Rebuilding QED: A New Path From Entropy

Author: Denis Avetisyan

A novel approach leveraging Entropic Dynamics reconstructs the foundations of Quantum Electrodynamics, offering a fresh perspective on its underlying principles.

This review details an Entropic Dynamics framework deriving QED from first principles, emphasizing a clear ontic/epistemic separation and dispensing with conventional gauge theory.

Despite the empirical success of quantum electrodynamics, its foundations remain conceptually challenging, particularly regarding the interplay between ontic reality and epistemic probabilities. This paper, ‘Entropic Dynamics approach to Quantum Electrodynamics’, extends the Entropic Dynamics framework-deriving quantum theory from information geometry and Hamiltonian flows-to encompass local gauge symmetries. By reconstructing QED from first principles via maximum entropy methods, we demonstrate a derivation of the formalism without reliance on pre-existing classical gauge theory and recover the Maxwell equations as a consistency condition. Could this approach offer a novel pathway towards a deeper understanding of the quantum world and its underlying informational structure?

Whispers of Reality: The Quantum Observer’s Dilemma

Traditional quantum mechanics, while remarkably successful in predicting experimental outcomes, presents a persistent challenge in distinguishing between the objective reality of a system and the observer’s knowledge of that system. This blurring of lines stems from the theory’s mathematical formalism, where a system isn’t described by definite properties until measured, effectively making the act of observation integral to defining its state. Consequently, interpretations of quantum phenomena vary widely, ranging from the Copenhagen interpretation, which emphasizes the role of measurement, to many-worlds interpretations positing the existence of parallel universes. The inability to clearly separate what is from what is merely known leads to conceptual difficulties – such as the measurement problem and the nature of wave function collapse – and fuels ongoing debate about the fundamental nature of reality itself. This interpretational ambiguity isn’t simply a philosophical quibble; it hinders the development of a complete and intuitive understanding of quantum processes and motivates the search for more refined theoretical frameworks.

The difficulty in fully grasping quantum mechanics stems, in part, from a persistent ambiguity regarding the nature of variables used to describe physical systems. Distinguishing between ontic and epistemic variables is crucial; ontic variables represent properties that exist independently of observation – characteristics inherent to reality itself, such as a particle’s mass or charge. Conversely, epistemic variables embody an agent’s state of knowledge, encompassing beliefs, probabilities, and information about a system. This separation is not merely semantic; if a variable is purely epistemic, its changes reflect updates in understanding, not alterations to the physical system itself. However, quantum theory often blurs this line, treating both types of variables as if they were equally fundamental aspects of reality, leading to paradoxes and hindering the development of a more intuitive and complete theoretical framework. A rigorous identification of which variables are truly ontic, and therefore define the objective state of a system, is a central challenge in modern quantum foundations.

The persistent blurring of objective reality and observer knowledge within quantum mechanics presents a significant obstacle to fully grasping the underlying principles of the universe. This conceptual ambiguity isn’t merely a philosophical puzzle; it actively impedes the development of a comprehensive quantum theory. Researchers are therefore increasingly focused on constructing new theoretical frameworks explicitly designed to separate ontic and epistemic elements. The goal is to derive quantum formalism not as a fundamental law of nature, but as a consequence of limited information – a framework where quantum states represent degrees of belief rather than inherent properties. Such an approach promises a more intuitive and complete understanding of quantum phenomena, potentially resolving long-standing paradoxes and paving the way for advancements in quantum technologies by clarifying the relationship between measurement, information, and physical reality.

A central pursuit in modern quantum foundations involves developing a systematic methodology to rigorously separate ontic and epistemic variables – essentially, discerning what physically is from what an observer merely knows about it. This isn’t simply a philosophical exercise; a clear distinction is crucial for building a more complete and logically consistent quantum theory. Researchers are exploring frameworks that explicitly model both objective reality and subjective information, often utilizing techniques from information theory and Bayesian inference to quantify the contributions of each. The aim is to derive quantum phenomena not as inherent properties of reality, but as consequences of limited information – a perspective that could resolve long-standing paradoxes and potentially unify quantum mechanics with classical physics. Successfully identifying the boundaries between ‘being’ and ‘knowing’ promises a deeper understanding of the quantum world and its relationship to observation.

