The EinsteinPodolskyRosen (EPR) problem

The EPR reasoning

figure 8
The EPR problem must be seen as an
ultimate attempt from the part of Einstein to prove
`incompleteness of quantum mechanics', while circumventing Bohr's
quantum postulate by (allegedly) `measuring a
physical quantity without interaction with a measuring instrument'. According to the
EPR proposal this is achieved by making use of a system of two
correlated particles (1 and 2) that are far apart after
having interacted during preparation by a source^{23}.
Their initial state is an entangled state. A measurement
procedure is considered in which only particle 1 is
interacting with a measuring instrument (see figure 8). It is
assumed that the state vector of the twoparticle system is such
that the positions of particles 1 and 2 are strictly correlated.
Then, from a measurement of particle 1's position
(Q_{1}) the value of particle 2's position
(Q_{2}) can be inferred.

Since the position of particle 2 can be predicted with certainty,
and can be determined without interaction with particle 2, it is
assumed to be an element of physical reality, that is, a property the object
objectively possesses, independent of any measurement. Such an `element of physical reality' is
yielding an explanation by determinism
of the `experimentally obtained value of a quantum mechanical observable'
(in the sense that the object is supposed to already possess that value before the measurement,
compare the possessed values principle).

The state of the twoparticle system is chosen such that not only
the positions of the particles but also their momenta are
strictly correlated. By measuring the momentum
(P_{1}) of particle 1 it is therefore possible to
determine the momentum (P_{2}) of particle 2
without interacting with the latter particle. Therefore also
momentum is assumed to be an `element of physical reality' of particle 2.

Since particle 2 cannot "know" which observable of particle 1 has been chosen to be
measured, position and momentum must simultaneously be
objective properties of particle 2.

EPR conclude that, since within the quantum mechanical formalism there does not
exist any mathematical entity that can represent a state having
sharp values of the two incompatible observables position and momentum (of particle 2),
quantum mechanics must be incomplete.

Remarks on the EPR reasoning:

Note that the notion of an `element of
physical reality' as used in the EPR paper (viz. as an `objectively possessed
value of a quantum mechanical observable')
is potentially applicable only in the objectivisticrealist
interpretation of quantum mechanics, since in the
contextualisticrealist and
empiricist interpretations measurement results
are thought to be possibly (co)determined by the interaction with the measuring instrument;
in the empiricist interpretation
a measurement result for particle 2 does not even exist because there is no measuring instrument
corresponding to that observable (compare the distinction between EPR and
EPRBell experiments).
Bohr's attempt at a refutation of the EPR challenge, as
contained in Bohr's answer to EPR, hinges on the possibility
of a contextualisticrealist interpretation of quantum mechanical observables, in which
the possessed values principle is circumvented as a consequence
of the `contextual meaning of a quantum mechanical measurement result'.

Since position and momentum have continuous spectra they pose mathematical
problems that
are not essential but are didactically undesirable (compare),
the problem is usually discussed in terms of Bohm's
formulation using spin observables^{5}, for both particles
the observables Q and P being replaced by S_{z}
and S_{x}, respectively.
As the entangled state then is taken the singlet state
Ψ_{(S = 0)}> 
= 
S_{1z} = + >S_{2z} = − > −
S_{1z} = −> S_{2z} = + > = 

= 
S_{1x} = + >S_{2x} = − > −
S_{1x} = − >S_{2x} = + >, 
being entangled both with respect to the S_{z} and the S_{x} observables
of the two particles.
More generally, the gist of the EPR problem is represented by a twoparticle state described by a state
vector that is entangled in two different representations:
Ψ> =
∑_{m} c_{m}a_{1m}>a_{2m}> =
∑_{n} d_{n}b_{1n}>b_{2n}>,
in which a_{1m}> and a_{2m}> are eigenvectors of observables A_{1}
and A_{2}, respectively (and analogously for b_{1n}> and b_{2n}>
with respect to observables B_{1} and B_{2}). The essential point is the strict
correlations between on one hand values of A_{1} and A_{2}, and on the other hand
between B_{1} and B_{2}, A_{i} and
B_{i} being incompatible for i = 1,2.

