Publication and dataset for "Has Anything Changed? Tracking Long-Term Interpretational Preferences in Quantum Mechanics"

Accepted: 24 May 2025 © The Author(s) 2025 Petr O. Jedlička [email protected] 1 Faculty of Philosophy and Arts, University of West Bohemia, Sedláčkova 19, Pilsen 306 14, Czechia 2 Institute of Philosophy, Czech Academy of Sciences, Jilská 361/1, Prague 1, 110 00, Czechia 3 Department of Physics and NTIS– European Centre of Excellence, University of West Bohemia in Pilsen, Univerzitní 8, Pilsen, 301 00 , Czechia 4 Institute of Information Theory and Automation, Czech Academy of Sciences, Pod Vodárenskou věží 1143/4, Prague 182 00, Czechia Has Anything Changed? Tracking Long-Term Interpretational Preferences in Quantum Mechanics Petr O.Jedlička1,2 · ŠimonKos3· MartinŠmíd4· JiříVomlel4· JanSlavík3 Foundations of Science https://doi.org/10.1007/s10699-025-09993-0 Abstract As we approach the centennial anniversary of modern quantum mechanics, this paper revisits the foundational debates through a new poll within the research community. Inspired by the survey by Schlosshauer, Kofler, and Zeilinger at the specialized 2011 Quantum Physics and the Nature of Reality conference, we expanded our recruitment to include a more representative sample of the broader community of physicists with the aim of revealing potential shifts in scientists’ views and to compare our findings with those from several previous polls. While quantum foundations still lack a consensus interpretation, our results indicate a persistent preference for the Copenhagen interpretation. This enduring support likely reflects both the educational emphasis on the Copenhagen interpretation and its pragmatic appeal in avoiding complex metaphysical questions and introducing new notions (e.g., other worlds or the pilot wave). Our findings thus underscore the relative stability of interpretational preferences over the past decades. Keywords Quantum foundations · Quantum interpretations · Copenhagen interpretation · Everett’s interpretation · De Broglie–Bohm interpretation 1 Introduction There is a long history of foundational debates in quantum mechanics dating back to its early years, attributable to its profound impact on established views of reality, causality, and measurement. The so-called Copenhagen interpretation, primarily based on the views 1 3 P. O. Jedlička et al. of Bohr and Heisenberg, emerged in the late 1920s and early 1930s. However, the term itself was not coined until 1955 when Heisenberg (1958) introduced it in defense against the unorthodox de Broglie–Bohm alternative1. Notably, even Bohr and Heisenberg ostensibly differed on several issues, such as mathematical formalism and the role of measurement (Camilleri & Schlosshauer, 2015). This interpretation was initially challenged by Einstein’s thought experiments, mostly on the grounds of purported incompleteness at two Solvay conferences. His line of argumentation became the core of the Einstein–Podolsky–Rosen paper in 1935, which highlighted what they perceived as existing problems of quantum mechanics but did not lead to any alternative interpretation. Equally important for subsequent developments was the notion of hidden variables and the pilot-wave theory, proposed by de Broglie and presented in his 1924 thesis and at the 1927 Solvay conference. Among other initial skeptics with lingering doubts about the Copenhagen interpretation was Schrödinger. Nevertheless, the Copenhagen interpretation acquired a status close to hegemony over the years. Yet, its tenets have been questioned over the years by alternative theories or interpretations, among them Bohmian mechanics (1952), Everett’s many-worlds interpretation (1957), and various quantum-information interpretations and their offshoots, such as the ensemble interpretation, consistent histories interpretation, and quantum Bayesianism. Interest in foundational questions has been sustained by ongoing experimental and theoretical progress, including work on Bell’s inequalities and their tests, decoherence, and quantum information. In this debate, various interpretations experience swings in popularity in the community of physicists, without a final resolution or consensus that goes beyond accepted mathematical formalism and undisputed experimental results. On the other hand, there are also minimalist views which deny the necessity of discussing interpretations at all or consider mathematical formalism itself to be an interpretation (Fuchs & Peres, 2000). 