January 14, 2000 LBNL-44712
Signals, Influences, and Information
\footnote{This work was supported in part by the Director, Office of Science,
Office of High Energy and Nuclear Physics, of the U.S. Department of Energy
under Contract DE-AC03-76SF00098.}
Henry P. Stapp
Lawrence Berkeley National Laboratory
University of California
Berkeley, California 9472
ABSTRACT
Relativistic quantum field theory predicts that no {\it signal} can
travel faster than the speed of light. No violation of this property
has ever been observed. However, recent experiments reinforce the
idea that some sort of faster-than-light {\it influence} exists.
These experiments validate some predictions of quantum theory that are
incompatible with certain formulations of the following theoretical
condition: the truth of a statement about what one experimenter can
observe at an earlier time cannot depend on which experiment another
experimenter will at a later time freely choose and then perform. The
usual forms of this locality condition are based on an assumption of the
existence and pertinence of hidden-variables. That assumption is alien to the
precepts of quantum theory and its use clouds the
significance of those results. In this work an approach fully
compatible with the principles of quantum theory is used to deduce a strong
logical requirement on any model of nature, hidden-variable
or not, that is compatible with both the principles and predictions of quantum
theory and a weak form of the causality condition described above. This strong
requirement entails, for example, that the most common idea of physicists
of what is happening during a quantum measurement requires transfer of
information over a spacelike interval. It is argued that this transfer does
not violate the demands of the theory of relativity in a quantum context and,
moreover, supports a von Neumann-type information-based conception of
physical reality.
Introduction
Albert Einstein, and two younger colleagues, Boris Podolsky and
Nathan Rosen, published in 1935, in The Physical Review, one of the
most famous papers in physics [1]. In it they raised a question about
the place of quantum theory within the general program of constructing
an adequate theory of physical reality. They did not challenge
the accuracy or logical coherency of quantum theory, but rather
used the predictions of that theory, plus a certain locality condition
drawn from the theory of relativity, to conclude that quantum theory,
as it was then formulated, was incomplete.
Thirty years later John Bell [2], developing the work Einstein et. al.,
showed that any theory in which the outcomes---or even the probabilities
of outcomes---of measurements are fixed by ``hidden variables'' that exist
and have definite values independently of which of the alternative possible
measurements is actually performed, and that reproduce the predictions of
quantum theory, must involve an influence that acts backward in time in
some frame. The influence in question is a dependence of the truth of a
statement about which outcome will appear to an observer at
an earlier time upon which experiment a far-away experimenter will, at some
later time, freely choose, and then perform.
The use of hidden variables makes Bell's work essentially
different from that of Einstein et. al.. The latter authors formulated
their arguments so as to avoid {\it assuming} the existence of any
entities that are not present in quantum theory. Leon Rosenfeld [3] described
Bohr's frustration during the many weeks that it took him
to construct his reply [4] to Einstein's argument, and Bohr himself
later admitted [5] to the ``inefficiency of expression which must have made it
very difficult to follow the trend of the argumentation''. This difficulty
that Bohr encountered makes it clear that the essence of Einstein's
argument was not fully captured by Bell's hidden-variable results.
The experiments discussed by Einstein et. al. were ``gedanken experiments''.
Bohm and Aharonov [6] clarified the Einstein argument by formulating it in
terms of performable experiments. Experiments similar to the one they proposed
were eventually performed [7, 8], and gave results in accord with
the predictions of quantum theory. Recently, some more spectacular
variations [9, 10, 11, 12] have been carried out, and they demonstrate, in the
context of Bell's hidden-variable arguments, the existence of
faster-than-light influences acting over distances of more than 10 kilometers.
Lucien Hardy [13] has considered a different kind of experimental
arrangement that allows the arguments to be simplified. Hardy-type experiments
are performable [14], and they will almost surely be performed.
In the following section I describe the logical structure of the Hardy
setup. [The experimental details are given in refs. 13, and 14.]
Then in section 3 I shall formulate a ``weak causality'' condition
that asserts that there is at least one coordinate system such that an
outcome that has already appeared to certain observers at an earlier time
cannot depend upon which experiment an experimenter at some later time will
freely choose, and then perform. I argue that this weak causality condition
is compatible with the orthodox precepts of quantum theory, and
believe it to be compatible also with all the predictions of quantum theory.
