Reprinted from Physics Today, July 1995

I have a serious concern that I would like to present to the physics community at large. It appears to me that there is a small but dedicated group of scientists-some with quite respectable reputations—who nevertheless dabble in things that most of us would not call science. (The terms "pseudoscience" and "pathological science" come to mind.) Occasionally attempts are made to dress up this type of work and anoint it with the trappings of "real science" and then usher it into publication in prestigious journals along with mainstream material—giving it the mantle of undeserved legitimacy.

For example, in the 1 July 1994 issue of Physical Review A there appeared an article by Henry P. Stapp, "Theoretical Model of a Purported Empirical Violation of the Predictions of Quantum Theory.''(1) This paper develops an acausal theoretical model of nonlinear quantum mechanics that is loosely based on work by Steven Weinberg. It is clear that this article was specifically created to explain the apparently anomalous results found in experiments designed to establish the physical reality of supposed paranormal phenomena: Stapp's reference (8) is to the telekinesis experiments of Helmut Schmidt, published in the Journal of Parapsychology.(2) Schmidt claims to have demonstrated that human beings are able to use psychic powers to retroactively alter the decay rate of naturally occurring radioactive isotopes months before the actual expenment took place. Schmidt's conclusion— which Stapp has tried to model theoretically in PRA—is that the test subjects used their psychic powers to alter the laws of quantum mechanics and Einstein causality.

Several scientific investigations have dismissed previous paranormal experiments by Schmidt as statistically and scientifically unsound, at the very least.(3) The latest experiments—summarized in reference (2)— have not been reproduced. At the very least, these acausal "telekinesis" experiments seem too controversial and pseudoscientific for there to be theories appearing in Physical Review A purporting to explain them. It's one thing for the physics community to be open-minded but entirely another for us to be supporting parapsychology and promoting pseudoscience. You can be sure that Schmidt, in his future publications in the Journal of Parapsychology, will reference Stapp's paper and claim that a theory that explains all his experimental data has been published in the flagship journal of the American Physical Society.

There is another interesting point. When you read Schmidt's paper (2) you find that it is not itself a report of an experimental result but rather a summary and statistical analysis of five experimental results—all by Schmidt—published in the Journal of Parapsychology from 1986 to 1993. Each of those experiments tested "psychic" subjects for their ability to acausally and telekinetically alter the generation in the past of random numbers based on the decay of radioisotopes. Each of Schmidt's five corresponding papers reports data that, although suggestive, are not statistically significant. In the summarizing paper(2)—the one that Stapp actually refers to—Schmidt averages the results of his previous five experiments. Upon doing so he finds a statistically significant indication of acausal telekinetic activity. Each of the five experiments was camed out with Schmidt as principal investigator and first author, with the names of one or two coinvestigators appearing as second or third author. For the fifth experiment, published immediately preceding Schmidt's summarizing paper (2) in the same issue of the Journal of Parapsychology, Schmidt's coauthor and coexperimenter is none other than Stapp.(4) Hence Stapp's theory paper in PRAI is in fact a theoretical explanation for Stapp's own experiment. It seems odd that this connection was nowhere mentioned by Stapp in his PRA article.

The Physical Review editorial board has informed me that some changes have been made in the guide to authors and referees to reduce the possibility of such papers' being published in the future. However, it is not clear to me that this solves the problem, or even that the physics community at large is even aware that there is a problem. Should we take the extreme "open-minded" position and let such papers appear, rather than be accused of censorship? Or should we put our foot down and say, "Articles dealing with parapsychology should not be published in PRA— period." (I'm not advocating that papers like Stapp's not be published at all, but there are more appropriate forums, for example, the Journal of Parapsychology.) In any case, only we as physicists can decide this. I hope that this missive will stimulate interesting public debate on this topic. One might argue that a more appropriate approach for criticizing an article in PRA would be to submit an official comment to PRA. In fact, I and four coauthors are preparing such a comment. We will discuss our concerns about the physical theory of Stapp as well as the experiments of Schmidt. The purpose of this letter is not to discuss the nuts and bolts of a particular physical problem but to bring out into the open my concerns about the philosophy and direction of physics as a whole.