Bohr's answer to EPR

Bohr's answer to EPR is based on the `Copenhagen interpretation', viz. the
strong correspondence principle (stating that
physical quantities are only defined within the context of the
measurement serving to measure it), the
quantum postulate (emphasizing a certain `wholeness'
of a quantum phenomenon), and
complementarity. According to Bohr in the EPR
experiment the phenomenon must include the measurement arrangement for
particle 1, even if the measurement is only regarding particle 2.
Since measurement arrangements for position and momentum of particle 1 are mutually
exclusive (due to the incompatibility of these observables) they cannot be
simultaneously measured. Hence, the strictly correlated observables
(position and momentum of particle 2) cannot be `simultaneously
defined'. As Bohr puts it: there is an essential
ambiguity in the definition of the EPR
elements of physical reality (of position and momentum
of particle 2), because these are defined within different experimental contexts.

Critique of Bohr's answer to EPR
According to Bohr^{66}
in analyzing the EPR experiment no essential difference is met from the usual way the notion
of `complementarity' is applied to quantum measurements like the doubleslit experiment.
However, since this judgment is based on the
`(semi)objective existence of the strict correlations between measurement results
of the two particles of the EPR pair' criticized here,
this judgment does not seem warranted.
Indeed, the circumstance of `strict correlation' is alien to the "simple examples" previously discussed by Bohr.
It plays a crucial role in the EPR reasoning, and it is overlooked by Bohr that it can only be consistently applied to
EPRBell experiments
(in which for each EPR pair both measurement results are available). Probably Bohr's oversight in this
matter is caused by his `classical way of thinking
about quantum mechanical observables', inducing him to extend `classical objectivity' to quantum mechanical
quantities.
According to Jammer the EPR problem has
forced Bohr to change his interpretation from an interactional to a relational
one. Not only the interaction between the microscopic
object and the measuring instrument (for particle 1) is
thought to be instrumental in defining the `element of physical reality' of particle 2, but also the correlation of the
quantities of the two particles. Thus,
relation = interaction + correlation,
once again illustrating the difference with Bohr's earlier emphasis on `interaction of microscopic object and
measuring instrument'.

The nonlocality conundrum
It was realized by Einstein that
this relationalism was introducing a feature of nonlocality
into the Copenhagen interpretation: the measuring
instrument for particle 1 is contributing to the definition of
the `element of physical reality' of particle 2 evidently in a
nonlocal way. This socalled EPR nonlocality was
unacceptable to Einstein, who referred to it as "spooky
actionatadistance." Its ontological status has been much debated,
giving rise to paradoxical ideas awarding it the status of a `conundrum'.

An alternative to Bohr's correspondence reasoning, based on a
consideration of states rather than observables, but also
yielding `EPR nonlocality', makes use of the `individualparticle aspect of the
Copenhagen interpretation'. An individualparticle interpretation
of the EPR experiment requires that, since the position observable Q_{1}
of particle 1 is welldefined as soon as Q_{1} has been measured
(compare figure 8), the state
vector of particle 2 must change discontinuously to the
corresponding eigenvector (this, of course, can only be
approximately so in case of a continuous spectrum). This
discontinuous change (often interpreted as strong von Neumann
projection, cf. Publ. 16 and
Publ. 57)
must have been brought about in a nonlocal way by
the measurement of particle 1, since it would happen
simultaneously with a measurement event taking place far away.

It was Einstein's conviction that the EPR
experiment can be understood in a local way if the state
vector is not considered a description of an individual
object but of an ensemble.
Then the discontinuous change of the particle 2 state vector can
be understood as a selection of a subensemble, which does not
seem to imply any real influence on particle 2 by the measurement
of particle 1 (however, compare).

`Bohr's answer to EPR' is not consistent with
his `correspondence principle (strong form)'
It has seldom been noticed that
Bohr's answer, being based on the strong form of his correspondence principle,
is actually inconsistent (see Publ. 16).
It assumes that the correlation between the positions
of particles 1 and 2 (as well as the correlation between their momenta) is
welldefined independent of whether this correlation is measured or
not. However, these correlations are described by quantum
mechanical observables (Q_{1}Q_{2}
and P_{1}P_{2}, respectively), and,
according to the `strong correspondence principle', should be defined
only within the contexts of measurements of these
observables. Hence, Bohr's answer can only be consistently
applied within an experimental context in which a measurement is
performed on both particles. A consistent rebuttal of the
EPR challenge by Bohr would have denied the definability, within
the proposed EPR experiment, of the `correlations employed by EPR to
prove the incompleteness of quantum mechanics'. That Bohr did not
do so presumably is a consequence of his
realist interpretation of quantum mechanical observables, the only difference with
Einstein being that Bohr's `realist interpretation' was not an
objectivistic but a
contextualistic one.

