ABSTRACT: This article compares two previously described mathematical psi models. The teleological model emphasizes the space-time independence of psi and the close relationship between ESP and PK. But this model leads to a divergence problem in the sense that the role of future observers seems exaggerated. The quantum collapse model avoids this problem. But this model may appear less attractive insofar as some of the space-time independence is lost and the relationship between ESP and PK is weakened. Experiments that might show the inadequacy of on or the other model are discussed.

At an early stage of psi research, one could hope to understand psi by a straightforward extension of physics. It seemed reasonable to interpret telepathy in terms of "mental radio waves" and psychokinesis (PK) in terms of some "mental force" But this changed when precognition was discovered and, more generally, when experiments showed the surprising insensitivity of psi to physical parameters suc as space, time, and the complexity of the task. Psi appeared increasingly implausible, suggesting a need for major changes in our thinking.

But, even with psi and current physics incompatible, there seems no need yet to abandon the general mathematical physical approacl to the problem. On the contrary, physics is rather flexible and open to changes. And the abstract mathematical method of modern physics has been very successful in helping us to understand phenomena that seemed at first intuitively implausible.

Several mathematical psi models have been developed by different researchers (see Millar, 1978). None of these presently available models can be considered as a satisfactory psi theory. Nevertheless these models are stimulating for the design of new experiments and the formation of new concepts.

In the following, I will review two of these models, compare their merits and their shortcomings, and discuss experiments to possibly show their inadequacies.

Since the first model has already been discussed in the parapsychological literature (Schmidt, 1975; 1978), a brief review will be sufficient. But the second model is published only in a rather technical version (Schmidt, 1982), so that some more detailed explanations are appropriate.

The model begins with an ensemble of all the possible world histories with their corresponding probabilities as they would be predicted by conventional physics. And, to introduce an element of noncausality, the model postulates a psi law that modifies the probabilities for the different world histories. This law is teleological in the sense that, for example, the outcome of a coin flip depends on its implications for the future history of the world. This is certainly implausible, but so is precognition. What matters is rather that this teleological law could be formulated in a mathematically simple form (without too many ad hoc assumptions) and that the resulting model is self-consistent. In our case, this law is very simple, and provides for a space-time independence of psi. At the same time, the psi law is Lorentz-covariant, that is, it fits into the space-time frame provided by Einstein's relativity theory.

The model does not claim to "explain" psi. It does not even try to discuss what happens inside a subject's head. It rather assumes subjects (the psi sources) with given abilities and then studies how a world with such odd elements as psychics can still be reasonable as a whole. This restricted scope of the model is in accordance with the experimental work aimed at the physical characteristics of psi (like its dependence on space, time, and task complexity) rather than at its psychological or spiritual aspects.

Let me list here the most important features of the teleological model:

1.

2.

3.

4.

5.

An interesting implication is that, in cases of delayed feedback, the relevant feature is the subject's mental state at the time of the feedback rather than at the time of the "test."

6.

The listed features seem closely linked, insofar as each one is an integral part of our model. But if we do not want to commit ourselves to any theoretical model, the first five features still appear as interesting hypotheses to be studied independently.

Quantum theory describes a physical system in terms of a state vector (or wave function). This vector can be considered as a set of parameters specifying the state of the system. There seems to be no question of how to use these vectors to make successful calculations and predictions. But there is still controversy about the interpretation of the state vectors.

Consider, for example, a binary random generator that randomly selects a red or green lamp to be lighted, with probabilities

When an observer looks at the outcome, he sees either the red or the green lamp lighted. At this stage, one feels, Nature must have definitely decided for one outcome. In the language of quantum mechanics, the original state vector, |STATE>, has made a quantum jump, or has been reduced, into either the state |RED> or the state |GREEN>. But the Schrodinger equation, which describes the change of the state vector with time, has no provision for such a sudden quantum jump. Then, how is this transition brought about? Is it a physically real process or some artifact resulting from an improper interpretation? Let me mention four different approaches:

The provocative idea that the equations of physics deal not with Nature per se, but with our knowledge about Nature, makes quantum theory self-consistent. At the same time, this seems to imply a very special role for the human observer, making him basically different from, say, an observing TV camera. The situation appears particularly puzzling when an observer tries to describe a system that includes another observer, as in Schrodinger's cat paradox, or in the paradox of Wigner's friend (d'Espagnat, 1976).