References

1. H. P. Stapp, Phys. Rev. A 50, 18 (1994).

2. H. Schmidt, J. Parapsychol. 57, 351 ( 1993).

3. C. E. M. Hansel, The Skeptical Inquirer, Spring 1981, p. 26. R. Hyman, ibid., p. 34. J. E. Alcock, Science and Supernature, Prometheus, Buffalo, N. Y. (1990), pp. 81-181. 4. H Schmidt, H. P. Stapp, J. Parapsychol. 57, 331(1993).

JONATHAN P. DOWLING

US Army Missile Command

Redstone Arsenal, Alabama"

STAPP REPLIES:

A scientist does not become "dedicated" to pseudoscience by accepting a challenge to examine purely physical facts created under highly controlled conditions. Indeed, to refuse to look at such physical evidence on ideological grounds would be pseudoscience.

Let me describe the special circumstances that led me to submit my theory paper to the Physical Review. I was approached during a conference by Helmut Schmidt, who asked me why in view of my long-standing interest in the apparent nonlocality associated with Bell's theorem, I never referred to his experiments, which seem to indicate the existence of a similar kind of effect. I replied, frankly, that the results he claimed seemed to me so astounding that I would sooner believe in the occurrence of a procedural flaw, or even outright fraud, than in the reality of the claimed effect; since I lacked the expertise and time to do confirming experiments myself I simply remained silent.

He answered that there was a very simple procedure that I could carry out in my own office, involving only printed numbers and no dealings with human subjects, that should allow me to confirm the reality of the claimed effects (which are backed up by the claims of other "psi" researchersl) without my having to make any assumptions at all about his competency or integrity. I listened, and we eventually set up a protocol that satisfied me, and I agreed to carry out the specified procedure.

I received by mail (in batches) a set of thick cardboard sheets. Each sheet had a set of rows, with each row consisting of a pair of short strips of black tape. After receiving a batch I waited for at least a week, and on a day prescribed by the fixed protocol, I extracted from the weather table of The New York Times, by a fixed recorded procedure known only to me, a pair of "random numbers" that I then used as seed numbers in a computer program devised by myself and divulged to no one (until after the experiment was completed). This program generated from the seed numbers a set of pairs of (pseudo) random signs (sigmali, sigma2i), with one pair of signs for each row i. The sign sigmali specified, according to the preestablished protocol, which one of the two black strips in row i I would peel off. Under the removed strip in row i was a (signed) number ni, which I multiplied by the sign sigma2i. I then computed, by a standard, preestablished procedure, taken from a statistics book, the "positive bias" of the sequence of numbers sigma2i ni. Since I had multiplied each incoming number ni by a randomly selected sign sigma2i that I had generated independently, I expected no statistically significant positive bias, and that is what I found.

I then sent the set of signs sigma2i to Schmidt, and some months later, after receiving a go-ahead from Schmidt, I removed the remaining strips of black tape (in the batch) and computed, by the same preestablished procedure, the positive bias of the sequence sigma2i ni' formed from the newly revealed numbers ni'. I expected, for the same reasons as before, to find no statistically significant positive bias, and that is what I found.

During the interval between the time I sent to Schmidt the signs sigma2i and my uncovering of the numbers ni' Schmidt supposedly had his subjects trying by mental effort to positively bias the numbers sigma2i ni'. On the basis of four earlier experiments of a generally similar kind, Schmidt predicted that I would find the sequence of numbers sigma2i ni', unlike the control sequence sigma2i ni, to be positively biased to about three standard deviations or more—something that would be expected to occur by chance only once in about a thousand trials.