Then in section 4 I deduce from this weak causality condition, and four
pertinent predictions in the Hardy setup, a logical requirement on any model,
hidden-variable or not, that satisfies both weak causality and these
predictions. This logical requirment can be used to rule out various
local models, in a way similar to the way that Bell's theorem
rules out local hidden-variable models. As an example, I show that
this logical requirement rules out a ``standard'' no-hidden-variable idea of
nature that is suggested by the words of Dirac and of Heisenberg, and is
probably held, at least informally, by most quantum physicists, insofar
as all backward-in-time influences are excluded in {\it every} Lorentz frame.
In the final section I discuss the significance of these results for the
future developments of physics, and argue that the logical requirement
mentioned above provides support for an informational conception of physical
reality that, on the basis of the mathematical structure of quantum theory,
is the most natural candidate. This conception is normally rejected first
on the grounds of its profound difference from our familiar
notion that the world is made mainly of `matter' whose properties are, at
least macroscopically, similar to the matter postulated in classical physical
theory, and second on the grounds that it conflicts with the theory of
relativity. As regards this second objection, I argue that this informational
conception of physical reality does not conflict with the theory of
relativity, even though it involves faster-than-light transfer of information.
\vspace{.2in}
{\bf 2. The Hardy Setup}
\vspace{.2in}
The experimental setup is similar to the ones considered in Bell's
theorem. There are two spacetime regions, L and R, that are
``spacelike separated''. This means that they are situated far apart
relative to their extensions in time, so that no point in either region can be
reached from any point in the other without moving faster than the speed
of light.
In each region an experimenter freely chooses between two possible
experiments. Each experiment will, if chosen, be performed within that region,
and its outcomes will appear to observers within that region.
Thus neither choice can affect anything in the other region
without some influence that acts over a space-like interval.
The two possible experiments in L are labelled L1 and L2.
The two possible experiments in R are labelled R1 and R2.
The two possible outcomes of L1 are labelled L1+ and L1-, etc.
The Hardy setup involves a laser down-conversion source that emits a pair
of correlated photons [13, 14]. The experimental conditions are such that
quantum theory makes four (pertinent) predictions:\\
1. If (L1,R2) is performed and L1- appears in L then R2+ must appear in R.\\
2. If (L2,R2) is performed and R2+ appears in R then L2+ must appear in L.\\
3. If (L2,R1) is performed and L2+ appears in L then R1- must appear in R.\\
4. If (L1,R1) is performed and L1- appears in L then R1+ must* appear in R.
The three words ``must'' mean that the specified outcome is predicted
to occur with certainty (probability unity). The word ``must*'' means
that for any small $\epsilon > 0$ the source can be fixed so that
the specified outcome is predicted to occur with probability $1-\epsilon$.
\vspace{.2in}
{\bf 3. Formulation of the Locality Assumption.}
\vspace{.2in}
The basis is this work is a certain weak causality assumption.
This assumption depends on the notion that experimenters can be
considered free to choose between the alternative possible experiments
that are available to them. Bohr often stressed that the choices made
by experimenters should be considered to be free, and in his debate with
Einstein he never claimed that, because only one course of events
actually occurs, one cannot, in the discussion of the connection
of a physical theory to physical reality, consider what that theory says about
alternative possibilities. Indeed, that way of evading Einstein's
challenges would have been contrary to his claim that:
``The freedom of experimentation, presupposed in classical physics,
is of course retained and corresponds to the free choice of experimental
arrangements for which the mathematical structure of the quantum
mechanical formalism offers the appropriate latitude.''[15]
Given this idea of freedom the weak causality assumption asserts that:
``For some system of coordinates with a monotonically increasing time
variable $T$, if an experiment is performed, and a definite outcome has
been observed prior to some time $T$, then this observed outcome is fixed
and settled, independently of which experiment will be freely chosen and
performed at times later than $T$.''
This assumption of `no influence backward in time' is part of the general
idea that universe evolves from the past into the future, with our free
choices left open until the instant they are made. I know of no quantum
precept that rules out this idea, and I believe it to be compatible with
the predictions of quantum theory.
\vspace{.2in}
{\bf 4. A Logical Requirement.}
\vspace{.2in}
Consider a theory of reality in which the choices made by the
experimenters can be treated as free variables, and such that given any
one of the various combinations of conditions that the experimenters can
choose to set up, the theory specifies that a set of outcomes that is
compatible with the predictions of quantum theory will appear. Suppose,
moreover, in accordance with our weak causality condition, that, for some
coordinate system, any outcome that appears (to observers) at one time is
fixed and settled at that time independently of which way any future free
choice by an experimenter will go.