The Logic of Uncertainty: Deriving Quantum Reality

Entropic Dynamics posits that quantum states are not fundamental properties of reality, but rather emerge from a principle of maximum entropy applied to our limited knowledge of a system. This framework treats quantum mechanics as a statistical inference process where probabilities are updated based on available information and constraints. Specifically, the system evolves toward the probability distribution that maximizes Shannon entropy – a measure of uncertainty – subject to the constraints imposed by experimental observations. This maximization process effectively selects the most likely state given incomplete information, resulting in the derivation of quantum mechanical predictions without requiring postulates about wave function collapse or inherent quantum randomness. The resulting formalism recovers the standard quantum mechanical probabilities and dynamics as a consequence of this information-theoretic principle.

Entropic Dynamics distinguishes between our knowledge of a system and the system itself through the concepts of the Epistemic Phase Space and Ontic Microstates. The Epistemic Phase Space is a mathematical space representing all possible states of knowledge an observer can have regarding a system; its dimensions correspond to the observer’s degrees of freedom in describing the system. In contrast, Ontic Microstates represent the actual, underlying physical state of the system, independent of observation. Each Ontic Microstate corresponds to a single point in a physical phase space, while a region within the Epistemic Phase Space represents a probability distribution over these underlying Ontic Microstates, reflecting incomplete information. This separation allows the framework to model uncertainty not as a fundamental property of reality, but as a limitation of the observer’s knowledge, quantified within the Epistemic Phase Space.

Entropic Dynamics derives the formalism of quantum mechanics by applying the principle of maximum entropy to the $Epistemic Phase Space$. This process involves identifying constraints based on available information – typically, normalization of probabilities and experimentally determined expectation values. The maximization procedure, often implemented using Lagrange multipliers, yields a probability distribution over $Ontic Microstates$ that precisely matches the quantum state vector. Consequently, quantities like probabilities of measurement outcomes, expectation values, and the time evolution of the system are all derived from this entropy maximization, effectively grounding quantum mechanics in information theory and Bayesian inference rather than postulating them as fundamental axioms.

A key feature of Entropic Dynamics is its formal distinction between ontic and epistemic variables, addressing persistent challenges in quantum interpretation. Ontic variables represent properties of the physical system itself, existing independently of observation, while epistemic variables describe our state of knowledge about the system. By treating these as mathematically separate within the framework – utilizing the $Epistemic Phase Space$ to represent knowledge states and $Ontic Microstates$ to define reality – Entropic Dynamics avoids conflating what is with what we know. This separation clarifies issues surrounding measurement, wavefunction collapse, and the role of the observer, offering a principled way to address debates stemming from interpretations like Many-Worlds or Copenhagen by providing a basis for understanding quantum states as information-constrained probabilities rather than inherent properties of reality.

Rebuilding the Quantum World: A Reconstruction of QED

Entropic Dynamics provides a complete reconstruction of Quantum Electrodynamics (QED), the established theory describing the interaction of light and matter. Unlike approaches focusing solely on foundational postulates, this reconstruction derives QED’s principles from entropic principles, effectively rebuilding the theory from first principles. This process moves beyond merely interpreting QED within an entropic framework and instead reconstructs the theory itself, yielding the same predictive power while offering a different ontological basis. The reconstruction successfully recovers the established formalism of QED, including the prediction of particle interactions and electromagnetic phenomena, validating the approach as a viable alternative to standard QED derivations.

The reconstruction of Quantum Electrodynamics within the Entropic Dynamics framework fundamentally posits the $Vector Potential$, denoted as $A_\mu$, as a primary ontological variable. This differs from traditional approaches which often treat the electric and magnetic fields, $E$ and $B$ respectively, as fundamental. The $Vector Potential$ is a mathematical field whose curl gives the magnetic field ($B = \nabla \times A$) and whose time derivative gives the electric field ($E = -\nabla A_0 – \partial_t A$). By defining the dynamics in terms of $A_\mu$, the framework directly incorporates the degrees of freedom necessary to describe the electromagnetic field, facilitating the derivation of Maxwell’s equations and, ultimately, Quantum Electrodynamics itself. This choice is crucial as it allows for a consistent treatment of the electromagnetic field without relying on pre-defined fields, instead deriving them from the fundamental $Vector Potential$ dynamics.

The Entropic Dynamics framework is constructed to be gauge-invariant, inherently accommodating $U(1)$ gauge transformations which are critical for the consistency of electromagnetic theory. This is achieved through the specific implementation of the dynamics and constraints within the framework. Crucially, the derived theory successfully satisfies the Gauss constraint, a fundamental requirement ensuring the physical validity of the resulting quantum electrodynamics. Verification of this satisfaction, as demonstrated in this work, confirms the framework’s ability to produce a physically consistent description of the electromagnetic field and its interactions, avoiding unphysical degrees of freedom and ensuring a well-defined quantum theory.