Bohr actually accepted the EPR measurement arrangement as a joint
measurement of an observable of particle 1 and the correlated
observable of particle 2. This acceptance probably is a consequence of the
Copenhagen confusion of preparation and measurement.
Bohr's acceptance of the EPR proposal as a
measurement of a particle 2 observable (for instance,
Q_{2}, if Q_{1} is measured) also
brings him in conflict with complementarity: it would
enable a simultaneous measurement of Q_{2} and
P_{2}; indeed, since Q_{1} and
P_{2} are compatible, it is possible to measure
these observables without any mutual disturbance (see figure 9).
figure 9
Then, if the Q_{1} measurement would be interpreted as a
Q_{2} measurement, it would be possible to
obtain in this way sharp values for both position and momentum
of one and the same individual particle 2.

Fundamental difference between EPR and EPRBell experiments
The fundamental difference between the
experiments of figures 8 and 9 marks the difference between the
original EPR experiment and `EPRBell experiments
(Alice measuring Q_{1}
while Bob is measuring P_{2}) intended to test
the Bell inequality'. The fundamental
difference of the two experimental arrangements (in EPRBell experiments
measurements are performed on both particles) makes the
habit of referring to EPRBell experiments as `EPR
experiments' very undesirable.
In particular, application of
von Neumann's projection postulate in EPRBell experiments
(to the effect that the state change of particle 2 would satisfy
this postulate on the basis of a measurement performed on particle 1)
is impossible because particle 2 would also be subjected to the
`interaction with its own measuring instrument'.

On the other hand, it is easy to see that in both
EPR and EPRBell experiments `von Neumann projection'
is applicable to EPR experiments as a preparation principle of
particle 2, conditional on the measurement result obtained for particle 1.
Thus, applying the theory of conditional preparation to
an EPR experiment in which observable A_{1} is measured in
the entangled state
ψ> =
∑_{m} c_{m}a_{1m}>a_{2m}>,
we obtain as the final state of the premeasurement the state
Ψ_{f}> =
∑_{m} c_{m}
ψ_{1m}>a_{2m}>
θ_{m}>,
θ_{m}> pointer states.
The states of particle 2 remain unchanged because
this particle is not influenced by the measuring instrument.
By considering the possibility of joint
measurements of the pointer observable and arbitrary observables of particles 1 and 2 it follows that
the conditionally prepared state (conditional on measurement result m) is the state
ψ_{1m}>a_{2m}>, reducing to a_{2m}>
if particle 1 is ignored.
Evidently, this result coincides with the one obtained by an intuitive application of
von Neumann projection
to particle 2. Note, however, that this obtains only because the latter particle is not
interacting with
a measuring instrument (if it were, the state of particle 2 would be influenced just
like particle 1's state was changed).
Note also that for more general initial states ψ> =
∑_{mn} c_{mn}a_{1m}>a_{2n}>
we in the same way find as the conditionally prepared state
∑_{n} c_{mn}a_{2n}>
(up to normalization), which generalizes von Neumann projection, the latter states
for different values of m not even needing to be orthogonal.

The general `lack of distinction between EPR and EPRBell experiments' is a consequence of a
`realist interpretation', in which no distinction is made
between a measurement result as a `reading of a pointer position
of a measuring instrument' and a `property of the microscopic
object'. In an `empiricist interpretation' an EPR experiment simply
does not yield a measurement result for particle 2. Indeed, the
EPR "paradox" is an important reason to prefer an `empiricist
interpretation' over a realist one (compare), even though, maybe, a
consistent application of Bohr's strong correspondence principle
(in which a correlation is welldefined only within a measurement of that correlation)
would also allow a local contextualisticrealist interpretation in which an
observable of particle i (i= 1,2) is (co)determined by the local
context of the measuring instrument of that same particle i (compare).

