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10.2 Probabilities and Propensities

In the early development of quantum physics, Born realised that the quantum theory did not predict the precise state after a collision, but only the `possibility of a definite state' (Born [1926]). The wave fields were not actual fields, but only determine the probability of the presence of quanta. What is new in the quantum theories is this emphasis on probabilities. In his `ensemble interpretation' of quantum mechanics, Born tried to take these probabilities as relative frequencies in an ensemble. An `ensemble' here is a real or imagined collection of systems that are as similar as we can make them. The probabilistic nature of quantum mechanics means that not all systems in the ensemble will behave in the same way, and only the relative numbers of the different outcomes is predicted from quantum theory. The ensemble interpretation of probabilities leaves quite open the significance of probabilities for individual systems:     the `propensity' notion of probability (see chapter 2) is designed to provide just such a meaning for attribution of probabilities to single systems. Even if we are have only one radioactive atom, for example, surely some meaning can be given to the likelihood of the decay event occurring in different intervals of time.


Jammer [1966, p. 286] relates how

Laws of nature, as Born and Heisenberg contended $\ldots$determined not the occurrence of an event, but the probability of the occurrence. For Heisenberg, as he later explained it 10.1 , such probability wave are ``a quantitative formulation of the concept of `dynamis', possibility, or in the later Latin version, `potentia', in Aristotle's philosophy. The concept of events not determined in a peremptory manner, but that the possibility or `tendency' for an event to take place has a kind of reality - a certain intermediate layer of reality, halfway between the massive reality of matter and the intellectual reality of the idea or the image - this concept plays a decisive role in Aristotle's philosophy. In modern quantum theory this concept takes on a new form; it is formulated quantitatively as probability and subjected to mathematically expressible laws of nature.''
Unfortunately Heisenberg does not develop this interpretation much beyond the sort of generality of the above statements, and the concept of `potentiality' remains awkwardly isolated from much of his other thought on this subject 10.2 .   It is unclear even what he means by `potentia'. Herbert [1985], in describing Heisenberg's ideas, imagines them to be more emphemeral than substantial:
Heisenberg's half-real universe of potentia is reminiscent of certain oriental views developed in contexts far removed from quantum physics:
This floating world is but a phantasm
It is a momentary smoke
Though ghostly and transitory, Heisenberg's shimmering ocean of potentia is the sole support for everything we see around us. The entire visible universe, what Bishop Berkeley called ``the mighty frame of the world,'' rests ultimately on a strange quantum kind of being no more substantial than a promise 10.3.
We will see below that, far from being as emphemeral as a promise, the propensities of the physical world are perfectly real and substantial. They are in fact the very substances out of which all things are made.



The present concept of `continuant' is also very similar to Nicholas Maxwell's notion [1982, 1985, 1988] of smearon or propensiton.

``Smearons'', as understood here, are hypothetical fundamental physical entities, having characteristics somewhat like the ``wave packets'' of orthodox QM in being smeared out in space like a wave function, but being unlike orthodox wave packets in having physically real nonlocal characteristics that in general exist in space and evolve in time independently of methods of preparation and measurement. What is smeared out in space is the propensity of one smearon to interact in a probabilistic, quasiparticle-like way with another smearon, should the appropriate physical (smearon) conditions to do so arise. The state vectors of QM are to be interpreted as characterising the actual physical states of smearons. The physical states of smearons evolve deterministically, in accordance with Schrödinger's time dependent equation (for elementary QM) as long as no probabilistic particle-like interactions between smearons occur. Probabilistic particle-like interactions between smearons involve changes of state which violate Schrödinger's time dependent equation even though no measurement is made. If appropriate physical conditions arise for an unlocalized smearon, in a state $\phi$, to interact in a probabilistic way with just one of many other highly localized smearons, then, roughly speaking, the probability that the unlocalized smearon interacts with the smearon LOcalized in dV is given by $\mid\phi\mid^{2}dV$ (this being a microrealistic reformulation of Born's original [1926] probabilistic interpretation of wave mechanics, which appealed explicitly to measurement). Smearon QM is thus a theory that is, in the first instance, exclusively about how smearons physically evolve and interact with one another in space and time independently of preparation and measurement. Measurements are probabilistic interactions between smearons which just happen to be recorded by physicists. Stable macro objects are the outcome of many probabilistic interactions between smearons. (Maxwell [1982] p. 609)
The causal analysis of section 7.2 can therefore be used to provide a philosophical justification and elaboration of the idea of smearons or propensitons, where it is remembered that propensitons only localise themselves intermittently.  
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Next: 10.3 Waves, Particles and Up: 10. Quantum Substances Previous: 10.1 Classical and Quantum
Prof Ian Thompson


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