Beyond Completeness: Reconciling Observation and Reality in Quantum Mechanics

Author: Denis Avetisyan

A new analysis contrasts leading interpretations of quantum mechanics, advocating for a pragmatic focus on empirical observation over the pursuit of a fully realized underlying reality.

The elliptope visually defines the permissible correlations between three random variables, as constrained by equation $3.2$.

This review argues for the superiority of the Bohrian approach, rooted in methodological realism, over purely metaphysical interpretations like the (neo-)Everettian approach.

The persistent challenge of interpreting quantum mechanics stems from differing assumptions about what constitutes a complete physical theory. This paper, ‘Methodological Realism and Quantum Mechanics’, distinguishes between completeness as a total description of reality and completeness as sufficient conceptual resources for describing any phenomenon. By contrasting the (neo-)Everettian and (neo-)Bohrian interpretations, it argues for the latter’s grounding in methodological realism-prioritizing empirical adequacy over metaphysical completeness. Ultimately, this analysis illuminates how these seemingly opposed views may, in fact, offer mutually supporting perspectives-but begs the question of whether a truly unified interpretation of quantum mechanics is even necessary or desirable.

Beyond Classical Boundaries: Reconciling Quantum Reality

Many early attempts to reconcile quantum mechanics with established understandings of reality adhered to a framework of metaphysical realism. This perspective posited that quantum states, described mathematically by the wave function $ \Psi $, correspond to definite, pre-existing properties of a physical system, much like position and momentum in classical physics. Researchers sought to map these quantum states onto a concrete ontological structure-a ‘real’ world composed of objects possessing inherent characteristics-believing a complete description of this underlying reality would resolve the probabilistic nature of quantum measurement. However, this approach proved challenging, as assigning definite values to quantum properties before measurement contradicts the inherent uncertainty predicted by the theory and creates conceptual difficulties in defining a complete and consistent reality independent of observation.

Attempts to reconcile quantum mechanics with a classically-defined reality encounter fundamental difficulties due to the inherent probabilistic nature of quantum phenomena. Unlike classical physics, which predicts definite outcomes given initial conditions, quantum mechanics describes reality in terms of probabilities, meaning a system doesn’t possess pre-defined properties until measured. This challenges the notion of a complete, objective reality independent of observation, as defining such a reality requires assigning definite values to quantum states, a process that seemingly introduces the measurement problem. Consequently, efforts to map quantum states onto a fixed ontological structure struggle to account for the uncertainty and superposition central to quantum behavior, leading to conceptual paradoxes and the ongoing debate surrounding the interpretation of quantum mechanics. The very act of seeking a ‘complete reality’ may be misaligned with the fundamental principles governing the quantum world.

The attempt to understand quantum systems through the lens of classical physics encounters fundamental limitations due to the inherent reliance on concepts like definite properties and predictable trajectories. Classical ontology assumes objects possess intrinsic characteristics independent of observation, and follow deterministic paths – a framework demonstrably at odds with the probabilistic and contextual nature of quantum mechanics. Observations at the quantum level reveal that properties aren’t fixed until measured, and a particle’s “trajectory” isn’t a well-defined path but rather a superposition of possibilities described by a wave function, $ \Psi $. Consequently, a successful description of quantum phenomena demands a departure from these classical foundational assumptions, prompting physicists to explore alternative ontological frameworks that prioritize probabilities, relations, and the role of measurement in defining reality itself. This shift isn’t merely a mathematical adjustment, but a re-evaluation of what it means for something to exist at the most fundamental level.

A Pragmatic Lens: Methodological Realism and Quantum Theory

Methodological realism posits a functional understanding of physical theories, defining their primary purpose as the accurate description of observable phenomena rather than the revelation of an objective, underlying reality. This approach diverges from traditional realism, which assumes a correspondence between theoretical constructs and an independently existing world. Instead, methodological realism emphasizes the predictive power and empirical adequacy of a theory as the criteria for its acceptance, irrespective of whether its elements correspond to ‘real’ entities. Consequently, the focus shifts from ontological questions – such as “what is ultimately real?” – to epistemological ones concerning the reliability and scope of the theory’s predictions. This pragmatic framing allows for the evaluation of a theory based on its utility in explaining and predicting experimental outcomes, without requiring a commitment to its metaphysical truth.

The emphasis on predictive success, as central to methodological realism, addresses longstanding ontological challenges in quantum mechanics by shifting the primary goal of theoretical physics. Rather than attempting to determine the “true” nature of quantum entities – a pursuit complicated by issues like wave function collapse and non-locality – this approach prioritizes the accurate description and prediction of experimental results. This does not deny the existence of an underlying reality, but asserts that defining it is not a necessary condition for utilizing quantum mechanics effectively. Consequently, the validity of a quantum theory is determined by its ability to consistently and accurately forecast observable phenomena, evaluated through rigorous empirical testing and statistical analysis, rather than its adherence to classical intuitions about objective existence or a specific metaphysical interpretation of the quantum state $ \Psi $.

