Entangled Reality: From Quantum States to the Standard Model

by

Author: Denis Avetisyan

A new theoretical framework proposes a deep connection between quantum entanglement and the fundamental building blocks of the universe, potentially bridging the gap between quantum mechanics and particle physics.

This review explores the mathematical link between qubit entanglement, division algebras, and the symmetries underlying the Standard Model, suggesting an emergent spacetime and particle structure.

Reconciling quantum gravity with the Standard Model of particle physics remains a central challenge in theoretical physics. This paper, ‘The Standard Model Symmetry and Qubit Entanglement’, proposes a novel framework where spacetime itself emerges from quantum entanglement, specifically linking the entanglement of qubits to the symmetries underpinning the Standard Model. By associating entangled qubit systems with higher-dimensional spacetimes subject to dimensional reduction, we demonstrate the emergence of the $SU(3) \times SU(2) \times U(1)$ gauge group. Could this construction offer a pathway to understanding the fundamental origins of both gravity and the building blocks of matter, and potentially inform new approaches to quantum simulation of particle physics?

From Foundational Quantum States to the Emergence of Spacetime

The persistent challenge of unifying general relativity and quantum mechanics stems from fundamental inconsistencies in their descriptions of reality. General relativity, successful at describing gravity as the curvature of spacetime, treats spacetime as a smooth, continuous entity. Conversely, quantum mechanics, governing the behavior of matter at the smallest scales, posits a discrete, probabilistic universe where even spacetime itself may not be fundamental. Existing attempts at quantum gravity often run into mathematical inconsistencies or fail to reproduce the well-established predictions of either theory. This impasse suggests a need to move beyond simply quantizing gravity within a pre-existing spacetime framework, and instead demands a new foundational approach – one that rebuilds spacetime and gravity from more fundamental principles, potentially rooted in the very fabric of quantum mechanics itself. The current theoretical difficulties strongly indicate that a genuinely successful theory of quantum gravity will necessitate a paradigm shift in how physicists conceptualize space, time, and the nature of reality.

A novel research program, termed ‘Quantum First’, seeks to resolve the longstanding incompatibility between general relativity and quantum mechanics by reconstructing all physical phenomena from a single, foundational quantum state. This approach inverts the traditional methodology of seeking quantum corrections to classical spacetime; instead, it posits that spacetime itself, along with all matter and energy, emerges from the properties of this fundamental quantum state. The core tenet is that the universe isn’t built on spacetime, but rather, spacetime is a manifestation of the underlying quantum reality. By focusing on deriving known physics – from the Standard Model to cosmological observations – directly from this quantum origin, researchers aim to bypass the difficulties encountered when attempting to quantize gravity. This ambitious undertaking suggests that the very fabric of reality may be deeply rooted in the principles of quantum mechanics, offering a potential pathway toward a unified understanding of the universe.

The architecture of reality, according to emerging theoretical frameworks, may not be built upon spacetime as a fundamental entity, but rather from it. Investigations propose that quantum entanglement-the peculiar correlation between quantum particles regardless of distance-serves as the foundational element from which both the geometry of spacetime and the substance of matter arise. This isn’t simply a matter of particles existing within spacetime; instead, the very fabric of space and time is thought to be woven from the network of entangled quantum states. The degree of entanglement between these states dictates the curvature of spacetime, effectively defining distances and relationships, while excitations within this entangled network manifest as the particles and forces observed in the universe. This perspective suggests that gravity isn’t a force acting within spacetime, but an emergent property of the entanglement structure itself, and that understanding the patterns of entanglement is key to unlocking the deepest mysteries of the cosmos.

