In trying to develop a theory of chance, I have so far drawn largely on a metaphysical picture inspired by classical physics, and have used statistical mechanics as my central example of chance arising in physical theories. It has proven difficult to develop an adequate theory of chance. But perhaps things will look different if we turn to quantum mechanics. The theory of quantum mechanics is extremely well confirmed. It is doubtful whether it is strictly true in its current form, due to the well-known conflict between quantum mechanics and the general theory of relativity, but it is an outstandingly good example of a successful physical theory, and it represents a stark break from earlier models of the physical world. Perhaps by tapping into these resources, we can develop an adequate metaphysics of chance. The quantum mechanical world It is widely believed that quantum mechanics is starkly opposed to classical physics, because quantum mechanics claims that the world is governed by fundamentally indeterministic laws. As it happens, this common belief oversimplifies somewhat. Quantum mechanics is a theory that is formulated in relatively mathematical terms, quite removed from concepts of directly observable physical entities. Consequently, there is a great deal of room for interpretation of the meaning of the mathematics. Indeed, there are at least three interpretations of quantum mechanics which are serious candidates for giving an adequate account of how the mathematics relates to reality.
In trying to develop a theory of chance, I have so far drawn largely on a metaphysical picture inspired by classical physics, and have used statistical mechanics as my central example of chance arising in physical theories. It has proven difficult to develop an adequate theory of chance. But perhaps things will look different if we turn to quantum mechanics. The theory of quantum mechanics is extremely well confirmed. It is doubtful whether it is strictly true in its current form, due to the well-known conflict between quantum mechanics and the general theory of relativity, but it is an outstandingly good example of a successful physical theory, and it represents a stark break from earlier models of the physical world. Perhaps by tapping into these resources, we can develop an adequate metaphysics of chance. The quantum mechanical world It is widely believed that quantum mechanics is starkly opposed to classical physics, because quantum mechanics claims that the world is governed by fundamentally indeterministic laws. As it happens, this common belief oversimplifies somewhat. Quantum mechanics is a theory that is formulated in relatively mathematical terms, quite removed from concepts of directly observable physical entities. Consequently, there is a great deal of room for interpretation of the meaning of the mathematics. Indeed, there are at least three interpretations of quantum mechanics which are serious candidates for giving an adequate account of how the mathematics relates to reality.
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its core concepts (amplitudes, global phases, etc.) can not be directly accessed and its interpretation is still the subject of intense debate, more than 100 years since it was introduced. So, a fundamental question is why this particular mathematical model is the one that nature chooses, if indeed it is the correct model. In the past two decades there has been a renewed effort to determine what physical or informational principles define quantum mechanics. In this paper, recent attempts at establishing reasonable physical principles are reviewed and their degree of success is tabulated. An alternative approach using joint quasi-probability distributions is shown to provide a common basis of representing most of the proposed principles. It is argued that having a common representation of the principles can provide intuition and guidance to relate current principles or advance new principles. The current state of affairs, along with some alternative views are discussed.
Abstract Quantum mechanics is our most successful and versatile account of the basic constituents of matter, of their interaction and of their compounds. We introduce the theory via a sketch of its history and lay out its mathematical structure in some detail. Before this background we address the important and controversial question of how to interpret that structure. We contextualise our own position, which is linked to our account of ontological emergence as detailed in Chap. 2 , and which is mathematically best expressed in the Heisenberg picture of quantum dynamics. Indeterminism and irreversible processes are fundamental for our approach. We discuss the dialectics of the deterministic challenge to our position and argue that indeterminism in the form of quantum randomness has turned from a philosophical riddle to a technological resource. This claim is supported by a discussion of quantum information science, including some of its basic protocols. Towards the end of the chapter we argue that agency and quantum mechanics come as a package deal. For one, quantum mechanics describes the world as offering open possibilities for the future at a fundamental physical level, which is needed for real higher-order organisation, including agency. Of course, this does not in any way show that the actual existence of agents in our world is guaranteed. But it does show that general agency scepticism has no basis in physics. Second, we show that quantum mechanics is best understood as a theory that describes our agential interactions with nature, and not as a theory that represents nature from the point of view of an inert, detached observer.