Schmidt and I had agreed beforehand that the result would be published regardless of whether the outcome confirmed his expectations or not, and hence my negative result was duly published in Jonathan Dowling's reference (4). That reference described also what Schmidt had done; I myself had no involvement in any aspect of the experiment beyond what I did in my office, which I have described above.

The procedure that I myself carried out was purely a "physics experiment." Since all the relevant numbers were in my possession and were stored in a secret and secure place, there was, according to orthodox physical ideas, no way for Schmidt to produce a systematic positive bias in the set of numbers sigma2i ni'. I described my physics experiment in detail in the original version of the paper I sent to the Physical Review but was forced by the referee and editors to exclude that part of my paper from the published version.

It was within the specific context of simple and clean physical experiments of this particular kind that I put forth my quantum mechanical model of how results of the kind predicted by Schmidt could be explained by merely making a small change in the Schrodinger equation that would produce no observable effects in any purely physical experiment heretofore performed by physicists. Because of the existence of this model we cannot rationally rule out the possibility that the "Schmidt effect" exists merely on the grounds that this effect is incompatible with what we already know about the laws of nature. I believe it would now be useful to perform additional experiments of the kind described here to resolve the discrepancy between the null result that I obtained and the positive combined result of the five experiments reported by Schmidt. From the physicist's point of view the entire system of human beings and physical devices that are producing the cardboard sheets is simply a black box, and no assumptions about its properties are required to draw the conclusion, if the positive bias predicted by Schmidt were to occur systematically, that some aspect of our orthodox understanding of the laws of physics is seriously incorrect. Hence if a significant number of physicists of established high repute were to obtain results in line with the combined results reported by Schmidt, and the effect were to hold up, a finding of first magnitude importance in physics would be obtained. On the other hand, a negative result would provide direct empirical evidence in support of the widespread view among scientists that experiments that purport to show the existence of "psi" phenomena will fail when sufficiently rigorous conditions are enforced.

Reference 1. D. L. Radin, R. D. Nelson, Found. Phys. 19, 1499 ( 1989).

HENRY P. STAPP

Lawrence Berkeley Laboratory

Berkeley, California

Physics Today, July 1995

3. Theoretical Model

This section describes a relatively simply theoretical model that could account for the reported phenomena. In order to retain the mathematical structure of quantum theory almost intact, I shall exploit the ideas of von Neumann (9) and Pauli (10), according to which the von Neumann process number 1 (reduction of the wave packet) is physically associated with the mental process of the observer.

Henry uses the traditional Copenhagen interpretation. Is his identification of mental process with collapse of the wave function stuck to that interpretation? It would appear so because there is no collapse in the many-worlds interpretation and also it is not in the Bohm nonlocal hidden variable interpretation. If Stapp is right , his idea provides a test of the Copenhagen interpretation.

My own idea is different. My idea is stuck in the Bohm interpretation. It says that mental process is beyond quantum mechanics and requires the very kind of violation of the statistical predictions of orthodox quantum mechanics that Stapp actually models for "intention" below. In Bohm's picture, this violation is caused by a feedback-control loop between living matter and its quantum wave function. Dead matter does not have this loop which is a kind of nonlocal quantum "elan-vital" or "the Ghost in the Machine" sort of idea. The difference is that it is not a supernatural idea but is part of "post-modern physics".

It is interesting that two of our most rigorous-minded mathematical physicists should both be inclined to favor an idea that is so contrary to our common-sense idea of the nature of the physical world. Most physicists have, I think, preferred to accept the common-sense idea that the world of macroscopic material properties is factual: e.g., that the Geiger counter either fires or not fire independently of whether any observer has witnessed it; and that the mark on the photographic plate is either there or not there, whether or not anyone observes it. Yet it is difficult to reconcile this common-sense intuition with the mathematical formalism of quantum theory. For there is in that mathematical representation no natural breakpoint in the chain of events that leads from the atomic event that initiates the chain to the eventual brain event that corresponds to the resulting conscious experience. From the perspective of the mathematical physicist any imposition of a breakpoint at any purely physical level is arbitrary and awkward: it breaks the close connection between mathematics and the physical world in a way that is mathematically unnatural, and that moreover lacks any empirical or scientific justification. From a purely mathematical perspective it seems preferable to trust more the uniformity of nature's link between mathematics and the physical world than to inject, without any logical reason, our notoriously fallible intuitions about the nature of physical reality.