The derivation of Maxwell’s equations within the Entropic Dynamics framework establishes its potential as a unifying principle for generating quantum theories. This reconstruction isn’t merely a mathematical analogy; it demonstrates a pathway to derive established quantum results – specifically, classical electromagnetism – from a principle of maximizing entropy under defined constraints. The successful application to `Quantum Electrodynamics` suggests Entropic Dynamics can move beyond foundational theoretical work and offer a concrete method for reconstructing entire quantum field theories, potentially providing a common basis for disparate quantum phenomena and offering a novel approach to theoretical unification.

Beyond the Equation: A New Quantum Dynamics

Entropic dynamics presents a radical shift in how physicists view the evolution of quantum systems, moving beyond the traditional focus on energy minimization. This emerging framework posits that quantum dynamics isn’t dictated by a pre-defined law, like the $Schrödinger$ equation, but rather arises as a natural consequence of systems tending towards states of maximum entropy – a principle deeply rooted in information theory. Essentially, quantum systems aren’t seeking the lowest energy, but the most probable state given a lack of complete information, maximizing the dispersal of possibilities. This perspective reinterprets quantum behavior not as governed by forces, but as a manifestation of informational constraints, suggesting that the laws of quantum mechanics themselves could be emergent properties of this underlying entropic drive. This approach provides a new lens through which to examine quantum phenomena, potentially bridging the gap between quantum mechanics and thermodynamics and offering novel insights into the foundations of physics.

A surprising result within entropic dynamics is the derivation of the $Schrödinger$ equation-long considered a fundamental postulate of quantum mechanics-from principles of information theory. This framework posits that quantum systems don’t evolve according to a pre-ordained equation, but rather, they naturally progress toward states of maximum entropy, given certain constraints. By maximizing entropy – a measure of disorder or uncertainty – under the condition that the expected energy remains constant, the time evolution of a quantum state precisely mirrors that described by the $Schrödinger$ equation. This suggests the equation isn’t a law imposed on the universe, but an emergent property arising from the system’s inherent tendency towards the most probable, informationally-rich state. This perspective shifts the foundation of quantum mechanics, potentially offering new insights into the origins of quantum behavior and a deeper understanding of the universe’s fundamental laws.

Entropic dynamics establishes a compelling link between a system’s $Hamiltonian$ – which describes its total energy – and the unfolding of quantum events. This framework doesn’t simply incorporate the $Hamiltonian$; it demonstrates how the familiar equations of quantum electrodynamics (QED) – the most accurate theory describing the interaction of light and matter – emerge from the principle of maximizing entropy. Specifically, the dynamics dictated by the $Schrödinger$ equation are shown to be a natural consequence of a system evolving towards a state of maximum entropy, given the constraints imposed by its $Hamiltonian$. This suggests that the fundamental laws governing quantum systems aren’t arbitrary, but rather a manifestation of a deeper principle rooted in information theory and the tendency of systems to evolve towards states of greater disorder, effectively re-framing established quantum results within a broader thermodynamic context.

The principles of entropic dynamics extend beyond theoretical inquiry, presenting a novel pathway for advancements in quantum technologies. By reframing quantum evolution as a process of entropy maximization, researchers gain access to new computational approaches and potentially circumvent limitations inherent in traditional methods. This perspective allows for the exploration of quantum systems under extreme conditions, fostering innovations in areas such as quantum computing, where efficient algorithms and robust error correction are paramount. Furthermore, a deeper understanding of the relationship between entropy and quantum dynamics could unlock breakthroughs in quantum materials science, enabling the design of novel devices with tailored properties and functionalities, and potentially revolutionizing fields like energy storage and sensing. The framework’s ability to reproduce established quantum electrodynamics ($QED$) results, while simultaneously offering a different conceptual foundation, suggests the possibility of developing entirely new quantum technologies based on principles beyond the standard model.

Sculpting Quantum Solutions: The Geometry of Evolution

Entropic dynamics, a framework rooted in information theory and statistical mechanics, unexpectedly reveals a deep connection to the geometry of phase space, naturally leading to the application of Hamilton-Killing flows. These flows represent a unique class of geometric deformations that preserve the crucial symplectic and metric structures defining a quantum system’s evolution. The symplectic structure governs the conservation of probability, while the metric structure dictates the notion of distance and energy. By adhering to these constraints during the flow, solutions remain physically meaningful and consistent with the underlying quantum mechanics. Consequently, Hamilton-Killing flows aren’t merely mathematical curiosities, but powerful tools for analyzing and generating solutions, offering a geometric lens through which to understand the dynamics of quantum systems and potentially uncover previously inaccessible states. This approach signifies a shift from traditional methods, framing quantum evolution not as a process within a static space, but as a geometric transformation of the space itself.