For parapsychologists, hidden variables are tempting, because they show some noncausal and space-independent features. If I could change a hidden variable at my location, this might imply a simultaneous change at some distant location. That need not disturb physicists, because in their model hidden variables cannot be observed and measured. But if the mind had some nonphysical way to change and measure hidden variables, psi effects could result. Walker and others have explored some of the possibilities for constructing psi models based on hidden parameters (Mattuck & Walker, 1979; Walker, 1975).

But as soon as an observer becomes consciously aware of the outcome, Wigner proposes, the observer's mind induces a reduction from the ambiguous ghost state into one of the "physically reasonable" states |RED> or |GREEN>. Thus, by interfering with the Schrodinger equation, the mind helps in maintaining one single reality.

Wigner had already wondered if the human mind, playing such an active role in shaping physical reality, might not contribute some PK effect in the process. The quantum collapse model to be discussed pursues this idea.

The detailed mathematical description of this model has been presented elsewhere (Schmidt, 1982). The model introduces, at the phenomenological level, a mathematical formalism that would provide the reduction of the state vector under an observation. The main requirements that led to this particular formalism were that the formalism should be mathematically as simple as possible but at the same time quite general, applicable to all situations.

To save the reader from having to go into the details of the quantum formalism of the original paper, I have summarized in the Appendix some of the general ideas and mathematical results for the simple case of a binary random decision.

In the model, the act of observation induces a gradual reduction from the original ghost state (|GHOST> = |STATE> of Eq. 1) into the well-defined states (|RED> or |GREEN>).

To formulate this transition mathematically, I shall introduce the three time-dependent functions

This shows an exponential decay of the ghost state, with the final result, after a sufficiently long time (

The value of the positive alertness parameter determines the speed of the state vector reduction. The choice of the name for this parameter should suggest that a highly alert observer might produce a faster reduction than a sleepy one. But even though state vector reduction is necessary for PK to operate, the speed of this reduction does not determine the size of the PK effect (perhaps, you don't have to be in an alert state to produce PK effects). The PK effect is given by another parameter,

A nonvanishing value of the PK coefficient

The Eqs.

This mechanism implies that simultaneous PK efforts by two subjects are rather inefficient, because each subject contributes to the attrition of the ghost state, thus leaving less for the other subject to work on. The Appendix shows explicitly that the PK score produced by two subjects, working simultaneously or consecutively, cannot be higher than the score obtained by the better of the two subjects working alone. This is very different from the situation in the teleological model and explains why the quantum collapse model has no diveregence problem.

A most interesting suggestion of the quantum collapse model is that some aspects of consciousness could be operationally defined by its ability to collapse the state vector. Conventional physics is not able to measure this collapse. But with the PK mechanism serving as a measuring probe, a successful PK subject could tell the difference between the collapsed and the noncollapsed state, because only the noncollapsed state would respond to PK efforts.

We might even look for consciousness effects from animals. To test whether, for example, a dog can collapse a state vector, we would compare the outcome of two types of tests in which the decisions made by our binary generator would or would not be preinspected by the dog before the human subject applied his PK effort. If the preinspection makes a difference, this would be our evidence for dog consciousness.

The model does not specify clearly what constitutes a conscious observation that should reduce the state vector. In the case of the dog, it might be necessary to activate the animal's attention by enforcing each red signal by a simultaneous food reward. And with a human subject, a passive observation where the observer immediately forgets the outcome, or a subliminal perception that does not fully enter consciousness, might produce only incomplete reduction. All these questions could be answered experimentally.

In this context, the results of two previous experiments might be interesting. In a PK experiment with prerecorded targets (Schmidt, 1976), the subjects listened to sequences of 256 clicks that were randomly channeled to the right or left ear. The PK target was to obtain more clicks on one specified side. The clicks were generated at a rate of 10 per second so that the subject could clearly notice the individual decisions but could not spend much time "digesting" the information. Half of the clicks were generated momentarily and presented once. The other half were prerecorded and presented four times in succession. The scoring rate on the repeatedly presented clicks was found to be higher (at a moderate level of significance) than the rate on the only-once-presented events.