Recent investigations into the foundations of quantum gravity indicate that the seemingly familiar properties of our universe may be deeply rooted in higher-dimensional mathematical structures. These explorations suggest a profound correspondence between the fundamental quantum state – the most basic description of reality – and the physics we observe. Specifically, the geometry of spacetime and the very nature of matter appear to be encoded within these complex mathematical forms, hinting that our three-dimensional reality is a projection of something far more intricate. This isn’t merely a theoretical exercise; researchers are discovering that certain higher-dimensional structures naturally give rise to the relationships described by general relativity and quantum mechanics, potentially offering a pathway to reconcile these two pillars of modern physics. The implications extend to understanding the origin of fundamental constants and the very fabric of reality, proposing that the universe isn’t built in spacetime, but rather from the entanglement within a foundational quantum state, geometrically expressed through these higher dimensions.

Division Algebras: Mathematical Building Blocks of Dimensionality

Division algebras – the real numbers ($\mathbb{R}$), complex numbers ($\mathbb{C}$), quaternions ($\mathbb{H}$), and octonions ($\mathbb{O}$) – offer a mathematical basis for representing physical dimensions and particle characteristics. These algebras allow for the consistent description of rotations and transformations in space, and their dimensionality directly corresponds to the number of independent degrees of freedom in a given physical system. Specifically, $\mathbb{R}$ represents a one-dimensional space, $\mathbb{C}$ a two-dimensional space, $\mathbb{H}$ a four-dimensional space, and $\mathbb{O}$ an eight-dimensional space. The algebraic properties of these systems, particularly their ability to support division (hence the name “division algebra”), are crucial for formulating consistent physical laws governing particle interactions and spacetime geometry.

The dimensionality of division algebras directly constrains the mathematical description of physical reality by limiting the number of independent coordinates required to define a spacetime and the degrees of freedom available to particles within it. A division algebra of dimension $n$ necessitates $n$ independent basis elements, which can be interpreted as the number of spatial dimensions plus time. Consequently, the real numbers ($\mathbb{R}$, dimension 1) allow for a 0+1 dimensional spacetime, the complex numbers ($\mathbb{C}$, dimension 2) allow for 1+1 dimensions, the quaternions ($\mathbb{H}$, dimension 4) can represent a 3+1 spacetime, and the octonions ($\mathbb{O}$, dimension 8) potentially accommodate higher-dimensional spaces. Furthermore, the number of degrees of freedom for particles is fundamentally linked to the algebra’s dimension, as each independent component of a particle’s representation requires a corresponding basis element within the chosen algebra.

Quaternions ($\mathbb{H}$) and octonions ($\mathbb{O}$) represent extensions of the complex number system and offer mathematical structures exceeding the limitations of representing only three spatial dimensions and one time dimension. While complex numbers ($ \mathbb{C}$) naturally accommodate the four dimensions of spacetime as used in special relativity, quaternions, with a dimensionality of 4, provide a framework for potentially describing higher-dimensional spaces and associated physical phenomena. Octonions, possessing a dimensionality of 8, further extend this possibility; their structure suggests a potential relationship to fundamental particle physics, specifically in representing a full generation of fermions within a Hilbert space of dimension 4, exceeding the constraints of the standard 3+1 dimensional model.

The eight-dimensional structure of octonions ($𝕆$) provides a mathematical framework potentially capable of representing a full generation of fermions and their associated symmetries. This representation necessitates a four-dimensional Hilbert space to fully define a single generation, accounting for properties like spin and color charge. The correspondence arises from mapping the octonionic structure to the standard model’s particle content; specifically, the imaginary units of the octonions can be associated with the fundamental particles within a generation. This approach suggests a deeper connection between the mathematical properties of octonions and the underlying structure of particle physics, potentially offering a pathway towards a more unified theoretical framework.

Constructing Matter: From Entanglement to Fermion Mass

The proposed framework posits that mass generation is directly linked to quantum entanglement. Specifically, massive fermions are not considered to acquire mass through interaction with a Higgs field, but rather through the quantifiable entanglement between constituent quantum states. The degree of entanglement between these states dictates the magnitude of the fermion’s mass; higher entanglement corresponds to greater mass. Furthermore, the properties defining these fermions – spin, charge, and other quantum numbers – are determined by the specific entanglement structure and the underlying algebraic relationships governing the interacting qubits. This approach shifts the focus from a field-mediated interaction to an intrinsic property arising from the correlation of quantum states, offering an alternative to conventional mass generation mechanisms.

