Modules ModulesIn this chapter, we discuss important modules such as Wollaston prisms, Newtonian prisms, beam splitters, phase shifters, mirrors, and null modules.Modules are pieces of apparatus placed at various strategic positions in the information void and are designed to influence labstate amplitudes at signal detectors.Modules are therefore a critical component in the quantized detector network (QDN) approach to quantum mechanics (QM).Modules are not classified as either real or virtual detectors, because no information is extracted from them.Their function is solely to influence quantum amplitude propagation between stages in specific ways.Even empty space (the vacuum) can be regarded as a module, for the propagation of signals through nominally "empty" space is a fundamental subject in its own right.A particularly important example illustrating how nontrivial that can be is the Hubble-Doppler red shift of light from distant galaxies.In the QDN description of the double-slit (DS) experiment, shown in Figure 10.2, the stage Σ 1 detectors labeled 1 1 and 2 1 may be considered as on the V 2 side of the wall W , where V 2 is the information void between stages Σ 1 and Σ 2 .Viewed in this way, the wall may be interpreted as a part of the apparatus that is positioned in the information void region V 1 so as to influence the signals obtained at detectors 1 1 and 2 1 .Virtually all experiments have similar components of apparatus in the information void.We shall call any such piece of apparatus a module.Modules are necessary to the architecture of the experiment, are situated in the information void, and therefore are not detectors.Examples of modules are Stern-Gerlach (SG) inhomogeneous field magnets, Wollaston prisms, mirrors, phase changers, and so on.Even empty space, otherwise known as the vacuum, should be regarded as a module.Each module has its own physical properties.These include the number of detectors feeding amplitudes into that module and the number of detectors that
Modules ModulesIn this chapter, we discuss important modules such as Wollaston prisms, Newtonian prisms, beam splitters, phase shifters, mirrors, and null modules.Modules are pieces of apparatus placed at various strategic positions in the information void and are designed to influence labstate amplitudes at signal detectors.Modules are therefore a critical component in the quantized detector network (QDN) approach to quantum mechanics (QM).Modules are not classified as either real or virtual detectors, because no information is extracted from them.Their function is solely to influence quantum amplitude propagation between stages in specific ways.Even empty space (the vacuum) can be regarded as a module, for the propagation of signals through nominally "empty" space is a fundamental subject in its own right.A particularly important example illustrating how nontrivial that can be is the Hubble-Doppler red shift of light from distant galaxies.In the QDN description of the double-slit (DS) experiment, shown in Figure 10.2, the stage Σ 1 detectors labeled 1 1 and 2 1 may be considered as on the V 2 side of the wall W , where V 2 is the information void between stages Σ 1 and Σ 2 .Viewed in this way, the wall may be interpreted as a part of the apparatus that is positioned in the information void region V 1 so as to influence the signals obtained at detectors 1 1 and 2 1 .Virtually all experiments have similar components of apparatus in the information void.We shall call any such piece of apparatus a module.Modules are necessary to the architecture of the experiment, are situated in the information void, and therefore are not detectors.Examples of modules are Stern-Gerlach (SG) inhomogeneous field magnets, Wollaston prisms, mirrors, phase changers, and so on.Even empty space, otherwise known as the vacuum, should be regarded as a module.Each module has its own physical properties.These include the number of detectors feeding amplitudes into that module and the number of detectors that
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.
Interferometers IntroductionThe discussion of modules and computerization in previous chapters gives us the means to consider empirically useful quantized detector networks (QDN).In this chapter we shall focus on a particular class of network known as interferometers.Interferometers play a crucial role in quantum mechanics (QM) because they demonstrate the "paradox" of wave-particle duality in a direct way.On the one hand, discrete signals are detected by the observer and those signals are usually interpreted as particles or quanta.On the other hand, the observed frequencies built up over many runs show effects interpreted as due to the interference of waves.In the previous chapter, we used computer algebra (CA) to discuss the Wollaston interferometer (WI), a relatively simple interferometer.We shall use the same approach in the following discussion of the Mach-Zehnder interferometer (MZI), apparatus that allows the observer to investigate optical transmission through various materials. The Mach-Zehnder InterferometerThe basic structure of an MZI is given in Figure 13.1.A source S of light sends a monochromatic, unpolarized beam 1 0 into one input channel of beam splitter B 1 .Output channel 1 1 is deflected by mirror M 1 onto a module labeled φ that contains some medium under investigation, such as a crystal or liquid.The net effect is to create a phase change in that deflected beam by an amount φ, and then that modified beam, 1 2 , is passed into beam splitter B 2 .The second output channel, 2 1 , from B 1 , meanwhile, is deflected by mirror M 2 into beam splitter B 2 .The two deflected beams, 1 2 and 2 2 , that pass into B 2 interfere and are finally monitored by detectors 1 3 and 2 3 .Our analysis of the MZI follows the CA approach used for the WI in the previous chapter.
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 In this chapter, we discuss some of the differences between apparatus and systems under observation (SUOs). The discussion is phrased in terms of self–intervening networks , wherein partial quantum outcomes in an early stage of an apparatus can alter future configurations of that apparatus. To explain what we mean, we introduce the following classification of experiments. Note that reference to apparatus here includes real and virtual detectors, and real and virtual modules. Virtual detectors and modules are mathematical fictions that are introduced into the formalism for convenience. Type-Zero Experiments Many important experiments involve signal propagation through “empty space.” We classify these as type zero (T0). The feature of T0 experiments qualifying for this classification is that the observer has no control of the modules in the information void. Examples are experiments in astrophysics, where the observer can choose which source to observe and how they observe it, but has no influence on the physical properties of whatever lies between source and detector. If there are gas clouds between source and detector, the observer can only recognize that fact after the experimental data are analyzed. An important modern variant of T0 experiments involves map location via the Global Positioning System (GPS): signals sent from Earth to geostationary satellites and received by mobile devices back on Earth have traveled through Earth's atmosphere and through empty space, where special relativistic and general relativistic effects have to be taken into account (Ashby, 2002). Before the rise of experimental science, most “experiments” were based on visual observations, which are principally of T0 classification. The advent of the telescope and the microscope did not change things in this respect. Indeed, it has been suggested that science did not progress in antiquity precisely because of the philosophical principle that the only valid experiments could be of T0, as these do not introduce the artificiality of constructed modules into observation, which (it was argued) would give a false perspective on “reality.” The logic of that argument is superb, but it is a dead-end principle in science. Several sciences such as geology, archaeology, and, indeed, cosmology started off with periods of basic observation rather than experimentation. During such initial stages of these sciences, the observations could be classified as T0 experiments.
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.
Motivated by Feynman's 1983 paper on the simulation of physics by computers, we present a general approach to the description of quantum experiments which uses quantum bit registers to represent the spatio-temporal changes occurring in apparatus-systems during the course of such experiments. To illustrate our ideas, we discuss the Stern-Gerlach experiment, Wollaston prisms, beam splitters, Mach-Zender interferometers, von Neumann (PVM) tests, the more general POVM formalism, and a variety of modern quantum experiments, such as two-particle interferometry and the EPR scenario.