The Neo-Bohrian approach, operating within the framework of methodological realism, prioritizes the extension of classical physics into the quantum realm rather than positing a fundamentally different ontological structure. This is achieved by focusing on the limits of classical concepts and their gradual modification as predictive accuracy demands, rather than outright replacement. The methodology avoids introducing entirely new entities or principles where classical approximations remain viable, seeking to maintain a degree of correspondence between classical and quantum descriptions. This strategy results in a less disruptive transition between the two theories, allowing for established physical intuition and mathematical tools to be leveraged in the development of quantum models, and minimizing the perceived conceptual gap between the classical and quantum worlds.

Completeness and the Multiverse: The Many-Worlds Interpretation

The assessment of completeness within quantum mechanics fundamentally shapes the diverse interpretations of the theory. This concern centers on whether the mathematical formalism and postulates of quantum mechanics provide a sufficient and exhaustive framework for describing all physical phenomena, or if additional, unstated assumptions or mechanisms are required. Interpretations diverge based on their response to this question; those accepting incompleteness often propose hidden variables or modifications to the theory, while interpretations like the Many-Worlds Interpretation strive for completeness by accepting the standard formalism as fully descriptive, even if it implies counterintuitive ontological consequences such as the existence of parallel universes. The debate regarding completeness therefore isn’t merely a technical detail, but a defining characteristic separating different approaches to understanding the foundations of quantum mechanics.

Gleason’s Theorem, a mathematical result in quantum mechanics, demonstrates that the probabilities assigned to measurement outcomes are uniquely determined by the mathematical structure of Hilbert space and the projection postulate. Specifically, it proves that any physically plausible assignment of probabilities to events must adhere to the Born rule, ensuring a consistent probabilistic framework. However, while establishing a unique probability measure – a key indicator of a complete theory in the sense of predictive power – Gleason’s Theorem remains silent on the interpretation of this probability. It does not specify whether the probabilities represent frequencies of events in a single universe, or instead reflect the existence of multiple, non-interacting universes each realizing a different outcome, leaving the ontological structure of quantum mechanics open to various interpretations such as the Copenhagen interpretation or the Many-Worlds Interpretation.

The Neo-Everettian interpretation addresses the completeness of quantum mechanics by proposing a fully deterministic ontology. This is achieved through the Many-Worlds Interpretation (MWI), which asserts that the quantum state does not collapse upon measurement. Instead, all possible outcomes of a quantum event are physically realized, each branching into a separate, independent universe. Consequently, the wave function, described by the Schrödinger equation, evolves unitarily and completely describes reality, eliminating the need for additional postulates regarding wave function collapse and providing a complete account of quantum phenomena. This approach views the observed probabilities in quantum mechanics not as inherent randomness, but as arising from the observer’s perspective within a single branch of the multiverse.

The Quest for Hidden Certainties: Limits of Classical Intuition

The Hidden-Variables Program arose from a dissatisfaction with the probabilistic nature of quantum mechanics, positing that the wave function offered an incomplete description of physical reality. Proponents believed that beneath the apparent randomness lay a set of unobserved parameters – “hidden variables” – which, if known, would allow for the precise prediction of quantum outcomes, restoring a deterministic worldview. This approach sought not to disprove quantum mechanics, but to provide a more fundamental, ‘complete’ theory where quantum probabilities merely reflected a lack of knowledge about these underlying variables. The intention was to explain quantum phenomena as arising from local, realistic causes, much like classical physics, by supplementing the wave function with information about the specific state of each particle – essentially, filling in what was perceived as missing from the quantum picture of the universe.

Initial efforts to mathematically dismiss hidden-variable theories, most notably by John von Neumann, appeared to definitively prove their impossibility, suggesting quantum mechanics’ inherent randomness wasn’t due to missing information. However, careful scrutiny revealed flaws in von Neumann’s reasoning, opening a brief window for renewed exploration. While these initial cracks were addressed, subsequent and more rigorous work – particularly Bell’s theorem and the associated experimental tests – firmly established that any local hidden-variable theory would necessarily conflict with the predictions of quantum mechanics. These results didn’t simply invalidate a specific approach, but highlighted a profound challenge: the very notion of explaining quantum phenomena with a classical, deterministic framework – one where properties are predetermined and only revealed through measurement – appears fundamentally incompatible with the observed behavior of the quantum world. This ultimately shifted the focus from attempting to ‘complete’ quantum mechanics to understanding and interpreting its probabilistic nature.

