IF, AS HEISENBERG SUGGESTED, potentia indeed constitute an ontologically fundamental species of reality, then the mathematical representation of the quantum mechanical evolution of the matrix of potentia to the matrix of probabilities-that is, the valuation of potentia as probabilities between zero and one-ought to be heuristically useful in understanding the ontological implications of this evolution.The mathematical representation should prove helpful in visualizing not only the process described by quantum mechanics but also, as we shall see in the following chapters, the process described by Whitehead.The basic formalism introduced and explored in this chapter is intended to be comprehensible to readers unfamiliar with mathematics.Some familiarity with the Pythagorean theorem and the addition of vectors will be useful, but not necessary.
IF, AS HEISENBERG SUGGESTED, potentia indeed constitute an ontologically fundamental species of reality, then the mathematical representation of the quantum mechanical evolution of the matrix of potentia to the matrix of probabilities-that is, the valuation of potentia as probabilities between zero and one-ought to be heuristically useful in understanding the ontological implications of this evolution.The mathematical representation should prove helpful in visualizing not only the process described by quantum mechanics but also, as we shall see in the following chapters, the process described by Whitehead.The basic formalism introduced and explored in this chapter is intended to be comprehensible to readers unfamiliar with mathematics.Some familiarity with the Pythagorean theorem and the addition of vectors will be useful, but not necessary.
Abstract Heisenberg was a very dedicated Kantian, and viewed the discoveries of early twentieth century physics as disqualifying of the Kantian metaphysical worldview. He made an effort – not an especially successful one – to reconfigure the Kantian critique by replacing noumena with the quantum-level reality, and proposed a new entity as mediative between the quantum realm and the subject. The new entity, potentia (borrowed from Aristotle, and altered to serve Heisenberg’s purpose) fulfills that role by means of its hybrid nature: it’s partly mental, partly a reification of probabilities. This dual nature allows epistemic access to the probabilistic nature of quantum-level interactions, out of which our phenomenal world is realized when a measurement is made. How well this notion serves the purpose of rehabilitating the Kantian critique is questionable, as Heisenberg’s conception is problematic and, perhaps, internally inconsistent. My dissertation follows Heisenberg’s development of potentia, examines how well it addresses the failure of the Kantian problem, and asks whether his proposal is an obscurum per obscurius. Thereafter I introduce a number of other, similar proposals to potentia, consider them on their own merits, compare them to Heisenberg’s conception, and use this conjunction of potentia proposals to made a judgment regarding whether the use of potentia is a philosophically defensible way of addressing the recondite problems of quantum mechanics.
Amid the wide variety of interpretations of quantum mechanics, the notion of a fully coherent ontological interpretation has seen a promising evolution over the last few decades. Despite this progress, however, the old dualistic categorical constraints of subjectivity and objectivity, correlate with the metrically restricted definition of local and global, have remained largely in place – a reflection of the broader, persistent inheritance of these comfortable strictures throughout the evolution of modern science. If one traces this inheritance back to its ancient roots in Plato and Aristotle, it is clear that the coherence, scientific utility, and historical durability of the various natural philosophies that followed have been directly proportional to their commitment, tacit or explicit, to object-oriented realism. As Simondon might put it, it is a commitment to the primacy of individuated substance over the process of individuation. For Whitehead, it is the misplaced assimilation of becoming to being, of potentiality to actuality. Quantum mechanics has challenged this commitment with a combined breadth and depth of force that far exceeds any other theory in the history of science. The theory’s objectively demonstrable empirical application is manifest only by way of a fundamentally subjective, context-dependent mechanism of measurement. More compelling still, actual system states are always actualizations of locally contextualized yet globally conditioned potential system states, such that “globally objective” reality is no longer merely the object of local measurement, but also its product. Thus, any coherent, ontological interpretation of quantum theory must include a conceptual framework by which objectivity and subjectivity, actuality and potentiality, global and local, being and becoming, individuated fact and process of individuation, are no longer understood as merely epistemic, mutually exclusive category pairs descriptive of an already extant, closed reality – but rather as mutually implicative ontological categories explicative of an ontogenetic, open reality-in-process.
