Abstract Since the Modal-Hamiltonian Interpretation (MHI) is based on the formalism and the minimal interpretation of Standard Quantum Mechanics (SQM), this chapter may seem superfluous: it could be argued that everyone knows what SQM is. However, as remarked in the previous chapter, the identification of SQM is not as immediate as is usually assumed. Therefore, if an interpretation of quantum mechanics is to be precisely developed, the underlying theoretical commitments must be clear from the very beginning. The second reason why this chapter is not superfluous is that the MHI differs from the traditional Hilbert space formulation of SQM by adopting the algebraic formalism as its departing point. Although this might seem a minor formal detail, it will play a central role in the ontological picture arising from the MHI interpretation, as will be seen in Chapter 10.
Abstract Since the Modal-Hamiltonian Interpretation (MHI) is based on the formalism and the minimal interpretation of Standard Quantum Mechanics (SQM), this chapter may seem superfluous: it could be argued that everyone knows what SQM is. However, as remarked in the previous chapter, the identification of SQM is not as immediate as is usually assumed. Therefore, if an interpretation of quantum mechanics is to be precisely developed, the underlying theoretical commitments must be clear from the very beginning. The second reason why this chapter is not superfluous is that the MHI differs from the traditional Hilbert space formulation of SQM by adopting the algebraic formalism as its departing point. Although this might seem a minor formal detail, it will play a central role in the ontological picture arising from the MHI interpretation, as will be seen in Chapter 10.
Abstract In Chapter 4, the MHI was introduced in terms of interpretative postulates that define the ontological reference of each physical term of quantum mechanics in its standard formulation. On the basis of that presentation, an ontology of properties, framed in the algebraic formalism of quantum mechanics, was proposed. The aim of this chapter is to set out in detail the structure of the ontology proposed by the MHI, now with the technical metaphysical resources developed in the previous chapter. In particular, the nature of the properties that constitute the fundamental ontological items is discussed, and it is argued that quantum systems are not objects at all, but mere collections of properties that do not retain their identity either synchronically or diachronically. More precisely, quantum systems turn out to be non-objectual bundles of properties.
Abstract Since the aim of this book is to introduce the Modal-Hamiltonian Interpretation (MHI) in a comprehensive way, this chapter focuses on the family of Modal Interpretations of quantum mechanics, to which the MHI belongs. The purpose is, then, to recall the common features of the Modal Interpretations as well as the differences between them. In particular, the original proposal of van Fraassen is presented, and the Biorthogonal-Decomposition Modal Interpretation, the Spectral-Decomposition Modal Interpretation, the Atomic Modal Interpretation, and the Perspectival Modal Interpretation are described, pointing out their advantages and limitations.
Abstract Standard Quantum Mechanics is a theory that has been applied to many concrete physical situations and by means of which an impressive amount of experimental evidence has been accounted for. Therefore, a “good” interpretation must not only meet the traditional interpretative challenges of the theory, but must also show its agreement with the orthodox practice of physics. This chapter is devoted to argue for the physical relevance of the MHI by applying it to well-known models and experimental results, which will be presented in the usual physical language. In particular, it is applied to the free particle, free particle with spin, harmonic oscillator, free hydrogen atom, Zeeman effect, fine structure, decoherence, the Born-Oppenheimer approximation, the problem of symmetry in quantum chemistry.
Abstract In the present chapter, the Modal-Hamiltonian Interpretation (MHI) is introduced in terms of interpretative postulates. These postulates distinguish between type-properties and case-properties, and define quantum systems as bundles of properties. The Hamiltonian of the system plays a central role in the definition of systems and subsystems. Moreover, according to the MHI-Actualization Rule, the selection of the preferred context is based on the Hamiltonian. In this chapter, the MHI is introduced in a neutral way, without discussing its advantages over other proposals. The arguments supporting it will become clear in the following chapters, where its physical relevance will be explained (Chapter 5) and it will be applied to solve traditional interpretative challenges (Chapter 6).
This chapter, based on the background information of the previous chapter, will review the formalism of quantum mechanics – its fundamental mathematical structure (the basic contents of Hilbert space representation and operator algebra representation) and physical assumptions (kinematics, dynamics, and measurement theory). These are the premise and foundation for discussing the quantum histories interpretation. Then, in combination with the viewpoints of some literature in recent years, we will explore what is the interpretation of quantum mechanics, analyze the relationship between the theory of quantum mechanics and its interpretation, and declare the author’s basic stance on these two issues. These two are the primary issues that all interpretive work in the philosophy of physics will face (not limited to the interpretation of quantum mechanics), and the necessary clarification here is also conducive to the subsequent discussion. Three common terms – theory, formalism, and interpretation – are explicated and differentiated by offering the necessary definitions of their meanings, based on the works of Acuña and Ruetsche. The clarification will help to make the subsequent related discussions more precise.
The paper investigates the existence and the nature of quantum indeterminacy in a particular realist interpretation of quantum mechanics, that is, the Modal Hamiltonian Interpretation (MHI)-together with an ontology of properties for quantum systems. In doing so, it serves a twofold purpose. First, it advances the debate on quantum ontology by showing precisely how and why indeterminacy arises in a quantum world-as described by the MHI. Second, it offers a naturalistic example of genuine metaphysical indeterminacy, an example coming from our best physics.