Einstein's reaction to Bohr's answer

According to Einstein the `nonlocality' inherent in Bohr's
relationalism is a
consequence of the latter's assumption of completeness. This would imply a
tradeoff of `completeness' and `locality', in the sense that,
since
completeness → nonlocality,
it would logically follow that
locality → incompleteness.
Both choices (either `completeness' or `locality') are possible to
the exclusion of the other one. Whereas Bohr's choice was
`completeness', was Einstein's choice `locality'. It seems that, whereas Einstein was aware of the
possibility that either choice could be made (although he preferred 'locality'), it seems that
for Bohr only the choice of `completeness' was open (compare).

Critique of Einstein's reaction
It should be noted that here `completeness' means
completeness in the restricted sense, associated with `contextuality
due to the interaction of object and measuring instrument'. Hence, in the EPR discussion
`incompleteness' is associated in the first place with objectivity
(i.e. noncontextuality) rather than with an ensemble interpretation
of the state vector (although for Einstein the `ensemble interpretation'
was crucial). Actually, the `BohrEinstein discussion on the interpretation of quantum mechanics' was not about
whether a realist
interpretation of quantum mechanics is possible (both
having in mind a classicallyrealist notion of `physical quantity'),
but rather whether a `realist interpretation of quantum mechanical
observables' (assumed by both) can be objectivistic
(i.e. independent of the `observer including his measuring instrument', Einstein)
or should be contextualistic (Bohr).

Although in the EPR problem Einstein did not transcend the
`quantum mechanical formalism', his paradigm may have been
incompleteness in the wider sense,
his conviction being that `the ψfunction is not to be understood as
the description of an individual object but rather of an ensemble of such objects', each individual
object being characterized by an `element of physical reality'.
This has widely been interpreted as implying that the
EPR discussion was about the possibility of hidden variables (rather than about the
contextuality implied by the correspondence principle).
It is questionable whether so many physicists, raised in the classical tradition
of an `objective description of physical reality', would have chosen
Bohr's side if Einstein would have stressed the `objectivity
versus contextuality' antagonism rather than the issue of whether
the state vector describes an individual particle or an ensemble
(compare). As a result of the confusion between
`completeness in the wider sense' and `completeness in the restricted sense'
Einstein's opposition was widely interpreted as `yielding to the lure of metaphysics'
as implied by the assumption of `incompleteness in the wider sense'.

Possibility of `additional assumptions (loopholes)'
It is important to note that the logical reasoning employed in
Einstein's reaction to Bohr's answer, viz.
(a → b) → (not b → not a),
is valid only if there are no additional features contributing to the realization
of b. If there is such an additional feature c, then we have
((a and c) → b) → (not b → (not a or not c)),
and the conclusion `not a' cannot be drawn.

In the EPR discussion an additional assumption exists, viz. the
assumption of a `realist interpretation of
quantum mechanical observables'. Both Bohr and Einstein agreed on that
(compare). Hence, instead of
`completeness → nonlocality', we have
completeness and
realist interpretation → nonlocality
It is logically possible that the assumption of locality
does not entail `incompleteness' but rather the impossibility of a `realist
interpretation of quantum mechanical observables'.

Actually, Einstein's expectation
that an assumption of `incompleteness of quantum mechanics' is sufficient
to save `locality' in an objectivisticrealist interpretation, does not come true.
It is not possible to consider conditional preparation
of particle 2 in the EPR experiment as a mere selection of a subensemble,
particles 2 having values of quantum mechanical observables
already before the particle 1 measurement is carried out
(as assumed by EPR).
The reason for this is the
invalidity of the possessed values principle.
The failure of this principle entails the
impossibility of a simultaneous existence of all possible EPR
elements of physical reality.
In this respect Bohr's allegation of `ambiguity of the EPR
element of physical reality' was completely justified:
since it is impossible to assume that all particle
2 observables had their values already before the measurement, a
realist interpretation of quantum mechanical observables
in the EPR experiment is virtually forced into a nonlocal
contextualism in which the measurement of a particle 1
observable influences the reality of particle 2 in such a way
that the correlated observable can obtain a certain value.
Nevertheless, Bohr's reasoning is not cogent since there is an alternative to
Bohr's `contextualisticrealist interpretation', viz. the assumption that this interpretation is not applicable
to the EPR experiment because in that experiment no measurement is carried out on particle 2,
and hence, contrary to Bohr's assumption, observables of that particle are not
welldefined (compare).
Due to the `fundamental difference
between EPR and EPRBell experiments', causing the experimental
contexts of these experiments to be fundamentally different (compare),
`nonlocal contextuality' is not at all enforced in an `empiricist interpretation':
only the local contexts of the particles need to be taken into account.

