In this and the following chapter I apply the present interpretation of quantum mechanics to coupled systems of the type studied by Einstein et al. (1935), Bohm (1951), Bell (1964), and Aspect et al. (1982a, 1982b) (to name just a few seminal contributors to the large and growing literature on this topic). The main conclusions were already anticipated in Chapter 1. In the present interpretation, quantum mechanics offers a detailed theoretical account of the physical events and processes that underlie the correlations exhibited in measurements on such systems. This account depends both on the postulation of irreducible properties of compound systems, and also on the treatment of measurement as a quantum mechanical interaction. In the present chapter I present technical details of this account, and in the next chapter I explore its metaphysical aspects and implications, especially for the notions of holism and causal explanation. For concreteness, I restrict attention here to systems composed of two spin-½ atomic systems: The generalization to other pairs of systems with different spins is straightforward. Such systems may result from a prior interaction between the two component systems, or they may be produced de novo (as a positron-electron pair may be produced by annihilation of a γ-ray). Call the component systems A, B and the compound system A⊕B . The system representative of A⊕B will be a subspace of the tensor product Hilbert space H A ⊗H B .
In this and the following chapter I apply the present interpretation of quantum mechanics to coupled systems of the type studied by Einstein et al. (1935), Bohm (1951), Bell (1964), and Aspect et al. (1982a, 1982b) (to name just a few seminal contributors to the large and growing literature on this topic). The main conclusions were already anticipated in Chapter 1. In the present interpretation, quantum mechanics offers a detailed theoretical account of the physical events and processes that underlie the correlations exhibited in measurements on such systems. This account depends both on the postulation of irreducible properties of compound systems, and also on the treatment of measurement as a quantum mechanical interaction. In the present chapter I present technical details of this account, and in the next chapter I explore its metaphysical aspects and implications, especially for the notions of holism and causal explanation. For concreteness, I restrict attention here to systems composed of two spin-½ atomic systems: The generalization to other pairs of systems with different spins is straightforward. Such systems may result from a prior interaction between the two component systems, or they may be produced de novo (as a positron-electron pair may be produced by annihilation of a γ-ray). Call the component systems A, B and the compound system A⊕B . The system representative of A⊕B will be a subspace of the tensor product Hilbert space H A ⊗H B .
As the previous chapter made clear, in the present interpretation quantum mechanics gives a rather specific account of EPR-type correlations and what underlies them. In the present chapter I argue that this account is genuinely explanatory (rather than merely an idle overlay on a simple description of the observed correlations), and that this constitutes a significant advantage of the present interpretation over certain rival interpretations, on which quantum mechanics is unable to offer an adequate explanation of the observed correlations. In order to make this argument it will prove necessary to examine the character of causal explanation in theoretical science, and in particular to develop a coherent metaphysics of a kind of holistic, nonseparable, causal explanation. I take the development of such a coherent metaphysics to constitute a significant task independent of the details of the present interpretation of quantum mechanics. Quantum mechanics is a mine of metaphysical insights, and I hope here at least to have exposed a rich seam. The first task is to defend the adequacy of the present account of EPR-type correlations as at least a coherent description of what may underlie the observed correlations. I foresee three main challenges to its descriptive adequacy. The first is to claim that the account is incompatible with the relativistic requirement that there can be no direct causal connection between spacelike-separated events, and must therefore be rejected. A weaker version of this challenge is to claim that although the incompatibility just mentioned may not by itself entail rejection of the account, it does seriously undermine its claim to be genuinely explanatory.
In Section 2.4 we learned that a composite quantum system, composed of two subsystems A and B , is associated with a tensor product space HA ? HB . Composite quantum systems have already played an important role in many instances in this text, especially in open systems and measurement models. In this chapter we dive deeper into tensor product spaces, discovering some strange implications of the quantum theory of composite quantum systems. As a result of its tensor product structure, quantum theory has embedded into it the phenomenon of entanglement , which is often seen as the foremost quantum feature. As early as in 1935 it puzzled Erwin Schrödinger, who introduced the German term Verschränkung [127] and Albert Einstein, who, together with Boris Podolski and Nathan Rosen, used the specific example of an entangled state to argue that quantum theory is incomplete [58]. In the 1960s John Bell demonstrated that the consequences of entanglement are incompatible with the Einstein– Podolsky–Rosen model of local realism [11], [12]. In recent years entanglement has been recognized as the resource for quantum information processing. Nowadays entanglement theory is a highly developed subject, and we can present only the mathematical basics. For the reader with a deeper interest in entanglement we recommend the recent reviews by Horodecki et al . [80] and Plenio et al . [118], which also cover the quantum information aspects of entanglement. To simplify our discussion we will assume that the Hilbert spaces are finite dimensional.
Since this book is closely connected to quantum mechanics, these introductory words will briefly and informally recall some postulates of this theory. Interested readers are urged to consult traditional books on quantum mechanics to complement the discussion ahead and for descriptions of experimental evidence that give rise to the postulates. In physics there are several “equivalent formulations” of quantum mechanics, and a catalogue of the most important appears in [StyO2]. The discussion here is restricted to the nonrelativistic case.
