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.
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.
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 In this chapter we move beyond the classical register scenario discussed in the previous chapter, extending the discussion to experiments described by timedependent quantum registers of varying rank. We apply our previous discussion of the signal basis representation (SBR), the computational basis representation (CBR), signal operators, signal classes, and the CBR of signal operators to the quantum case. Our discussion of dynamics covers persistence, that is, the stability of apparatus, observers, and laboratory time, and the Born probability rule. We state the principles of quantized detector network (QDN) dynamics and show how they apply to the description of quantum experiments. We discuss the signal theorem and path summations. Persistence Our first step is to clarify what QDN assumes about the evolution of apparatus in time, because this affects the modeling. QDN is designed to reflect the behavior of apparatus in the real world and so it is not assumed in general that a given observer's apparatus is constant in time, even during a given run of an experiment. Although many experiments appear to be carried out with apparatus that persists over any given run of the experiment, and indeed, perhaps over all the runs of that experiment, that is just an incidental factor that reflects no more than an economy in construction. In practice it is invariably easier and more economical to use the same equipment over and over again rather than use it once, throw it away after each run, and build a new version ready for the next run. Lest this be thought of as a trivial point, it is nevertheless an integral and costly feature of many experiments, involving maintenance and upgrading. Indeed, in laboratories such as the Large Hadron Collider, actual run time is a small fraction of total project time. A related, significant issue has to do with the concept of ensemble , discussed in the Appendix. Persistence has everything to do with time scale , specifically, the relative laboratory time over which any piece of equipment can be meaningfully discussed as such. The degree of persistence of apparatus is as contextual as anything else in physics. If a run is relatively brief, say, over in very small fractions of a second, as in high-energy particle scattering experiments, then in such an experiment, the apparatus will behave as if it persists forever.
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.
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.
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 show how the quantized detector network (QDN) formalism describes the double-slit (DS) experiment. This is arguably the simplest experiment that demonstrates quantum affects such as wave–particle duality and quantum interference. It continues to be the focus of much debate and experiment (Mardari, 2005), because theoretical modeling of what is going on reflects current understanding of quantum physics and hence physical reality.We will apply QDN to two variants: the original DS experiment and the monitored DS experiment, where an attempt is made to determine the imagined path of the particle. The DS experiment is widely acknowledged by physicists to be of importance to the understanding of quantum mechanics (QM). So much so that in 2002, the single electron version, first performed by Merli, Missiroli, and Pozzi (Merli et al., 1976), was voted by readers of Physics World to be “the most beautiful experiment in physics” (Rosa, 2012). The DS experiment can be discussed in terms of three stages, shown in Figure 10.1. By the end of the preparation stage, Σ 0 , a monochromatic beam of light or particles has been prepared by a source P , such as a laser. The beam emerges from point O and then passes through an information void V 1 to the first stage, Σ 1 , which consists of a wall or barrier W . This wall has two openings denoted A and B that allow parts of the beam to pass through into another information void V 2 and onto the second and final stage Σ 2 , which consists of a detecting screen S . The screen S is in general some material that can absorb and record particle impacts. In reality, any screen will consist of a finite number of signal detectors, such as photosensitive molecules, but the typical QM modeling is done as if there were a continuum of sites on the screen, such as C , that could register particles.