The persistent failure of hidden-variable theories to reconcile quantum mechanics with classical determinism has profoundly shifted the landscape of physical interpretation. Attempts to supplement the quantum wave function with unobserved parameters, aiming for a complete and predictable description of reality, consistently encounter mathematical and conceptual roadblocks. This isn’t merely a technical difficulty; it highlights a deeper incompatibility between the quantum world and classical intuitions about objective properties and causal relationships. Consequently, physicists are increasingly compelled to explore interpretations that accept probability as a fundamental aspect of the universe, rather than an indication of incomplete knowledge. These approaches, such as the Many-Worlds Interpretation or consistent histories, forgo the search for hidden certainties and instead grapple with the implications of a reality where outcomes are inherently probabilistic, challenging long-held assumptions about the nature of existence itself.

Bridging Classical and Quantum Worlds: A Path Forward

The architecture of quantum systems, despite their inherent complexity, benefits from a surprising connection to the well-established principles of classical physics. Boolean Algebra, a system of logical operations, offers a powerful tool for dissecting the possible states and measurements – the ‘observables’ – within a quantum realm. Similarly, the principle of free mobility, traditionally applied to rigid bodies moving in space, provides a conceptual scaffold for understanding how quantum states evolve over time. This isn’t to suggest a direct equivalence, but rather that these classical concepts furnish a familiar, intuitive framework for analyzing the logical relationships between different quantum properties and the dynamics governing their changes. By leveraging these established principles, physicists can more effectively model and interpret the behavior of quantum systems, bridging the gap between abstract theory and observable phenomena, and ultimately, gaining a deeper understanding of the universe at its most fundamental level.

While classical physics furnishes a valuable conceptual scaffolding for approaching quantum systems, direct transference of its principles demands nuanced scrutiny. The inherent discreteness and probabilistic nature of quantum phenomena often diverge significantly from the continuous and deterministic framework of classical mechanics. For instance, attempting to define quantum observables solely through Boolean algebra, while logically consistent, fails to fully encapsulate the non-commuting relationships characteristic of quantum operators like momentum and position, described by the Heisenberg uncertainty principle $ \Delta x \Delta p \ge \frac{\hbar}{2}$. Consequently, interpretations relying exclusively on classical analogs risk obscuring the uniquely quantum behaviors – such as superposition and entanglement – that differentiate these systems and necessitate a revised understanding of physical reality.

This work advocates for a renewed focus in quantum mechanics research, emphasizing the development of interpretations that are both logically consistent and supported by experimental evidence. The analysis suggests that progress hinges on bridging the gap between theoretical frameworks and empirical observations, potentially through the application of methodological realism – a philosophical approach prioritizing the explanatory power of scientific models. Specifically, the Many-Worlds Interpretation emerges as a promising avenue for exploration, offering a conceptually complete, albeit counterintuitive, account of quantum phenomena. Future studies should therefore prioritize rigorous philosophical examination alongside continued empirical testing, aiming to refine and validate interpretations that accurately reflect the nature of quantum reality and its observable consequences.

The pursuit of understanding, as demonstrated by the contrast between Everettian and Bohrian interpretations of quantum mechanics, hinges on recognizing the limits of complete description. The article highlights how the Bohrian approach prioritizes methodological realism-what can be empirically observed-over a fully realized metaphysical picture. This resonates with Richard Feynman’s assertion: “The first principle is that you must not fool yourself – and you are the easiest person to fool.” Just as self-deception hinders accurate perception, an insistence on completeness, when the evidence points toward inherent uncertainty, obstructs a genuine grasp of the quantum realm. The model, in this case, functions as a microscope, and the data, the specimen-both require rigorous scrutiny to reveal the underlying patterns, accepting that a perfect, all-encompassing view may be fundamentally unattainable.

Where Do We Go From Here?

The persistent tension between demanding a complete metaphysical picture and accepting a pragmatically sufficient one continues to define the quantum landscape. This work suggests that prioritizing methodological realism – focusing on what can be reliably observed and measured – offers a more fruitful path than striving for ontological completeness. However, it is crucial to acknowledge that ‘reliable observation’ is itself a subtly shifting target. Future investigations should carefully check data boundaries to avoid spurious patterns arising from limitations in experimental design or data analysis. The pursuit of non-Boolean algebras, as a means of refining the logic underpinning quantum states, remains a potentially valuable, if demanding, avenue.

A continuing challenge lies in reconciling the predictive power of quantum formalism with the intuitive demands of realism. While the Bohrian approach, with its emphasis on operational definitions, avoids the ontological commitments of Everettian interpretations, it does not entirely dispel the feeling of an incomplete description. Further research might explore whether alternative formalisms-beyond both standard quantum mechanics and its many-worlds variants-could offer a more satisfying balance between predictive accuracy and conceptual clarity.

Ultimately, the question may not be whether quantum mechanics is a complete description of reality, but rather what constitutes completeness in the first place. A rigorous examination of the assumptions embedded within this very question-and a willingness to abandon cherished metaphysical preconceptions-will likely be essential for navigating the conceptual challenges that lie ahead.

Original article: https://arxiv.org/pdf/2512.02169.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/