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12.2 Objective Actualisation - some proposals The problem addressed in the remainder of this chapter is the specification of the precise conditions for the actualisation of propensities. Propensities have been construed to be propensities for actualising events, but we have not yet said when these events occur, or even under which conditions they become more likely. In the terminology of chapter 2, while the propensities may be the `principal cause' of the actualising, we have still to determine the conditions or `instrumental causes' of their operation. This is because dispositions in general have to have appropriate conditions before they have a non-zero probability of manifesting themselves. Indeed, the very ascription of dispositions made this clear: Object S has the disposition P to do action A $\equiv$ if S is in some circumstance C, C depending on P and the character of A, then there will be a non-zero likelihood of S doing A. The suitable `circumstance C' was considered in chapter 2to be defined by multiple spatial relations to other objects, but this is not a necessary definition: it could just as well be defined by differences of energy, of numbers of interactions, of durations, or of gravitational effects on the space-time metric, to name some of the conditions that have been proposed. These options will be considered in detail below. It will turn out to be rather implausible that the conditions for the actualisation of the fundamental `propensities for actual events' depends simply on spatial distances, though at one time this was seriously considered.     12.2.1 Simple schemes Faber [1986] provides a useful catalogue of what he calls `materialistic hypotheses' for answering the question ``When precisely does the transition to actuality occur, and what sort of causality is responsible for it?''.   All these hypotheses follow Heisenberg's recommendation that, although measurements result in actualities, it is `during the physical, not the psychical act of observation'12.1. Faber discusses seven simple schemes as follows; the eighth I have added to his list.     1. Actuality from present or future connections to our senses This suggestion would resolve the problem of measurement, by ensuring that whenever any set of outcomes will lead to different interactions with human senses, then one of those outcomes will actually occur. Presumably this will also apply for the senses of non-human sentient beings, but what about experiments controlled by computers? One can easily imagine   (elaborating on possibilities described in Deutsch [1986]) that there are situations where a computer has been programmed to make a measurement, but not to tell us, or anyone, the actual result. According to this first scheme, the whole computer would have to be in a superposition of states, and could never be said to have definitely gone into a state of having registered any outcome as distinct from any opposing outcomes. It seems peculiar to have objective actualising conditions depend on some ultimate outcome connected with sentient perceptions: I doubt that this connection could be made sufficiently definite. It would also be hardly a `materialist' theory if there were dependencies of this sort.     2. Actuality from Composite Objects Perhaps individual particles follow the laws of quantum mechanics, but the complexity of composite systems means that irreversible phenomena occur which are equivalent to the actualisation of one of a selection of possibilities. The difficulty here is in specifying the necessary degree of complexity, for composite objects that are quite complex have been observed to show quantum diffraction and interference effects. Whole atoms and molecules show interference oscillations in one and two slit experiments, and (as discussed in chapter 11,) large crystals can interact with particles without specific or actual interactions with any single atom in the crystal. It therefore appears that compositeness, by itself, is not a sufficient condition for the actualisation of propensities.     3. Actuality from Macroscopic Objects All the known cases of actualisation of propensities, as observed to occur with ordinary physical measuring apparatus, involve large or macroscopic objects. Perhaps it is sufficient for actualisation that macroscopic objects be involved: perhaps there is a new law of physics which says that macroscopic properties, for example, cannot be in a superposition of possibilities, but must settle for one option or another. Experiments certainly don't rule this out, for it is a `minimal inductive generalisation' of the type of experiments that have already been performed, but, as Faber [1986] points out, it is a rather odd and ad hoc hypothesis. We would be much happier if we had some physical criterion, preferably from general principles, which distinguished those properties which are sufficiently `macroscopic' from those which are not. This criterion would have to allow such `large' systems as lasers and superconducting metals to be in un-actualised quantum states, while allowing some quite small systems, such as micro-electronic integrated circuits, to be in definite and actual states.     