Alternative possible measurements must be treated as mutually exclusive:
one can speak of the outcome of a measurement only under the condition that
it is performed, and two alternative possible measurements cannot both
be performed.
Let this theory be applied to the Hardy setup.
Suppose the experimental setup is such that region L is later than time $T$
and region R is earlier than time $T$.
Suppose the actually selected pair of experiments is (L1,R2),
and that L1- appears in L. Then prediction 1 of quantum theory entails
that R2+ must have already appeared in R prior to $T$. The
no-backward-in-time-influence condition then entails that this outcome R2+
is fixed and settled at time $T$ independently of which way the later
free choice L will eventually go: the model must leave the already fixed
value R2+ undisturbed even if the later free choice in L were to be L2
{\it instead of} L1.
Under this alternative condition (L2,R2,R2+) the notion of a result
for L1 is banned. But L2 must have an outcome, which, by virtue of
prediction 2 of quantum theory, must be L2+. This gives, for this model,
the following condition:
Assertion A(R2):
If (R2,L1) is performed and L1- appears in L, then if, instead, the choice
in L had gone the other way, the model must specify that
outcome L2+ would have appeared there.
This is an expression, in the context of the Hardy experimental
setup, of the no-backward-in-time-influence condition.
Now let Assertion A(R1) be defined to be Assertion A(R2) with R2 replaced
by R1. Then A(R1) can be proved to be false.
To verify this claim suppose that this claim is false, and hence that
A(R1), like A(R2), is true. That is, suppose that:
If (R1,L1) is performed and L1- appears in L, then if, instead, the choice
in L had gone the other way, the model must specify that
outcome L2+ would have appeared there.
Under this condition (R1,L2,L2+), the prediction 3 of quantum
theory asserts that the outcome in R must be R1-. However, according to our
weak causality condition, with R1 in place of R2, the {\it later} choice
between L1 and L2 in L cannot affect what the earlier outcome in R was.
So also under the original conditions (R1,L1,L1-) the outcome in R must
have been R1-. But that contradicts prediction 4.
Thus the following logical requirement holds:
Any model that conforms to the stated assumptions {\it must}
make A(R2) true and A(R1) false.
The argument for this logical requirement makes no use
hidden-variables, or of the idea that a locality condition
should be introduced by imposing a factorization condition involving
hidden variables. It demands, rather, that:
1) The choices made by the experimenters can be treated as free
variables;
2) For any of the possible experimental conditions that these
experimenters might freely choose to set up, if that set of conditions
is put in place, the theory guarentees that there will appear to observers
a set of outcomes of {\it that particular set} of
experiments that agree with the predictions of quantum theory; and
3) The fixing of outcomes does not depend on future free choices.
Physical theories do not specify simply the one unique course of events
that actually occurs. Classical physical theories specify an infinite set of
physically possible worlds only one of which is actual. And quantum theory
gives predictions for each of the possible experimental arrangements that
the experimenters can freely choose to perform. The weak causality condition,
which makes earlier fixings independent of the future free choices, entails,
as shown above, the existence of certain necessary logical connections
between mutually exclusive alternative quantum possibilities.
The three conditions just listed are, I think, usually tacitly assumed by
most orthodox quantum theorist, but I have here made those tacit
assumptions explicit. These assumptions are somewhat akin to the assumption
of the existence of hidden variables, but, unlike that assumption, they
do not require an assumption that there exists, in addition to the properties
and entities that are parts of the mathematical machinery of quantum theory,
some ``hidden'' variables that exist and have definite values
independently of which experiment will be performed, and which must be
averaged over to get the statistical predictions of quantum theory. The
present line of argument replaces that hidden-variable assumption with
the weak causality assumption.
The most `standard' quantum idea of how nature works is the idea that once
the experiment has been set up, and a definite question is thus posed as to
whether some specified outcome will appear under that specified condition,
{\t then, and only then}, ``Nature Chooses the Outcome''. This idea is
suggested both by Dirac's terminology that, in regard to the occurrence of
phenomena for which only statistical predictions can be made, we are
concerned with a choice on the part of `nature' [16], and Heisenberg's idea
that a ``transition from the `possible' to the `actual' takes place during
the act of observation [17].
Assertion A(R2) places conditions on Nature's Choices in
L under the two different conditions, L1 and L2, that could be set up there.