I build upon Heisenberg’s proposal in 1958 that quantum states are ontologically real “potentia.” On this view reality consists in ontologically real Possibles and ontologically real Actuals. Then measurement converts Possibles to Actuals. This ontological hypothesis, explicit in Heisenberg’s proposal, suggests a natural place for “mind.” Mind converts Possibles to Actuals. This role for mind is a scientific hypothesis open to test. Modest evidence now supports the hypothesis. If very well confirmed, such results alter the foundations of quantum mechanics and afford a role of mind in the becoming of the universe. More, the ontological proposal is not a substance dualism, for potentia are not substances. Thus, this proposal for the role of mind does not seem to inherit many of the problems raised in a substance dualism such as Descartes’ Res cogitans and Res extensa, (Descartes), or in a substance neutral monism such as Russell, (Russell). The proposal is radical. Far more evidence is needed.
This author has been engaged over the past several years in the effort to develop certain basic intuitions into a fully mathematical theory. These evolving intuitions first began with the idea that the economist's notion of utility might more truly be represented mathematically by a normed measure on the commodity space rather than by a point function, the value of the measure on a particular set of goods having the sense of a relative propensity of the individual to select a good in that set. With this idea there came in turn, quite naturally, the insight that utility and probability are one and the same thing. And accordingly it emerged that the theory we were seeking would not be restricted to the economic behavior of human beings, nor even to the behavior in general of human beings: it would pertain, in utmost generality, to all behavior of all systems. Thus, it must affirm that all behavior is the evolution of stochastic processes, and that all systems are stochastic processes. Consistent with this the structural elements of stochastic processes are seen as the fundamental, objective, real entities, the ultimate building-blocks of reality. These are eventualities and acts and-according to the traditional mathematical representation of stochastic processes, also-probabilities. This structural aspect of the theory under development puts into sharp evidence its wide divergence from the classical scientific conception of reality. Our intensive search failed to discover a dynamical law for the proposed new theory within the mathematical context of the traditional, σ-field-real-valued-measure representation of stochastic processes. We therefore have gone on to a higher level of possible mathematical representation. This particular representation would have collections of eventualities represented by lattices of certain configurations in a unitary space. Closed linear manifolds are among these configurations, and indeed the formalism of quantum mechanics falls into the context of this representation. But the general lattice element in the kinds of lattices being investigated is more complicated than a linear manifold, being heuristically comparable with an acute-angle cone of vectors. These configurations are formulated by means of a ƒlanking relation between linear manifolds. One such lattice has been developed. Others are currently being sought through variations on the notion of flanking. The fact that probabilities present themselves in the unitary space representation-as is familiar from quantum mechanics-as parameters of the relationship between linear manifolds suggests that probability is not a fundamental structural concept. It is consequently indicated that eventualities and acts alone are the basic elements of real structure. Accordingly, the dynamical law must be formulable in terms of these elements only. There is a natural suggestion of what the law might look like. Even at the present early stage of development of the new theory being sought it is possible to cite many pieces of empirical evidence vouching for its exclusive validity. Such evidence is particularly noteworthy in the domain of human behavior.
This chapter depicts the spectrum between reality and potentiality, generally by providing diagrams, graphs, and variables along with their corresponding details and explanations. Hilbert spaces here are remarked with different values to represent what will actually happen or to reach the “satisfaction” — realization of the anticipated outcome — that was mentioned in the previous chapter. Aside from the spaces, there are also vectors which stand for the characteristics of the portrayed person, group, object, etc. Coefficients of the variables define the level of possibility that the alternative outputs will occur. The appearance of the outcome states is dependent on our expectations, which are anchored to objective reality. Of course, there are inevitable, uncontrollable outside forces than can come into the picture, and these externalities are termed “trace-over.” Also, the three advantages of the ontological interpretation of quantum formalism are universality of the scope of the interpretation of quantum mechanics, permissiveness to locate the paradox of quantum nonlocality, and its interposition between the altercations in physics.
This chapter tries to pinpoint the epistemological information that a scientist (or an epistemologist) anxious to keep away from "metaphysical" commitments of any sort may nevertheless derive from quantum physics. But, valuable as it is (mainly as a guide for discriminating the genuinely scientific questions from those of a more "mixed" sort) this standpoint is not to be raised to the status of a universal way of thinking that would be the only admissible one. Within the veiled reality conception Einstemian separability, applies to empirical, not to independent, reality; which means that special relativity theory does not concern independent reality. In his mature years Heisenberg developed a conception of the world in which quite a central role is played by the notion of potentia. He associated wave functions to potentia. In a sense, Heisenberg's approach is ontological, but his ontology is of a subtle kind, for along with actuality it leaves room for potentialities.