4. Actuality from Alternative Interactions Perhaps, whenever a quantum particle can interact with any of a number of other systems, it ends up with actually interacting with only one (or none) of them.   Bussey [1984], [1986] proposes, for example, that wave packet reduction (i.e. actualisation) occurs during particle-particle interactions whenever `individual atoms change state'. This is similar to the hypothesis considered in chapter 11 , concerning whether all interactions could be actual events, and hence had to definitely occur or not occur. We saw there that it could not be true, as there is good experimental evidence (the crystal diffraction case, for example) that interactions can occur without actualising. Bussey tries to meet this objection by holding that when atoms bound together in a crystal form a compound system, such systems behave as individual quantum-mechanical entities in their own right. The crystal `as a whole' does not change state after the diffraction, or at least not its internal state (if Bussey were to make this distinction properly), and hence does not produce actualising. The difficulty is that there is considerable arbitrariness in what exactly constitutes a `compound system'. Ordinary quantum mechanics does not draw any sharp distinction between compound systems and fortuitous clusters of particles with energies near bound-state 12.2 or resonance energies.     5. Actuality from Irreversible Interactions The actualisation of propensities seems intimately connected with the occurrence of irreversible processes. Perhaps actualisations are just the consequence of irreversible events? The trouble with this option is finding a definition of `irreversible events'.   One could attempt to base irreversibility on thermodynamics, such as its Second Law. An irreversible event could be one during which entropy increases. But is an increase of entropy an objective process, or is it a consequence of our necessarily incomplete knowledge, and of our use of probabilities to represent out ignorance?   Heisenberg [1958] advocated the use of thermodynamics and entropy to define irreversible events, but in the end had to admit that irreversibility `is a consequence of the observer's incomplete knowledge of the system and in so far not completely ``objective''.' My approach is to accept that propensity actualisations occur, and then define irreversibility in terms of such events. As we saw in chapter 10, however, some physicists have taken the opposite view, and hold that there is an objective sense of `irreversibility', in large thermodynamic systems for example, from which they can derive the irreversibility of measurement events in the quantum domain.     Prigogine [1980, 1984] and Rae [1986] hold, for example, that irreversible changes do not occur in quantum physics specifically.   Rather, they occur principally in large complex systems in which there are sufficient instabilities that `chaotic behaviour' follows. This means that any arbitrarily small change in a starting condition will result in completely different future behaviour. Their theory, however, does not remove the need for some non-local phenomena in the universe. Furthermore, although it declares that there is a transition between the reversible quantum world and the irreversible thermodynamic world, it does not say exactly at what point this transition occurs. Talk of `large complex systems' merely brings back the problems of proposals 2 and 3 above. Until specific suggestions are made for the microscopic basis of the supposedly fundamental `irreversible events', this proposal remains a `philosophy of nature', rather than becoming a specific theory.             6. Actuality from Superpositions not inter-transformable Schlegel [1980] has proposed that quantum superpositions can only contain components that can be transformed into one another by what he calls the `modified Lorentz group' (m.L.g.). These include the standard velocity transformation, spatial translation and rotation, space but not time inversion, and charge conjugation. This allows, for example, the superposition of momenta of a whole crystal, but not the superposition of unexposed and exposed photographic grains. The uncertainty, however, is whether the m.L.g. applies to a whole system, or whether it applies particle by particle. Schlegel does not want to apply to individual sub-systems, to avoid the case of a photographic grain being transformed by a series of steps, each of which is within the m.L.g. We suppose therefore that we can only apply transformations to systems as a whole. Consider, however, the case of a system (such as a neutron) decaying into several particles with variable distributions of kinetic energy (as is the case with the proton, electron and neutrino from neutron decay). Now the Lorentz transformations needed to bring together all kinetic energy combinations are all different, because transformations to different rest frames are required. We would therefore predict that all continuously different kinetic energies are actualised separately. This is not observed experimentally, as it would mean that each observed outcoming particle would be a wave packet of zero energy dispersion, and hence of completely indeterminate time duration. It would also mean that there could be no EPR-style non-local correlations between the various particle spins.       