2 Past Polls Scientific surveys cannot settle foundational questions in physics, but they can provide insight into how the research community’s perspectives evolve in response to theoretical advancements and experimental developments. In the context of quantum mechanics, polls tracking interpretational preferences offer a snapshot of prevailing attitudes. Over the years, multiple surveys have aimed to map these preferences, examining not only the most favored interpretations but also the underlying associations between different conceptual positions. The polls on quantum foundations in the past have been conducted mostly at conferences– by Tegmark (1998), Schlosshauer et al. (2013), Norsen and Nelson (2013)– or as online polls by Sivasundaram and Nielsen (2016), with dual goals: determining preferred interpretations and elucidating views on central questions (randomness, entanglement, measurement, observer, etc.), and examining whether there are any correlations between the 1 Although de Broglie’s and Bohm’s pilot-wave interpretations are today often merged into one, they also differ in several aspects. De Broglie (1987) originally conceived the wave as a physical wave in threedimensional space, and later further developed this theory. Bohm completed the pilot-wave theory to include the quantum potential and generalized it for the many-particle cases; however, his version does not require the physical existence of a particle-generated quantum wave. See also Croca et al. (2021), or Castro, Bush, and Croca (2024). 1 3 Has Anything Changed? Tracking Long-Term Interpretational Preferences… answers. In the following, we will provide a chronologically ordered short overview of their main findings from these polls. Tegmark’s original paper (1998) sought to correct common confusion around certain postulates in Everett’s many-worlds interpretation and explain its metaphysical and epistemological consequences. Another reason for conducting the poll was to dispel the then widespread notion of the hegemony of the Copenhagen interpretation and the argument that MWI is only a minority stance held by physicists with “non-standard views” about science. Among 48 participants in Tegmark’s poll, which took place in August 1997 at the University of Maryland quantum mechanics workshop, the Copenhagen interpretation secured first place when 27% of participants voted for it. However, MWI came in second with 17%, followed by the Bohmian interpretation at 8%, leading Tegmark to view these results as a sign of waning interest in the once-dominant Copenhagen interpretation. He also noted that, apart from the universal computational practices, the choice of interpretation of quantum phenomena remains purely a “matter of taste”. At the conference Quantum Physics and the Nature of Reality, held in July 2011 at the International Academy Traunkirchen in Austria, Schlosshauer et al. (2013) repeated the poll on the favorite interpretation, with a total of 33 participants (a mix of affiliations in physics, philosophy, and mathematics). To gain more comprehensive insights, they expanded its scope to 16 multiple-choice questions covering the most relevant issues and open questions about quantum foundations, i.e., quantum ontology and behavior, the nature of measurement and observer, relations between classical and quantum worlds, and our possible knowledge of them, as well as meta-questions concerning future developments of the field, changes in interpretations, etc. Among the findings that received strong support were the following: superpositions of macroscopically distinct states are in principle possible (67%); randomness is a fundamental concept in nature (64%); Einstein’s view of quantum theory is wrong (64%); personal philosophical prejudice plays a large role in the choice of interpretation (58%); the observer plays a fundamental role in the application of the formalism but plays no distinguished physical role (55%); physical objects have their properties well defined prior to and independent of measurement in some cases (52%); the message of the observed violations of Bell’s inequalities is that unperformed measurements have no results (52%). When the answers were correlated, the authors found diverse relationships, some of which “transcended the traditional lines” such as Bohr-versus-Einstein, nonrealist-versusrealist, and epistemic-versus-ontic. While some of the patterns in data were expected, such as those who regarded the measurement problem as a pseudo-problem also tended to favor the Copenhagen interpretation (with its nuanced original arguments concerning these issues), refute Einstein’s view, and