Let us summarize what we have achieved, which mathematical problems remain to be solved, and where we should go in the future to achieve a faithful image of nature for fundamental particles and all their interactions that fully reflects the state-of-the-art knowledge of quantum field theory. Sections 4.2 and 4.3 of this final chapter may be considered as a program for future work.

The Nature of Quantum Field Theory

Lagrangian quantum field theory, the branch of quantum field theory that has delivered spectacular predictions in fundamental particle physics, is plagued by divergencies and lacks mathematical rigor. We consider these mathematical difficulties to be self-imposed because the field idealization, which implies limiting procedures, is made too easily and too early in the development of the theory. In doing so, the natural physical ultraviolet and infrared cutoffs given by the Planck length and the size of the universe are dauntlessly ignored.

In this book we have elaborated that, when guided by a number of pertinent philosophical considerations, we naturally arrive at a perfectly healthy, intuitive version of quantum field theory. All the crucial ingredients to quantum field theory can be established a priori, not just as an a posteriori reaction to the occurrence of divergencies or other problems associated with the representation of an infinite number of degrees of freedom. In this section, we briefly summarize the key elements of the theory, that is, of our mathematical image of nature, and discuss some implications for the ontology of the most fundamental theory of matter.

The Image

We choose to consider space and time as prerequisites for developing physical theories. Although we clearly need to respect the space–time transformation behavior of special relativity, we can rely on separate concepts of space and time provided that we choose a particular reference frame. Time appears explicitly in the fundamental evolution equation of our approach; spatial dependencies are eliminated by Fourier transformation.

Philosophical doubts about our ability to handle uncountable sets of degrees of freedom lead us to consider finite volumes of increasing size instead of an infinite space. We thus obtain a countable set of momentum vectors providing a priori infrared regularization. Philosophical considerations moreover suggest that irreversibility, or dissipation, occurs naturally.We thus obtain a dynamic smoothing of fields providing a priori ultraviolet regularization.

“ALL men by nature desire to know,” states Aristotle in the famous first sentence of his Metaphysics. Knowledge about fundamental particles and interactions, that is, knowledge about the deepest aspects of matter, is certainly high if not top on the priority list, not only for physicists and philosophers. The goal of this book is to contribute to this knowledge by going beyond the usual presentations of quantum field theory in physics textbooks, both in mathematical approach and by critical reflections inspired by epistemology, that is, by the branch of philosophy also referred to as the theory of knowledge.

This book is particularly influenced by the epistemological ideas of Ludwig Boltzmann: ”… it cannot be our task to find an absolutely correct theory but rather a picture that is as simple as possible and that represents phenomena as accurately as possible” (see p. 91 of [1]). This book is an attempt to construct an intuitive and elegant image of the real world of fundamental particles and their interactions. To clarify the word picture or image, the goal could be rephrased as the construction of a genuine mathematical representation of the real world.

Consciously or unconsciously, the construction of any image of the real world relies on personal beliefs. I hence try to identify and justify my own personal beliefs thoroughly and in various ways. Sometimes I rely on philosophical ideas, for example, about space, time, infinity, or irreversibility; as a theoretical physicist, I have a limited understanding of philosophy, but that should not keep me from trying my best to benefit from philosophical ideas. Often I rely on successful physical theories, principles or methods, such as special relativity, quantum theory, gauge invariance, or renormalization. Typically I need to do some heuristic mathematical steps to consolidate the various inputs adopted as my personal beliefs. All these efforts ultimately lead to an image of nature, in the sense of a mathematical representation, but they are not part of this image. The final mathematical representation should convince by its intrinsic logical clarity, mathematical rigor, and natural beauty.

Emphasis on the importance of beliefs, even if they are justified by a variety of philosophical and physical ideas, may irritate the physicist. The philosopher, on the other hand, is used to the definition of knowledge as true justified belief. But how can one claim truth for one's justified beliefs?

Introduction

Our concern in this chapter is locality in quantum mechanics (QM). Locality is a heuristic physics principle based on the following propositions.

No Action-at-a-Distance

All the evidence points to the principle that physical actions, taken within restricted (localized) regions of space and time by observers or other agencies such as systems under observation (SUOs), do not cause instantly observable effects on other SUOs at large distances. This does not apply to mathematical/ metaphysical concepts such as quantum wave functions or correlations, as these are conceptual objects (Scarani et al., 2000). Statements about instantaneous wave function collapse are vacuous (have no empirical significance) and are therefore not an issue of significance in physics. Such statements are an issue to theorists who objectivize wave functions, as in Hidden Variables (HV) theory.

Action-at-a-distance is generally regarded as anathema by most physicists. For example, Newton's law of universal gravitation is well known for mathematically encoding action-at-a-distance. There is direct evidence, however, in the form of a letter written by Newton to Bentley, that Newton believed that gravity acting “at a distance through a vacuum without the mediation of anything else” was an absurdity (Newton, 2006).

The no action-at-a-distance principle is encoded in quantized detector networks (QDN) by the requirement that labstate preparation and consequent signal detection never occur at the same stage.

Causal Transmission

All physically observable consequences of local actions taken by an observer or SUO are transmitted by identifiable physical processes, such as electromagnetic waves or neutrinos. There is no such thing as magic or action-at-a-distance.

In QDN this proposition is taken into account implicitly in the labstate outcome amplitudes at each stage, as these model how information is propagated from stage to stage. When necessary, the information void can be modeled as if there were fields and/or particles propagating through it, giving scope for different mathematical models, such as Euclidean space, curved spacetime, noncommuting spacetimes, and so on. The structure of the information void is essentially a discussion of whatever modules have to be taken into account between labstate preparation and signal detection.

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 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.

In a routine optical telescope scan of a distant galaxy, astronomer Alice saw nothing unusual. Her radio astronomer colleague Bob, however, reported intense radio activity in that galaxy. Who had the true view of the galaxy?

This is the sort of question discussed in this book. If you said that Bob had the “true” view of the galaxy, you would be quite normal. Normal, in the sense of average, or typical, or even reasonable. But if you went on to read the rest of this book and understand its main message, you might then give a different answer to that question.

It is not a trick question, however. The “correct” answer is not “Alice has the true view of the galaxy.” Neither is it “Neither of them” nor is it “Both of them.”

This preface is not the place to discuss possible alternative answers to the above question; you should be able to work one out based on the principles discussed in the main text of this book. Although the question is easy to state, the answer we give in the last chapter is simple neither to explain nor to justify. It is best discussed using a lot of words and rather sophisticated mathematical models and technologies. These are introduced, developed, and applied after intensive preliminary discussions of the issues concerned.

Our answer is intimately bound up with the laws of observation as they pertain to quantum processes, the subject matter of this book. These laws are the rules that underpin modern, empirically based perceptions of physical reality (our term for the world of experience). It has taken over two thousand years of philosophical, natural philosophical, and empirical inquiry into the physical universe for some of these rules to be discovered, particularly the ones involving quantum processes. These latter have been understood for only the last hundred years or so, and what they mean is still an active subject of debate. The old question of how many angels can dance on the head of a pin is nothing compared with the question of what the wave function means in quantum mechanics.

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.