There is no suggestion at this point for any need for any faster-than-light
transfer of information: there is just a specified condition on what Nature
can do in L, provided R2 is chosen in R. But this same condition on what
Nature can do in L {\it cannot hold} if R1 is chosen in R. Thus there is
a constraint upon what Nature can do in L that either {\it must} exist
or {\it cannot exist} depending upon which free choice is made in R.
It is impossible for such a condition to be valid if there can be
no transfer of any kind of information backward in time in any frame.
Thus this line of argument, which is logically and structurally different
from some other recent arguments [18] that lead to somewhat similar results,
gives a conclusion that is like that of Bell's theorem, but does not depend on
assuming the existence of hidden variables.
This result does not mean, however, that the information cannot travel
{\it continuously} from one region to the other. In the Heisenberg
picture, which most theorists prefer, rather than the Schroedinger
picture that I have used here, the entire spacetime structure of expectation
values is specified at each stage of the accumulation of facts, and one can
trace the flow of information from one region to the other by tracing first
back to the source of the correlation, and then forward to the other region.
A flow of information along this path would conflict with the idea of
no-backward-in-time-influence, but allows one to say that, in some sense,
causation is always transmitted by direct contact. The possibility of
viewing things in this way is built into orthodox relativistic quantum
field theory, in the Heisenberg picture. Several authors [19] have emphasized
the possibility of viewing the causal connection in this way.
\vspace{.2in}
{\bf 5. The Informational Character of Physical Reality.}
\vspace{.2in}
Einstein objected strongly to the Copenhagen stance that physicists
should settle for merely a set of rules that predict connections between
our observations. He, John Bell, and many other eminent scientists
believed that we should strive to construct a theoretical conception of an
underlying physical reality. A principal stumbling block has always been
the mysterious causal structure, which seems to defy rational explanation.
However, in the growing physics literature about proposed conceptions
of physical reality, the candidate that is by far the most reasonable,
given what we know about the mathematical structure of quantum theory,
is rarely mentioned. This omission apparently stems from
two causes. The first is its profound conceptual departure from the
prevailing idea that physical world is made mainly of matter/energy:
the second is a flawed idea of the demands of the theory of relativity
in an indeterministic quantum context. I shall address here this latter point.
The theory of relativity was originally formulated within classical physical
theory, and, in particular, for a deterministic theory. In that case the
entire history of the universe could be conceived to be laid out for all
times on a four-dimensional spacetime manifold. The idea of ``becoming'',
or of the gradual unfolding of reality, has no natural place in
this conception the universe: there is no reason why each of us should
be moving along our own world line ``in synch'' with each other:
our experiences would be independent of where anyone else's psyche is
situated along his own world line. In fact, this entire picture of nature
is grossly out of touch with the progressively unfolding character of the
world we actually experience.
Newton's idea of a universal `now', advancing with the passage of time, is,
of course, much closer to the way we experience nature. But it was banished
by the theory of relativity as a totally useless notion, within a classical
{\it deterministic} universe. Within that context no significant
use can be found for that idea, which was therefore dropped from physical
theory. On the other hand, all of the causal mysteries in quantum theory
stem precisely from the attempt to banish Newton's `now' in the
context of a quantum universe that produces definite outcomes of
freely chosen experiements.
Nonrelativistic quantum theory is based on the Newtonian idea of `now'.
In that version of quantum theory all the needed faster-than-light
tranfers of information are made automatically by the mathematical structure,
and they are instantaneous. Once that basic feature is accepted,
all causal mysteries of the kind under discussion here vanish.
Relativistic quantum field theory is the accepted relativistic
generalization of nonrelativistic quantum theory. That theory has many
relativistic properties: all of its predictions are independent of the
frame used to define the advancing sequence of constant-time surfaces `now',
and, in fact, these constant-time surfaces --- the instantaneous `nows' ---
can even be replaced by a set of advancing non-flat spacelike surfaces. These
surfaces give, automatically, the locus of the needed ``instantaneous''
transfers of information. Thus these transfers can be achieved in a variety
of ways, without affecting the predictions of the theory, one of which is
that no {\it signal} can be transmitted faster than light.
[A ``signal'' is {\it controllable} transfer of information: a transfer
that allows a sequence of bits composed by a sender to be conveyed to a
receiver.]