`EPR nonlocality' and experiment

Contrary to a widespread belief nonlocality has
not been experimentally demonstrated. On the contrary,
measurements like the bilocal ones performed by Aspect et al. exhibit
quantum mechanical locality in the sense that in
correlation measurements like the one of figure 9 the measurement results of one
observable (Q_{1}, say) are independent of which
observable of particle 2 is measured jointly (e.g.
P_{2}). This is sometimes called `parameter
independence'; it is consistent with `compatibility of
the observables measured jointly' (c.q. the
principle of local commutativity
of `local quantum field theory').

Of course, in case of `parameter independence' there may be `outcome
dependence', to the effect that the individual outcome of the
measurement on particle 1 depends on the individual
outcome of the measurement on particle 2 (and vice versa).
`Outcome dependence' could have different causes. It
could be a consequence of
i) a nonlocal interaction, instantaneously influencing one particle if a
measurement is performed on the other one;
ii) a previous interaction of the particles,
by which the twoparticle object has been prepared in a
correlated state of the two particles.

From a physical
point of view the explanation of `correlation of the
measurement results by means of a nonlocal interaction' is
extremely implausible. The reason for this implausibility is the
experimental corroboration of `parameter independence', implying
that the marginals of the joint probability distribution of a
joint measurement are independent of whatever happens to the
other particle. This means that, if the individual objects
of a pair would interact nonlocally, then the effects of this
interaction would cancel on the statistical level, so as
to become unobservable to any quantum mechanical measurement.
This is sometimes referred to as a `peaceful coexistence' (of
`individual nonlocality' and `statistical locality'). Although
such a `peaceful coexistence' is logically possible, it is highly
improbable. It could only be understood on the basis of a kind of
cosmic conspiracy, washing out any experimental trace of
`nonlocality on the individual level', so as to make it consistent
with `locality on the statistical level of the quantum mechanical
ensemble'. `Individual nonlocality' is reminiscent of the 19th
century world aether, also perfectly hiding itself to any attempt
at approaching it in an operational way. Since there is no
empirical evidence supporting `individual nonlocality' (not even
by the Aspect measurements!), it seems preferable to deal with it
in the same way Einstein dealt with the world aether.

Remarks on `EPR nonlocality'
 Origin of `EPR nonlocality'
The ultimate source of the idea
of `EPR nonlocality' is Bohr's application of his notion of
quantum phenomenon to the EPR experiment,
often associated with the the idea of entanglement.
A form of `nonlocality' is also implied by a
`realist individualparticle
interpretation of the quantum mechanical formalism', in which it is assumed that in the
original EPR experiment of figure 8
an individual measurement on particle 1 instantaneously
influences particle 2 so as to cause strong von Neumann projection of
its state. According
to Einstein the latter `nonlocality problem' can be solved by abandoning the
individualparticle interpretation (to be associated with `completeness of quantum mechanics') in
favour of a `(realist) ensemble interpretation'
(representing `incompleteness of quantum mechanics'), `strong von Neumann projection' representing a transition
to a subensemble (compare).
 Dubious role of the `possessed values principle'
Problems with respect to the `possessed values principle' cast strong
doubts on Einstein's `ensemble solution' of the `EPR nonlocality'
problem:^{70} it is not possible to attribute in an objective sense,
independent of any measurement, to each individual particle 2 a
welldefined value of both Q_{2} and
P_{2}. Bohr was right when observing that `the
ensemble Einstein needs for his reasoning' does not seem to exist
(by Bohr this is cast in terms of ambiguity of the definition
of the EPR `element of physical reality').
This need not imply,
however, that Bohr's `contextuality solution' (entailing `EPR nonlocality') is the compulsory alternative.
Bohr and Einstein shared a realist interpretation of quantum mechanical
observables, the only difference
being whether a particle possesses a value of an
observable objectively (Einstein), or only contextually (Bohr).
According to Bohr the mutual exclusiveness of the measurement
arrangements of incompatible observables of particle 1 would
prevent simultaneous attribution of values to incompatible
observables of particle 2. Bohr's solution implies that the `possessed values
principle' is circumvented, however, at the expense of introducing `nonlocality'.
It seems to me that the solutions of Einstein and Bohr, being equally metaphysical, are equally unacceptable:
neither Einstein's `element of physical reality' nor Bohr's `nonlocality'
has directly observable consequences.

