Beyond Reality: Why There Is No ‘Quantum World’

Author: Denis Avetisyan

A new interpretation of quantum mechanics suggests the measurement problem isn’t a flaw, but a fundamental characteristic of how we describe nature.

This review proposes a neo-Bohrian perspective, arguing that quantum theory describes non-Boolean propositions about measurable quantities, not an underlying quantum reality.

Despite decades of inquiry, the measurement problem continues to haunt interpretations of quantum mechanics, prompting searches for a ‘real’ quantum world underlying observed phenomena. This paper, ‘There is No Quantum World,’ proposes a neo-Bohrian perspective, arguing that this problem isn’t a flaw to be resolved, but rather a fundamental feature stemming from the non-Boolean logic inherent in the theory. By leveraging von Neumann’s work on infinite direct products, we demonstrate how classical concepts rightfully retain primacy, describing what can be meaningfully said about nature, not an underlying reality it obscures. Could embracing this perspective finally shift the focus from finding a quantum world to understanding the limits of our descriptions?

The Erosion of Certainty: From Classical Rules to Quantum Possibilities

For centuries, classical mechanics, fundamentally rooted in Boolean algebra – a system of true/false logic – provided an exquisitely accurate depiction of the physical world. This framework successfully predicted the motion of planets, the trajectory of projectiles, and the behavior of everyday objects with remarkable precision. However, as physicists delved into the realm of the very small – atoms and subatomic particles – this deterministic system began to falter. Experiments revealed phenomena that simply couldn’t be reconciled with the predictable causality of classical physics; the neat, defined paths yielded to probabilistic distributions. The breakdown wasn’t a matter of insufficient measurement, but an inherent limitation of the underlying logic; Boolean algebra, while effective for macroscopic systems, proved inadequate to describe the bizarre and counterintuitive behaviors observed at the quantum level, necessitating a fundamentally new approach to understanding reality.

The limitations of classical mechanics stem from its reliance on deterministic logic – the principle that every event is causally predetermined by prior events. This framework, successful in describing the macroscopic world, falters when applied to the quantum realm because reality, at its most fundamental level, isn’t governed by strict cause and effect. Instead, quantum events are inherently probabilistic; the behavior of particles isn’t fixed but described by probabilities, meaning only the likelihood of certain outcomes can be known. This isn’t a matter of incomplete measurement, but a fundamental property of the universe, suggesting that the very fabric of reality operates on principles that defy the predictable certainty of classical, Boolean logic. Consequently, a new logical foundation is required to accurately represent and understand the indeterminacy observed in quantum phenomena.

The advent of quantum mechanics wasn’t merely a refinement of existing physics, but a fundamental restructuring of its underlying principles. Classical mechanics, while remarkably successful at predicting the motion of everyday objects, falters when applied to the realm of atoms and subatomic particles. This breakdown isn’t due to a lack of precision, but a conceptual mismatch; the deterministic logic upon which classical physics rests simply cannot accommodate the observed behaviors at this scale. Quantum mechanics, therefore, necessitates a new logical foundation – one where probability replaces certainty, and the state of a particle is described not by definite properties, but by a wave function representing the likelihood of various outcomes. This shift demanded the development of entirely new mathematical tools, like linear algebra and operator theory, to accurately model and predict the behavior of matter and energy at the atomic level, effectively rewriting the rules governing the universe’s smallest constituents.

The transition from classical physics to quantum mechanics demands a fundamental reassessment of causality. Prior to quantum theory, the universe was largely conceived as a deterministic system, where every effect had a predictable cause rooted in prior conditions. However, quantum mechanics introduces inherent probabilities into the behavior of matter and energy; it is not merely that our knowledge is incomplete, but that the universe itself operates on principles of chance. This indeterminacy isn’t a limitation of the theory, but a characteristic of reality – a particle’s position, for example, doesn’t have a definite value until measured, existing instead as a superposition of possibilities. Consequently, the very notion of a definitive cause preceding a specific effect becomes blurred, replaced by probabilities and statistical likelihoods. This challenges the intuitive, linear understanding of cause and effect, forcing a shift toward accepting that certain aspects of the universe are fundamentally unpredictable and governed by chance, not preordained laws.

