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} 1. A. Einstein, N. Rosen, and B. Podolsky, Phys. Rev. {\bf 47}, 777 (1935). 2. J.S. Bell, Physics, {\bf 1}, 195 (1964); and in {\it Speakable and Unspeakable in Quantum Mechanics.} Cambridge Univ. Press, Ch. 4; J. Clauser and A. Shimony, Rep. Prog. 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Stapp, ``Basics of von Neumann-Wigner Quantum Theory'', [http://www-physics.lbl.gov/~stapp/stappfiles.html]; in Journal of Consciousness Studies, {\bf 6}, 143 (1999); and in {\it Quantum Future: from Volta and Como to the Present and Beyond}, eds. Ph. Blanchard and A. Jadczyk, Springer, Berlin, 1999, p.156 \end{document}