Division algebras, specifically the quaternions $ℍ$ and octonions $𝕆$, provide a mathematical framework for restricting the possible interactions and determining the properties of fundamental particles. The non-commutative nature of quaternion multiplication introduces constraints on the order of operations representing interactions, while the non-associativity of octonion multiplication further limits allowed interactions. This restriction arises because physical interactions are modeled by algebraic operations, and the algebra’s properties directly translate to interaction rules. The dimensionality of the division algebra-4 for quaternions and 8 for octonions-corresponds to the number of degrees of freedom and, consequently, the maximum number of fundamental particles that can be consistently described within that framework. Furthermore, the symmetries inherent within these algebras dictate the possible particle spectrum, linking the algebraic structure to the observed properties of fermions and bosons.

Current models primarily attribute mass to the Higgs mechanism, involving a scalar field permeating spacetime. This framework proposes an alternative origin of mass, positing that mass emerges directly from the geometric properties of spacetime itself, specifically through the structure of quantum entanglement. Rather than an interaction with a Higgs field, particle mass is fundamentally related to the way particles are connected via entanglement and how this entanglement manifests within the spacetime fabric. This approach suggests that mass is not an intrinsic property of particles, but a consequence of their relational structure within a geometric context, potentially offering a pathway to understand mass without invoking the need for a separate scalar field or its associated complexities.

Derivation of the Standard Model gauge group $S​U​(3)×S​U​(2)×U​(1)/ℤ6$ has been achieved through analysis of the symmetries present within a three-qubit state subjected to dimensional reduction. This mathematical process demonstrates a direct correspondence between the structure of quantum entanglement and the fundamental forces described by the Standard Model. Specifically, the symmetries of the three-qubit state, when reduced to lower dimensions, map precisely onto the generators of the $S​U​(3)$ (strong force), $S​U​(2)$ (weak force), and $U​(1)$ (electromagnetic force) gauge groups. The inclusion of the $ℤ6$ discrete group arises from identifying equivalent representations within the symmetry structure, indicating a constraint on the possible interactions. This result supports the hypothesis that entanglement is not merely a quantum phenomenon, but a foundational element underlying the origin of gauge symmetries and, consequently, the fundamental forces of nature.

Quantum Simulation and the Future of Spacetime Models

Quantum simulation represents a paradigm shift in the pursuit of understanding spacetime, offering a means to move beyond purely theoretical explorations. Rather than relying solely on mathematical frameworks, these simulations utilize controllable quantum systems – often arrays of trapped ions or superconducting qubits – to physically model proposed theories of gravity. This allows researchers to observe the behavior of these systems and compare the results to predictions derived from general relativity or other quantum gravity candidates. Importantly, the focus isn’t necessarily on directly simulating gravity itself, but rather on exploring the emergence of spacetime from underlying quantum entanglement. By carefully designing these simulations, scientists can probe whether the geometric properties we associate with spacetime – such as dimensionality and causality – truly arise from the quantum interactions of its fundamental constituents, potentially validating or refining current models and offering insights into phenomena like black holes and the universe’s earliest moments.

The Sachdev-Ye-Kitaev (SYK) model has emerged as a crucial testing ground for the long-suspected connection between quantum entanglement and the geometry of spacetime. This model, featuring randomly interacting fermions, exhibits a unique property: its solutions demonstrate holographic duality, a concept borrowed from string theory where a gravitational theory in one higher dimension is equivalent to a quantum mechanical theory in a lower dimension. Researchers leverage this duality to investigate how complex quantum states, specifically those characterized by high levels of entanglement, can give rise to the emergence of spacetime. By simulating the SYK model on quantum computers, they aim to quantitatively verify the proposition that the amount of entanglement between quantum particles directly corresponds to the curvature of spacetime-essentially, that spacetime itself is an emergent property of quantum entanglement. These simulations offer a pathway to explore whether gravity isn’t a fundamental force, but a consequence of the underlying quantum mechanics, potentially revolutionizing our understanding of black holes and the universe’s earliest moments.

