4.7 Quantum physics

In the above sections, power and propensity have been described generically, where propensities are those powers that manifest themselves in terms of probabilities for different outcomes. To allow for quantum physics and its probabilities, we need just such propensities. The question of whether propensities are in fact needed for describing nature is linked to the accuracy of quantum physics. I will not decide that question now. I only wish to argue that quantum processes can be described by means of propensities, and that quantum substantial objects can be identified as those more fundamental propensities which appear in some form or structure.

Quantum mechanics describes the probabilities of actual outcomes in terms of a wave function or at least of a quantum state of amplitudes that varies with time. The public always asks what the wave function is, or what the amplitudes are amplitudes of. Usually, we reply that the amplitudes are ‘probability amplitudes’, or that the wave function is a ‘probability wave function’, but neither answer is ontologically satisfying since probabilities are numbers, not stuff. We have already rehearsed the objections to the natural world being made out of numbers, as these are pure forms. In fact, ‘waves’, ‘amplitudes’ and ‘probabilities’ are all forms, and none of them can be substance. So, what are quantum objects made of? What stuff?

According to Heisenberg,^4.11the quantum probability waves 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.^4.12It is unclear even what he means by ‘potentia’.

Herbert (1985), in describing Heisenberg’s ideas, imagines them to describe a world more ephemeral than substantial, imaging that “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." (p. 195)^4.13We instead argue that, far from being ‘as ephemeral as a promise’, the propensities of the physical world are perfectly real and substantial and may in fact be the very substance of all things.

We now propose, according to our pragmatic realism, that propensities can be the stuff of quantum objects. We describe those objects as having the forms of wave functions spread out in space and time. Such forms, with a spatiotemporal range, are best viewed as fields.^4.14Quantum objects themselves can be conceived of as ‘fields of propensity’ according to the general manner of this chapter. This concept of substance is similar to Nicholas Maxwell’s notion (2010,1988) of smearon or propensiton. Substantial objects with such natures are particularly relevant for quantum mechanics, since it is now found that the concept of a corpuscle with definite extension, hardness, etc., is markedly inadequate. As yet, however, no philosophically adequate replacement has been generally accepted. With the help of the new proposal of ‘propensity fields’, we can try to understand some of the more puzzling quantum features such as the reason for ‘non-localities,’ and the nature of ‘measurements.’

One feature of the present account of substance is that such objects need not be located in small fixed volumes of space as, for example, the corpuscles or particles of classical physics would be. The propensity fields that have been defined do not need to have any special ‘center’ distinguishable from all the other places in the field. They may have no center at all that could be regarded as the ‘true substance’ whereby the surrounding field could be regarded as just the ‘sphere of influence’ of the central substance.^4.15

It is commonly believed, e.g. by Molnar (2003) and by many physicists, that high energy scattering experiments allow us to conclude that fundamental particles like electrons, quarks, etc. are point particles, like real objects of zero size. However, this inference is incorrect. What the experiments show is that there is no lower limit to the size that the wave packet of an electron (for example) may be compressed. They never show that there is actually a point particle, as this would contradict the Heisenberg Uncertainty Principle by requiring infinite energy to be used in producing it. Some other objects (e.g. atoms or nuclei) do have a lower limit of compression, and this is interpreted as arising from a composite internal structure. No matter how small we then compress the wave packet for an atom’s centre of mass motion, the atom as a whole cannot be made arbitrarily small. At all times, both fundamental particles and composite objects have some varying finite size that depends on time and circumstances and may be legitimately said to occupy the volume of this size in space. Whether they also fill that volume depends on the probabilities of interaction with instruments, which may be small or large and so are a matter of degree in a similar manner to the way that air ‘fills’ a room according to its pressure.

A substance-field of propensities may have a variable spatial size. Sometimes it behaves more like a spread-out wave, and when at other times it interacts, it behaves like a localized particle. A propensity field can have practically any extensive shape over the places that are possible for it. We can allow that propensity fields are described by some kind of field equation such as the Schrödinger or Dirac equation including interaction potentials. The fields would be subject to boundary conditions set by the results of past actions. This gives continuous and wave-like propagation into the future, and it allows them to propagate as wave packets around obstacles or potentials which would stop classical atoms. They can even tunnel through barriers, as the probability for a definite interaction may be reduced but will still be non-zero. It becomes reasonable to expect the diffraction, interference and tunneling effects we know in quantum physics from the solutions of Schrödinger’s equation, even though we have no general grounds yet for choosing any particular equation.

We do not now need to believe that somewhere, as it were hidden away behind the propensities, there really exist particles waiting to appear. This is not the case. Questions like ‘Where is the electron and what is its speed?’ have no answer, because there never exists such a thing as a small corpuscular electron. The only things that exist are propensity fields and the inter(actions) they produce. Propensity fields are not vague, indeterminate or smeared-out particles. They are perfectly definite entities in their own right. It may not be determinate in advance which actions a propensity field will produce, but that does not mean that the propensity field is any the less real or definite when considered as a thing in itself. Its field structure can be described using perfectly definite mathematics. Its existence is as real and substantial as any existing object. In fact propensity fields are the very substantial ingredients out of which all things are made. Nothing can be more substantial than them.

Kaempffer (1965), for example, after pointing out the “erosion of naive pictures of particles” goes on to suggest that the word particle stand for a quantum mechanical state [a wave field], characterized by a set of quantum numbers, which is associated, in principle, with an identifiable event such as the momentum transfer in a “collision". We can follow him as he redefines the meaning of the word ‘particle’ to refer to something like propensity fields.

The concept of substances as dispositional contains the essential idea that they do something: that the dispositions are for some kind of event. Such events are characterized generically as ‘actual events’, because they have definite properties once they exist and are selections between distinct possibilities that are arrayed like a field. In quantum mechanics, these actual events are just the process of ‘reduction of the wave packet’ that physicists and philosophers have long discussed and sought for both theoretically and experimentally. The treatment of quantum objects as substance-dispositions implies that such reduction or selection events do occur.