Rewriting Quantum Reality: A New Path to Interpretation

Author: Denis Avetisyan

A novel approach to understanding quantum theory focuses on reconstructing its core principles from operational foundations, potentially resolving long-standing interpretational debates.

The study dissects the inherent subjectivity within physical theories, demonstrating how interpretational biases - stemming from linguistic choices and framing - inevitably shape understanding, even when grounded in seemingly objective systems like classical point mechanics. — The study dissects the inherent subjectivity within physical theories, demonstrating how interpretational biases – stemming from linguistic choices and framing – inevitably shape understanding, even when grounded in seemingly objective systems like classical point mechanics.

This review proposes a reconstructive methodology for deriving the quantum formalism, addressing interpretational bias and revealing deeper physical insights from experimental practices.

For a century, quantum theory has challenged our fundamental understanding of physical reality, yet a systematic and coherent interpretation remains elusive. This paper, ‘Systematizing the Interpretation of Quantum Theory via Reconstruction’, argues that prevailing interpretative methodologies suffer from inherent biases, prioritizing the formal over the informal aspects of the theory. To address this, we propose a ‘reconstruction-based interpretation’ – deriving quantum formalism from foundational principles – as a means to identify all potentially relevant facts and circumvent existing limitations. Could this approach not only resolve interpretational challenges but also reveal deeper physical principles and a richer conception of quantum reality?

The Cracks in Classical Certainty

For centuries, classical mechanics provided an immensely successful framework for understanding the physical world, accurately predicting the motion of everything from planetary orbits to billiard balls. However, this deterministic system breaks down when applied to the realm of atoms and subatomic particles. Experiments reveal behaviors – such as wave-particle duality and quantum superposition – that have no classical analogue and lead to demonstrable paradoxes. For instance, attempting to pinpoint an electron’s position with increasing accuracy fundamentally disturbs its momentum, a contradiction of classical predictability formalized by Heisenberg’s uncertainty principle: $ \Delta x \Delta p \geq \frac{\hbar}{2}$. These inconsistencies aren’t mere measurement errors; they represent a fundamental limit to how accurately classical descriptions can model the quantum world, prompting a search for entirely new theoretical foundations.

Bell’s theorem and subsequent “no-go” theorems represent a pivotal challenge to classical physics by demonstrating the inherent incompatibility between local realism and the predictions of quantum mechanics. These theorems don’t disprove quantum mechanics; instead, they rigorously prove that any theory attempting to explain quantum phenomena must relinquish at least one of two deeply held classical assumptions. Locality, the idea that an object is only directly influenced by its immediate surroundings, and realism, the belief that physical properties have definite values independent of measurement, are both cornerstones of classical intuition. Experiments designed to test Bell’s inequalities – mathematical expressions derived from the assumptions of local realism – consistently violate these inequalities, effectively ruling out the possibility of a local realistic description of the quantum world. This isn’t merely a matter of incomplete knowledge; the theorems establish a fundamental limit on how accurately quantum systems can be understood through classical lenses, forcing a reconsideration of concepts like entanglement and non-locality.

The demonstrable inadequacies of classical mechanics when applied to the quantum world compel a profound reconsideration of fundamental physical principles. Existing frameworks, built upon assumptions of locality and realism, consistently clash with experimental observations, suggesting that the very nature of reality at the smallest scales may be radically different than previously conceived. This isn’t merely a matter of refining existing models; rather, it demands an exploration of entirely new conceptual foundations – potentially challenging deeply held beliefs about causality, determinism, and the objectivity of measurement. The implications extend beyond physics, prompting philosophical inquiry into the relationship between observation, information, and the constitution of reality itself, as scientists grapple with a universe that appears fundamentally probabilistic and non-intuitive.

Classical physics, prior to Maxwellian electrodynamics, conceptualized reality as a hierarchy encompassing overarching principles, fundamental categories like space and time, metaphysical axioms, and the physical principles of Newtonian mechanics.

Rebuilding Quantum Mechanics: A Pragmatic Approach

The Quantum Reconstruction Program diverges from traditional approaches to quantum mechanics by prioritizing a derivation of the mathematical framework – including operators, Hilbert spaces, and the Schrödinger equation – directly from a set of foundational physical postulates. This methodology intentionally avoids reliance on pre-existing metaphysical interpretations or assumptions about the nature of reality, such as wave-particle duality or the role of the observer. The aim is to establish quantum mechanics as a logically consistent and experimentally verifiable theory based solely on observable phenomena and their associated mathematical descriptions, rather than interpretations that may not be directly testable. This approach seeks to minimize the influence of potentially misleading philosophical considerations and focus on predictive power and empirical validation as the primary criteria for a successful theory.