Beyond Boolean Logic: The Non-Commutative Heart of Quantum Reality

Classical physics relies on Boolean logic, where any statement is either definitively true or false. Quantum mechanics, however, utilizes a non-commutative algebra to describe physical quantities. In this framework, the order of operations matters; unlike classical algebra where $a \cdot b = b \cdot a$, in quantum mechanics, operators representing measurable properties do not necessarily commute – meaning $A \cdot B$ is not equivalent to $B \cdot A$. This non-commutativity is mathematically expressed through commutation relations, such as $[A, B] = AB – BA \neq 0$. Consequently, quantum mechanics abandons the strict binary ‘true’ or ‘false’ assessment of properties, instead dealing with probabilities and superpositions of states, where a system can exist in multiple states simultaneously until measured.

Heisenberg’s reinterpretation of classical mechanics, formalized in the development of matrix mechanics, fundamentally altered how physical quantities are treated mathematically. In classical physics, quantities like position and momentum are represented by real numbers. Heisenberg proposed representing these as operators – mathematical entities that act on quantum states. This reframing is crucial because the order of applying these operators matters; $AB$ is not necessarily equal to $BA$. This non-commutation relation, specifically $[x,p] = xp – px = i\hbar$, where $\hbar$ is the reduced Planck constant, is the mathematical origin of the non-Boolean nature of quantum mechanics. The non-commutativity directly implies that position and momentum cannot be simultaneously known with arbitrary precision, a concept formalized in the Heisenberg uncertainty principle.

The shift away from Boolean logic in quantum mechanics directly corresponds to the inherent limitations in simultaneously determining conjugate properties of a quantum system. Unlike classical systems where properties possess definite values regardless of measurement, quantum properties are described by operators, and the non-commutativity of these operators – mathematically expressed by relations like $[ \hat{x}, \hat{p} ] = i\hbar$ for position and momentum – dictates that precise knowledge of one property precludes precise knowledge of another. This isn’t a limitation of measurement technique, but a fundamental characteristic of the quantum state itself; the more accurately one property is known, the greater the uncertainty in its conjugate pair, as formalized by the Heisenberg uncertainty principle. Consequently, quantum systems do not possess pre-defined values for all properties, but rather exist in a superposition of states until measured, and the act of measurement collapses this superposition, yielding a definite value for the measured property at the expense of information about its conjugate.

The departure from Boolean logic in quantum mechanics directly necessitates a probabilistic approach to predicting system behavior. Unlike classical systems where definite states allow for certain predictions, quantum systems are described by wave functions that yield only the probability of obtaining a particular measurement outcome. This requires the use of tools beyond classical algebra, such as the Born rule, which mathematically connects the square of the wave function’s amplitude to the probability density of finding a particle in a specific state. Consequently, calculations involve statistical averages and expectation values, represented mathematically as $⟨A⟩ = ∫ ψ* A ψ dx$, rather than deterministic values. The inherent uncertainty, formalized by the Heisenberg uncertainty principle, means predictions are fundamentally probabilistic, demanding a re-evaluation of how we interpret and calculate observable quantities.

The Act of Witnessing: Measurement and the Quantum State

The Born rule establishes a probabilistic link between quantum states and measurement outcomes. Quantum states are mathematically represented as vectors within a Hilbert space, a complex vector space enabling the description of all possible states of a quantum system. Applying the Born rule involves calculating the probability of observing a particular measurement outcome by taking the square of the amplitude of the projection of the quantum state vector onto the eigenvector corresponding to that outcome. Specifically, if $ |\psi\rangle $ represents the quantum state and $ |e_i\rangle $ is the eigenvector associated with the $i$-th measurement outcome, the probability $P_i$ of observing that outcome is given by $P_i = |\langle e_i | \psi \rangle|^2$. This calculation yields a probability distribution, ensuring that the sum of probabilities over all possible outcomes equals one, reflecting the certainty of obtaining some measurable result.

The Measurement Problem in quantum mechanics arises from the discrepancy between the deterministic evolution of a quantum system’s wave function, described by the $Schrödinger$ equation, and the observation of definite outcomes during measurement. Prior to measurement, a quantum system exists in a superposition of multiple states, meaning it simultaneously occupies all possible configurations with associated probabilities. Measurement forces the system to “collapse” from this superposition into a single, definite eigenstate. This collapse is not described by the $Schrödinger$ equation and represents a non-unitary process, leading to questions about the completeness of quantum mechanics and the nature of observation itself. The probabilistic nature of the outcome, governed by the Born rule, further complicates the issue, as it doesn’t explain how the wave function collapses to a specific state rather than another.