7. Actuality from no general characteristic Cartwright [1983] argues that there is no general characteristic that describes the reduction of the wave packet (the actualising of potentialities). Rather, it is a natural process that happens all the time in many different ways. However, the examples she gives of when actualisation is supposed to happen are not correct. Actualisation does not necessarily occur at the point of decay of radio-active nuclei or the preparation of an ion in a particular state with a specific projection of its angular momentum in the direction of a magnetic field, as in the Stern-Gerlach experiment.   All these schemes, Faber [1986] points out, are deficient in some way. Some (such as nos. 1 and 5) turn out to not be sufficient definite in an non-subjective sense for them to be objective conditions for actualisation,     unless (after Prigogine and Rae) physical theory is deliberately extended to provide the required objective sense. Others (such as nos. 2, 4, 6 and possibly 7) are almost certainly wrong empirically: we know that nature just does not behave like that. The remaining one (number 3) is somewhat odd and ad hoc.     8. Actuality from point localisations in space and time N. Maxwell [1976], in outlining a propensity interpretation of quantum mechanics, suggested that actual events could be at specific points in space and time, and hence amounted to position measurements of quantum systems. All other kinds of quantum mechanical `observables' we taken to be reducible to combinations of position measurements, as in Feynman and Hibbs ([1965], p. 96). We have already seen in chapter 11 the deficiences in having point actualisations. 12.2.2 Schematic Proposals There are a group of proposals which suggest that there is a specific duration of propensity fields before actual events occur.   In the language of quantum mechanics, they propose that there is a specific duration of coherent superpositions before there is a reduction of the wave packet. These proposals are only partly elaborated, in that they still have free parameters that have not been specified. Some of them refer to the existence of hidden physical mechanisms which would have to be postulated, but about which we know nothing as yet.       1. Actualisations outside a `correlation length' One proposal for an `objective reduction of the wave packet' comes from Einstein. In response to the difficulties in interpreting the long-range correlations in his proposed EPR experiment, he suggested ``that the current formulation of the many-body problem in quantum mechanics may break down when particles are far enough apart.''12.3 There could then be a certain distance, such that particles separated by more than this distance spontaneously reverted to statistical mixtures of actual states, rather than remaining in superpositions. This prospect,     however, is made specific by Bell's inequalities (Bell [1964]), and experiments have shown that there do remain non-local correlations between quantum systems which may be separated by even large laboratory distances.     2. Actualisations from some `effective temperature'     Baracca, Bohm et al. [1975] propose that, due to some unavoidable couplings with a `sub-quantum level', there is some `effective temperature' T for both the sub-quantum and quantum systems, to reflect the equilibrium distribution of energy. There would then be a `critical time' $\tau_0 = \hbar / kT$ for the maximum duration of superposition and correlations (k being Boltzman's constant). However, they do not suggest any plausible values for this temperature.       3. Actualisations as localisation to gaussians wave-packets Ghirardi et al. [1986] propose that there may be a new spontaneous process of localisation of quantum wave functions, so that quantum substances end up actually as one of a number of gaussian wave-packets. They choose the parameters governing the rate of this process so that it happens more rapidly, the more variables there are in the many-body wave function   $\Psi ( \vec{x}_1 , \vec{x}_2 , \ldots ,t).$ Benatti et al. [1987] show how this ensures that large macroscopic pieces of measuring apparatus very rapidly have one actual state, and not a superposition of different states. 