**Einstein Locality:** In 1935 Albert Einstein, in collaboration with
Boris Podolsky and Nathan Rosen, published a landmark paper entitled
"Can quantum mechanical description of physical reality be considered
complete?" (Einstein, 1935) Einstein had already been engaged for
several years in a discussion with Niels Bohr about the completeness of
quantum theory. In the1935 paper Einstein did not challenge the claim of
the quantum theorists that their theory was complete in the
pragmatic/epistemological sense that it gives all possible empirically
testable predictions about connections between the various aspects of
"our knowledge". In the 1935 paper Einstein et. al. effectively accepted
this claim of epistemological completeness, but defined the question
they were addressing to be the completeness of quantum mechanics as a
description of physical reality.

"Physical reality" is a slippery concept for scientists, when it becomes
separated from empirically testable predictions. Hence Einstein and his
colleagues were faced with the difficult task of introducing this term
into the discussion in a way that could not easily be dismissed as vague
metaphysics by a physics community which, greatly impressed by the
empirical successes of quantum mechanics, was in no mood to be sucked
into abstruse philosophical dialectics. Yet Einstein and his colleagues
did succeed in coming up with a formulation that shook the complacency
of physicists in a way that continues to reverberate to this day.

The key to their approach was to tie the needed characterization of
physical reality to a peculiar *nonlocal* feature of the quantum
mechanical treatment of two-particle systems.

The mathematical rules of quantum theory permit the generation of a
state of two particles that has predicted properties that appear, at
least at first sight, to violate a basic precept of the special theory
of relativity, namely the exclusion of instantaneous (i.e.,
faster-than-light) action at a distance.

Quantum theory generally allows any one of several alternative possible
measurements to be performed on a particle that lies in some
experimental region R. The choice of the measurement to be performed in
R is treated in quantum mechanics as a boundary condition that can be
"freely chosen" by the experimenter. According to the Copenhagen
interpretation, performing the measurement is supposed to affect the
particle being measured in a way such that the observed outcome
specifies the measured property of the state of the particle *after* the
measuring process is complete. But then if two alternative possible
measurements are *mutually incompatible*, in the sense that either one
or the other can be performed, but not both at the same time, then there
is no logical reason why the particle should have at the same time well
defined values of *both* of the two properties.

The mathematical structure of quantum theory does in fact involve
various properties of a particle that cannot, within that theoretical
structure, have simultaneously well defined values. Potential
inconsistencies are evaded by claiming that any two such theoretically
incompatible properties are also empirically incompatible, in the sense
that they cannot be measured simultaneously. But Einstein et.al.
constructed an argument designed to show that the values of certain of
these properties are, nevertheless, simultaneous elements of physical
reality. Such a demonstration would render quantum mechanical account
incomplete, as a description of physical reality!

To bring "physical reality" into the discussion, in conjunction with the
question of completeness, Einstein et. al, noted that the basic precepts
of quantum theory ensure that there is a state (wave function) of two
particles that has the following properties:

1\. The two particles lie at the time of a measurement performed on
particle 1, in two large regions that lie very far apart.

2\. There is a pair of measurable properties, X~1~ and P~1,~ which are
the location and the momentum of particle 1, respectively, that are
neither simultaneously representable nor simultaneously measurable; and
also a pair of measurable properties, X~2~ and P ~2,~ of particle 2 that
are, likewise, neither simultaneously representable nor simultaneously
measurable.

3\. The prepared state of the two particle system, before the
measurement is performed on particle 1, is such that measuring the value
of X~1~ determines the value of X~2~, whereas measuring the value of
P~1~ determines the value of P~2~.

These properties entail that the experimenter in the region where the
first particle lies can come to know either X~2~ or P~2~ , depending
upon which measurement he chooses to perform. This choice controls
physical measuring actions that are confined to the region where
particle 1 is located, and this region is very far from the region where
particle 2 is located. Consequently, any physically real property of the
faraway particle 2 should, according to the precepts of the theory of
relativity, be left undisturbed by the nearby measurement process: the
distance between the two regions can be made so great that the physical
consequences of performing the measurement on particle 1 cannot reach
the region where particle 2 is located without traveling superluminally:
faster than the speed of light.

These considerations permit Einstein et. al. to introduce "physical
reality" by means of their famous "criterion of physical reality":

> If, without in any way disturbing a system, we can predict with
> certainty (i.e., with probability unity) the value of a physical
> property, then there exists an element of physical reality
> corresponding to this physical property.