consider quantum randomness as fundamental etc., others defied easy interpretation. However, the overall conclusion was that despite the mature mathematical formalism and predictive success, quantum theory still does not lend itself to a consensual interpretation. In 2013, Norsen and Nelson (2013) ran a sequel to this poll with 76 participants at a conference Quantum Theory Without Observers III, held in Bielefeld, Germany. Here, the results again demonstrated the existence of “sub-communities with quite different views,” and led the authors to believe that “there is probably even significantly more controversy about several fundamental issues” than had been revealed in previous polls. The authors also found strong support for the de Broglie–Bohm interpretation among the participants 1 3 P. O. Jedlička et al. (63%), compared to only 4% for the Copenhagen interpretation, which they inferred was the result of the invitation process favoring scientists with kindred “realist” views. Sivasundaram and Nielsen (2016) conducted an online poll with a slightly different set of questions, polling 149 physicists of all specializations from eight universities in several countries, which secured a sample of physicists that is the most representative of all polls. The Copenhagen interpretation garnered the highest rate with 39%, with only 6% for Everett’s interpretation (many worlds or/and many minds), 2% for the de Broglie–Bohm interpretation, and 17% in total for other interpretations. Altogether, 36% of the sample had no preferred interpretation. Crucially, the authors came to the conclusion that “foundational concepts in quantum mechanics are still a topic that only a minority of physicists are familiar with,” although they deem it important. 3 Methodology 3.1 Questionnaire Our questionnaire was based on the 16 multiple-choice questions formulated by Schlosshauer, Kofler, and Zeilinger. For the polls, we selected 10 questions that we deemed most relevant (there was a limited total length for the poll questionnaire). Prior to full deployment, the questionnaire was piloted with several physicists not specializing in quantum foundations. Feedback led to minor wording adjustments that improved clarity without changing substantive content. No further validation was performed. Here are the questions and response options (for those used in further analysis with their italicized abbreviations): Q1. What is your opinion about the randomness of individual quantum events (such as the decay of a radioactive atom)? (Rnd): The randomness is only apparent (RndApp); There is a hidden determinism (HidDet); The randomness is irreducible (RndIrred); Randomness is a fundamental concept in nature (FundRnd). Q2. Do you believe that physical objects have their properties well defined prior to and independent of measurement? (Wdp): Yes, in all cases; (Yes); Yes, in some cases: (Some); No; I’m undecided (NotKnow). Q3. Is the quantum mechanical description of reality by a wave function complete? To which alternative are you inclined? (Wdr): No, the wave function description of reality is not complete (A. Einstein) (Einstein); The description of reality by a wave function is complete (N. Bohr) (Bohr); I don’t know, there is another way. (Other) Q4. The measurement problem is (Msr): A pseudo-problem (Pseudo); Solved by decoherence (Decoher); Solved/will be solved in another way; A serious difficulty threatening quantum mechanics (Serious); None of the above (None). Q5. What interpretation of quantum states do you prefer? (Qs): Epistemic/informational (Epistem); Ontic (Ontolog); A mix of epistemic and ontic (Comb); Purely statistical (e.g., ensemble interpretation) (Stat); Other. Q6. The observer (Obs): 1 3 Has Anything Changed? Tracking Long-Term Interpretational Preferences… Is a complex (quantum) system: (Complex); Should play no fundamental role whatsoever; Plays a fundamental role in the application of the formalism but plays no distinguished physical role: (ApplForm); Plays a distinguished physical role (e.g., wave-function collapse by consciousness). Q7. Which interpretation of quantum mechanics do I prefer? (Qm) Copenhagen (quantum mechanics is a complete description of the microworld, measurement is an intervention from the classical world) (Copenhag); Everett’s (in measurement the world breaks down into multiple worlds– all possibilities are realized in some world– i.e. many worlds or many minds) (Everett); De Broglie–Bohm (particle moves in a deterministic potential and randomness is in the initial conditions)2 (Bohm); Other (Other). Q8. Superpositions of macroscopically distinct states (Val): Are in principle possible (PrincPos); Will eventually be realized experimentally (Experim); Are in principle impossible (ImpPrinc); Are impossible due to a collapse theory. Q9. How often have you switched to a different interpretation? (Chn): Never (Never); Once (Once); Several times (Several); I have no preferred interpretation: (NoPref). Q10. How much is the choice of interpretation a matter of personal philosophical prejudice? (Phl): A lot (Much); A little (Little); Not at all (NotAtAll). 