The Quantum Reconstruction Program’s Operational Framework establishes a methodology for defining quantum phenomena strictly through experimentally accessible contexts and measurable quantities. This approach deliberately limits theoretical constructs to those directly linked to observation, eschewing interpretations that extend beyond the scope of potential measurements. Specifically, the framework focuses on defining states and dynamics based on the minimal set of operations required to prepare and measure a system, thereby grounding the mathematical formalism of quantum mechanics in physically realizable procedures. This prioritization of observable phenomena over hypothetical entities aims to resolve foundational ambiguities and provide a more robust basis for the theory, focusing on what can be known rather than how reality fundamentally is.

The Operational Indistinguishability Postulate posits that the indistinguishability of identical particles is not a statement about their intrinsic nature, but a consequence of the limitations imposed by operational definitions within the Quantum Reconstruction Program. Specifically, any experimental procedure designed to differentiate between two identical particles – those with identical measurable properties like momentum, spin, and charge – will necessarily yield the same result, regardless of the procedure employed. This postulate avoids attributing any pre-existing, non-operational properties to particles and instead defines indistinguishability as a fundamental constraint on measurement. Mathematically, this is reflected in the symmetry requirements of the wavefunction $ \Psi $ under particle exchange, which arises directly from demanding that observational outcomes remain unchanged when labeling identical particles is varied. The postulate, therefore, forms a foundational element in reconstructing quantum mechanics from purely operational principles.

Einstein reconstructed Lorentz transformations by establishing logical dependencies and forcing reconsiderations of fundamental axioms related to space, time, matter, and interaction.

The Math Underneath: Quantum States and Dynamics

Quantum states are mathematically represented as vectors within a complex vector space, known as a Hilbert space. This space allows for the description of quantum phenomena through complex numbers, where the squared magnitude of the complex amplitude represents the probability of observing a particular state. The use of complex numbers is fundamental, enabling the representation of wave-like behavior and interference effects. Superposition, a key principle of quantum mechanics, is directly manifested through linear combinations of these state vectors; a quantum state can exist as a combination of multiple basis states simultaneously, represented as $|\psi\rangle = \sum_{i} c_i |\phi_i\rangle$, where $c_i$ are complex coefficients and $|\phi_i\rangle$ represent the basis states. The complex nature of the vector space is crucial for accurately modeling the probabilistic and wave-like aspects of quantum systems.

Quantum states evolve in time according to unitary transformations, mathematically represented by unitary operators. These operators, acting on the state vector in Hilbert space, preserve the inner product, which corresponds to the probability amplitude. Consequently, the total probability, calculated as the sum of the squared magnitudes of the amplitudes, remains constant over time – a fundamental requirement for a physically consistent system. Specifically, if $|\psi(t)>$ represents the quantum state at time $t$, its evolution is described by the time-dependent Schrödinger equation: $i\hbar \frac{d}{dt}|\psi(t)> = H|\psi(t)>$, where $H$ is the Hamiltonian operator and the solution is given by $|\psi(t)> = U(t)|\psi(0)>$, with $U(t)$ being a unitary operator ensuring probability conservation.

Local tomography refers to the process of reconstructing the complete quantum state, represented as a density matrix $ \rho $, from a set of measurements performed on a subsystem of the overall system. This is achieved by collecting sufficient measurement statistics that, when analyzed using reconstruction algorithms, yield an accurate estimate of $ \rho $. The ability to perform local tomography is vital because it validates the program’s predictive capacity; a successful reconstruction demonstrates that the system’s future behavior can be accurately forecast based solely on accessible, local data. Crucially, it bypasses the need for global state knowledge, making the program applicable to scenarios where full system access is impractical or impossible, and allows for verification of the internal consistency of the model against experimental results.

The principle of Symmetric Transition Probabilities, formalized as $P(x \rightarrow y) = P(y \rightarrow x)$, dictates that the probability of a quantum system transitioning from state $x$ to state $y$ must equal the probability of transitioning from $y$ to $x$. This constraint arises from the requirement of a consistent and physically realistic dynamical description. Without this symmetry, the resulting evolution would violate fundamental principles of quantum mechanics, potentially leading to non-unitary time evolution or inconsistencies in observable quantities. Specifically, the symmetry ensures that the transition rates between states are reciprocal, preventing preferential directional behavior not dictated by the system’s Hamiltonian and maintaining the integrity of probabilistic predictions.

