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.

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