4. Actualisations from logarithmic terms in Schrödinger's equation     Bialynicki-Birula and Mycielski [1976] considered adding a potential term to Schrödinger's equation that is proportional to the logarithm of the probability density:   $$H \psi - b \log \mid a \psi \mid ^{2} ~ \psi = i \hbar \frac{\partial \psi }{\partial t},$$ (12.1)   then there are soliton-like solutions: wave functions which do not continuously spread, but are stabilised with a finite extent $\ell = \hbar/(2mb)^{1/2} ,$ and hence could perhaps be taken to represent particles and not just propensities for events. Here, H is the usual quantum Hamiltonian, a is a constant for dimensional reasons, and b is a positive constant with units of energy which determines the magnitude of the non-linear effects. The non-linear soliton equation (12.1) was not designed for the actualisation of potentialities, and does not give proper selections of alternative branches of the $\Psi$ function, but,   as Shimony [1986] points out, it does allow us to quantify the departures from ordinary quantum mechanics. Very accurate neutron diffraction experiments have been   performed (see Zeilinger [1986]), and these have all supported ordinary quantum mechanics, and to date have placed upper bounds on b of about $3 \times 10 ^ {-15} eV$. This figure would mean that the soliton solutions would spread to as large a diameter as 3 mm before being stabilised by the non-linearities. It is remarkable, Zeilinger admits, that even the nonlinear theory has to admit the existence of macroscopic quantum objects.       5. Actualisations from statistical fluctuations in the Hamiltonian If there were statistical fluctuations in the potentials appearing in the quantum mechanical Hamitonian, Pearle [1976, 1986] points out that the Schrödinger equation behaves like a diffusion equation. The probabilities of different branches diffuse in a random walk and end up either at zero or unity. In this way, the reduction process is the physical product of an underlying `Brownian motion' in some physical medium as yet unknown.   Bohm and Bub [1966] present a similar scheme. 12.2.3 Quantitative Proposals We now come to a group of proposals which make specific numerical predictions for the duration of propensity fields before actual events occur. They do not contain any free parameters which could be arbitrarily and independently adjusted, so we have here the beginnings of fully fledged physical theories.         1. Actualisations from energy differences The original proposal along these lines is that of Bedford and Wang [1975], when they suggested that superpositions of states of energy difference $\Delta$E only last for a time $\Delta t = \hbar / \Delta E$ before spontaneously collapsing into actually one or other of the states, in a statistical mixture. That is, interference oscillations between states of different energy could only last for one cycle before they became actually one particular state. Any measurement apparatus will have alternative states different in energy, so all equipment will very rapidly revert to actually be in just one of its states. Bedford and Wang [1977] then realised that there are counter-examples to this hypothesis. A photon originating in two radiotransmitters of different frequency will interfere at distances beyond that predicted by the criterion.   Quantum beat experiments (Andrä [1970]) show interference oscillations lasting for many cycles without sign of abatement. Bedford and Wang [1977] therefore revised their criterion, to have it necessary for actualising that the several systems with energy differences must (a) be in a state which has no factorisation (i.e. is not really an uncorrelated product of two free fields), (b) be effectively non-interacting, and (c) be relatively unaffected by environmental fluctuations.       2. Actualisations from inelastic energy differences N. Maxwell [1982] refined the criterion of Bedford and Wang, and only allowed inelastic or rest mass energy differences to give rise to actualisations. Inelastic energy differences $\Delta$E are those between two bound states and/or resonances of a given system. If the system is treated as a compound whole, then it its rest mass m will differ by $\Delta m = \Delta E/ c^{2}$. Restricting the actualising criterion in this way avoids the refutations of the Bedford and Wang hypothesis above, but we still have to keep the `non-interacting' condition. Maxwell proposes that the interval $\Delta t = \hbar / \Delta E$be counted from the cessation of any interactions, and so is timed while there are no interference effects. The idea is that if there have been interference effects, and then they disappear for a whole cycle, actualisation then makes them disappear permanently. If there was going to have been interference oscillations again, then actualisation means that there is an experimental difference with ordinary quantum mechanics. Maxwell [1982, 1986, 1988] proposes some crucial experiments, though it would be rather difficult to set up the necessary coherent arrangements. Maxwell [1986] recognises that his criterion will have to be generalised to allow for (a) multiple inelastic states, (b) a statistical half-life of $\Delta$t, rather than a fixed duration, and (c) the gradual cessation of interactions, as coupling potentials never cut off absolutely.     