None of these results of relativistic quantum field theory imply or
suggest that one can get by without transferring information
about newly fixed local facts (i.e., definite outcomes) backward in time in
{\it some} Lorentz frame: on the contrary, such a transfer of
information, when a new fact become fixed in one place, is what relativistic
quantum field theory automatically gives. The notion that such transfers could
be banished within a quantum context, or do not exist, or {\it cannot} exist
because of requirements of the theory of relativity, is a complete fallacy,
within the context of a quantum theory that requires local experiments to
have definite outcomes that are independent of future free choices. There is
no suggestion at all in the mathematics of relativistic quantum field theory
that any such banishment is possible. Within the explicit formalism the
definite outcome at the earlier time is representable by a change in the
(global) state, which can influence in various ways what can appear very far
away at a slightly later time. In particular, the ``initial state'' of a
quantum system is specified by some set of facts, and when new fact becomes
fixed a new global ``initial state'' of information becomes defined.
The argument in the earlier sections is simply a demonstration of the
difficulty of imposing a banishment on backward-in-time influences {\it in all
Lorentz frames} by examining, not the explicit underlying mathematical
structure of relativistic quantum field theory, but merely the predictions
of that theory themselves, in a context where measurements are assumed to
have definite outcomes, `yes' or `no', that do not depend on future free
choices made by experimenters.
But how can one deal, theoretically, with this idea of
instantaneous tranfers of information? The answer is this: Heed
what the founders of quantum theory said! They insisted,
in Dirac's words [20] that ``the wave function represented
our knowledge of the system, and the reduced wave function
our more precise knowledge after measurement.'' There is, of course,
nothing puzzling in the fact that ``our knowledge'' about
a far-away system can change the instant we learn something
new about a nearby system, when this nearby system is correlated in a known
way with that far-away one. ``Our knowledge'' certainly does behave in
exactly that way..
The founders recognized what the mathematics was telling them,
and fitted their language to it. But they were reasonable men.
While insisting that the representation of a system, within
their new theory, was a representation only of ``our knowledge'',
and denying the usefulness of any deeper description of
the atomic system it represented, they recognized that human
knowledge could not be called ``physical reality'' in the traditional
sense of that word. So they initially retreated to the position that
the theory was {\it complete} in the scientifically important sense,
even though it did not give a complete description of physical reality
in the usual sense.
Bohr [4], in his arduous effort to answer Einstein et.al., isolated
the root problem. It is with the conception of ``physical reality.''
The latter authors asked the question: Can quantum-mechanical description
of physical reality be considered complete? In their argument that
quantum-mechanical description was not complete they assumed that aspects
of physical reality measurable by one experimenter could not be disturbed
by which experiment a faraway experimenter performed. Bohr
answered that, in the situation under discussion, there was
``no question of a mechanical
disturbance of the system under investigation during the last critical
stages of the measuring procedure. But even at this stage there is
essentially the question of {\it an influence on the very conditions that
define the possible types of predictions regarding the future behaviour of
the system.} Since these predictions 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.''
This answer to Einstein et. al. was the product of a great effort
by Bohr, and it deserves serious attention. In it he denies
the possibility of a ``mechanical'' disturbance of the system, but allows
for an influence on ``physical reality''. The forbidden ``mechanical''
disturbance can be identified as a disturbance attributable to a
transmission of energy/mass from cause to effect, whereas the
allowed influence on ``physical reality'' is an influence in another domain,
a domain of {\it information} that {\it encompasses} our knowledge, and the
predictions we can derive from it our knowledge. Thus in order to meet
rationally the challenge of Einstein et. al. without undermining the ideas
of relativistic quantum field theory Bohr in effect allowed the quantum state
to represent {\it an informational type of physical reality} in which a free
choice made by one experimenter could exert an influence
of a kind forbidden in a mechanical type of physical reality.
John von Neumann [21] had the audacity to follow consistently where the
mathematics itself led, and reached a similar conclusion. Because quantum
theory naturally allows for interacting systems to be treated as components
of larger systems, the study of the process of measurement in quantum theory
led to the inclusion of the entire physical universe in the quantum system.
This approach cast out a relic, the awkward and seemingly logically
inconsistent notion of a classical world standing between the quantum system
and the consciousness of the observer. The quantum mechanical
state of the physical universe became, thereby, not just a tool
for computation but a conceivable representation of the mathematical
structure of physical reality itself. In the von Neumann approach
the anthropocentric limitation of the Copenhagen approach is removed, and
quantum state becomes a global compendium of locally specified objective
{\it bits} of information, where each bit is specified by an objective
answer to a yes-no question.
Accepting what the mathematics is saying produces, then, a radically
altered conception of physical reality: the physical world is metamorphed
from a largely matter-like structure riding in some obscure way on a
sea of micro-potentialities, into a single giant informational
structure. What the mathematics proclaims is that the physical world is an
informational structure, rather than a material one.
