QDN (quantized detector networks) is a description of quantum processes in which the principal focus is on observers and their apparatus, rather than on states of SUOs (systems under observation). It is a realization of Heisenberg's original instrumentalist approach to quantum physics, and can deal with time dependent apparatus, multiple observers and inter-frame physics. QDN is most naturally expressed in the mathematical language of quantum computation, a language ideally suited to describe quantum experiments as processes of information exchange between observers and their apparatus. Examples in quantum optics are given, showing how the formalism deals with quantum interference, non-locality and entanglement. Particle decays, relativity and non-linearity in quantum mechanics are also discussed.
QDN (quantized detector networks) is a description of quantum processes in which the principal focus is on observers and their apparatus, rather than on states of SUOs (systems under observation). It is a realization of Heisenberg's original instrumentalist approach to quantum physics, and can deal with time dependent apparatus, multiple observers and inter-frame physics. QDN is most naturally expressed in the mathematical language of quantum computation, a language ideally suited to describe quantum experiments as processes of information exchange between observers and their apparatus. Examples in quantum optics are given, showing how the formalism deals with quantum interference, non-locality and entanglement. Particle decays, relativity and non-linearity in quantum mechanics are also discussed.
Motivation The aim of this book is to introduce, develop, and apply quantized detector networks (QDN), an information-based, observer-centric approach to quantum mechanics (QM). Six reasons motivating our development of QDN are the following. Avoidance of Metaphysical Speculation There is such a variety of unproven (and unprovable) speculation concerning the interpretation of QM that the subject of this book, QDN, may appear at first sight to be yet another in this growing branch of metaphysics. In fact, our motivation is precisely the opposite. QDN was intended from the outset to reduce the level of metaphysics in the application of QM. To achieve this, our strategy is to move the traditional focus of attention away from systems under observation (SUOs) and toward the observers of those SUOs. In QDN, wave functions represent not states of SUOs but states of apparatus. We shall call such states labstates , to distinguish them from states of SUOs (which do have a place in QDN). It is only labstates that observers can ever deal with directly. In this respect, QDN is an attempt at a more laboratory-based description of quantum physics than standard QM, focusing as much on how an experiment is done as on the results of that experiment. For example, instead of talking about the wave function of an electron, QDN talks about the labstate of the signal detectors that allow us to say anything about that electron in the first place. That is all, there is nothing deeper. Whether or not electrons actually “exist” is thereby relegated to an inessential metaphysical issue that we can choose to ignore. It is important to understand what QDN does not say as much as what it does say. QDN does not say that electrons do not “exist”. QDN merely asks for an empirical definition of “existence”. QM Is Much More Than a Calculational Device Many physicists hold the utilitarian view that the success of quantum theory in predicting experimental data is sufficient for their purposes, and that further inquiry is really the business of metaphysics and therefore outside the scope of science proper. We cannot say that this is entirely unreasonable. However, we take the view that QM represents such a radical departure from the principles of classical mechanics (CM) that this pragmatical view cannot be all there is to the subject.
Introduction The quantized detector network (QDN) formalism was designed from the outset to deal with detector networks of arbitrary complexity and rank. However, there is a price to be paid. A qubit register of rank r is a Hilbert space of dimension 2 r , so the dimensionality of quantized detector networks grows exponentially with rank. For example, a relatively small system of, say, 10 detectors involves a Hilbert space of dimension 2 10 = 1 , 024. Even such a relatively small system cannot be dealt with easily by manual calculation, because quantum mechanics (QM) involves entangled states. Labstates in QDN are far more complex (in the sense of having far more mathematical structure) than the corresponding states in a classical register of the same rank. Some of the mathematical entanglement and separability properties of quantum labstates are discussed in Chapters 22 and 23. The quantum entanglement structure of labstates poses a ubiquitous and serious problem, for both theorists and experimentalists. At this time, there is significant interest in quantum entanglement, particularly regarding its use in quantum computing, but theoretical understanding of entanglement is still surprisingly limited. On the experimental side, quantum computers with 2000 qubits are currently being developed (D-Wave Systems, 2016). There is scope here for the application of QDN to networks of rank going into the many thousands. For those sorts of systems under observation (SUOs), quantum entanglement makes calculations by hand far too laborious to be of any practical use. Fortunately, three factors come to our aid here, making the application of QDN to large-rank networks a potentially viable proposition. Modularization We saw in previous chapters that QDN deals with discrete aspects of observation, despite the fact that standard QM and relativistic quantum field theory (RQFT) deal with continuous degrees of freedom. This discreteness comes in three forms, referred to us as stages, nodes, and modules, and all of that is due to three inescapable physical facts. First, all real observations take time and involve discrete signals in finite numbers of detectors. Second, real apparatus is constructed from atoms, not continua. Third, these atoms form finite numbers of well-characterized modules, as discussed in the previous chapter. Contextuality A critically helpful fact here is that in any particular experiment, the contextual subspaces that the observer needs to deal with will usually be of significantly lower dimensions than that of the full quantum registers involved.
We discuss the QDN (quantized detector network) approach to the formulation and interpretation of quantum mechanics. This approach gives us a system-free approach to quantum physics. By this, we mean having a proper emphasis on those aspects of physics which are observable and an avoidance of metaphysical concepts, which by definition are incapable of verification and should play no role in science on that account. By focusing on only what experimentalists deal with, i.e., quantum information, we avoid the ambiguities and confusion generated by the undue objectification of what are complex quantum processes.
Introduction In this chapter we discuss how quantized detector network (QDN) theory can be extended to cover the creation and decommissioning of apparatus, from the perspective of observers and their laboratories. This extension will be referred to as extended QDN. It allows us to discuss bit power sets, laboratories, the universal register, contextual vacua, and the creation of quantized detector apparatus. This extended formalism is used to describe the Elitzur–Vaidman bomb-tester experiment and the Hardy paradox experiment. A central concept running through this book is that of the observer , the enigmatic “ I ” of I think therefore I am . The problem is that, despite the many triumphs of quantum mechanics (QM), the physics of the observer and observation is still not well understood. Regardless of how observers are defined and whether classical or quantum principles are involved, physicists generally believe that classical information in some form is extracted from systems under observation (SUOs) in actual physics experiments. In all branches of science, their language reflects this belief: experimentalists talk of measuring an electron's spin or the mass of a new particle, and so on. The conceptual issues in quantum mechanics such as wave–particle duality, quantum interference, and nonlocality gave the first indication that all might not be well with this perspective. We need only to look at the photon concept to appreciate some of the problems with the idea that photons are particles (Paul, 2004). There are experiments where a photon (that is, a signal) is detected from a crystal, but the atom “from whence it came” cannot be identified, suggesting that a cooperative process is involved, rather like the phonon concept in the physics of crystals. The problem we have with the photon-as-particle concept is the gap in logic. If the particle interpretation is taken literally, then obvious questions about the physical structure or its equivalent of such particles spring up. Does such a particle have a “surface”? If it has a surface, what is that surface made of? These and other simple (minded) questions quickly lead to the conclusion that the particle concept is a convenient and economical objectification of context. In other words, a useful illusion.