Putting the Fire in the Equations; Generating multilevel dynamical processes in Physics and Psychology

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13.3 When actualities are selections of alternatives Principle of Selection 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. Derivative Dispositions Actual events are produced in a two-stage process, with the propensities for the actual events themselves being derivative from the propensities for virtual events. Two Stages of Propensities First there are `free-field propensities' (satisfying equation (11.1)), and these interact by means of virtual events to produce many-body wave functions $\Psi$ (satisfying equation (11.2), or its replacement in relativistic quantum field theory). These many-body wave functions then describe the propensities for actual events, which are selections from within the range of the $\Psi$-function satisfying the Principle of Selection. Space for Virtual Events is marked not by definite positions, but by equivalence classes of sets of positions, all of which are `essentially the same' as far as the production of actualising propensities is concerned. Gauge Invariances Extensiveness in the space for virtual events is relational in a real (absolute) sense. This relational structure can be equivalently formulated as the `gauge invariance' of all physical laws with respect to choices within the following equivalence classes: 1. Interactions imply extensive relations in space and time, rather than definite and absolute positions. It makes no difference to any interaction or event if the whole universe were to be shifted over in space, or delayed arbitrarily in time, or rotated about any axis. 2. Interactions use potentials which are arbitrary with respect to additions of certain kinds of spatio-temporal functions, and hence generate complex-valued wave functions which have a corresponding arbitrariness in their phase. 3. Interactions in quantum field theory operate in arbitrarily small regions of space-time, and hence almost always need a variable renormalisation to correct the self-energies (i.e. masses) of the particles, and to correct the coupling-strengths of the interaction terms. 4. Interactions can be between identical particles, for which, as they can be arbitrarily interchanged, we need to apply the Pauli Exclusion Principle. Unchanging Continuant (Substance) is field of propensity for virtual (not actual) events.

    

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

Email: IJT@generativescience.org