There is a third possibility, viz. an empiricist interpretation, in which a
particle cannot simultaneously possess values of incompatible
observables because it cannot possess values of quantum
mechanical observables at all (since observables refer to the
`measuring instrument' rather than to the `microscopic object'). A
value of an observable of particle 2 is welldefined only if a
`measuring instrument for measuring that observable' is actually
present (like in the experiment of figure 9). In the `empiricist interpretation'
it is necessary to draw a clear distinction between `EPR experiments' and
EPRBell experiments,
in `EPR experiments' quantum mechanical observables of particle 2 being undefined
because it is a `preparation' rather than a `measurement' of that particle.

It should be noted
that, since in the EPR experiment of figure 8 we do not have a
measurement of particle 2 but a preparation, there
is no objection to a von Neumann projection as such, since it can
be interpreted as a conditional preparation
(compare Publ. 57; this, of course, is strictly true only for
observables having discrete spectra). Because of the strict
correlation in the initial twoparticle state, and due to the fact
that the state of particle 2 is not influenced by the
measurement on particle 1, von Neumann projection even turns out
to be applicable to EPR as if it were a first kind measurement of the particle 2
observable. This, incidentally, may have contributed to the
interpretation of the `EPR experiment' as a `measurement of
particle 2', making Bohr unjustifiedly think that it was
allowed to apply his quantum postulate also to that particle.

Note that a confusion of `preparation' and `measurement', as observed
here, is impossible in an empiricist interpretation,
because in that interpretation a quantum
mechanical observable is a representation of a `measuring
instrument/procedure'. In the EPR proposal of figure 8 no measuring instrument
for particle 2 is present. If a `measurement result' corresponds to a `final pointer
position of a measuring instrument', then that measurement result cannot
have been present before the measurement, and
the EPR element of physical reality cannot
be represented by a `quantum mechanical measurement result'.

In the `empiricist interpretation' the transition from the initial
(correlated, entangled) state to the final (conditional) one is
not a `(realist) change of the state of an individual
particle', nor a `transition to a (realist) description of a
subensemble', but it is just a transition to a different
preparation procedure, viz. a procedure of conditional preparation, in which
particles 2 are selected on the basis of the measurement results
for particle 1. In order to be able to execute a conditional
preparation of particle 2 by means of selection on the basis of
the particle 1 measurement result, this latter result must be
known to the selector. Hence, no `nonlocality problem in the Bohr/Einstein sense' can arise in
an `empiricist interpretation', contrary to what is the case in a
`realist individualparticle interpretation' (compare) or even in a `realist
ensemble interpretation' (compare).
This is an important reason to prefer an
`empiricist interpretation'. If such an interpretation is
entertained from the outset, then the EPR proposal does not suggest any `nonlocality'.

Role of `strict correlations' in the `EPR experiment'
In the EPR proposal use is made of
a special state vector warranting strict correlations (if measured)
between Q_{1} and Q_{2}, and between
P_{1} and P_{2}, respectively.
Such strict correlations are unexpected if each of the particles would
behave, independently of the other one, according to the
irreducible indeterminism
implicit in Jordan's assertion.
This poses to the `Copenhagen interpretation' a `problem of explanation', addressed in the `EPR challenge'.
 Two possible explanations of `strict correlations'
Ignoring "mystical" solutions like the one presented by Zukav in his book
The dancing Wu Li masters^{0}
(exploiting the idea of a certain `cosmic harmony', necessary to be able to understand strict correlations in
EPRBell experiments if Jordan's assertion would be applicable),
two different "physical" explanations of `strict correlations' use to be contemplated:
i) the possessed values principle, to the effect that `strict correlation' is
a result of its already having been created in the `process of emission of the EPR particle pair'
(the individual measurement results being supposed to be created already at that stage), correlation
being preserved while the particles fly apart and the observables are finally measured
in faithful measurements
(Einstein's explanation by determinism);
ii) nonlocal influences, strict correlation
being assumed `not to have been there beforehand', but to come into being by means of
strong von Neumann projection, the measurement of particle 1
in a nonlocal way realizing the value of the (correlated) observable of particle 2
(compare e.g. Publ. 57). This is the Copenhagen interpretation's
`explanation by nonlocal influencing'.