If a measurement were to be performed in the region where particle 2 is
located then the quantum theorist could argue that this measurement
could disturb the particle, and hence there would be no reason why
properties X~2~ and P~2~ should exist simultaneously. But the situation
under consideration allows either of the two (simultaneously
incompatible) properties of particle 2 to be determined (predicted with
certainty) without anything at all being done in the region where that
particle 2 is located, and hence, according to the ideas of the theory
of relativity, "without in any way disturbing that system". Thus
Einstein and his colleagues infer, on the basis of their criterion of
physical reality, that *both* properties are physically real. However,
these two properties cannot be represented simultaneously by any quantum
mechanical wave function. Hence Einstein et.al. "conclude that the
quantum mechanical description of physical reality given by wave
functions is not complete."

Anticipating an objection Einstein et.al. complete their argument by
saying:

> One could object to this conclusion on the grounds that our criterion
> of reality is not sufficiently restrictive. Indeed, one would not
> arrive at our conclusion if one insisted that two or more physical
> quantities can be regarded as simultaneous elements of reality *only
> when they can be simultaneously measured or* *predicted.* On this
> point of view, since either or the other, but not both simultaneously,
> of the quantities P \[here P~2~\] or Q \[here X~2~\] can be predicted
> they are not simultaneously real. This makes the reality of P and Q
> depend upon which measurement is made of the first system, which does
> no disturb the second system in any way. No reasonable definition of
> reality can be expected to permit this.

If one examines the situation considered by Einstein et. al. in the
explicit formulation of relativistic quantum field theory given by
Tomonaga (1946) and Schwinger (1951) one finds that the quantum state
(wave function) of particle 2 after the measurement is performed on
particle 1 depends not simply on which measurement is performed on
particle 1, but jointly upon which measurement is performed and what its
outcome is.

In a general context it is neither problematic nor surprising that what
a person can *predict* should depend not only upon which measurement he
performs, but also upon what he learns by experiencing the outcome of
that experiment, and hence upon both which measurement is chosen and
performed, and which outcome then appears.

In *classical* relativistic physics an *outcome* in one region can be
*correlated* to an *outcome* in a faraway region\-\--that is space-like
separated from the first\-\--without their being any hint or suggestion
of any faster-than-light transfer of information. Such correlations can
arise from a common cause lying in the earlier (preparation) region from
which each of the two later experimental regions can be reached by
things traveling at the speed of light or less.

In relativistic quantum field theory, as in relativistic classical
theory, merely performing the measurement action on particle 1 does not
affect any measurable or predictable property of particle 2. In both the
classical and quantum versions the subsequent *outcome* pertaining to
particle 1 is *correlated* (through the earlier initial preparation) to
a predictable and measurable outcome pertaining to the faraway particle
2. Thus, although this experimenter's choice and his consequent action
on particle 1 have, by themselves, no *direct* faraway effects, this
choice and action\-\--by determining the physical significance (X~1~ or
P~1~ ) of the local outcome, and thereby also the physical significance
(X~2~ or P~2~ )of the correlated faraway outcome\-\--do influence the
*nature* of the particular property of the faraway property of particle
2 that is revealed to the experimenter who is performing the measurement
on particle 1, by his experiencing the outcome of the experiment that he
has chosen and performed. But this sort of "influence" would, as in the
classical case, fall far short of any indication of the need for any
superluminal action at a distance, or of any superluminal transfer of
information about the nearby free choice to the faraway region. All that
has happened, in both the classical and quantum cases, is that the
nearby experimenter has learned the value of an outcome that is
*correlated* to the value of the outcome that a particular faraway
experiment would have if the faraway experimenter were to choose to
perform that particular experiment.

To identify what makes the quantum case different from classical case
suppose one has two balls, one red and one green, and one hot the other
cold. Suppose they are shot in opposite directions into two far-apart
labs. Simply measuring the color of the ball reaching the first lab does
not immediately disturb in any way anything in the other lab. But
knowing the outcome of this color measurement allows one to know
something about what will be found if color is measured also in the
second lab. *But in the classical case this real property of the system
that arrives in the second lab would not be nullified or eradicated if
one had chosen to measure temperature instead of color*. It is the
claimed *nullification* of one *kind* of property of particle 2 or
another, on the basis of which kind of experiment is performed on
particle 1, that distinguishes the quantum case from the classical one.
It entails the need for some sort of leaping of the information about
which action was chosen and performed on particle 1 to the region where
particle 2 is being measured. The need for this nullification arises
from the fact that no wave function can represent a well defined value
of both X~2~ and P ~2.~

In spite of this apparent violation of the notion that no information
about the free choice made in region 1 can get to region 2, relativistic
quantum field theory is compatible with the basic requirement of
relativity theory that no "signal" can be transmitted faster than light.
A *signal* is a carrier of information that allows a receiving observer
to know which action was taken by a distant sender. Because the receiver
does not know, superluminally, which *outcome* was observed by the
sender, she, the receiver, cannot know, superluminally, which action was
taken by the sender. Hence no signal can be sent.

