Chapter 15. The History of Quantum Mechanics

V. S. Olkhovsky

It shortly described a far from being completed history of quantum mechanics-quantum theory of measurements.Furthermore, there was a relatively recently finished chapter of quantum mechanics which for a long time had not been resolved.This chapter is dedicated to time as a quantum observable, canonically conjugated to energy.And the mathematical reasons for its principal resolving are explained.

Pieter Kok

Kefu Zhu

To revisit and analyze the histories formalism of quantum mechanics, this chapter will refer to the basic idea of the nomological interpretation of the quantum wave function as described in the previous chapter. The quantum wave functions can be interpreted as nomological and non-ontological elements of Bohmian mechanics. This inspires us that, in quantum histories formalism, the multiple conditions/criteria of determining the possible families of histories, whose validity can be examined by reasonable tests regarding the properties of subsystems, can be argued as lawful or nomological, while the quantum histories can be argued as the fundamental physical reality. We will specifically focus on this novel depiction of the formalism concerning quantum reality, which enables us to reconsider the numerous objections to the histories interpretation that were raised in previous chapters and re-examine/resolve from the nomological perspective the several aforementioned ontological and logical issues of quantum histories interpretation. However, there still remain challenging issues in the understanding of quantum histories.

Jean Bricmont

Daniel R. Bes

Kefu Zhu

This chapter discusses the main points and thought sources of the quantum histories interpretation. Section 3.1 introduces its core concepts, theoretical assumptions, and basic formalism first, as well as how probability calculations and propositional reasoning are performed here, and shows how this interpretation depicts the process by which (quasi-)classicality is derived from quantum histories. Section 3.2 sorts out the five important thought sources from which it emerges: the Copenhagen interpretation, Feynman’s sum-over-histories formulation of quantum mechanics, Wigner’s measurement theory, Everett’s relative state interpretation or many-worlds interpretation, and the mechanism of decoherence. Their respective correlations, similarities, and differences with the quantum histories interpretation are briefly analyzed. In the appendix to this chapter, three notorious paradoxes showing intractable aspects of quantum mechanics, namely the Einstein-Podolsky-Rosen (EPR) paradox, Wheeler’s delayed choice gedankenexperiment, and Frauchiger–Renner paradox, are formulated via history chain operator analysis in the quantum histories formalism.