3.2 Data Collection The poll was conducted as part of a project on scientific objectivity at the four largest Czech research institutions: Czech Academy of Sciences, Charles University in Prague, Masaryk University in Brno, and University of South Bohemia, along with their research institutes. It was hosted on a local online platform and administered via email, which provided main information about the project. Respondents were incentivized with a coupon for an online bookstore upon completion. To maintain consistency with previous polls, we included in our analysis only those responses from participants whose main specialization was in mathematics, physics (including applied physics), and information science. We imposed a cut-off time limit and excluded entries completed in under eight minutes, as we considered this duration to be the minimum to meaningfully respond to the entire questionnaire. This approach yielded a total of 40 valid questionnaires, although the response rate varied per question since answering the questions was not mandatory (the number of respondents N is specified for each question). Additionally, the response choices were limited to only one option in our poll, so we make only relative comparisons with the results from other polls in our paper. 3.3 Statistical Analysis In the results section, we first provide simple descriptive statistics comprising the distributions of response options in the graphical representation, which corresponds to the original paper by Schlosshauer, Kofler, and Zeilinger. These results were subsequently analyzed and compared with the Schlosshauer, Kofler, and Zeilinger results and results of the other 2 Although de Broglie’s interpretation is often labelled deterministic, it should, sensu stricto, be regarded as merely causal (de Broglie, 2021). 1 3 P. O. Jedlička et al. polls. In the second part, we opted for Bayesian network analysis (BNA) and Chi-square tests combined with the Spearman correlations to reveal further relationships between the variables. To investigate the interrelationships between questions, we employed Bayesian networks (BNs), which are probabilistic models that utilize graphs to visualize independence and dependence relations between variables (Pearl, 1988; Jensen & Nielsen, 2007; Koller & Friedman, 2009). These models are particularly well-suited for nominal variables, which is the case for our questions. To ascertain the graphical structure of the BN model, we employed a learning algorithm that maximizes the Akaike Information Criterion (AIC), which is calculated as the log-likelihood of observed data given the model minus the number of model parameters. The penalty component of AIC serves to prevent overfitting of data by overly complex models. All computations were performed in R using the bnlearn package (R Core Team, 2021). The resulting model is presented as a Complete Partially Directed Acyclic Graph (CPDAG) of the learned Bayesian network, a hybrid graph that can contain both directed and undirected edges that represents an equivalence class of Bayesian networks. (The CPDAG has the same skeleton as all BNs from the equivalence class it represents. Furthermore, only edges that have the same direction in all Bayesian networks of the equivalence class are directed in concordance with these BNs. See R Core Team (2021) for details.) To assess the degree of confidence in each edge, we ran the learning algorithm 40 times, removing one respondent in each iteration, and computed the relative frequency of each edge’s presence in the model. Additionally, we investigated the relationship between variables by examining correlations of binary indicators for selected response options. To quantify the dependence, we used the Chi-square test, and to determine the direction of the relation, we employed the Spearman correlation. To obtain robust results, we proceeded in a similar way as above: we computed the correlations 40 times, each time excluding a single observation. Consequently, we calculated the relative frequencies of test results that were significant at the 0.05 level. The code and the dataset are available at h t t p s : / / g i t l a b . c e s n e t . c z / u t i a / p u b l i c / q u a n t u m - i n t e r p r e t a t i o n s . 