Beyond Quantum: Mapping the Theoretical Landscape

The Quantum Reconstruction Program represents a significant departure from traditional validation of quantum mechanics, instead functioning as a framework for theoretical expansion. This program meticulously dissects the fundamental postulates underpinning quantum theory, not to confirm their accuracy, but to identify the minimal set of assumptions necessary for its operation. By isolating these core principles, physicists can then systematically explore alternative mathematical structures and probabilistic rules that also satisfy these postulates. The result is the development of Generalized Probabilistic Theories – frameworks that, while consistent with observed quantum phenomena, may predict different behaviors under novel conditions or offer insights into scenarios beyond the reach of standard quantum mechanics. This approach doesn’t seek to disprove quantum mechanics, but rather to map its place within a broader landscape of possible physical theories, potentially revealing deeper connections and unveiling previously unknown laws governing the universe.

The pursuit of theories beyond quantum mechanics hinges on a precise dissection of its fundamental principles – its core postulates. Researchers are now systematically identifying these foundational axioms, not to dismantle quantum theory, but to define the boundaries of its essential characteristics. This allows for the construction of alternative theoretical frameworks that, while adhering to these same postulates, predict demonstrably different physical behaviors. By exploring these Generalized Probabilistic Theories, scientists can rigorously test the necessity of specific quantum features – such as superposition or entanglement – and potentially reveal deeper, more encompassing laws governing the universe. This process isn’t about finding flaws in quantum mechanics, but understanding why it works, and what other logically consistent, yet distinct, realities might also be possible, expanding the landscape of theoretical physics beyond its current limitations.

By systematically examining the foundational principles of quantum mechanics, researchers are unveiling connections to more universal physical laws. This investigation isn’t simply about confirming existing quantum predictions; it’s a deliberate effort to discern the broader context within which quantum phenomena operate. The process involves identifying core postulates – the fundamental assumptions upon which quantum theory is built – and then exploring alternative theoretical frameworks that adhere to those same principles. While these alternative theories may predict different outcomes in specific scenarios, their shared adherence to the core postulates suggests a deeper, underlying unity. This pursuit of generalized probabilistic theories, grounded in the established framework of quantum mechanics, holds the potential to reveal previously unknown physical principles and ultimately, expand the boundaries of human understanding regarding the nature of reality itself.

The burgeoning field of quantum information – encompassing technologies like quantum computing, cryptography, and sensing – provides both the necessary tools and compelling motivations for extending quantum mechanical frameworks. Recent progress in manipulating and measuring quantum states with unprecedented precision allows physicists to rigorously test the boundaries of the theory and explore potential deviations. Moreover, the drive to build practical quantum devices necessitates a deeper understanding of the underlying principles, prompting investigation into generalized probabilistic theories that might offer advantages in specific applications. This technological impetus, coupled with enhanced experimental capabilities, creates a synergistic environment where theoretical exploration and practical innovation mutually reinforce each other, paving the way for a more complete understanding of reality and potentially unlocking novel technologies beyond the current quantum landscape.

The Minimal Interpretation: A Pragmatic Path Forward

Quantum theory, despite its predictive power, is frequently veiled by interpretative biases arising from an overemphasis on mathematical formalism at the expense of direct experimental engagement. This prioritization can lead researchers to favor elegant, yet potentially misleading, theoretical constructs over insights gleaned from observable phenomena. The tendency to build interpretations primarily upon the mathematical structure – the equations and operators – risks obscuring the fundamental physical principles at play. Consequently, the true implications of quantum mechanics, particularly regarding the nature of measurement, locality, and realism, become distorted through a lens heavily influenced by mathematical convenience rather than empirical validation. A focus on rigorous experimental testing, coupled with a willingness to challenge preconceived theoretical notions, is therefore crucial for accurately deciphering the profound messages embedded within the quantum realm and avoiding interpretations that diverge from observable reality.