In particular, the mathematical structure is appropriate for describing a
reality that consists of an objective accumulation of a discrete {\it facts}
each of which comes into being as a whole. Each fact is the answer to a
yes-no question that is represented in a mathematically well-defined way,
and the dynamical laws of quantum physics are the rules that specify how the
new facts are added to the old ones to form an evolving accumulation of
objective mathematically represented facts.
Two things block the general acceptance of this coherent objective conception
of physical reality that quantum theory lays at our feet. The first is inertia
of old ideas. The second is an exaggerated idea of the demands of
the theory of relativity in an indeterministic quantum setting. I shall
remark here on the second.
Relativistic quantum field theory is compatible with the theory of
relativity (at least at the scale we are concerned with here). To
the extent that it specifies definite outcomes of the quantum measurements
that we freely choose to perform, it is {\it filled} with instantaneous
influences. Newton's `nows', the preferred constant-time surfaces, which
were useless ornaments in deterministic classical physics, become the
foundation of a rationally coherent mathematical representation of an
unfolding indeterministic universe: they are the loci of the perpetual
adjustments of the informational structure. Rather than blinding ourselves
to what the mathematics is telling us, because it conflicts with old
intuitions of matter-based causation, and trying to look outside
quantum theory for physical reality, we may instead follow the other option,
which is to change our conception of the character of physical reality, by
bringing it in line with the properties of a mathematical
structure that fits all the known empirical facts, namely the structure
provided by von Neumann's approach to quantum theory.
We have now, of course, something the founders lacked: a natural empirically
determined candidate for defining the advancing sequence of global
instantaneous ``nows''. It is the big-bang rest frame revealed by the
background black-body radiation. Although a conception of a nature that
extends beyond the narrow bounds of `our knowledge' and encompasses an
informational structure in which our knowledge can be naturally embedded
may or may not contribute to a deeper understanding the atomic physics
experiments with which the founders of quantum theory were primarily
concerned, the ideal of the unity of science that motivates much of scientific
progress is well served by a conception of nature that can cover the
huge range of sizes from the atoms through humans to the cosmos. In the
context of the effort to rationally accommodate all this within one
coherent framework the twentieth century can be viewed as a
transitional century from a matter-based conception of physical reality
to an information-based one.
What is the significance for physics of these considerations?
One aspect concerns the efforts of the many scientists who are
uncomfortable with the Copenhagen view that physics must limit itself to
`our knowledge', and hence must turn its back on attempts to conceptualize
an encompassing reality in which our knowledge is naturally embedded.
What needs to be be recognized in the search for a broader theory is that
the application to {\it indeterministic} quantum theory of ideas of the
theory of relativity that were appropriate in the context of
{\it deterministic} classical physical theory is problematic: if the
broader theory is to accommodate the idea of definite factual outcomes of
freely chosen experiments, in the spirit of Bohr, then the relativistic
requirements can be imposed without restriction on the theory {\it considered
as a theory of predictions about our knowledge}, while admitting at the more
fundamental level of physical reality itself the concept of an advancing
sequence of global `nows' to accommodate the needed rapid transfers of
information. The notion that such transfers of information inherently
conflict with properly formulated relativistic requirements and hence cannot
be present in physical reality can rationally be rejected, as Bohr himself
affirmed, albeit obliquely, in his reply to Einstein et. al..
The other aspect concerns the significance of the many ``nonlocality''
experiments that have already been performed or that will be performed. The
results of the preceding sections buttress the intuitive idea of many
physicists that these experiments, by confirming the predictions of quantum
theory in these particular cases, are telling us that a certain idea spawned,
in a deterministic context, by the theory of relativity must be applied in
an appropriately limited way within the context of indeterministic quantum
theory. That is, the significance of the results of these nonlocality
experiments goes beyond the mere confirmation, or deduction, of the fact that
hidden-variables cannot exist: they indicate rather the need to curtail a
certain over-extension of the requirements of the theory of relativity that
has, for three quarters of a century, caused physicists to abandon prematurely
the hope constructing a rationally coherent conception of physical reality.
\begin{center}
\vspace{.2in}
\noindent {\bf Acknowledgements}
\vspace{.2in}
\end{center}
I thank A. Shimony, J. Finkelstein, and P. Eberhard for comments that
contributed to the final form of this paper.
\begin{center}
\vspace{.2in}
\noindent {\bf References}
\vspace{.2in}
\end{center}
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