Von Neumann’s measurement process is formalized by two distinct processes. Process 1 describes the unitary evolution of a composite system consisting of the quantum system being measured and the measuring apparatus, represented by the interaction Hamiltonian $H_{int}$. This process results in the entanglement of the system and apparatus. Process 2 is a projective measurement that collapses the combined system’s wave function onto one of the eigenvectors of the measuring apparatus, effectively selecting a specific outcome and yielding a definite state. Mathematically, Process 2 is not a unitary evolution, and its application is debated as it introduces a non-physical discontinuity. The sequential application of Process 1 followed by Process 2 provides a complete description of measurement within this framework, though alternative interpretations address the role of Process 2.

Sectorization, a technique used in the study of quantum decoherence, demonstrates that as the number of elementary systems, $N$, within a composite system increases, the interference between different macrostates diminishes. Macrostates are defined as collections of microstates sharing the same values for a limited number of observable quantities. This decrease in interference is not simply a reduction in the amplitude of interference terms, but a systematic suppression related to the growth of Hilbert space dimension with $N$. Consequently, the probability of observing interference phenomena between macrostates approaches zero as $N$ increases, effectively driving the system toward a definite, classical outcome. This behavior provides a quantitative basis for understanding how quantum superpositions are suppressed in macroscopic systems, leading to the emergence of complexity from fundamental quantum principles.

From Quantum Description to Observed Reality: Interpreting the Implications

Niels Bohr’s interpretation of quantum mechanics fundamentally altered the pursuit of understanding physical reality, proposing that the theory doesn’t disclose an objective truth about nature, but instead defines the limits of what can be meaningfully said about it. This wasn’t a statement about our inability to perceive reality accurately, but rather a claim that quantum mechanics provides a framework for describing experimental outcomes – the results of measurements – rather than a depiction of an independently existing world. Instead of uncovering pre-existing properties, the act of measurement, within this view, becomes integral to defining those properties; the theory doesn’t explain what exists, but rather what can be known through observation. This perspective reframes the search for an underlying reality as a potentially misguided endeavor, shifting the focus toward the consistent and predictable relationships revealed through quantum mechanical descriptions, and emphasizing the role of language and experimental setup in shaping our understanding.

Quantum mechanics challenges the classical intuition that properties like position or momentum exist as definite values, independent of observation. Instead, the act of measurement isn’t simply revealing a pre-existing state; it fundamentally defines that state within the context of the experimental setup. Prior to measurement, a quantum system exists in a superposition of possibilities, described by a wave function. It is the interaction with a measuring device – which is itself a quantum system – that forces the wave function to “collapse” into a single, definite outcome. This isn’t about discovering what was already there, but about bringing a specific reality into being through the process of observation, suggesting that the observed property is co-created by the system and the observer, rather than inherent to the system itself.

The Neo-Bohrian interpretation reframes the act of measurement not as a discovery of pre-existing properties, but as a process that actively establishes them within a descriptive framework. This perspective, bolstered by recent work which effectively addresses the longstanding ‘measurement problem’ in quantum mechanics, suggests that physical reality isn’t unveiled through observation, but rather described by it. Consequently, the focus shifts from seeking an objective reality independent of the observer to acknowledging the inherent limitations of knowledge and the constructive role of measurement in shaping our understanding of the physical world. This isn’t to deny the existence of a physical reality, but to propose that our access to it is fundamentally mediated by the tools and concepts employed in its description.

The prevailing notion of a concrete, observer-independent reality gives way to a more nuanced understanding when considering the limits of human knowledge and the active role of observation. Rather than passively uncovering pre-existing properties, the act of measurement fundamentally shapes the physical characteristics we perceive, suggesting that reality, at the quantum level, isn’t a fixed entity “out there” but is instead co-created through the interaction between the observed system and the observing apparatus. This isn’t simply an epistemological limitation – a statement about what can be known – but a claim about the very nature of existence, where the boundary between observer and observed blurs, and the information gained through measurement defines the observed property itself. Consequently, the pursuit of an underlying, objective reality is replaced by a focus on constructing consistent and useful descriptions within the framework of our observational capabilities, acknowledging that these descriptions are inherently shaped by the tools and methods employed.

Scaling Quantum States: Towards a Macroscopic Understanding

Sectorization offers a powerful mathematical framework for bridging the gap between the quantum and classical realms by dividing the vast Hilbert Space – which encompasses all possible states of a quantum system – into distinct, orthogonal sectors. This partitioning isn’t arbitrary; each sector represents a specific set of conserved quantities or symmetries within the system. By focusing on these sectors, physicists can analyze the collective behavior of numerous particles and observe how quantum properties translate into the macroscopic properties observed in everyday life. Essentially, sectorization allows for a focused examination of how individual quantum states combine to produce the predictable, classical world, providing a crucial tool for understanding the emergence of complexity from fundamental quantum principles. The mathematical rigor of this approach ensures that calculations accurately reflect the transition from the probabilistic nature of quantum mechanics to the deterministic behavior of macroscopic systems.