4 Results and Discussion In this section, we summarize the results of our poll, providing a short commentary that also discusses and compares them with the results of previous polls. 4.1 Descriptive Statistics A majority of the participants in our poll supported the idea that randomness is a fundamental concept in nature, with over three-fifths choosing this answer (Fig. 1). This view is prevalent in the community of physicists, as similar results were also obtained in the Schlosshauer, Kofler, and Zeilinger and the Sivasundaram and Nielsen polls. The exception was the Norsen and Nelson poll, where it received little support (less than a quarter). Conversely, there was low support for the ideas that randomness is only apparent or that there is a hidden determinism, again with the notable exception of the Norsen and Nelson poll. 1 3 Has Anything Changed? Tracking Long-Term Interpretational Preferences… The most common response in our poll was ‘yes, in some cases’ (Fig. 2), which was consistent with the Schlosshauer, Kofler, and Zeilinger and the Norsen and Nelson polls. In the Norsen and Nelson poll, participants generally believed that the properties are well-defined in all cases, or at least in some cases, whereas Sivasundaram and Nielsen results diverged substantially, with ‘no’ being the most favored answer. Into this single question, we condensed the essence of questions 3 and 4 from the Schlosshauer, Kofler, and Zeilinger questionnaire, focusing on Einstein’s view of quantum mechanics and Bohr’s view of quantum mechanics. Our results indicated somewhat stronger leanings towards the notion that the wave function description of reality is incomplete, Fig. 2 (Q2, Wdp): Do you believe that physical objects have their properties well defined prior to and independent of measurement? (N = 39) Fig. 1 (Q1, RnD): What is your opinion about the randomness of individual quantum events (such as the decay of a radioactive atom)? (N = 38) 1 3 P. O. Jedlička et al. aligning with Einstein’s stance and contrary to Bohr’s views (Fig. 3). However, over twofifths of the scientists were undecided and expected another solution. Previous polls showed divergent responses: participants in the Schlosshauer, Kofler, and Zeilinger poll largely considered Einstein’s views to be incorrect or likely to be disproven in the future (three quarters); the Norsen and Nelson poll participants generally disliked both Bohr’s views (close to three quarters), as well as Einstein’s (almost half). A third of the participants in our poll remained undecided (Fig. 4). Other polls did not show a general consensus either. For instance, in the Sivasundaram and Nielsen poll, a third of the participants did not prefer any of the variants, whereas in both the Schlosshauer, Kofler, and Zeilinger and the Norsen and Nelson polls, the most preferred (although vaguely defined) solution was that the problem will be “solved in another way.” In our poll, the “purely statistical (e.g., ensemble interpretation)” prevailed (Fig. 5). The results in other polls are mixed, with the Norsen and Nelson participants showing a higher Fig. 4 (Q4, Msr): The measurement problem is: (N = 37) Fig. 3 (Q3, Wdr): Is the quantum mechanical description of reality by a wave function complete? To which alternative are you inclined? (N = 36) 1 3 Has Anything Changed? Tracking Long-Term Interpretational Preferences… preference for an ontic interpretation and the Schlosshauer, Kofler, and Zeilinger favoring a mix of epistemic and ontic interpretations. The dominant view in our poll is that the observer is a complex (quantum) system (Fig. 6), which was also the most common view in the Sivasundaram and Nielsen poll. Results in the other two polls (the Schlosshauer, Kofler, and Zeilinger and the Norsen and Nelson) are inconclusive. Only a small, single-digit fraction in our poll, as well as in the Schlosshauer, Kofler, and Zeilinger and the Norsen and Nelson polls, subscribe to the view that the observer plays a distinguished physical role (e.g., wave-function collapse by consciousness). Following pilot testing, we simplified the options for this question to include the three most popular interpretations (Copenhagen, Everett’s, de Broglie–Bohm) but also left room for participants to propose their preferred interpretation (“Other” option) in an open quesFig. 