The sender, who knows both which experiment he has freely chosen and
performed, and which outcome has appeared, knows, on the basis of his
knowledge of both the theory and this outcome, more about what the
receiver will experience than the receiver herself can know.

Quantum theory, by focusing on knowledge and prediction, is able neatly
to sort out these observer dependent features. The theory carries one
step further Einstein's idea that science needs to focus on what actual
observers can know and deduce on the basis of their own observations.
But quantum theory places a crucial restriction on definability that
classical relativistic theory lacks: a person by his choice of probing
action performed in one region can cause one *type* of property in a
faraway region to become *undefined* *in principle*, within the theory,
because an incompatible *type* of property becomes defined there.

In the book "Albert Einstein: Philosopher-Physicist" Einstein (1951,
p.85) gives a short statement of his locality condition:

> The real factual situation of the system S~2~ is independent of what
> is done with the system S~1~, which is spatially separated from S~2~.

The problem of reconciling this condition with quantum theory is that
quantum theory is a theory of predictions (about outcomes of
observations) not a theory of reality. The probing action performed on
system S~1~ by the experimenter does not, by itself, *disturb* in any
way the real factual system S~2~. This action, by itself, does not allow
any new prediction to be made about any outcome of any measurement made
on S~2~. Hence one may quite reasonably claim that "the real factual
situation of the system S~2~" is not disturbed by the mere action of
performing the faraway measurement. And it is in no way surprising that
what kind is predictions one can make about the faraway correlated
system depends upon what kind of nearby measurement is chosen.
Einstein's challenge is to the quantum theoretical claim that if the
quantum state, which pertains to predictions, allows no predictions
about a property then that property is in reality ill-defined.

If one accepts the quantum claim that the property itself is ill-defined
if the property is ill-defined in the quantum theoretic state then the
argument of Einstein et.al. shows that the condition of
no-faster-than-light action is violated in quantum theory. It is
violated because the choice made in one region determines, no matter
which outcome occurs, which *kind* of properties of the faraway particle
becomes, within the quantum framework, ill defined.

The conclusion is that Einstein's argument leads, *within the quantum
theoretical framework*, not to a proof of some incompleteness of quantum
theory, but rather to a proof of the existence within theory of a
faster-than-light transfer to a faraway region of the information about
which measurement is performed in the nearby region.

This conclusion depends, however, on accepting the basic precept of
quantum theory that if two properties of a system cannot be
simultaneously represented by a wave function and one of these two
properties is defined then the other cannot exist. Einstein rejected
that premise. The question thus arises: Can the requirement of no
superluminal transfer of information be upheld if one rejects the
quantum precept that properties that cannot be simultaneously
represented by any quantum state cannot be considered to be
simultaneously definite.

This question has been studied by John Bell (1964) and others within the
special context of theories that postulate the existence of pertinent
real hidden-variables. \[Bell's Theorem\]. Those arguments show that,
within this hidden-variable context, the answer to the question posed at
the end of the preceding paragraph is 'No'! Once the notion is accepted
that decisions as to which measurements are performed are controlled by
free choices that can go either way, it is impossible to reconcile *even
merely the* *predictions* of quantum theory for all of the then-allowed
alternative possible measurements with the demand that there be no
superluminal transfer of information about which measurements are freely
chosen

Primary

Bell, J.S. (1964): On the Einstein Podolsky Rosen paradox, *Physics*,
195-200.

Einstein, A., Podolsky, B., and Rosen, N., (1935): Can quantum
mechanical description of physical reality be considered complete?
*Phys. Rev*. 47, 177-180.

Einstein, A. (1951): in *Albert Einstein: Philosopher-Scientist*, (ed.)
P. A. Schilpp, Tudor, New York.

Secondary

Cushing J./E. McMullin (1989): *Consequences of Qth*

Howard, D. (1989): contribution to Cushing/McMullin volume, pp. 224-47

Howard, D. (2004): contribution to Standford Encyclopedia of Philosophy

Lange, M. (2002): *Philosophy of Physics*, Ch. 9

Henry P Stapp, LBNL, University of California, Berkeley.