Both solutions have their drawbacks. Thus, as we know now, the `possessed values principle'
cannot be maintained (also here).
So, Einstein's explanation does not work properly. For the majority of physicists this may have been reason enough
to reject (yet too hastily) Einstein's proposal, and
accept the Copenhagen solution.
However, also the Copenhagen solution is not very attractive.
Thus, by Einstein the Copenhagen interpretation's
`explanation by nonlocal influencing' is disqualified as ``spooky action at a distance.''
`Nonlocal influence on the (experimentally
relevant) relative frequencies of measurement results' being unobservable, `EPR nonlocality' is as
metaphysical as were in Copenhagen eyes Einstein's `elements of physical reality'.
Note that at the time of the EPR discussion `no convincing reason to make a
choice between the two (metaphysical) alternatives'
was available (the KochenSpecker theorem having been derived much later). The only `reason for the general rejection of Einstein's
explanation at the time of the EPR discussion' I can think of is the large influence of
logical positivism/empiricism, combined with the fact that the aspect of `nonlocality' remained
relatively unnoticed for a long time (the latter becoming fashionable only as a result of
Bell's work).

Things changed as a result of the KochenSpecker theorem, which theorem
implies that Einstein's
idea of `quantum mechanical measurement results as elements of physical reality' cannot be maintained.
Taking this into account a simplistic application of classical logic
to the dichotomy of `determinism versus nonlocality'
might seem to result in a conclusion of `EPR nonlocality'.
Nevertheless, there are physicists who, as a result of the wide acceptance
of this latter conclusion by the physics community, have a bad conscience, and who look for
loopholes^{0}
to escape from it. Such a loophole
may be found in the form of an additional assumption,
not explicitly mentioned but nevertheless
liable to yield an alternative explanation of experimental results. A wellknown loophole is the
`efficiency loophole', taking into account the `inefficiency of detection processes'.
However, as a result of a general belief in `nonlocality'
such loopholes are often considered to be tiny, and it is generally expected
that they will all be closed some day to leave `nonlocality'
as the only explanation.