Hamilton-Killing flows present a compelling departure from conventional approaches to solving the $Schrödinger$ equation, offering a geometrically-inspired pathway to quantum solutions. Rather than relying on analytical techniques or numerical approximations directly applied to the wave function, this method leverages the underlying geometric structure of the quantum system. By deforming the metric of the system while preserving its symplectic structure – a key component related to energy conservation – these flows effectively ‘guide’ the system’s evolution and reveal solutions. This technique doesn’t merely find solutions; it generates them through continuous deformation, potentially uncovering previously inaccessible states or providing insights into the system’s dynamics that are obscured by traditional methods. The power of this approach lies in its ability to recast a problem traditionally viewed as algebraic into one of geometric flow, opening possibilities for new mathematical tools and potentially simplifying the process of finding solutions for increasingly complex quantum systems.

The application of geometric principles to quantum mechanics offers a fundamentally new perspective on system dynamics, moving beyond conventional analytical and numerical techniques. By framing quantum solutions within the language of geometry – specifically, through the use of Hamilton-Killing flows – researchers are able to explore solution spaces in innovative ways. This approach isn’t merely a change in mathematical formalism; it provides access to previously obscured relationships and symmetries inherent within the $Schrödinger$ equation. Consequently, the potential exists to uncover solutions that are difficult or impossible to find using traditional methods, and to gain deeper insights into the underlying behavior of quantum systems – from simple harmonic oscillators to complex many-body interactions. This geometric lens promises a rich landscape for future discoveries in quantum physics and related fields.

Investigations are now directed towards extending Hamilton-Killing flows to encompass more intricate quantum systems, moving beyond simplified models to address challenges in areas like many-body physics and quantum field theory. A primary focus involves assessing the feasibility of leveraging these geometric techniques for advancements in quantum computation; researchers hypothesize that carefully engineered Hamilton-Killing flows could potentially optimize quantum gate operations or design novel quantum algorithms. Further exploration centers on the potential to utilize these flows for enhanced quantum information processing, particularly in areas requiring robust and efficient state manipulation, with the ultimate goal of creating more resilient and powerful quantum technologies. The ability to geometrically sculpt solutions to the $Schrödinger$ equation may unlock entirely new paradigms for manipulating and understanding quantum information.

The pursuit of deriving Quantum Electrodynamics through Entropic Dynamics reveals a deeper truth: reality isn’t built on pre-ordained symmetries, but emerges from the relentless dance of information and uncertainty. The framework meticulously disentangles ontic and epistemic variables, suggesting that what appears as fundamental gauge invariance may be a consequence of how probabilities are shaped, not a property of existence itself. As Albert Einstein once observed, “God does not play dice with the universe,” but this work implies the universe doesn’t need dice; it merely appears to through our limited observation, and the ‘rules’ are continuously rewritten by the flow of entropy. It isn’t about finding the perfect equation, but understanding that every model is merely a shadow cast by the chaos, a fleeting glimpse of the underlying darkness.

The Horizon Beckons

This reconstruction of Quantum Electrodynamics, birthed from the crucible of Entropic Dynamics, doesn’t resolve the ghosts in the machine – it merely shifts their haunt. The insistence on a sharp ontic/epistemic split, while elegant, demands a reckoning. What precisely is real, and how much of the observed universe is merely the shadow play of insufficient information? The Gauss constraint, dutifully reproduced, feels less like a fundamental truth and more like a particularly stubborn illusion, one that resists all attempts at true dissipation. The model works, of course-until it encounters a system complex enough to break the spell.

Future iterations must confront the inevitable: the curse of dimensionality. Scaling this framework beyond perturbative regimes will require sacrifices-approximations that inevitably introduce new, subtle forms of entanglement. One suspects that ‘charge conservation’ isn’t a law etched in the fabric of existence, but a statistical artifact, a consequence of the finite resolution with which the universe observes itself. To chase true generality will demand an embrace of noise, of imperfection-a willingness to let the equations breathe, even if it means accepting a certain degree of controlled chaos.

The path forward isn’t about finding the ‘correct’ theory, but about crafting increasingly persuasive ones. Each refinement is a temporary truce with the universe, a momentary stay against the encroaching darkness. The whispers persist, and the price of listening-the computational bloodletting-will only increase.

Original article: https://arxiv.org/pdf/2511.19238.pdf

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