6 (Q6, Obs): The observer (N = 35) Fig. 5 (Q5, Qs): What interpretation of quantum states do I prefer? (N = 34) 1 3 P. O. Jedlička et al. Despite these reservations, our findings confirm steady and relatively strong support for the Copenhagen interpretation among those who have picked an interpretation to begin with, which has been quite a consistent pattern over a 25-year period but probably also earlier when such polls were not common. Thus, the fluctuations regarding interpretations and some seminal questions appear to stem mostly from the biased audience at specific quantum foundation events rather than from the evolution over time. Our findings, therefore, do not lend much support to Tegmark’s initial claim from 1997 that “the prevailing view on the interpretation of quantum mechanics appears to be gradually changing,” as the preferences in interpretations have remained rather stable since then. Most importantly, however, our results suggest that there is still a significant amount of uncertainty in the community, and many practitioners simply remain undecided about their preferences– particularly the general physicists’ community approached in our and the Sivasundaram and Nielsen poll, which in greater numbers stated that they do not have a preferred interpretation. Physicists, for the most part, seem to be aware of the inherent “shakiness” of quantum foundations, as is apparent from the answers to the meta-questions concerning the evolution of one’s own views and about the influence of personal philosophical prejudice (Q9 and Q10). Here, the responses indicate that physicists understand that the lack of a more comprehensive theory leaves substantial room for their personal views or prejudices, as the most common answer in all polls was that the prejudice “matters a lot” in the choice of interpretation. Acknowledgments We thank the reviewers for their valuable comments. We also thank the poll participants and the other members of the project team who helped collect the data. Author Contributions Petr Jedlička: Conceptualization; Data curation; Investigation; Formal analysis; Methodology; Writing– original draft; Šimon Kos: Conceptualization; Data curation; Investigation; Martin Šmíd: Formal analysis; Methodology; Visualization; Writing– original draft; Jiří Vomlel: Formal analysis; Methodology; Visualization; Writing– original draft; Jan Slavík: Conceptualization; Methodology; Funding Open access publishing supported by the institutions participating in the CzechELib Transformative Agreement. P.O.J. was supported by Grant No. 18–08239 S of the Czech Science Foundation. Š.K. was supported by the project Quantum materials for applications in sustainable technologies (QM4ST), funded as Project No. CZ.02.01.01/00/22_008/0004572 by Programme Johannes Amos Comenius, call Excellent Research. This work was supported by the European Regional Development Fund project “Beyond Security: Role of Conflict in Resilience-Building” (reg. no.: CZ.02.01.01/00/22_008/0004595). Data Availability The code and the dataset that support the findings of this study are available at: h t t p s : / / g i t l a b . c e s n e t . c z / u t i a / p u b l i c / q u a n t u m - i n t e r p r e t a t i o n s . Declarations Competing Interests The authors declare no competing interests. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 1 3 Has Anything Changed? Tracking Long-Term Interpretational Preferences… References Castro, P., Bush, J. W. M., & Croca, J. (Eds.). (2024). Advances in Pilot Wave Theory– From Experiments to Foundations. Boston Studies in the Philosophy and History of Science, 344. Springer. h t t p s : / / d o i . o r g / 1 0 . 1 0 0 7 / 9 7 8 - 3 - 0 3 1 - 4 9 8 6 1 - 9 _ 1 Croca, J. R., Castro, P., Gatta, M., & Moreira, R. N. (2021). Louis de Broglie realistic research program and the experimental detection of quantum waves. Annales De La Fondation Louis De Broglie, 46(1), 197–215. Camilleri, K., & Schlosshauer, M. (2015). Niels Bohr as philosopher of experiment: Does decoherence theory challenge Bohr’s doctrine of classical concepts? Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 49, 73–83. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . s h p s b . 2 0 1 5 . 0 1 . 