The Greek Concept of Matter and Quantum Uncertainty

Lydia Jaeger FAITH Magazine March-April 2009

Lydia Jaeger is Director of Studies at the Institut Biblique de Nogent-sur-Marne

From its outset, quantum mechanics has been a source of intrigue; the picture it presents of the microscopic world being so different to that of everyday experience gained from normal-sized entities, between the atomic scale and the vast spaces of the cosmos. Many efforts have been (and are still being) made to understand the strangeness of the quantum world; a plethora of interpretations, often divergent, have been proposed. In the context of our study, it is relevant to introduce two approaches which allow a link with the Greek notion of matter; they specifically ask the question as to what extent the developments in physics in the 20th century should make us reconsider the critique of this notion, which the idea of creation gives rise to.

Werner Heisenberg, one of the founders of quantum theory, explicitly made the connection between the probabilistic nature of quantum mechanics and Greek matter, in its role of potentia; he tried in this way to make sense of attributing a state vector to an individual quantum system. While the probability theorems of this theory allow us accurately to predict the behaviour of a sufficiently large group of identical quantum entities, the wave function of an individual quantum system describes itspofenf/al to produce certain outcomes when appropriate measurements are taken. This potentia therefore constitutes an intermediate level of reality, between quantum systems and the observation of certain outcomes when a measurement is taken. It sustains the change in a quantumsystem which is caused by taking a measurement. In this way, it plays a role comparable to matter, which, for Aristotle, is the substrate which accommodates changes.[1]

However, the analogy established is misleading. In quantum mechanics, the idea of probability only applies to groups of systems and not to individual systems; in particular, no measurement exists for the supposed probability property for an individual system. Moreover, the wave function contains all the information about the state of the system (provided that it is pure). This wave function can be expressed without recourse to any probabilistic notions (if we represent the state vector of the system in an arbitrary orthonormal basis). The potentia that Heisenberg postulates cannot therefore amount to an extra level of reality, in addition to the objective properties of the system. Recent results have indeed been able to show that probabilistic predictions in quantum mechanicslogically follow, without any additional postulates, from the description of individual quantum systems, with the aid of the wave function, which can be expressed, as we have seen, in a completely non-probabilistic way and the assumption that the objective properties of the system can be obtained by measurements with certainty.[2] Thus it is impossible to consider the probabilistic structure of quantum mechanics when applied to groups of systems as pointing towards an intermediate level of reality, the so-called potentia.

A second connection between quantum theory and the Greek concept of matter is profiled in the debate on the possible incompleteness of quantum mechanics. The famous article by Albert Einstein, Boris Podolsky and Nathan Rosen in 1930 triggered this debate, since it demonstrated, for the first time, non-local correlations between two systems which have interacted in the past, as predicted by quantum mechanics. This consequence of the formalism seemed so unacceptable to Einstein that he concluded from it that quantum theory would only give a partial description of reality, leaving out a more fundamental domain. The debate took a new and decisive step with the work of J.S. Bell. He managed to show that the probabilistic nature of quantum predictions is not the result of our limited knowledge:we arrive at contradictory results if we postulate that quantum theory is only a partial description of a hidden reality.

This result cautions against the temptation to perceive, in the probabilistic nature of quantum mechanics, an indication of its incompleteness. Quantum theory does not contain any sign of a deeper reality of which it only furnishes a partial description. Thus, it is not warranted to infer from the strangeness of the microscopic world a limit that mathematical description might encounter at that level. As much as Galilean physics, contemporary physics is based on the conviction that mathematical processes apply to our "lowly" world; we are not talking about merely approximate realisations of mathematical forms which would only exist in the world of Ideas. In this respect, it is noteworthy that laws of exact mathematical form govern the probabilistic predictions of quantum mechanics. Asindicated, (complex) mathematical considerations even allow us to deduce the statistical predictions of quantum mechanics, solely starting with the non-probabilistic descriptions of individual quantum systems. It is therefore wrong to believe that there would be another level of reality behind the atomic world and that mathematical description would there come to an end. On the contrary, quantum mechanics describes a real order, even if this order reveals strange features which are unintuitive to common sense. We should not be too surprised: after all, our common sense is derived from the world of macroscopic objects, and transposing this to the atomic world is not at all obvious.

These considerations show that the presumption of order stemming from faith in a Creator God is not impaired by quantum mechanics. In particular, creation makes us immune against the fundamental motive owing to which Einstein saw in the uncertainty of quantum theory a sign of its incompleteness: in a strictly deterministic worldview our ignorance is the only possible source of indeterminate events. Over against such a view, the biblical perspective stresses the contingency of natural order, as it is dependent on the free act of creation.
This is an extract of a paper given to the joint conference of the American Scientific Affiliation and Christians in Science in Edinburgh, August 2007. The author thanks Peter Mittelstaedt for very helpful comments.

[1]Werner HEISENBERG, Physics and philosophy: the revolution in modem science, New York, Harper & Row, 1958, ch. IX.
[2]P. MITTELSTAEDT, The interpretation of quantum mechanics and the measurement process,
Cambridge UP., 1998, p. 47-57, 62-64.

Faith Magazine

March - April 2009