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Next: 12.2 Objective Actualisation - Up: 12. Measurements and Other Previous: 12. Measurements and Other

12.1 The Problem of Measurement

We have postponed until now the question of the exact prerequisites for a measurement or actualising event to occur. This is because the question of measurement is to some extent independent of the previous discussions. Much of those discussions have been concerned about `what exists', whereas the problem of measurement concerns which particular causal factors influence the actualisation of propensities, that is, the `reduction of the wave packet' of quantum mechanics.

Traditionally, the question of measurement in quantum world has been most problematic. Because measurements seem to have effects on particular quantum systems that are probabilistic, and are not described entirely by Schrödinger's equation, they have given rise to many and varied debates. Questions have been continually raised concerning some of the deepest questions in philosophy, such as whether the world exists independently of our observations or of our minds, whether physical substances exist and/or have any definite properties, whether indeed anything could be said to have definitely happened to the exclusion of its alternatives. Many of these general questions about the nature of reality have been answered by the general theory of actualities and potentialities of this book, but there still remain many specific questions concerning exactly when and how measurements and other actualisations do occur.

In chapter 10, actualisation was assumed to be a spontaneous mode of action of propensities, whereby potentiality was transformed into an actuality at a specific place in space and time, and whereby future potentialities were restricted to take into account the consequences of that event having definitely happened. It was pointed out that this function could be used to replace the special category of measurements that had been postulated in quantum theory ever since von Neumann [1929].   For measurements were also assumed to have definite outcomes without equivocation, to be historically irreversible, and to be essentially projections of the wave function at some time onto one of a selection of eigenstates of some `measurement observable'. Von Neumann called this process the reduction of the wave packet, and had to postulate it separately from the time evolution governed by Schrödinger's equation. In our philosophy of nature, however, it is to be expected that propensities, as well as having forms of distribution in space and time, also have a characteristic mode of operation wherein some one possibility becomes actualised to the exclusion of its competitors. Although quantum measurements can be performed for any of a wide range of quantum variables, and actualisations were assumed to be always point localisations in space-time, it was argued, following Feyman and Hibbs [1965] and N. Maxwell [1976], that arbitrary quantum mechanical measurement processes could always be reduced to essentially a set of localisations in space and time.

In chapter 11,   however, it was pointed out that point localisations in ordinary space and time are not acceptable, as they result in completely indeterminate momenta and energy, and as they give subsequent wave functions (propensity fields) which are not largely selections of what was present before the measurement. Therefore, the concept of point actualising was reconsidered, and found to refer to point localisations in a tree-structured space of selections of branches of the wave function.     In this way, we could more accurately follow what was called the Principle of Selection: that the effects of the actualisation are a selection of the field extent not only at the time of the actualisation, but also at all subsequent times.

As it stands however, the Principle of Selection does not have a precisely defined meaning, as it is not clear what does or does not constitute a `selection' of a propensity field. It could be strictly interpreted, to mean that no probability at any future spacetime point be changed apart from the overall renormalisation that is necessary to bring a whole branch to unit probability. This has the effect of ruling out any actualisation that eliminates any interference terms that would otherwise be present. It would only allow the selection of one of a set of branches that were already disjoint, and had no overlaps or interference possibilities of any kind. If particular actualising events could be made to follow this strict rule, then the quantum measurement problem would be solved entirely, though in a way which is perhaps too perfect. The significance of this `perfection' will become apparent when we consider various `imperfect' schemes later in this chapter. Those schemes will be `imperfect' because there will be probability changes (following the selection) that are not just overall renormalisations. As probability changes are in principle observable, it should be possible to provide empirical evidence either for or against them. That is, `imperfect schemes' are not just interpretations which leave all predictions the same, but are in fact individual physical theories with specific experimental consequences.

A more serious criticism of basing physical laws on a strict Principle of Selection, is that it makes present events depend on propensities for all future times. They are of course present potentialities, so the knowledge of the future that is required is not the impossible `what will actually happen', but the more feasible `what is allowed by propensities in the present state'. Still, it does seem rather unusual to have `non-localities in time' of this kind. It is as if nature automatically knew all possible consequences of its present state, a knowledge denied to us mere mortals (but keenly sought after by scientists and politicians). I am not denying that it is logically possible, only that we should also consider conditions for actualising that depend only on features of the present local region of space and time. The remainder of this chapter will examine rules for actualising of that kind, and see which are compatible with the philosophy of nature that has been formulated so far.  

There are two principal ways of having actualisations occur on the basis of local features of the processes going on at that time. One way has the actualising events prompted by certain physical conditions pertaining at that time, and the other way has the actualising events prompted by certain mental conditions pertaining at that time. We could call these `objective actualising' and `mind-dependent actualising' respectively, and various schemes for them will be considered below.

    You may be surprised that I am considering `mind-dependent' actualising at all, as it seems to be counter to the main trend in my philosophy of nature. I have tried to resolve the difficulties of quantum mechanics by reformulating physics, rather than by introducing subjective elements, by redefining the relation between theory and reality, or by having consciousness `create reality' in some way. The fact that the physical world exists objectively does not mean, however, that minds are logically forbidden from existing objectively too. We are not committing ourselves to subjectivism if we take other persons' minds to have real influences in the world, as this would presumably be then a matter of fact, rather than of subjective judgement. We have to consider this possibility (alongside that of more mundane schemes), because many physicists and philosophers (e.g. Wigner and Popper) have argued from the likelihood of mind-dependent actualising to the reality (in some manner) of minds. One purpose of this chapter is to examine precisely this likelihood of mind-dependent actualising. It is by no means as likely as some people would like to think: in the next section we will see that many `objective' or mind-independent conditions can be proposed and made to work, and more attention should be paid to these proposals.

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Prof Ian Thompson


Author: I.J. Thompson (except as stated)