A strictly minimal physical interpretation of quantum theory prioritizes the foundational understanding necessary for its practical application in experiments, effectively mitigating the influence of interpretative biases. Rather than imposing complex metaphysical frameworks, this approach centers on the core principles – wave function evolution governed by the Schrödinger equation, probabilistic measurement outcomes, and the role of observation – as directly observable and quantifiable phenomena. By focusing solely on what is required to use the theory – predicting experimental results and designing new experiments – researchers avoid getting lost in abstract debates about the ‘true’ nature of reality. This pragmatic stance doesn’t necessarily resolve philosophical questions, but it allows for continued scientific progress by ensuring that interpretations remain grounded in empirical evidence and do not hinder the development of new technologies or deeper experimental investigations. The emphasis on operational definitions and predictive power, therefore, functions as a crucial safeguard against allowing mathematical elegance to overshadow physical relevance.

A minimal philosophical interpretation of quantum theory seeks to bridge the gap between its counterintuitive predictions and established philosophical thought, fostering a more unified understanding of reality. Rather than imposing pre-existing metaphysical frameworks, this approach prioritizes identifying the core philosophical commitments inherent within the mathematical formalism and experimental results themselves. By avoiding unnecessary philosophical embellishments, it allows quantum mechanics to be reconciled with diverse viewpoints – from realism and idealism to pragmatism – without forcing a single, potentially restrictive, interpretation upon the entire field. This careful approach doesn’t aim to ‘solve’ philosophical problems with physics, but rather to clarify the philosophical implications arising from the theory, ensuring that quantum mechanics is understood not as a challenge to all philosophical reasoning, but as a novel perspective within it, demanding a re-evaluation of established concepts like causality, objectivity, and the nature of existence itself.

Quantum phenomena are often described by characteristics that appear mutually exclusive, demanding a reconciliation through the principle of complementarity, particularly regarding persistence and nonpersistence. A quantum entity doesn’t simply exist in a defined state, nor does it entirely not exist; rather, its manifestation depends critically on the observational context. This isn’t merely a limitation of measurement, but an inherent property of quantum reality. Consider, for instance, the wave-particle duality: an electron can exhibit wave-like behavior, spreading through space as a probability distribution – a persistence of potential – yet collapses into a definite particle location upon measurement – a nonpersistence of that spread. This interplay isn’t paradoxical, but fundamental; both aspects are necessary for a complete description. Accepting that a quantum system simultaneously embodies both the potential for continued existence as a superposition and the definite actuality of a measured state, rather than forcing one to dominate, offers a more nuanced and accurate understanding of quantum behavior, moving beyond classical intuitions about definite properties and trajectories.

The Bohmian interpretation reformulates the Schrödinger equation to describe particle trajectories guided by a quantum potential.

The pursuit of a ‘reconstruction-based interpretation’ feels…optimistic. This article attempts to derive quantum formalism from fundamental principles, a noble goal, but one destined to become tomorrow’s tech debt. It’s reminiscent of building elegant cathedrals on shifting sand. As Paul Dirac once said, “I have not the slightest idea how it works.” The inherent ambiguity in quantum mechanics, the attempt to ground it in operational frameworks – it’s all well and good until production finds a way to violate those frameworks. The article suggests resolving interpretational bias through rigorous reconstruction; one suspects the archaeologists will find plenty of exceptions. They don’t write code – they leave notes for digital archaeologists.

So, What Breaks Next?

This exercise in systematizing quantum interpretation via reconstruction – elegantly deriving formalism from operational principles – feels suspiciously like rearranging deck chairs on the Titanic. The paper correctly identifies the core issue: interpretational bias creeping into the very foundations. But the assumption that a ‘correct’ derivation will somehow solve the measurement problem feels… optimistic. Production, as always, will find a way to disagree with the theory. It will likely expose the limitations of any chosen operational framework, and the inevitable approximations introduced during reconstruction.

The real challenge isn’t finding the ‘right’ derivation, but acknowledging that any such derivation is, at best, a useful fiction. The pursuit of metaphysical interpretations, even those seemingly grounded in operational rigor, should proceed with a healthy dose of skepticism. One anticipates a proliferation of competing reconstructions, each with its own preferred set of ‘fundamental principles’ – a new cottage industry of foundational squabbles, beautifully formalized.

Ultimately, this work highlights a recurring pattern: everything new is old again, just renamed and still broken. The next step isn’t more derivation, but more…reality. More experiments pushing the boundaries of quantum mechanics, relentlessly exposing the cracks in whichever reconstruction currently holds sway. Let the data be the judge, not the axioms. And prepare for the alerts.

Original article: https://arxiv.org/pdf/2512.18002.pdf

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