The Nomological Interpretation of the Wave Function

Vera Matarese

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.

K. T. Hecht

Valia Allori

In this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.

Kefu Zhu

The law of nature is a core concept in the philosophy of science, but there are significant differences among science philosophers regarding the necessity and connotation of this concept. The current understanding of the law of nature can be roughly divided into two categories – the regularity approach and the necessity approach. How to understand the status of quantum states is a core issue in the philosophy of quantum mechanics. The following analysis focuses on the nomological interpretation of the wave function of quantum mechanics proposed by some scholars of the Bohmian school. To defend this interpretation, supporters have put forward various arguments and carefully distinguished different meanings of “nomology”. This is not only related to the several major approaches to understanding the law of nature that already exist in the philosophy of science but also shows a different perspective from the literature. In particular, these new arguments provide a reference for re-examining the formalism of the quantum histories interpretation.