Motivated by Heisenberg's assertion that electron trajectories do not exist until they are observed, we present a new approach to quantum mechanics in which the concept of observer independent system under observation is eliminated. Instead, the focus is only on observers and apparatus, the former describing the latter in terms of labstates. These are quantum states over time-dependent Heisenberg nets, which are quantum registers of qubits representing information gateways accessible to the observers. We discuss the motivation for this approach and lay down the basic principles and mathematical notation.
Motivated by Heisenberg's assertion that electron trajectories do not exist until they are observed, we present a new approach to quantum mechanics in which the concept of observer independent system under observation is eliminated. Instead, the focus is only on observers and apparatus, the former describing the latter in terms of labstates. These are quantum states over time-dependent Heisenberg nets, which are quantum registers of qubits representing information gateways accessible to the observers. We discuss the motivation for this approach and lay down the basic principles and mathematical notation.
Motivated by Heisenberg's assertion that electron trajectories do not exist until they are observed, we present a new approach to quantum mechanics in which the concept of observer independent system under observation is eliminated. Instead, the focus is only on observers and apparatus, the former describing the latter in terms of labstates. These are quantum states over time-dependent Heisenberg nets, which are quantum registers of qubits representing information gateways accessible to the observers. We discuss the motivation for this approach and lay down the basic principles and mathematical notation.
Standard Quantum mechanics (SQM) deals with observers, frames of reference (apparatus) and systems under observation (SUOs). Heisenberg based his approach to quantum mechanics on a desire to avoid metaphysical (i.e. unobservable) concepts, dealing only in terms of experimentally observable quantities. Following this idea, we describe an approach to quantum mechanics which deals only with labstates, which represent the observer's quantum information about the apparatus. This approach is compatible and consistent with Hume's philosophy known as empiricism. We show that conventional ideas do not work without modification when we consider certain quantum experiments involving classical special relativistic transformations. We discuss the appearance of quantum horizons, which present a barrier to information transmission between initial and final state apparatus whenever these are in relative motion.
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.
Reality is that which, when you stop believing in it, does not go away. Philip K. Dick In Chapters 1 and 2 we developed the necessary mathematical apparatus and terminology that will be used throughout this book. Chapter 3 has provided some heuristics and gently led us to the threshold of quantum mechanics. It is now time to open the door, introduce the basic concepts and tools of the trade, and continue our journey to quantum computing. In Section 4.1 we spend a few words on the motivations behind quantum mechanics. We then introduce quantum states and how they are distinguishable from one another through observations. Section 4.2 describes observable physical quantities within the quantum framework. How observable quantities are measured is the topic of Section 4.3. The dynamics of quantum systems, i.e., their evolution in time, is the focus of Section 4.4. Finally, in Section 4.5, we revisit the tensor product and show how it describes the way in which larger quantum systems are assembled from smaller ones. In the process, we meet the crucial notion of entanglement, a feature of the quantum world that pops up again in the chapters ahead. QUANTUM STATES Why quantum mechanics? To answer this question, we have to hearken back in time to the dawn of the twentieth century. Classical mechanics still dominated the scene, with its double-pronged approach: particles and waves .
After some 80 years, the meaning of quantum theory remains as controversial as ever. The theory, as presented in textbooks, involves a human observer performing experiments with microscopic quantum systems using macroscopic classical apparatus. The quantum system is described by a wavefunction – a mathematical object that is used to calculate probabilities but which gives no clear description of the state of reality of a single system. In contrast, the observer and apparatus are described classically and are assumed to have definite states of reality. For example, a pointer on a measuring device will show a particular reading, or a particle detector will "fire" a definite number of times. Quantum systems seem to inhabit a fuzzy, indefinite realm, while our everyday macroscopic world does not, even though the latter is ultimately built from the former.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.