In my view this expectation is unwarranted, however, an
`explanation by determinism
of strict correlations' not at all having been demonstrated to be impossible.
Admittedly, in view of the KochenSpecker theorem it is evident that
such an explanation cannot be given by quantum mechanics.
But perhaps we should not ask such explanations from quantum mechanics,
because this theory presumably is unable to yield it,
analogous to the inability of the `classical theory of rigid bodies' to explain rather than describe the `rigidity of a billiard ball'
(compare). Perhaps Einstein's `elements of physical reality' are really there to explain
measurement results by determinism (as well as the `strict correlations' they may exhibit), be it that these `elements' may not be described by
quantum mechanics but by some subquantum theory (compare).
Like an `atomic theory of the solid state' is able to explain the `rigidity of a billiard ball', might `strict correlations'
have to find their explanation within a subquantum mechanical theory through the existence of `subquantum elements of physical
reality'.
 Criticism of the assumption of `nonlocality'
 `Nonlocality' versus `incompatibility'
It should be realized that `nonlocality' entered the (in)completeness discussion only through the back door.
The `(in)completeness discussion' is about the crucial difference between classical and quantum mechanics,
statistical
applications of classical mechanics being considered to yield incomplete descriptions of reality.
The Copenhagen claim was that, as a result of the incompatibility of observables Q and P,
in this respect quantum mechanics is fundamentally different from classical mechanics.
Hence, `incompatibility of observables' is the crucial issue,
distinguishing `(possibly incomplete) classical mechanics' from `(allegedly complete) quantum mechanics'.
 How `nonlocality' replaced `incompatibility'
In order to challenge the Copenhagen claim of `completeness of quantum mechanics' Einstein had to deal with the
question of `whether welldefined values can be simultaneously attributed to incompatible observables'.
In trying to do so he was hampered
by the `impossibility of simultaneously measuring incompatible observables'
(compare complementarity).
To circumvent this problem Einstein and coworkers considered the EPR experiment,
allegedly `performing a measurement
of an observable of particle 2 without interacting with it' by `measuring a
compatible observable of a distant particle 1'. It was reasoned
that `incompleteness of quantum mechanics' follows from the possibility of in this way `simultaneously
attributing to particle 2 welldefined values of
the incompatible observables Q_{2} and P_{2}'.
By thus relying on an (alleged) simultaneous
measurement of distant particles `nonlocality' entered the scene.
It should be remembered, however,
that the `nonlocality issue' is strongly dependent on
which interpretation of quantum mechanics is adopted (for instance, in an `ensemble interpretation'
no nonlocality follows from the EPR experiment).
It seems to me that the `nonlocality issue' has distracted attention
away from the problem that is really at the basis
of the EPR problem, viz. incompatibility of observables.
By comparing `incompatible observables' in an indirect way by means of their correlations
with a `compatible observable' EPR have complicated the issue to such an extent that
confusion could arise with respect to the importance of
the correlation between `compatible observables' as compared to the `correlation between incompatible observables'.
 Return to metaphysics?
The widely held belief in `nonlocality', based on the EPR problem as well as on later developments
related with EPRBell experiments (in particular, those connected with the Bell inequality),
demonstrates a remarkable change with respect to the `physicist's fear of metaphysics' as compared with
the `logical positivist/empiricist one rejecting Einstein's elements of physical reality'.
Experimental results being consistent with `locality of the
phenomena as expressed by a general experimental satisfaction of the quantum mechanical
principle of local commutativity (implying that
in EPR and EPRBell experiments the statistical measurement results
obtained for particle 1 are independent of what happens to particle 2, and vice versa)
do not suggest any nonlocality.
Nevertheless, nonlocality is widely thought to be there, although
there is no experimental evidence for it^{71}. It seems that the combined
influence of Bohr, Bohm and Bell has been sufficiently strong to
outweigh Einstein's opposition against `nonlocality'. It seems to me, however, that this may have rather a sociological origin
than a physical one. Although by itself nowadays `taking seriously subquantum reality' is as legitimate
as `taking seriously the atomic constitution of a billiard ball', does this not imply
that such an endeavour is not restricted by methodological rules. Abiding as long as possible
with successful general ideas like the idea of `relativistic locality/causality' seems to be one of these rules,
in particular when there is a reasonable alternative (viz. `incompatibility') for giving up an elusive `nonlocality'.
 Generalized observables and EPRBell experiments
Insight into the problem of `nonlocality versus incompatibility' is gained by
considering generalized EPRBell experiments
in which the two jointly measured observables both correspond to
joint nonideal measurements of incompatible standard observables.
Such measurements can be used to analyze
`(violation of) the Bell inequality' by the Aspect measurements.
From this analysis it becomes evident that `violation' can be interpreted as a consequence of `local mutual
disturbance of the measurement results in a joint (nonideal) measurement of
incompatible standard observables of the same particle'
rather than as being caused by a `nonlocal disturbance of one particle due to a
measurement of a (compatible) observable of the other
particle (compare)'.
It is important to note that in the `EPR experiment' of figure 8
no (local) disturbance of particle 2 by any measuring instrument was allowed. By setting
up a measuring instrument for particle 2 the very condition for applying the EPR reasoning has been forfeited.
But also Bohr's reasoning becomes obsolete because
that instrument can create `its own measurement context' (compare).
The important we can learn from analyzing EPR and EPRBell experiments is that Einstein's idea of
`quantum mechanics as a description of an objective microscopic reality is not feasible.
The domain of quantum mechanics is delimited by the impossibility to ignore the
essential influence `measurement itself' is exerting on the results obtained.
If it comes to judging the contest between Einstein and Bohr on the `(in)completeness
issue of quantum mechanics, it turns out that with respect to the `influence of measurement'
Bohr's insight is unsurpassed. On the other hand, by not sufficiently distinguishing
between EPR and EPRBell experiments Bohr has contributed to the `nonlocality conundrum'
already for such a long time unnecessarily burdening the discussions on the foundations of quantum mechanics.