In the frame of our quantum collapse model, this effect might be understood in the sense that, at the first presentation of the clicks, there was not enough time for the subject to absorb the whole information and thus to reduce the state completely. Therefore, subsequent PK efforts could lead to a strengthening of the observed PK effect.

Another possibly relevant result comes from a PK experiment with prerecorded and preinspected seed numbers (Schmidt, 1981). This experiment was performed in the following steps: (a) With the help of radioactive decays as source of randomness, a six-digit random number was generated and recorded. (b) This number was carefully inspected by the experimenter. (c) The seed number was fed into a computer "randomness" program to produce a binary quasirandom number sequence. (d) The binary sequence was displayed to the PK subject as a sequence of red and green signals (or in some other manner) while the subject tried to enforce the generation of many "red" signals.

In part of the experiment, step b was omitted (the experimenter's observation of the six-digit random number). In this case, the PK subject was the first person to observe the random result that originated from the radioactive decay. But the outcome of the experiment showed a PK effect also in the part where the experimenter had preinspected the seed numbers. Thus, there appeared no significant collapse, even though the experimenter had enough information to derive from the seed numbers, in principle, the finally displayed binary sequence.

This result might help us to a better understanding of what constitutes a "conscious observation" that collapses the state vector. Note that the seed numbers did not convey "meaningful information" to the first observer, or information that he could remember (a large block of seed numbers used for the experiment were inspected in one sitting). Refer to Schmidt (1982) for more information.

1. In the teleological model, all forms of psi seem intricately linked, and there is a high degree of symmetry between PK and precognition: A PK subject can be set up to act to predict future events, and a prophet can be made to acomplish PK tasks. In the quantum collapse model, however, PK seems to play a more dominant role, and the model might not be sufficient to account for all forms of precognition. Take as example the case where the subject tries to predict the outcome of a future random event. If this subject is the first to receive feedback on the results, then the subject can still succeed (by mentally enforcing the generation of the predicted event). But if somebody else looks at the results first, collapsing the state vector in the process, then the subject's efforts should be useless.

2. Both models agree insofar as only a "weak violation" of physics occurs; that is, the effects appear only in connection with random processes.

3. The space-time independence of psi is somewhat restricted by the quantum collapse model. The outcome of a PK experiment is still independent of the distance in space and time between the subject's effort and the random event. Experiments with prerecorded targets still work. But if two subjects make consecutive PK efforts on a random event, it matters which subject tries first. This feature may be an advantage of the quantum collapse model because it helps to eliminate the divergence problem.

4. The complexity independence is common to both models because the formalism makes no reference to the internal structure of the random generators.

5. Feedback is equally vital for both models.

6. There is no divergence problem in the quantum collapse model because a complete observation reduces the state vector so that PK effects from later observers are excluded.

For a most straightforward experimental comparison between the two models, consider a PK experiment where two subjects, A and B, make subsequent efforts at a total of

To evaluate the results, determine the deviations of the four scoring rates from chance under the four different conditions given by Table 1. Note that for opposite target directions in a trial, the subjects have opposite scores. Therefore, the definitions of the score deviations in the table have to specify (last column) to which of the subjects this score applies.

From the viewpoint of the teleological model, it should not matter whether A or B made the first effort; that is, apart from statistical fluctuations,

Deviation of scoring rates (S) | Subject order | Target direction | Subject who scored |
---|---|---|---|

S1 | A,B | Same | A |

S2 | A,B | Opposite | A |

S3 | B,A | Same | B |

S4 | B,A | Opposite | B |

Considering next the quantum collapse model, let us first assume that the feedback from each trial provides a complete observation with complete collapse of the state vector. Then the second subject cannot exert an effect; that is,

In the quantum collapse model, the possibility of an incomplete reduction of the states can be covered with the help of Equation A16. But because a PK effect is necessarily accompanied by some reduction of the state, the difference between the two models remains observable.