0 0 5 de Broglie, L. (1987). Interpretation of quantum mechanics by the double solution theory. Annales De La Fondation Louis De Broglie, 12(4), 1–22. de Broglie, L. (2021). Non-linear wave mechanics, a causal interpretation. Creative Media Partners. Fuchs, C. A., & Peres, A. (2000). Quantum theory needs no ‘interpretation’. Physics Today, 53, 70–71. Heisenberg, W. (1958). Physics and philosophy. Harper. Jensen, F. V., & Nielsen, T. D. (2007). Bayesian networks and decision graphs. Information science and statistics. Springer. https://doi.org/10.1007/978-0-387-68282-2 Koller, D., & Friedman, N. (2009). Probabilistic graphical models: Principles and techniques. The MIT Press. Norsen, T., & Nelson, S. (2013). Yet Another Snapshot of Foundational Attitudes Toward Quantum Mechanics. arxiv.org/pdf/1306.4646v2.pdf Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. Morgan Kaufmann. https://doi.org/10.5555/534975 R Core Team (2021). R: A Language and Environment for Statistical Computing, R Core Team, R Foundation for Statistical Computing. Vienna, Austria. https://www.R-project.org/ Schlosshauer, M., Kofler, J., & Zeilinger, A. (2013). A Snapshot of Foundational Attitudes Toward Quantum Mechanics. arxiv.org/abs/1301.1069 Sivasundaram, S., & Nielsen, K. (2016). Surveying the Attitudes of Physicists Concerning Foundational Issues of Quantum Mechanics. arxiv.org/abs/1612.00676 Tegmark, M. (1998). The interpretation of quantum mechanics: many worlds or many words? Fortschritte Der Physik, 46, 855. https://arxiv.org/abs/quant-ph/9709032 Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Petr O. Jedlička is a researcher at the Institute of Philosophy, Czech Academy of Sciences, specializing in scientific objectivity and various topics in the philosophy of science. He was a visiting researcher at the Centre for Philosophy of Natural and Social Sciences at the London School of Economics, where he focused on scientific reproducibility under the supervision of Professor Roman Frigg. He studied Philosophy and History of Science and Technology at the Faculty of Arts, and also completed coursework in Physics at the Faculty of Applied Sciences, University of West Bohemia. Šimon Kos is a physicist with an interest in the philosophy of physics. His research focuses on condensed matter physics, with a current emphasis on thin films deposited by magnetron sputtering, critical behavior of correlated electrons, and non-perturbative instanton effects. Over his career, he has contributed significantly to the study of heavy-fermion superconductors and the optical and spin properties of inorganic semiconductors. Kos has held research positions at leading international institutions, including Los Alamos National Laboratory and Cavendish Laboratory. Since 2009, he has been a docent at the Department of Physics, Faculty of Applied Sciences, University of West Bohemia. Martin Šmíd is a researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences, specializing in decision-making under uncertainty, stochastic models, and multistage stochastic optimization. He earned his Ph.D. in Econometrics and Operations Research from Charles University in Prague, where he currently serves as a researcher at the Faculty of Mathematics and Physics. His work spans a range of applied mathematical and economic topics, including scientific modeling. He has been the principal investigator of multiple research projects funded by the Czech Science Foundation. His research has been published in leading journals such as Annals of Operations Research. 1 3 P. O. Jedlička et al. Jiří Vomlel is a senior research fellow at the Institute of Information Theory and Automation, Czech Academy of Sciences. His research interests lie in the area of probabilistic methods in artificial intelligence. He specializes in computationally efficient probabilistic inference, structural learning of probabilistic graphical models, and their applications. He received his PhD in AI from the Czech Technical University in Prague in 2000 and spent three years as a postdoctoral researcher at Aalborg University in Denmark. He has been a member of research teams in about twenty research projects funded by European and Czech science foundations. He is an area editor of the International Journal of Approximate Reasoning. Jan Slavík was a distinguished physicist and educator associated with the University of West Bohemia in Pilsen. He worked at the Department of Physics at the Faculty of Applied Sciences, specializing in plasma physics and relativistic physics. His interests included the fields of plasma physics and thin films, thermomechanics, fluid mechanics, and general relativity at the Faculty of Mechanical Engineering, and the theory of physics education at the Faculty of Education. He was interested in the philosophy of physics, especially as related to foundations of quantum mechanics, as well as history and philosophy in general. 1 3