Henry Stapp, Physicist
Lawrence Berkeley National Laboratory



Reprinted from Physics Today, July 1995
An attack from a US Army physicist on Stapp and his theory of PK just presented. 
Stapp, like Harvard psychiatrist, John Mack, who studies UFO abductions, is 
under serious peer pressure (e.g. head of LBL where Stapp works) to supress his 
fringe research. This is a new threat to academic freedom in our elite 
universities. 
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. 
Sarfatti Commentary 
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.
Sarfatti Commentary 
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. 
Sarfatti Commentary 
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: 
Sarfatti Commentary 
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*.
Sarfatti Commentary 
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*.
Sarfatti Commentary Is this where the "strange loop" of Godelian self-reference 
comes in? The clean separation between the active transformer and the passive 
transformed is mended. No longer is the state vector the passive victim. It 
fights back. :-) Is this fusion between the operator and the state vector 
completes the self-referential feedback control circuit and is the mechanism of 
free will? 
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-).
Sarfatti Commentary Here is Stapp's original contribution beyond Weinberg's 
nonlinear theory. It is not the nonlinearity of Weinberg's theory that is the 
mechanism of "intentional" PK(i.e., psychokinetic) distortion of the statistical 
predictions of orthodox quantum mechanics, but, rather it is the new unorthodox 
anti-commutator {F,H"} in the equation of motion (in addition to the orthodox 
commutator [F,H']) of the quantum probabilities that comes from an explicit 
breaking of the symmetry of unitarity. No longer can we assume that the 
transition probabilities are frame-independent in Hilbert space because the 
generator of time evolution is not Hermitian. The historical transformations for 
living matter are, in this post-modern view of physics, essentially nonunitary. 
This lack of conservation of total probability is the quantitative measure of 
creative intelligence. Unitarity restricts us to less than monkeys typing random 
word salad on the keyboard of the cosmic computer. 
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.
Sarfatti Commentary The above remark is precisely the position advocated by 
Brian Josephson in his Mind-Matter Unification Project at Cambridge University. 
Like Stapp, Josephson has also been attacked for his unorthodox ideas. 
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.
Sarfatti Commentary 
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 
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