Theoretical model of a purported empirical violation of the predictions of quantum theory
(Originally published in Physical Review A, Vol.50, No.1, July 1994)
ABSTRACT: A generalization of Weinberg's nonlinear quantum theory is used to model a reported violation of the
predictions of orthodox quantum theory.
This work concerns the possibility of causal anomalies. By a causal anomaly I mean a theoretical or empirical situation in which
the occurrence or nonoccurrence of an observable event at one time must apparently depend upon a subsequently generated
(pseudo) random number, or willful human act.
Considerations of the Einstein-Podolsky-Rosen  and Bell's-Theorem  type entail  -- if many-world's interpretations are
excluded -- the occurrence of causal anomalies on the theoretical level, provided certain predictions of quantum theory are at least
approximately valid. However, those anomalies cannot manifest on the empirical level if the quantum predictions hold exactly .
On the other hand, slight departures from the exact validity of the quantum predictions  could lead to small but observable causal
Empirical causal anomalies have been reported in the past in experiments that appear, at least superficially, to have been
conducted in accordance with scientific procedures , and the protocols are becoming ever more stringent . I do not enter into
the difficult question of assessing the reliability of these reports. The scientific community generally looks upon them with
skepticism. But at least part of this skepticism originates not from specific challenges to the protocols and procedures of the works
of, for example, Jahn, Dobyns and Dunne , but from the belief that such
results are not compatible with well-established principles of physics, and
hence to be excluded on theoretical grounds. However, it turns out that small modifications of the
standard quantum principles would allow some of the most impossible sounding of the
reported phenomena to be accommodated. According to the report in Ref. , it
would appear that in certain experimental situations willfull human acts,
selected by pseudorandom numbers generated at one time, can shift, relative to
the randomness predicted by normal quantum theory, the timings of radioactive
decays that were detected and recorded months earlier on floppy discs, but
that were not observed at that time by any human observer. Such an influence
of an observer backward in time on atomic events seems completely at odds
with physical theory. However, a slight modification of normal quantum theory can accommodate the reported data.
In the scientific study of any reported phenomena it is hard to make progress without a theoretical description that
ties them in a coherent way into the rest physics.
The purpose of the present work is to construct, on the basis of an extension of Weinberg's nonlinear generalization
of quantum theory , a theoretical model that would accommodate causal anomalies of the kind described above.
Specifically, the present work shows that the reported phenomena, although incompatible with the main currents of
contemporary scientific thought, can be theoretically modeled in a coherent and relatively simple way by combining
certain ideas of von Neumann and Pauli abut the interpretation of quantum theory with Weinberg's nonlinear
generalization of the quantum formalism.
II. THE THEORETICAL MODEL
To retain the mathematical structure of quantum theory almost intact, I shall exploit the ideas of von Neumann  and Pauli ,
according to which the von Neumann process number 1 (reduction of the wave packet) is physically associated with the mental
process of the observer. 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 normal 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 does 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 anyone observes it or not. Yet
it is difficult to reconcile this common-sense intuition with the mathematical
formalism of quantum theory. For there is in that structure no natural
breakpoint in the chain of events that leads from an atomic event that
initiates the chain to the brain event associated with the resulting
observational experience. From the perspective of the mathematical
physicist the imposition of a breakpoint
at any purely physical level is arbitrary and awkward: it would break the close connection between mathematics and
the physical world in a way that is mathematically unnatural, and moreover lacks any empirical or scientific
justification. From a purely logical perspective it seems preferable to accept the uniformity of nature's link between the
mathematical and physical worlds, rather than to inject, without any logical or empirical 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 Schrodinger 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.
In fact, this point of view is not incompatible with the Copenhagen interpretation, which, although epistemological
rather than ontological in character , 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
According to this point of view, expressed however in ontological terms, the various possibilities in regard to the
detection of a radioactive decay remain in a state of "possibility" or "potentiality," even after the results are recorded on
magnetic tape: no reduction of the wave packet occurs until some pertinent mental event occurs.
By adopting this non-common-sense point of view, we shift the problem raised by the reported results from that of
accounting for an influence of willful thoughts occurring at one time upon radioactive decays occurring months earlier
to the simpler problem of accounting for the biasing of the probabilities for the occurrence of the thoughts themselves,
i.e., a biasing relative to the probabilities predicted by orthodox quantum theory.
This latter problem is manageable: Weinberg  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  has already pointed out that Weinberg's theory can lead to causal anomalies.
According to the interpretation of quantum theory adopted here, the mechanical recording of the detection
of the products of a radioactive decay generates a separation of the physical world
into a collection of superposed "channels" or "branches": the physical world, as represented
by the wave function of the universe, divides into a superposition of channels, one for each of
the different possible recorded (but unobserved) results. Contrary to
common sense the recorded but unobserved numbers remain in a state of
superposed "potentia," to use the word of Heisenberg. Later, when the
human 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 described by von Neumann .
FInally, when the psychological event of observation occurs, the state
of the universe will be reduced by a projection onto those brain
states that are singled out by the conscious experience of the observer .
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 kind reported: the probabilities associated with the
alternative possible brain events will necessarily, according to the orthodox theory, as explained by von Neumann,
agree with those that were determined earlier from the probabilities of the alternative possible detections of radioactive
decays: there could be no biasing of those probabilities due to a subsequent willful intent of an observer. However, a
generalization of Weinberg's nonlinear quantum mechanics allows the probabilities for the possible reductions of the
state of the brain of the observer to be biased, relative to those predicted by orthodox quantum theory, by features of
the state of the brain of the conscious observer. If such a feature were the activity of the brain that is associated with
"intent," then the effect of the anomalous term in the Hamiltonian would be to shift the quantum probabilities
corresponding to the various alternative possible conscious events toward the possibilities linked to his positive intent.
We turn, therefore, to a description of Weinberg's theory, in the context of the problem of the shifting of the
probabilities away from those predicted by orthodox quantum theory, and toward those defined by an "intent"
represented by particular features of the state of the brain of the observer.
Weinberg's nonlinear quantum theory is rooted in the fact that the quantum-mchanical 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.
[ technicalities deleted... ]
This example shows that the reported phenomena, although contrary to orthodox ideas about causality, can be model
within a Weinberg-type of nonlinear quantum theory if the Hamiltonian function
h(psi,psi*) is allowed to
If there are in nature nonlinear contributions of the kind indicated...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 Weinberg nonlinearities were intially introduced in the present context
because of Gisin's result, which showed that these nonlinearities could
lead to causal anomalies of the Einstein-Podolsky-Rosen (EPR) kind.
However, the considerations given above indicate that those nonlinearities
alone cannot produce anomalies of the kind reported in Ref. : a nonreal
h is apparently needed to obtain an effect of that kind.
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
If the purported acausal phenomena is a real physical eitect 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.
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