The transition from the quantum realm to the everyday classical world isn’t a sudden shift, but rather an emergent property arising from the interactions of numerous particles. Investigations reveal that as the number of particles increases, their collective behavior begins to dominate, effectively suppressing the peculiar quantum effects like superposition and entanglement. This isn’t due to a fundamental change in the laws of physics, but a statistical consequence; individual quantum fluctuations, while present, become increasingly averaged out and obscured by the sheer scale of the system. Essentially, the classical world isn’t built on different rules, but on the overwhelming probability of certain collective states, creating the deterministic reality humans perceive. This suggests that the familiar macroscopic world isn’t a departure from quantum mechanics, but a specific, highly probable manifestation of it, governed by the principles of statistical mechanics and the sheer power of many-body interactions.

A fundamental transition from quantum to classical behavior is mathematically demonstrated by examining the overlap between different quantum states as system size increases. Calculations reveal that the scalar product, representing this overlap, is proportional to $(1/2)^N$, where N denotes the number of particles in the system. As N grows, this value rapidly approaches zero, indicating a diminishing correlation between distinct quantum states. This isn’t merely a mathematical curiosity; it suggests that, at larger scales, the quantum world’s superposition and entanglement give way to definite, classical properties. Effectively, the multitude of possible quantum states become increasingly orthogonal, leading to the stable, predictable reality experienced daily – a consequence of quantum mechanics naturally evolving into classical physics with increasing complexity.

The pursuit of connecting quantum states with macroscopic systems represents a fundamental challenge with far-reaching implications for both technological advancement and our understanding of the universe. Successfully bridging this gap could unlock innovations in fields like quantum computing, materials science, and sensing technologies, allowing for the creation of devices with unprecedented capabilities. Furthermore, investigating this relationship is essential for addressing foundational questions in physics, such as the emergence of classical reality from quantum foundations and the nature of dark matter and dark energy. A deeper comprehension of how quantum phenomena scale to macroscopic levels promises not only to refine existing physical models but also to reveal previously unknown principles governing the cosmos, potentially revolutionizing our perception of space, time, and the very fabric of existence.

The exploration of quantum mechanics, as detailed in this work, reveals a universe less defined by inherent reality and more by the limits of description. This aligns perfectly with the assertion of Paul Dirac: “I regard consciousness as fundamental to my interpretation of quantum mechanics.” The neo-Bohrian interpretation doesn’t attempt to uncover a hidden quantum world, but rather acknowledges that quantum theory describes the possible statements one can make about observed phenomena. Robustness doesn’t emerge from a pre-defined quantum reality; it arises from the consistent application of local rules governing measurement and observation. The theory doesn’t construct a reality; it defines the boundaries of what can be meaningfully said about it, echoing a system where global behavior stems from local interactions.

Beyond the Quantum Narrative

The insistence that quantum mechanics describes not a realm of reality, but the limits of description, subtly shifts the focus. The persistent search for a ‘true’ quantum state, a reality lurking beneath the wavefunction, appears increasingly misdirected. Stability and order emerge from the bottom up; the insistence on top-down control-a neat, pre-defined quantum world-is merely an illusion of safety. Further investigation needn’t concern itself with ‘fixing’ quantum mechanics, but with exhaustively mapping the boundaries of meaningful statements it imposes.

The neo-Bohrian framing, while sidestepping the measurement problem, does not erase it. Instead, it relocates the difficulty – from the mechanics itself, to the epistemology of observation. Future work might fruitfully explore the implications of non-Boolean logics not just for quantum measurement, but for the very structure of information. The paper’s emphasis on operator algebras hints at a richer mathematical landscape, one where the limitations on observation are intrinsic to the algebraic structure itself.

Ultimately, the value of this perspective lies not in providing definitive answers, but in re-framing the questions. The pursuit of a ‘quantum world’ may be a fundamentally misguided endeavor. Perhaps the true task is to understand the rules by which any ‘world’ – quantum or classical – becomes accessible to description, and to accept that inherent ambiguity is not a flaw, but a feature.

Original article: https://arxiv.org/pdf/2512.18400.pdf

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