Following, then, the mathematics, instead of intuition, I shall adopt the assumption that the Schroedinger equation holds uniformly in the physical world. That is, I shall adopt the view that the physical universe, represented by the quantum state of the universe, consists merely of a set of tendencies that entail statistical links between mental events.

This point of view is, in fact, not incompatible with the Copenhagen interpretation, which, although epistemological in character rather than ontological,(11) rests on the central fact that in science we deal, perforce, with connections between human observations: the rest of science is a theoretical imagery whose connection to reality must remain forever uncertain.

According to this point of view, expressed however in ontological terms, the various possibilities, in regard to the detections of the radioactive decays, remain in a state of "possibility", or "potentiality", even after the results are recorded on magnetic tape, and the numbers are typed onto the sheets of cardboard: no reduction of the wave packet occurs until some pertinent mental event occurs.

Adopting this non-common-sense point-of-view shifts the problem from that of accounting for an influence of willful thoughts occurring at one time upon radio-active decays occurring months earlier to the simpler problem of explaining a biasing of the probabilities for the occurrence of the willful thoughts themselves, i.e., a biasing relative to the probabilities predicted by orthodox quantum theory.

The above paragraph is very important. I do not understand it very well. But it appears that Henry is trying to save Einstein causality. I thought the claim is that the irreversible records of the actual radio active decays do not obey the standard exponential decay statistics. Is Henry's idea that due to the limited sample we are seeing fluctuations away from the mean exponential and that somehow these fluctuations in the present capture or entrain or "correlate" the probability for the observer to "will" a +1 or a -1 or a particular color etc., whatever the protocol may be? In this case free will is an illusion and the observer-participator is a passive terminal channeling, so to speak in New Age terms, external causes.

This latter problem is quite manageable: Weinberg (5) has devised a nonlinear quantum mechanics that is very similar to quantum theory, but that can produce probabilities that are biased, relative to the probabilities predicted by linear quantum mechanics. Gisin (6) has already pointed out that Weinberg's theory can lead to causal anomalies.

According to our interpretation of quantum theory the mechanical registrations of the detections of the radio-active decays produces a separation of the physical world into a collection of superposed "channels" or "branches": the physical world, as represented by the wavefunction of the universe, divides into a superposition of channels, one for each of the different possible recorded (but unobserved) results. When the skeptic observes the control sequence {Cn^ = Cn sigma n} there is a projection onto those channels that are compatible with these observations. But, contrary to common-sense, the typed numbers under the remaining pieces of black tape are not yet fixed. Later on, when the "observer" looks at the device, the state of his brain will separate into a superposition of channels corresponding to the various alternative macroscopic possibilities, in the way already described by von Neumann.(9) Eventually, the state of the universe will be reduced by a projection onto those brain states that are compatible with the conscious experience of the observer. (12)

If the probabilities associated with the various alternative possibilities for the brain state are those given by orthodox quantum theory then there can be no systematic positive bias of the reported kind: the probabilities will necessarily, according to von Neumann's theory, agree with those that were determined earlier from the probabilities of the alternative possible detections of ratio-active decays, and there could therefore be no biasing of those probabilities due to the willful intent of the observer.

