Introduction to the Pilot Wave Theory

The Pilot Wave Theory, also known as de Broglie-Bohm theory or Bohmian mechanics, is a conceptual framework in physics that offers an alternative interpretation of quantum mechanics. Unlike the widely accepted Copenhagen interpretation, the Pilot Wave Theory posits that particles have definite positions, and the wave function merely guides the particles in their motion. This theory has gained attention as an intriguing and potentially useful approach to understanding quantum phenomena.

Quantitative Assessment of Research Efforts

While qualitative measures of the popularity of different interpretations of quantum mechanics have been attempted, such as the Snapshot of Foundational Attitudes Toward Quantum Mechanics, there has been no comprehensive attempt to quantitatively assess the amount of work done on the Pilot Wave Theory. This essay aims to provide such an assessment, based on a quantitative analysis of published research papers and publications.

Measuring Research Activity

Any measure of research activity must address the complexity and variability in the publication landscape. A straightforward count of the number of people or papers alone is insufficient, as the influence of a highly cited paper should be considered. For instance, a paper by J. S. Bell, a renowned physicist, would have a greater impact than an ordinary paper.

Interpretative Divisions

When excluding the Copenhagen interpretation, the Pilot Wave Theory, a.k.a. de Broglie-Bohm, a.k.a. Bohmian mechanics, has likely received as much attention, or perhaps more, than any other interpretation of quantum mechanics. Here, we can categorize different interpretations into leagues, based on the amount of regular research activity:

Premier League

- Copenhagen Interpretation (considered as the most widely accepted interpretation)

First Division

- Pilot Wave/Bohmian Mechanics - Many Worlds/Everett Interpretation (somewhat above Pilot Wave)

Lower Divisions

- GRW/Self-Assembly Models - QBism (Quantum Bayesianism) - Relational Quantum Mechanics While the Pilot Wave Theory is not the most prolific, it has maintained a steady stream of contributions to both its ontological foundations and to various extensions of the original theory, such as relativistic or quantum field versions.

Rationale for Quantitative Assessment

To gather a rough and ready measure of the amount of work being done on the Pilot Wave Theory compared to the Everett/Many Worlds interpretation, we can conduct a simple search on databases such as arXiv and the Phil-Sci Archive. We will focus on the Physics subject area and consider the period from 2015 to 2017.

Search Term Analysis

Search terms are crucial in conducting such analyses, as they can yield misleading results if not chosen carefully. For example, terms like “Bohm,” “de Broglie,” and “Many Worlds” can include other unrelated meanings. Therefore, we opt for terms that are more specific to the interpretations:

Pilot Wave:

- arXiv: 68 - PhilSci Archive: 19

Everett:

- arXiv: 25 (excluding one astrophysics paper by Mark Everett) - PhilSci Archive: 10 Over the two-year period of 2015 to 2017, these figures suggest that the Pilot Wave Theory is receiving more attention than the Everett/Many Worlds interpretation, although the sample may not be fully representative.

Additional Categorizations

For other interpretations, the following categories are established based on the same time period and sample size:

GRW/Self-Assembly Models:

- arXiv: 10 (after removing papers on Generalized Robertson Walker metrics) - PhilSci Archive: 4

QBism (Quantum Bayesianism):

- arXiv: 12 - PhilSci Archive: 3 While these figures are not conclusive due to the aforementioned limitations, they provide a general indication of the level of attention given to these interpretations.

Challenges in Quantifying Work Done

The most significant challenge in quantifying the amount of work done on the Pilot Wave Theory arises from the diversity of how “work” can be defined. If one counts strictly the research done on the interpretation itself, without considering historical contributions, the Pilot Wave Theory may appear less significant compared to other interpretations. However, if work is measured by the number of papers in which the interpretation serves as the foundational intellectual framework, the Pilot Wave Theory would likely outperform other interpretations by significant margins.

Conclusion

In conclusion, while the Pilot Wave Theory is not the most prolific in terms of research output, it has maintained a steady stream of contributions to both its ontological foundations and its extensions. The quantitative analysis presented here, utilizing databases such as arXiv and PhilSci Archive, suggests that more work is being done on the Pilot Wave Theory than on the Everett/Many Worlds interpretation. Nonetheless, this analysis should be viewed with caution due to the limitations inherent in the methodology and the search terms used.

Keywords

- Pilot Wave Theory - Bohmian Mechanics - Interpretations of Quantum Mechanics