The July 1994 edition of *New Scientist* contained an article by
Julian Brown with the rather surprising title "Martial arts students influence the past". For copyright reasons, we are unable to reproduce it here
so we shall describe its contents:

The article focusses on Berkeley physicist Henry Stapp's paper "Theoretical model of a purported empirical violation of the predictions
of quantum theory" published in *Physical Review A*,
July 1994. The paper is described as
"scientific heresy", probably as it was inspired by experiments carried out by
parapsychologist Helmut Schmidt in San
Antonio, Texas in 1992.

The intial claim is that Stapp *"has found a way of modifying
the basic equations of quantum theory
to permit people to influence things that
happened in the past"*.

Schmidt's experiments are described briefly. They involved a group of
martial arts students as subjects, being shown prerecorded random numbers
via an electronic display. The numbers had been generated some months
earlier by an apparatus involving a radioactive source and a decay counter
(radioactive decay timings being as "truly random" as anything one can find
in nature). The students attempted to exert a mental "influence" on the
visual display, whose behaviour was determined by the prerecorded numbers. In
this way, they would be supposedly influencing the statistical distributions
of the numbers themselves. *"Remarkably"*, the article claims, a
significant bias was found in the numbers, *"one that had a less than 1 in
1000 probability of occuring by chance"*. It is claimed that *"elaborate
precautions were taken to prevent any cheating"*. Precise descriptions of
experimental procedures in many similar experiments carried out by Schmidt can
be found in the numerous articles available in the RPKP archive.

Henry Stapp had acted as an independent monitor in Schmidt's experiments,
and while *"acknowledging the inherent heresy of the idea"*, he decided
to look further into the possibility that the martial arts students had
actually influenced the past. His idea was to develop a simple generalisation
of a modified "nonlinear" quantum theory introduced by
Steven Weinberg
of the University of Texas at Austin. Whereas the macroscopic world involves
countless nonlinear systems (from the rupture of an elastic band to the
collapse of a stock market), the standard model of quantum mechanics suggests
that the underlying behaviour of the microworld is entirely linear. Weinberg
was attempting to bridge this gulf between an explicitly nonlinear macroworld
and a purportedly linear microworld. He concluded that such an adaptation could not work, as the changes introduced would lead to "logical absurdities".
Stapp has apparently "sidestepped" Weinberg's concerns and developed his own
nonlinear version of quantum theory, one which accomodates Schmidt's findings.

Stapp claims that the nonlinearity he has introduced would allow a mental
influence on the outcome of quantum measurements. He is quoted as saying
* "Although quantum theory is a
beautiful theory and has been tested to very
high accuracy experimentally there is still
considerable doubt over what precisely
happens when a quantum system such as a
decaying radioactive atom is subjected to a
measurement.
Eugene Wigner
suggested that consciousness is involved in
a fundamental way. I don't know whether
he was right but if he was then this work
takes his ideas one step further."*

The article goes on to explain the ideas of "quantum superposition", i.e. that a radioactive atom can exist in two states simultaneously - one in which a decay has occurred and one in which it hasn't. Wigner suggested that the atom is forced into one of the two states only when the decay is monitored by a human observer. If this is the case, when Schmidt's apparatus generates random numbers, there would actually be a complicated superposition of states in which we could find all possible sets of numbers. As long as the numbers remain unobserved, it is claimed, the superposition would remain (this ignores the issue of "thermal decoherence" which prevents macroscopic quantum superpostions - this may be a significant oversight). In Schmidt's experiments the superposition would have remained until the martial arts students viewed the electronic display.

Even if Wigner's interpretation is correct (and not all
physicists accept it), standard
quantum mechanics would still predict a statistically unbiased outcome,
contrary to Schmidt's findings.
In Stapp's
adaptation of quantum mechanics, however,
the nonlinearity allows mental states
to *"skew the relative probabilities. Intent,
he says, could boost the chances of one
particular set of numbers being
selected over another."*

The crucial idea here seems to be a mathematical representation of the
subjects "intent" in terms of a quantum brain state, as well as the
representation of the superpostion of the possible number-states.
*"When one of the
martial arts students saw a signal on
the display, for example, the combined
system of numbers and brain
would have evolved into a new
quantum state. In Stapp's version of
quantum theory, the way this evolution
occurs would depend on a term that
involved the interaction of the
two- the numbers and the brain. It
is this term that could allow the
probabilities to be biased."*

Weinberg claims
he has not yet seen the paper, and therefore
is unable to comment on its details.
However, he has pointed out that
nuclear spin measurements provide evidence that any
nonlinear quantum mechanical effects
could contribute no more than one part in
10^27 of the energy of a nucleus.
*"That's a
fantastic level of precision. Any modification
of the theory is going to find it difficult
to meet that constraint. Furthermore,
another problem with nonlinear terms is
that they allow the possibility of signals that
can propagate faster than light.
That to me
just seems unacceptable."*

Stapp has responded by saying that he had yet to calculate the size of the effect his nonlinear term would have on energy levels in the nucleus. He believes, however, that the problem of faster-than-light signalling, which leads to a breakdown of causality, is connected to the seeming causality violation which is evident in Schmidt's data. So in a sense the martial arts students were able to "influence the past", but Stapp's theory provides a "causal" mechanism by which this can happen.