A generalization of Weinberg's nonlinear quantum mechanics allows the probabilities for the possible reductions in the brain state to be biased by the will of the conscious observer. Indeed, it allows part of the total probability to be shifted away from those possibilities to which the observer assigns negative "desire" or "value" and toward the possibilities to which he assigns positive "desire" or "value". We turn, therefore, to a description of Weinberg's theory, in the context of the present problem of the shifting of the probabilities away from those predicted by orthodox quantum theory, and toward those defined by a "desire" represented physically in the brain of the observer.

Stapp now makes a profound seemingly simple remark. He is not simply saying that any free field can be decomposed into independent simply oscillating normal modes. He uses the term "a general quantum system". Is this Stapp's original contribution or is it Steven Weinberg's? I think it is Weinberg's from my dim memory of glancing at his papers. It as novel and surprising a way of looking at quantum mechanics as was Richard Feynman's with the amplitude equal to the exponential of the classical action along the path and all indistinguishable paths adding coherently. This is about to become self-evident below.

Weinberg's nonlinear quantum is rooted in the fact that the quantum mechanical equations of motion for a general quantum system are just the classical equations of motion for a very simple kind of classical system, namely a collection of classical simple harmonic oscillators. Thus a natural way to generalize quantum theory is to generalize this simple classical system.

To describe this connection of quantum theory to classical simple harmonic oscillators let pn and qn, for n = 1,2..., be the classical canonical variables for a collection of simply harmonic oscillators. Define the dimensionless parameters

xn = qn(mw/2hbar)^1/2 (1.a)

and yn = pn(1/2hbarmw)^1/2 (1.b)

Then the collection of pairs

zn = xn + iyn

and

zn* = xn - iyn

is an equivalent set of variables, and the classical Hamiltonian can be written (with hbar =1) as

h(z,z*) = zn*Hnmzm = (z|H|z) (3)

... repeated indices are .. summed. The function h(z,z*) is bilinear: it is a linear function of each of its two (vector) arguments z and z*. The matrix Hnm is independent of z and z*: it is a diagonal matrix with positive elements, in the original basis. However (3) is written in a basis-independent way, and in the general representation Hmn is Hermitian, Hnm = (Hmn)*. The basis-independent quantity h is real:

The elegant notation looks quantum mechanical, but Henry, at first at least appears to be doing classical Hamiltonian theory here. So it should be possible to rewrite it as a Hamilton-Jacobi theory. Quantum mechanics is suddenly slipped in eq. (8) by what appears at first to be a Magician's trick.

The canonical classical equation of motion for a function f(z,z*) is

df/dt = {f,h}PB (5)

Here the right-hand side {..}PB is the classical Poisson bracket, which can be written in the form

{f,h}PB = -i(&f/&zn &h/&zn* - &h/&zn &f/&zn*) (6)

To obtain quantum mechanics as a special case one restricts the observables to bilinear forms:

f(z,z*) = zn*Fnm zm = (z|F|z) (7)

where F is independent of z and z*. Them

df(z,z*)/dt = {f,h} = -i(z|[F,H]|z) (8)

where [F,H] is the commutator. The variables zn and zn* can then be identified with the components PSIn = and PSIn* = of the general quantum system.

To pass to Weinberg's nonlinear quantum theory one allows the observables including the Hamiltonian to be real non-bilinear functions of z and z*, i.e., of PSI and PSI*, but imposes the condition that every observable be homogeneous of degree one in each of the variables z and z*:

zn&f/&zn = zn*&f/&zn = f (9)

This condition allows one to write

f(z,z*) = zn* &^2f(z,z*)/&zn*&zm zm = zn* Fnm zm = (z|F|z) (10)

where the Fnm are now no longer necessarily independent of z and z*.