In quantum mechanics, quantum nonseparability is at the core of philosophical debates regarding its meaning. In the context of the process matrix formalism, causal nonseparability characterises quantum processes (connecting the inputs and outputs of different local quantum operations) that are incompatible with any definite causal structure among interacting parties. One talks about indefinite causal orders. A famous example of causally nonseparable processes is called the quantum switch (QS). It is extensively studied in the literature in virtue of its simple architecture and its various implementations in laboratories.The present work will discuss the possible interpretations of the QS's causal nonseparability under the assumption that causal nonseparability is seen as pointing towards novel objective features of nature.It was first defended that a scientific realist approach towards the process matrix formalism, which is an operational theory generalising quantum mechanics, was as much legitimate as any possible antirealist reading, contrary to certain views found in the literature. The reason is that operational formalisms are ontologically and epistemically neutral.From there, the theoretical concepts of interest, namely causal nonseparability and its model-independent counterpart called noncausality, were analysed in more details, in order to highlight in what sense they are distinct from the standard notions of quantum nonseparability and nonlocality in quantum mechanics.The discussion then focused on noncausality. It was argued that noncausality has a strong connection with a notion of temporal nonlocality. In the same way that Bell nonlocality is given different underlying explanations depending on the details of the chosen quantum mechanics' account, noncausality pointing towards temporal nonlocality can be given a variety of underlying descriptions depending on the exact way to interpret the process matrix formalism.The last chapter focused precisely on this particular point, namely on the various ways to understand process matrices and causal nonseparability in a realist context. In order to explore the potential impact of causal nonseparability on spacetime,we shifted from the notion of (indefinite) causal structure to (indefinite) spatiotemporal ones. This shift was allowed under a set of reasonable assumptions regarding the properties of a physical spacetime manifold and the connection between an operational and relativistic notions of causal relations.While different readings were suggested for indefiniteness of spatiotemporal relations, we insisted in particular on an objective understanding appealing to the concept of metaphysical indeterminacy. It was argued that such an approach could prove useful in a more general theoretical context such as quantum gravity, while being already partly supported in standard quantum mechanics.
From the preceding exposition it follows that the quantum statistical representation of an individual atomic system does not imply any renunciation regarding further knowledge about the system. On the contrary the statistical character of quantum physics directly reflects the fundamental non-causal appearance of quantal recordings, and through the discovery of the complementarity of quantal phenomena a complete but necessarily statistical description of the atom has been accomplished. Furthermore quantum physics has afforded a statistical description of macroscopic bodies through their representation as assemblies of huge numbers of identical atomic systems, and, apart from accounting in a more fundamental way for the properties already described in classical physics(the correspondence principle, p. 36), quantum statistics explains several macroscopic phenomena which cannot be understood within the conceptual frame of classical physics only. It must be maintained, however, that when observing the properties of individual atomic objects the macroscopic observational apparatus cannot be represented in terms of atomic constituents because this would destroy the unambiguity of the description. The observational apparatus fulfils its basic function of being the spacetime frame of reference for the quantal recordings precisely through its description in classical physics alone. However, when refraining from the analysis of individual quantal processes it is possible to apply quantum statistics to macroscopic phenomena, that is, the causality of classical physical phenomena can be interpreted in the quantum formalism as the statistical result of the interplay of enormous numbers of atomic processes. It is possible, then, to talk of statistical causality as a fundamental aspect of physical reality.
This thesis aims to explore the relationship between the science, the philosophy and the esoteric imagination of the American physicist David Bohm (1917-1992). Bohm is recognized as one of the most brilliant physicists of his generation. He is famous for his ‘hidden variables’ interpretation of quantum mechanics. Bohm wrote extensively on philosophical and psychological subjects. In his celebrated book Wholeness and the Implicate Order (1882) he introduced the influential ideas of the Explicate and the Implicate orders that are at the core of his process philosophy. Bohm was also a very close disciple of the Indian teacher Jiddu Krishnamurti (1895-1986), whom he recognized to have had an important influence on his thought. Chapter 1 is a general explanation of what I intend to do, why my research is filling an important gap, introduce the field of Western esotericism as a scholarly subject and suggesting that it offers a fruitful way of approaching the thought of David Bohm. I also explain my research principles and a brief description of the philosophical standpoint from which I am approaching the material. Chapter 2 gives a description of the textual sources I used in my research. This is followed by a comprehensive literature review. Chapter 3 is a biographical essay where I give an account of Bohm’s life, career, works, major ideas and their development, stressing their significance for the development of Bohm’s holistic philosophy and his interactions with the esoteric. This chapter is an introduction to the main ideas of the dissertation. Chapter 4 revisits the genesis of the Causal Interpretation, Bohm’s first attempt to deal with the interpretation of quantum mechanics. I make emphasis on the philosophical developments that gave rise to it. I introduce all the relevant physics and give a detailed explanation of the problem of interpretation and Bohm’s first proposal. Chapter 5 is about the philosophical developments in Bohm’s thought brought by the Causal Interpretation. In particular I examine the influence that G. W. F. Hegel (1770-1831) had on Bohm’s thought and explain why I take the view that this is an esoteric influence. Chapter 6 reviews the developments in Bohm’s thought during the 1960’s. I describe Bohm’s search for radically new concepts in physics and his exchanges with several thinkers ending with his encounter with Jiddu Krishnamurti. Chapters 7 and 8 are devoted to the study of Bohm’s philosophy as he elaborated it after 1960. Chapter 7 concentrates on the idea of the Implicate Order and it also studies the Ontological Interpretation of Quantum Mechanics, Bohm’s last version of his interpretation effort, which is based on the Implicate Order. In chapter 8 I examine Bohm’s theory of how the mind and the body are connected through a ladder of consciousness formed by a series of Explicate and Implicate Orders, and finishes with an exposition of Bohm’s dialogue technique. In the last chapter I summarize my conclusions. An appendix is included with a brief overview of Bohm’s legacy. All the relevant details about the esoteric currents that Bohm encountered during his life and that are required to understand our argument are introduced as they are needed throughout the main body of the text.