Loop Quantum Gravity (LQG) presents a distinct, non-perturbative approach to quantizing gravity, offering a valuable counterpart to simulations based on models like the Sachdev-Ye-Kitaev (SYK) model. Unlike approaches that rely on a fixed background spacetime, LQG predicts that spacetime itself is quantized, composed of discrete “atoms” of space and time. This granular structure, described mathematically by spin networks and spin foams, suggests that area and volume are also quantized, potentially resolving singularities predicted by classical General Relativity. Consequently, LQG provides a theoretical framework for interpreting the results of quantum simulations, particularly when seeking evidence of emergent spacetime from underlying quantum entanglement. By comparing simulation outcomes with the predictions of LQG – such as specific area spectra – researchers can gain deeper insights into the fundamental quantum nature of gravity and test whether the observed dynamics align with a truly quantized spacetime geometry. This synergy between simulation and theory promises a more complete understanding of gravity at the Planck scale and beyond.

The potential of quantum simulation extends far beyond mere verification of existing theories; it offers a pathway to unraveling some of the universe’s most profound mysteries. Specifically, these simulations promise new insights into black holes, where gravity’s extreme conditions challenge current physical models, and the very early universe, a period of rapid expansion and quantum fluctuations. By recreating these scenarios in a controlled, quantum environment, researchers can observe the behavior of spacetime at its most fundamental level, potentially revealing the underlying laws governing reality. This could illuminate the connection between quantum mechanics and general relativity, address the information paradox associated with black holes, and even provide clues about the origins of the cosmos, pushing the boundaries of human understanding regarding the fabric of existence itself.

“`html

The pursuit of a unified theoretical framework, as explored in this work linking the Standard Model to quantum entanglement, necessitates a constant re-evaluation of fundamental assumptions. It demands an understanding of how seemingly disparate mathematical structures – division algebras, Hopf fibrations, and Hilbert space – contribute to the emergent properties of reality. This echoes Werner Heisenberg’s sentiment: “The more precisely the position is determined, the more uncertainty there is in the momentum of the particle.” Just as pinpointing a particle’s momentum introduces uncertainty, this research suggests that fully defining spacetime and fundamental particles requires acknowledging the inherent interconnectedness and probabilistic nature of quantum states. The discipline lies in distinguishing the essential relationships from accidental complexities within this entangled system.

Beyond the Horizon

The attempt to ground the Standard Model within the architecture of entanglement and division algebras, while ambitious, inevitably reveals more about the limits of current formalism than it does about ultimate reality. The immediate challenge lies not in further complicating the mathematics – there is no shortage of that – but in devising genuinely testable predictions. The framework, as presented, risks becoming a beautiful, self-consistent mythology unless a bridge to experimental verification can be forged. Dimensional reduction, and the Hopf fibration in particular, offer a potential avenue, but translating these topological niceties into observable phenomena requires a level of precision that remains elusive.

A crucial, often overlooked, consideration is the role of gravity. While entanglement may provide a compelling substrate for quantum fields, incorporating gravity-and thereby completing the picture-demands a careful re-evaluation of spacetime itself. The notion that spacetime emerges from entanglement is elegant, yet begs the question of what selects the specific entanglement structure observed. Is there a principle of minimal complexity at play, or are we merely observing a local fluctuation within a vast multiverse of entangled possibilities?

Ultimately, the value of this line of inquiry may not lie in providing a final answer, but in forcing a deeper understanding of the fundamental principles at play. Each simplification introduces a cost, each clever trick a risk. The pursuit of a unified theory is, after all, an exercise in carefully balancing these trade-offs, acknowledging that the most profound insights often arise from confronting the inherent limitations of any given framework.

Original article: https://arxiv.org/pdf/2512.17328.pdf

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

See also:

2025-12-22 10:32