“Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia

Abstract

Werner Heisenberg introduced the notion of quantum potentia in order to accommodate the indeterminism associated with quantum measurement. Potentia captures the capacity of the system to be found to possess a property upon a corresponding sharp measurement in which it is actualized. The specific potentiae of the individual system are represented formally by the complex amplitudes in the measurement bases of the eigenstate in which it is prepared. All predictions for future values of system properties can be made by an experimenter using the probabilities which are the squared moduli of these amplitudes that are the diagonal elements of the density matrix description of the pure ensemble to which the system, so prepared, belongs. Heisenberg considered the change of the ensemble attribution following quantum measurement to be analogous to the classical change in Gibbs' thermodynamics when measurement of the canonical ensemble enables a microcanonical ensemble description. This analogy, presented by Heisenberg as operating at the epistemic level, is analyzed here. It has led some to claim not only that the change of the state in measurement is classical mechanical, bringing its quantum character into question, but also that Heisenberg held this to be the case. Here, these claims are shown to be incorrect, because the analogy concerns the change of ensemble attribution by the experimenter upon learning the result of the measurement, not the actualization of the potentia responsible for the change of the individual system state which-in Heisenberg's interpretation of quantum mechanics-is objective in nature and independent of the experimenter's knowledge.

A Realist View of the Quantum World

“…However, claim (i) is false, in that there is no direct empirically evidence whatsoever for any role for consciousness in measurement, though it might appear to be the case if one were to mistake the acquisition of knowledge of a changed state of affairs for a change in the state of affairs itself; cf. [10]. As for claim (ii), it is purely speculative at this point.…”

“…Moreover, contrary to a widespread belief regarding Aristotle's theory of causation and explanation, no teleological ("final") cause appears in this case [11]. The associated non-deterministic change of state-vector evolution occurs precisely with the intervention of the measuring apparatus and the rest of the world as its proximate cause: There is not a lack of causation upon these events, but rather Aristotelian chance causation not captured by the fundamental quantum law of motion for closed systems which applies only to systems not being measured [10,11].…”

“…This manifestly interpretational rule provides a prescription for attributing meaning to statements about the properties of quantum systems incorporating Einstein's reality criterion [15] and allows the physicist to attribute state assignments on the basis of empirical data. In Heisenberg's approach to the quantum formalism, the complex amplitudes {c i } of the state |ψ = i |ψ i of a system, when squared, provide the objective probabilities {p i } of its being found upon measurement to possess the possible values of the corresponding properties [17]: The measured value of a property becomes definite (actual) with probability p r , as opposed to indefinite (potential) [5,10,11] upon a precise measurement providing outcome r by the measuring apparatus in conjunction with the remainder of the world which, again, is macroscopic and classically describable (cf. [8]).…”

Quantum Unsharpness, Potentiality, and Reality

“…46-47; cf. [7]. In particular, the possibilistic element of Aristotle's theory of causation is utilized: ".…”

“…For the remainder of the twentieth century, Heisenberg's view of causation and its notion of potential reality was viewed as insufficiently precise to be worthy of further consideration, and its relation to Aristotelian causation was considered tenuous, at best [5]. However, recently, the precise nature of the relation of Heisenberg's quantum potentiality to Aristotle's notion of potentia as a form of spontaneous causation has been clarified in a way that lends support to Heisenberg's claims of having extended potentiality from a qualitative to a quantitative notion [7,8]. In addition, developments in the theory of quantum probability and quantum measurement generalizing observables via the notion of positive operator measures (POMs) to which he contributed, Paul Busch (together with the current author, in [1]) offered a robust view of quantum mechanics as a realist theory of individual systems including a degree of reality for generalized observables based of the notion of unsharp quantum reality introduced by him and his coworkers.…”