Times do not say such a thing unless

they really know. As for me, I was truly astonished, for I thought you had the prize.” ’

Schrödinger had arranged for the award of a second, temporary fellowship for a Berlin

colleague, Arthur March. He had recently begun an affair with March’s wife Hildegunde.

On 30 May 1934 Hilde bore Schrödinger’s ﬁ rst child. They had made no secret of their

relationship but the baby, named Ruth Georgie Erica, was registered as the child of Hilde

and her husband. Both Hilde and Anny cared for the baby and, to all intents and pur-

poses, Schrödinger lived for a time as though with two wives.

Frederick Lindemann, who had worked behind the scenes to bring Schrödinger to

Oxford, was furious, calling Schrödinger a ‘bounder’. He struggled to persuade ICI to

The Paradox of

Schrödinger’s Cat

Oxford, August 1935