This chapter provides, we believe, for the apogee of what we think will form the base for success of the quantum physics–like applications. Readers are invited in this chapter to carefully study the two-slit interference experiment with agents (and the agent two-preference interference) for a variety of real potential functions.

This chapter starts with a discussion on models informing probability versus the case where probability is inherent in the model. The chapter also goes into detail to argue why a particular interpretation of quantum mechanics, Bohmian economics, can be useful in finance. We provide for an example of how such mechanics can be applied to daily returns on commodity prices. We also briefly look into the potential connection between Bohmian mechanics and a macroscopic fluid system.

The chapter begins by answering the question “how did physics, which originally represented the philosophy of nature, evolve into its modern phase of the philosophical as well as the scientific knowledge of nature” in terms of a brief history of physics. This is presented in the form of four chronological phases – ancient times, the scientific revolution, the birth of modern physics and the modern version of the quest for the nature of reality. This is followed by the authors’ interpretation of the generic structure of the physical theories of motion and by the application of the interpretation to the problem of “the motion of a particle under gravity”. We then introduce the reader to three key features which characterize financial and economic systems: markets, decision making, and the economic actor. The chapter goes into some detail on each of these three ingredients. The chapter ends by providing the abstracts of the remaining chapters.

We start in this chapter arguing why quantum probability is a good candidate for modelling purposes in decision-making contexts. The quantum formalism, in this chapter, centres around the argument that such formalism can accommodate paradoxical outcomes in decision making. Quantum probability offers a response to those decision-making contexts where a consistent violation of the law of total probability occurs. Strong results have been obtained in decision-making applications and we go into some detail to discuss the so-called QQ equality and the Aumann theorem.

One of the main purposes of this chapter is to explain, albeit in an abstract manner, how quantum physics–like models of the economics-finance contexts would differ from quantum math-like (or simply, quantum-like) models. For this, the chapter begins by considering, what may be called, the “physical” foundations of quantum theory. These include the foundations pertaining to the theoretical, experimental, and interpretational aspects of quantum theory. With reference to the physical foundations, the chapter elaborates on certain expectations from agent-centric economics-finance models to qualify as “quantum physics–analogous”. Then, by briefly reviewing some of the prominent theories of analogical arguments and reasoning from the philosophy of science (for instance, Aristotle’s theory, Hesse’s theory, Gentner’s structure-mapping theory and Bartha’s articulation model), the chapter ends by proposing a strategy for the systematic construction of quantum physics–analogous models of economics and finance.

In this last chapter of the book, we keep coming back to the potential function and we attempt to connect it to more precise ideas in finance, including that of the agent heterogeneities. We also initiate a discussion on agent behaviour and causality and nonlocality. Our last words in this book will be centred on what comes next. One of the key queries we have is whether we can consider more complicated real potentials in the two-slit interference experiment with agents (and the agent two-preference interference). The other one is centred around the investigation on the nonexistence of “spooky” free will of the individual agents.

This chapter attempts to expound on basic and essential ideas (for further use in the book) from both classical and quantum mechanics. The chapter is somewhat technical in nature but only requires an elemental knowledge of calculus. The first three sections take a review of some of the elements of classical mechanics and classical statistical mechanics – the Euler–Lagrange and the Hamilton–Jacobi equations, the idea of an ensemble in the classical context, and the continuity equation for particle density. The remaining part is devoted to the elements of quantum mechanics – the connection between the Hamilton–Jacobi equation and the Schrödinger equation, the idea of an ensemble in the quantum context, the free particle wave function and operators, the uncertainty principle and the idea of the expectation value of an operator, and the concept of a wave packet.

This chapter (together with the next one) introduces probably the highlight of the book, i.e. it attempts to answer the important question: what can we now do with the quantum-physics like stance? An immediate, almost obvious, discussion centres around the analogies with the famed double-slit experiment. We set ourselves the task of answering how we can begin to enumerate, quite precisely, analogies between electrons and agents. As the reader will find out, we will need to move over several (important) hurdles, one of them being the perennially difficult analogy we need to make with the Planck constant. We then proceed in shaping the idea of two-preference interference, a concept of paramount importance in our quest to properly define the quantum physics–like research direction.

This chapter provides for a summary overview of some of the great movements in economic science. We discuss theory falsification and the historical role of the observable in economics. We provide for a brief overview of behavioural and experimental economics, as well as computational and neuroeconomics. We conclude the chapter with some ideas on the value of information in the price process.