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The difficulty with this ontology is that it is not clear how events cause succeeding events. We could always postulate `physical laws' sufficient for the purpose, but physical laws talk about such properties as `energy', `momentum' and `mass', etc., and these have no counterpart in a world that is made only of events. Whitehead  originally had the link between events to be some process of `prehension' modelled on perception. Stapp  has tried to adapt Whitehead's ideas for quantum physics, but he has had to assume that there are `geodesics' between events. `Each geodesic is associated with real mass m , and also with a momentum-energy vector p=mv, where v is the four-velocity defined by the direction of the geodesic.'4.2 This is to be regarded `as a mathematical condition on the overall spacetime structure of what emerges from the process of creation', but seems to admit ideas from classical physics in an ad hoc manner that is not compatible with the original ontology.
Cramer [1980, 1983, 1986] has proposed what he calls the `transactional interpretation' of quantum mechanics. This uses primarily an ontology of events, but again supplemented by links (here, waves) that propagate between events and carry energy and momentum. What is novel in this interpretation is that the waves propagate both forwards and backwards in time, and set up `transactions' between cause and effect events. However, these transactions cannot be set up in any temporal sequence, but must be `in place' before any single event can actually occur. This requires a `block universe' theory of time (see section 2.3), in which all future events are definite even at the beginning of the universe, and according to which nothing new becomes true when events (appear to) `happen'.
If Born's statistical interpretation were adopted, then quantum mechanics cannot say anything about individual systems. The way is now open to imagine some new `sub-quantum' level, containing (as yet) hidden variables, so that quantum probabilities are the result of fluctuations at this new level. Belifante  surveys some of these theories, and Bohm4.4  gives more details of a proposed sub-quantum level that is essentially classical in detail.
If a new `quantum logic' were adopted, then it is possible to keep an ontology of particles like corpuscles with definite properties, even though we are limited as to the inferences that we can draw. Quantum logic is usually `non-distributive', in that the distributive law of Boolean logic is now no longer valid. Gibbins  surveys the methods and scope of quantum logic. The logic has the disadvantages (or features) that truth tables cannot be used to check deductions, and that there is no scale (such as a Planck's constant) to make a gradual transition to the approximately classical world of macroscopic bodies.
The earliest proposal along these lines was that of Schrödinger, using the wave function of his formulation of quantum physics. In his view, physical reality consisted of waves and waves only, and he denied categorically the existence of discrete energy levels and quantum jumps. What appeared to be localised particles are really moving `wave packets', or localised concentrations of waves. This view has the difficulty, however, that the wave packets do not remain localised after any length of time. In rectilinear unperturbed motion, for example, the different frequencies in the wave packet move at slightly different velocities, so the wave packet will eventually become more and more spread out. After any kind of interaction, moreover, Schrödinger's equation requires that the wave packet can be split into parts which are moving in completely different directions. These alternatives remain as a superposition, leading to the question of whether there is ever a `reduction of the wave packet' that brings back a localised wave packet again. There is also the difficulty that the wave function for an n-particle system is defined over a `configuration space' of 3n dimensions, not over real (three dimensional) space. This allows interacting particles to be correlated with each other because of previous interactions, and prefigures the nonlocalities shown by Einstein, Podolsky and Rosen. It is now difficult to interpret the wave functions as real entities in physical space.
One modern variant of this `wave ontology' solves the problem of the `reduction of wave packet', by assuming that it never occurs! This is the `many worlds interpretation' of quantum mechanics, as proposed by Everett, Wheeler and Graham4.5. According to this interpretation, the Schrödinger wave function describes everything that there is in the world. If it splits up into two or more alternatives, then the whole universe (or at least some part of it4.6) is duplicated as many times as is necessary. And this happens at every interaction: the theory is generous on universes! The `benefit' of believing in this extravagant production of universes, is that there is then no need for any `reduction of the wave packet', and there are then fewer physical laws in the quantum world (only, there are more worlds!).
Even if these difficulties were solved (or ignored), there are still problems in the philosophy of nature, as it is not clear however what exactly is `waving' when a Schrödinger wave or a field goes by. This is the problem of substance again. It cannot be that a `wave function' makes up the physical world, since a `function' is a mathematical rather than a physical entity.
Both particles and waves are definite things that Newton knew about, but neither of these concepts by itself is adequate to describe the nature of quantum substances. Bohr, and Heisenberg later, want us to take what amounts to a strange and unpalatable mixture of the two concepts.
According to Maxwell , quantum substances are discrete propensitons. These `only evolve probabilistically intermittently in time, when relevant physical conditions arise, the values of propensities (or the states of propensitons) otherwise evolving deterministically'4.7. Specifying the nature of a propensiton amounts to specifying the laws governing these two kinds of time evolution:
The evolution of genuinely (discrete) propensiton die would have to be conceived of in something like the following terms. The propensiton die is tossed. As the die flies through the air it is gradually into six potential, virtual, ghostly dice, each with a different face uppermost, each with a different (probability) density (all equal in the case of unbiasedness), which may very well vary with time. When the six potential dice hit the table top, five vanish and one solid die remains. If the die is tossed repeatedly, the statistical outcomes are determined by the probability densities of the six virtual dice just before contact with the table top.4.8The `relevant physical conditions' for probabilistic events to occur are that the wave function splits up into two or more alternatives, and that there is an inelastic energy difference for some system between the alternatives. This will be discussed again in chapter 12, and amounts to one solution of the problem of measurement in quantum physics.
Next: 4.4 The Problem of Up: 4. The Peculiarities of Previous: 4.2 Quantum Experiments Prof Ian Thompson