When this theory is written in Hamilton-Jacobi form, maybe what happens is that the dependence of Fnm on z and z* causes a non-unitary source term in the conservation of current equation that accompanies the Hamilton-Jacobi equation with the quantum potential. The source term should explicitly depend upon the actual nonlocal hidden variable "n'" of the Bohm theory. For example, if we are doing non-relativistic nonlinear quantum mechanics of a single particle, n' is x' the actual position of the actual particle, where z = . This source term is "back-reaction" of the actual hidden variable on the quantum potential. That is, the nonlocal quantum potential not only "pilots" the particle but is also affected directly by the motion of the particle in a self-consistent feedback-control loop which causes deviations away from the statistical predictions of the linear theory. In other words, is Weinberg's nonlinearity in the Copenhagen interpretation equivalent to Bohm's back reaction? This may a wrong approach because at the end of Stapp's paper it becomes clear that non-Hermiticity of the Hamiltonian is what really matters.

The reality condition f(z,z*) = f(z,z*)* is equivalent to

Fnm = (Fmn)* (11)

The matrix elements Hnm are defined in an analogous way, and

df/dt = - i(z|[F,H]|z) (12)

This equation looks the same as the orthodox equation (3). Now, however, the operator parts cannot be separated from the state-vector parts, z and z*, because F and H can depend upon z and z*.

We now apply this formalism to our situation. Let the general wave function PSI be written as

PSI = Sum(i) ai PHIi CHIi (13)

where the CHIi denote states of the brain, and the PHIi are a set of mutually orthogonal states of the rest of the universe. Suppose, for simplicity, that at t = 0 the state PSI has the form PSI = (a PHI+ + b PHI-) CHIo (14)

where PHI+ and PHI- are two macroscopically different states: suppose PHI+ corresponds to a world in which the recorded numbers have a positive bias, and PHI- corresponds to a state in which the recorded numbers have a negative bias. Suppose the state CHIo is represented for simplicity, by a compactly supported wave function in momentum space (say in one variable p) and that the interaction Hamiltonian is

H = (|PHI+> where Xop is the generator of translations in the variable p. Under the action of this Hamiltonian the state (14) evolves into

PSI(t) = aPHI+ CHI+(t) + bPHI- CHI-(t), (16)

where the states CHI+(t) and CHI-(t), expressed in momentum space, are displaced in opposite directions by an amount proportional to t.

Note that if F+ = |PHI+><(PHI+| and F- = |PHI-><(PHI-|

then

f+(t) =

and

f-(t) =

are both independent of t: the probability of finding the system in the positively (or negatively) biased state is not influenced by the action of the "measurement" process generated by the H specified in (15).

This constancy of f+(t) and f_(t) is a general consequence of the fact that the evolution is generated by a hermitian H that has no matrix elements connecting the states |PHI+> and |PHI-> More generally, if the Fi, i = 1,...,N, are a set of projection operators onto orthogonal states |PHIi> in PHI space, and H has no diagonal elements connecting any two different states |PHIi>, and if

PSI = Sum (i = 1 to N) aiPHIi CHIi

then

dfi(t)/dt = = 0

the probabilities fi(t) remain constant.

If the different states |PHIi> represent macroscopically different configurations (e.g., states in which different numbers are typed onto cardboard sheets) then it would be unreasonable to allow H to have any (significantly) nonzero matrix elements connecting them.

This argument is not altered by passing over to the nonlinear version of the equation of motion represented by (12). As long as H has no matrix elements connecting the macroscopically distinct states |PHIi> there will be no transitions between these states, and hence no change in the associated probabilities fi(t).

This argument apparently shows that Weinberg's theory by itself is not sufficient to produce the reported phenomena. To model this effect we take h(z,z*) = h'(z,z*) + ih"(z,z*), with h' and h" real. This generalization of Weinberg's theory is examined next.

From the homogeneity condition (9) one obtains, as before (see (10)),

h(z,z*) = zn*Hnmzm (17)

but now with

Hnm = Hnm' + iHnm"

where

Hnm' = (Hmn')* (18a)

and Hnm" = (Hmn")* (18b)

Weinberg's equation of motion for zn is

dzn/dt = -i (&^2h/&zn*&zm) zm = -iHnm zm (19)

Hence

dzn*/dt = iz*(Hmn' - iHmn") (20)

Consequently, the equation of motion for a real function f(z,z*) becomes

df/dt = (d/dt) = -I + (21)

Where {F,H"} is the quantum anti-commutator FH" + H"F. This anti-commutator term can contribute to df/dt even if H" is diagonal in (PHI+, PHI-).

