The sky is blue, and other reasons quantum mechanics is not underdetermined by evidence

Abstract: I criticize the widely-defended view that the quantum measurement problem is an example of underdetermination of theory by evidence: more specifically, the view that the unmodified, unitary quantum formalism (interpreted following Everett) is empirically indistinguishable from Bohmian Mechanics and from dynamical-collapse theories like the GRW or CSL theories. I argue that there as yet no empirically successful generalization of either theory to interacting quantum field theory and so the apparent underdetermination is broken by a very large class of quantum experiments that require field theory somewhere in their description. The class of quantum experiments reproducible by either is much smaller than is commonly recognized and excludes many of the most iconic successes of quantum mechanics, including the quantitative account of Rayleigh scattering that explains the color of the sky. I respond to various arguments to the contrary in the recent literature.

• The paper demonstrates that alternative quantum interpretations lack comprehensive empirical coverage compared to unitary quantum mechanics and QFT.
• It critically examines how Bohmian mechanics and collapse theories fail to model many phenomena accurately observed in non-relativistic quantum experiments.
• Wallace refutes the Quantum Underdetermination Thesis by arguing that experimental evidence overwhelmingly supports standard, unitary quantum mechanics.

Quantum Mechanics and the Fallacy of Underdetermination

The paper "The sky is blue, and other reasons quantum mechanics is not underdetermined by evidence" by David Wallace critically examines the prevalent belief in the field of quantum mechanics that several interpretations and theories, including the Everett interpretation, Bohmian mechanics, and dynamical collapse theories, are empirically indistinguishable. Wallace challenges the Quantum Underdetermination Thesis (QUT), which posits that these theories cannot be distinguished by empirical evidence and are thus equally valid. This essay offers a comprehensive overview of Wallace's argument and insights into its significance for the foundations of quantum mechanics.

Wallace argues that the assumption of empirical equivalence among these competing quantum theories is unfounded. He asserts that the scope of experiments that can be accurately described by Bohmian mechanics or dynamical collapse theories is much narrower than commonly perceived. Furthermore, he points out that many significant experimental successes of quantum mechanics, particularly in the domain of Quantum Field Theory (QFT), are beyond the reach of these alternative theories.

Wallace's paper provides several dimensions to the discourse:

1. Empirical Adequacy and Quantum Experiments: Wallace emphasizes that the range of quantum experiments that can be modeled entirely within non-relativistic quantum mechanics (NRQM) and, by extension, within Bohmian or dynamical-collapse frameworks, is limited. He illustrates through examples such as Rayleigh scattering and spectral lines that many everyday quantum phenomena involve interactions that are fundamentally quantum electrodynamical in nature and require QFT for their explanation.
2. Role of Quantum Field Theory: The author critically evaluates the inability of both Bohmian mechanics and dynamical collapse theories to extend beyond NRQM to QFT. He argues that the indirect relationship between microscopic quantum field theories and macroscopic phenomena in QFT challenges attempts to simulate these phenomena through alternative theories that rely on precise, microphysically stateable variables.
3. Critique of the Quantum Underdetermination Thesis: Wallace refutes the claims of QUT proponents by demonstrating that no current versions of Bohmian mechanics or dynamical-collapse theories cover the comprehensive empirical successes achieved by unitary quantum mechanics. He contends that if significant portions of quantum phenomena cannot be accounted for by these alternative theories, the thesis of empirical equivalence and hence underdetermination collapses under its own weight.
4. Future Directions and Implications: While suggesting that QUT is false due to the lack of comprehensive empirical coverage by alternatives beyond unitary quantum mechanics, Wallace acknowledges that the development of a hidden-variable or dynamical-collapse theory that is empirically competitive with QFT would theoretically provide an instance of underdetermination. Such an advancement, however, remains speculative and unsupported by current scientific achievements.

The paper's implications are far-reaching for both theoretical and practical aspects of quantum mechanics. Theoretically, Wallace's findings stress the importance of recognizing the empirical breadth of unitary quantum mechanics and challenge the position that quantum mechanics is underdetermined by evidence. Practically, this call to critically evaluate the actual empirical successes of alternative theories prompts the community to either substantiate or reconsider the pursuit of these theories in light of their limited scope.

In conclusion, David Wallace provides a robust critique of the notion that quantum mechanics is characterized by underdetermination. His analysis foregrounds the empirical inadequacies of Bohmian mechanics and dynamical-collapse models in the broader quantum mechanical landscape dominated by QFT. This recognition not only clarifies the standing of various interpretations in quantum mechanics but also reinforces the necessity of empirical success as a criterion for evaluating the validity and future potential of any scientific theory.