For the physicist, the ultimate goal of psi research would be the discovery of some novel microscopic law of Nature of great mathematical simplicity and beauty, from which all psi effects could, in principle, be derived. That law would qualify, from the physicist's viewpoint, as an "explanation" of psi.

But the phenomenological, macroscopic approach appears as a reasonable, and perhaps necessary, first step, as a basis for a later, more complete understanding.

The two particular psi models.were selected for the discussion because these models are relatively simple mathematically and because their easily testable predictions sharply disagree on a vital question of parapsychology: the degree to which the future may affect the present, that is, the extent of theo noncausality of psi.

We have indications of such noncausality from precognition tests, from PK tests with prerecorded targets, and from experiments that suggest an effect of a later checker on previously collected test results. Furthermore, this noncausality might be the source of the uncontrollability of psi, in the sense that the future, beyond our control, affects the results of a present experiment.

The teleological model, with its space-time-independent structure, provides for all these noncausal effects and derives PK, precognition, and the other forms of psi from one basic mechanism. But this attractive high degree of symmetry leads to a divergence problem in the sense that future observers obtain an unreasonably high influence on the present.

The quantum collapse model drastically reduces this PK effect from future observers. After a complete observation of a random event, there is no more opportunity left for future observers to affect the outcome. The model retains much of the space-time independence of psi. And precognition and PK effects on prerecorded targets can still occur. But some forms of precognition seem not to work as well as they should.

Thus, the two models might be too extreme, in opposite directions. And this makes the suggested Experiments particularly interesting.

Another difference between the two models might be emphasized. The teleological model can be formulated completely within the framework of classical physics. And the model makes no reference to any concept of consciousness. Thus, there is no logical necessity that the psi problem be related to the consciousness problem, or to quantum theory.

The quantum collapse model, on the other hand, assumes a close link between psi, consciousness, and quantum theory. The most provocative implication of this model is that the effect of consciousness in collapsing the state vector should be measurable, with the PK effect serving as a measuring probe.

Consider the simple case of a binary random generator that makes a decision on the lighting of a red or green lamp, with the associated probabilities

Before an observer has looked at the result, the status of the system is given by a state vector

Our model considers this "ghost state" as a physically real state but one in which Nature has not yet decided for one or the other possibility. Physical reality, at this stage, consists of a coexistence of two branches of reality, one with the red lamp lighted and one with the green lamp lighted.

After an observer has looked at the outcome of the random decision, there is no more ambiguity because the observer clearly sees either red or green.

The model assumes that it is the act of observation that gradually reduces the initial |GHOST> state (Eq.

Starting from the fully undecided state at time 0, we have

If

The parameter

The PK coefficient

The restriction of Eq.

Imagine two subjects with, parameters

It might be difficult to have two observers acting precisely at the same time. If one starts observing only slightly earlier, then he may already have reduced the state so that there is nothing left for the second observer to do.

But consecutive action of two observers can be interesting if the first observation is not complete. If, for example, the time was so short as to give the first observer only a subliminal glimpse at the outcome, the status after this observation would be given by

Simple calculation gives for the total PK effect in this case

For more details with a more general discussion of the reduction mechanism, see Schmidt (1982).

EVERETT, H. (1957). Relative state formulation of quantum mechanics.

MATTUCK, R.D., and WALKER, E.H. (1979). The action of consciousness on matter, a quantum mechanical theory of psychokinesis. In A. Puharich (Ed.),

MILLAR, B. (1978). The observational theories. A primer.

SCHMIDT, H. (1975). Toward a mathematical theory of psi.

SCHMIDT, H. (1976). PK effects with prerecorded targets.

SCHMIDT, H. (1978). Can an effect precede its cause? A model of a noncausal world.

SCHMIDT, H. (1981). PK tests with pre-recorded an d pre-inspected seed numbers.

SCHMIDT, H. (1982). Collapse of the state vector and psychokinetic effect.

WALKER, E.H. (1975). Foundations of paraphysical and parapsychological phenomena. In L. Oteri (Ed.),

WIGNER, E.P. (1962). Remarks on the mind-body problem. In I.J. Good (Ed.),