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.
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.
Heisenberg offered an interpretation of the quantum state which made use of a quantitative version of an earlier notion, , of Aristotle by both referring to it using its Latin name,potentia, and identifying its qualitative aspect with . The relationship between this use and Aristotle's notion was not made by Heisenberg in full detail, beyond noting their common character: that of signifying the system's objective capacity to be found later to possess a property in actuality. For such actualization, Heisenberg requiredmeasurementto have taken place, an interaction with external systems that disrupts the otherwise independent, natural evolution of the quantum system. The notion of state actualization was later taken up by others, including Shimony, in the search for a law-like measurement process. Yet, the relation of quantum potentiality to Aristotle's original notion has been viewed as mainly terminological, even by those who used it thus. Here, I reconsider the relation of Heisenberg's notion to Aristotle's and show that it can be explicated in greater specificity than Heisenberg did. This is accomplished through the careful consideration of the role of potentia in physical causation and explanation, and done in order to provide a fuller understanding of this aspect of Heisenberg's approach to quantum mechanics. Most importantly, it is pointed out that Heisenberg's requirement of an external intervention during measurement that disrupts the otherwise independent, natural evolution of the quantum system is in accord with Aristotle's characterization of spontaneous causation. Thus, the need for a teleological understanding of the actualization of potentia, an often assumed requirement that has left this fundamental notion neglected, is seen to be spurious. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.
Abstract: The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states---the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious “collapse of the wave function ” by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as “potentia ” or “objective tendencies ” are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. 1. Heisenberg and the epistemic conception of quantum states The epistemic conception of quantum states is the idea that quantum states are not descriptions of the properties of quantum systems but rather reflect the state assigning
Quantum mechanics has been enormously successful in explaining the behavior of microsystems such as molecules, atoms, and nuclei. We have seen that quantum mechanics describes a quantum system by the wave function ψ, which is the solution of the Schro¨dinger equation. The wave function determines the probability amplitudes (whose modulus squared gives the probability) for all possible outcomes of a measurement corresponding to an observable on the system. In general, the wave function does not uniquely predict the result of a measurement; it only provides a probability distribution for all possible results of the measurement on a quantum system. Only if the system happens to be in an eigenstate corresponding to the observable being measured, is the result of a measurement of this observable completely predictable. On the other hand, the results of measurements corresponding to a conjugate or non-commuting observable, on the same system in the same state, are indeterminate. Quantum mechanical description of physical systems raises profound questions: How are the wave function and the probabilities for different outcomes of a measurement to be interpreted? Does the wave function represent a single system or an ensemble of systems? Does the physical system actually have the attribute corresponding to the measurement in question or does the measurement itself create the attribute? These questions led to different interpretations of quantum mechanics, which were vigorously debated during the years of its discovery as also in the following decades. The new idea of indeterminacy was especially difficult to reconcile with the long-held view that a physical theory should aim at predicting accurately, and without ambiguity, the result of any measurement on any system, big or small. These debates not only gave us a deeper understanding of quantum mechanics but also changed profoundly the way we view the micro-world.
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.
In classical mechanics the state of a dynamical system at any particular time can be described by the values of a set of coordinates and their conjugate momenta, thus, if the system has n degrees of freedom, by 2n numbers. In quantum mechanics, on the other hand, we have to describe a state of the system by a wave function involving a set of coordinates, thus by a function of n variables. The quantum description is, therefore, much more complicated than the classical one. Let us consider, however, an ensemble of systems in Gibbs' sense, i.e. not a large number of actual systems which could, perhaps, interact with one another, but a large number of hypothetical systems which are introduced to describe one actual system of which our knowledge is only of a statistical nature. The basis of the quantum treatment of such an ensemble has been given by Neumann. The description obtained by Neumann of an ensemble on the quantum theory is no more complicated than the corresponding classical description. Thus the quantum theory, which appears to such a disadvantage on the score of complication when applied to individual systems, recovers its own when applied to an ensemble. It is the object of the present note to examine this question more closely and to show how complete the analogy is between the quantum and classical treatments of an ensemble.
In the Copenhagen approach to quantum mechanics as characterized by Heisenberg, probabilities relate to the statistics of measurement outcomes on ensembles of systems and to individual measurement events via the actualization of quantum potentiality. Here, brief summaries are given of a series of key results of different sorts that have been obtained since the final elements of the Copenhagen interpretation were offered and it was explicitly named so by Heisenberg-in particular, results from the investigation of the behavior of quantum probability since that time, the mid-1950s. This review shows that these developments have increased the value to physics of notions characterizing the approach which were previously either less precise or mainly symbolic in character, including complementarity, indeterminism, and unsharpness.