In classical physics there is, in accordance with common sense, an objective world ‘out there’. That world evolves in a clear and deterministic way, being governed by precisely formulated mathematical equations. This is as true for the theories of Maxwell and Einstein as it is for the original Newtonian scheme. Physical reality is taken to exist independently of ourselves; and exactly how the classical world ‘is’ is not affected by how we might choose to look at it. Moreover, our bodies and our brains are themselves to be part of that world. They, also, are viewed as evolving according to the same precise and deterministic classical equations. All our actions are to be fixed by these equations - no matter how we might feel that our conscious wills may be influencing how we behave. Such a picture appears to lie at the background of most serious 1 philosophical arguments concerned with the nature of reality, of our conscious perceptions, and of our apparent free will. Some people might have an uncomfortable feeling that there should also be a role for quantum theory - that fundamental but disturbing scheme of things which, in the first quarter of this century, arose out of observations of subtle discrepancies between the actual behaviour of the world and the descriptions of classical physics. To many, the term ‘quantum theory’ evokes merely some vague concept of an ‘uncertainty principle’, which, at the level of particles, atoms or molecules, forbids precision in our descriptions and yields merely probabilistic behaviour. Actually, quantum descriptions are very precise, as we shall see, although radically different from the familiar classical ones. Moreover, we shall find, despite a common view to the contrary, that probabilities do not arise at the minute quantum level of particles, atoms, or molecules - those evolve deterministically - but, seemingly, via some mysterious larger-scale action connected with the emergence of a classical world that we can consciously perceive. We must try to understand this, and how quantum theory forces us to change our view of physical reality.
When metaphysicians pay attention to theories in fundamental physics, they are usually interested in their implications for fundamental metaphysics: they want to know what the theories imply or suggest concerning the ultimate structure of reality. This essay, by contrast, is concerned with the “derivative metaphysics” of quantum mechanics. I will be considering a certain hypothesis about the fundamental structure of reality, which I will call H. I am interested in H because it strikes me as embodying the most obvious, flat-footed way to read an account of the fundamental structure of reality off the mathematical apparatus of elementary quantum mechanics. But I won’t be defending this claim here, or trying to argue that the members of H are more plausible than other accounts of the fundamental structure of reality inspired by quantum mechanics. Instead, my question is: if H were true, could there be (non-fundamentally speaking, of course) such ordinary objects as plants, planets and people? More specifically: could there be such ordinary objects as ourselves and the things we are familiar with, having more or less the ordinary properties we take them to have? And more generally: given that the fundamental structure of a possible world is such as to make H true, what is its correct description in ordinary terms? Of course, I care about these questions in part because I want to explore the extent to which we might have good reason to believe H, or something akin to it. But even if H turned out to be consistent with our ordinary knowledge about the world of ordinary objects, it would obviously take a lot more work to show that it has any serious claim on our credence. At a minimum, one would have to say something about how likely we should regard our evidence as being, given H; one would want to make some sort of survey of alternative hypotheses; and one would want to take into account our specialised scientific knowledge as well as our ordinary knowledge, including the facts that make trouble for elementary quantum mechanics and force us to look beyond it to quantum field theory and ultimately towards some kind of theory of quantum gravity.
Quantum probability and quantum mechanics The formalism of quantum probability theory Discussions of quantum mechanics are often confused by a lack of clarity about what exactly constitutes ‘quantum mechanics’. It is therefore useful to try at the start to isolate a consistent mathematical core of quantum mechanics, and consider anything that goes beyond this core to be ‘interpretation’. For us, this core is quantum probability theory. Quantum probability is a generalization of classical probability, and therefore I begin with a brief review of the latter. I assume that the reader has some familiarity with the ideas of probability theory. What follows is just to provide a quick review, and to establish some notation and terminology. In modern classical probability theory, probabilities are defined over algebras of events. The motivation is straightforward: we begin with a set of ‘primitive’, or ‘simple’, events (the ‘sample space’), and form an algebra of events by taking all logical combinations of the simple events. For example, let us take the simple events to be the possible results of rolling a six-sided die one time, so that the sample space is the set {1,2,3,4,5,6}. We then form an algebra of events from the sample space by taking all possible logical combinations of the simple events. Logical combinations include, for example, ‘either 3 or 5’ and ‘not 3 and not 2’.
The abstract theory of probability and its interpretation are briefly reviewed, and it is explicitly demonstrated that the formalism of quantum mechanics satisfies the axioms of probability theory. This refutes the suggestions which have occasionally been made that ‘‘classical’’ probability theory does not apply to quantum mechanics. Several erroneous applications of probability theory to quantum mechanics are examined, and the nature of the errors are exposed. It is urged that more attention be given to probability theory in the physics curriculum.