Stapp gives an explicit example in equations (23) to (24) in which the nonunitarity (i.e., H") causes df+/dt to be positive.

... Hence the probability associated with the state |PHI+> will build up, relative to the value |a|^2 prescribed by orthodox quantum theory.

This example shows that the reported phenomena, although contrary to orthodox ideas about causality, can be modeled within a Weinberg-type of nonlinear quantum theory if the Hamiltonian function h(PSI,PSI*) is allowed to be nonreal.

If there are in nature nonlinear contributions of the kind indicated in Eq. (23) then it seems likely that biological systems would develop in such a way as to exploit the biasing action. The biasing states, illustrated in the model by the state |CHI+>, could become tied, in the course of biological evolution, to biological desiderata, so that the statistical tendencies specified by the basic dynamics would be shifted in a way that would enhance the survival of the organism.

The Weinberg nonlinearities were initially introduced in the present context because of Gisin's result, which showed that these nonlinearities could lead to causal anomalies of the EPR kind. However, the considerations given above indicate that those nonlinearities alone cannot produce anomalies of the kind reported in ref. 8: a nonreal h is apparently needed to obtain an effect of that kind.

This is strange. Weinberg's nonlinearity, according to Gisin, is sufficient to allow causal anomalies on the nonlocal quantum connection, but it is not enough to permit the controlled intentional PK distortion of quantum statistics. What does Gisin mean by "causal anomalies"? Weinberg, says his theory permits use of the nonlocal quantum connection as a communication channel which is why he rejected it. The fact that an atomic physics experiment did not show the nonlinearity is not relevant because the present claim is that the new effects can only be seen in living matter. How can there be such violation of Eberhard's theorem without nonunitarity of the type modelled by Stapp?

Because the nonlinear aspect is not obviously needed, one could try to revert to a linear theory. Yet it is important to recognize that in the modeling of acausal effects one has available the more general nonlinear framework. If the purported acausal phenomena is a real physical effect and is explainable in terms of a nonreal h that arises solely in conjunction with nonlinear terms, as in the model given above, then orthodox quantum theory could become simply the linear approximation to a more adequate nonlinear theory.

References

l. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777-780 (1935).

2. J.S. Bell, Physics 1, 195-200 (1964).

3. H.P. Stapp, Phys. Rev. A47, 847-853 (1993); Phys. Rev. A46, 6860-6868 (1992); Bell's theorem in an indeterministic universe, Lawrence Berkeley Laboratory Report LBL-29836 (1993) (with D. Bedford) Submitted to Synthese.

4. P. Eberhard, Nuovo Cim. 46B, 392-418 (1978).

5. S. Weinberg Ann. Phys. (NY) 194, 336-386 (1989).

6. N. Gisin, Phys. Lett. A 143, 1-2 (1990).

7. H. Schmidt, J. Am. Soc. Psy. Res. 38, 267-291 (1976). R. Jahn, Y. Dobyns, and B. Dunne, Soc. of Sci. Expl. 5, 20S-232 (1991).

8. H. Schmidt, Observation of a psychoScinetic effect under highly controlled conditions, Soc. of Sci. Exp.

9. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princeton, 1955. Ch EII.

10. W. Pauli, quoted in Mind, Matter and Pauli, Chap. 7 of ref. 12.

11 H. P. Stapp, Amer. J. Phys. 40, 1098-1116, (1985).

12. H.P. Stapp, Mind, Matter, and Quantum Mechanics, Springer-Verlag, Berlin and Heidelberg, 1993.

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