3. Actualisations from gravitational differences     Penrose ([1986], [1987]), after considerations of various problems in cosmology and quantum gravity, thinks that wave function collapse is linked with gravitation. When two states of differing energy distribution are linearly superposed, the slightly differing space-time geometries that these energy distributions produce (according to general relativity) must also be superposed. $\ldots$ I would contend, therefore, that when two geometries involved in a linear superposition become too different from one another -- in some yet-to-be-determined precise sense -- then linear superposition fails to hold, and some effective non-linear instability sets in, resulting in one or other geometry winning out, the result being reduction Penrose [1986] originally thought that wave functions collapse when the the apparent lowering of entropy that such a process leads to is more than compensated by the rise in some kind of gravitational entropy. It could then be allowed as consistent with the Second Law of thermodynamics (that, in all processes, entropy must either increase or remain constant). He then added in postscripts that the criterion should be phrased in terms of the more clear-cut `graviton number'. On that view, ``wave function collapse takes place when the difference between the gravitational fields of the states under superposition amounts to at least one graviton's worth''. According to his calculations, this means that `actualisations' occur for droplets of water with diameters of around 10-5 m, which is sufficiently small for nearly all measuring apparatuses to have definite states rather than superpositions.   Similar ideas are put forward by Károlyházy et al [1986], who also consider the uncertainty in the spacetime metric predicted in general relativity if there were uncertainties or superpositions of energy distributions. They calculate the reduction rate, assuming that it occurs when uncertainties in the metric imply that the wave function $\psi$ propagates with uncertainties of up to half a cycle (i.e. a phase uncertainty of $\pi$). They do not know why or how wave packet reductions occur: they can only estimate very approximately how often they are likely to happen. Their conclusions are that atoms and nuclei have negligible probability of actualising in the known lifetime of the universe, but a ball of 1 cm diameter and terrestrial density will reach its phase uncertainty of $\pi$ within 10-4 s, and hence behaves as a classical object as expected. The largest uncertainties before actualising sets in are found to be for masses of 10-14 g: that of a colloidal grain, containing $\approx 10^9$ molecules, for which actualisations should occur only several times per hour. They proposal two experiments, preferably to be performed in weightless conditions in a space laboratory.   Comments From the point of view of experimental evidence to date, all three of these quantitative proposals are equally satisfactory. The Bedford and Wang proposals, however, are not as accurately formulated as they could be: the non-factorising and non-interacting conditions, they point out, have to be interpreted in an approximate rather than a precise sense. The second two proposals are more definite in their application, but are quite different from each other in their predicted rates of actualisation. N. Maxwell's proposal has actualisations happening quite quickly at every nuclear, atomic and molecular level. Because of his condition that timing starts only after interactions cease, however, the effects of actualising (the predicted losses of coherence) will be almost impossible to detect in practice. If his proposal is modified to allow for some kind of `progressive probability' for actualising as interactions progressively fall away, then there will be small but definite effects in a variety of scattering experiments. Such modifications are eagerly awaited. The proposals of Penrose and of Károlyházy predict a much slower rate of actualising. They allow wave packets to become quite large (on a molecular scale) before some gravitational differences trigger an actualising localisation again. Penrose does not see his process as `actualisation' at all, but as the symptoms of some new `non-linear instability' that might occur in other physical circumstances too. That is, he is still looking for some microscopic mechanisms which underly the quantum phenomena. Following Bell's Inequalities, of course, these will have to be non-local phenomena, but Penrose has not begun to publish any specific thoughts in this direction. One consequence of adopting one of the quantitative proposals of this section, is that there can then be a new objective sense for some of the notions proposed in the previous section for actualising. That is, if Maxwell, Penrose or Károlyházy proved to be correct, then we could find new objective meanings for the notions of `composite object', `macroscopic object', `alternative interactions' and `irreversible processes'. These could all be redefined in terms of some new objective process of actualising. This is particularly useful in the case of `irreversible processes', as then we would have a new microscopic foundation for thermodynamics.     In both classical and quantum physics, Prigogine [1980] points out, the reversibility of the microscopic laws makes it difficult to have a `real thermodynamics' with objective definitions of irreversibility and entropy, etc. If an `actualising' process were found to be fundamental, then a variety of objective proposals for an `entropy superoperator' could be considered (see Prigogine [1980], p. 168 for one such proposal). Thermodynamics could then be put on a new footing.

    

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

Email: IJT@generativescience.org