Fragmented Reality: A Quantum Link Between Energy, Dark Energy, and Spacetime

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Author: Denis Avetisyan

New research proposes that the very fabric of spacetime emerges from the fragmentation of the Universe’s quantum state, offering a novel perspective on dark energy and the nature of gravity.

This paper explores the implications of an SU(∞) Quantum Gravity framework for understanding energy-momentum, dark energy, and the emergence of classical spacetime through Hilbert space fragmentation and quantum entanglement.

Reconciling quantum mechanics with general relativity remains a central challenge in modern physics, demanding novel approaches to understanding gravity and cosmology. This paper, ‘Energy-momentum and dark energy in $\boldsymbol{SU(\infty)}$-QGR quantum gravity’, introduces a fundamentally quantum framework-$SU(\infty)$-QGR-where the Universe’s Hilbert space fragmentation generates emergent spacetime and symmetries. We demonstrate that this fragmentation leads to an effective action resembling Einstein’s equations, incorporating energy-momentum tensors for all components, and offers a potential explanation for both inflation and the observed late-time acceleration of the Universe-potentially linking dark energy to the quantum structure of the cosmos. Could the evolution of quantum states within this fragmented Hilbert space provide a deeper understanding of cosmological phenomena and the emergence of classical reality?

The Illusion of Smooth Spacetime

The persistent difficulty in formulating a consistent theory of quantum gravity stems from a fundamental incompatibility between general relativity and quantum mechanics. General relativity elegantly describes gravity as the curvature of spacetime, a smooth and continuous fabric, while quantum mechanics governs the probabilistic behavior of matter at the smallest scales. Attempts to merge these frameworks often result in mathematical inconsistencies, most notably the appearance of singularities – points where physical quantities become infinite. These singularities signal a breakdown in the theory’s predictive power, indicating that the universe, under extreme conditions like those near black holes or at the very beginning of time, behaves in ways current models simply cannot describe. The resulting paradoxes highlight the need for a new theoretical foundation that can smoothly reconcile the seemingly disparate realms of the very large and the very small, resolving these inconsistencies and offering a unified understanding of the cosmos.

The conventional picture of the universe relies on a smooth, continuous spacetime fabric, but emerging theoretical frameworks suggest this may be an approximation. At the most fundamental level, reality might not be a seamless expanse, but rather a highly fragmented quantum state-a mosaic of discrete, interconnected pieces. This concept challenges the foundations of both general relativity and quantum field theory, as it implies spacetime itself isn’t a pre-existing arena, but an emergent property arising from this underlying fragmentation. Describing this state necessitates moving beyond traditional field-based approaches and exploring models where spacetime geometry is a derived quantity, potentially linked to quantum entanglement and information density. Such a fragmented reality could resolve inconsistencies encountered when attempting to unify gravity with quantum mechanics, offering a pathway towards a complete description of quantum gravity and a deeper understanding of the universe’s origins.

The persistent cosmological constant problem – the vast discrepancy between theoretical predictions and observed values of dark energy – strongly suggests that current understandings of quantum gravity are incomplete. A fragmented view of quantum reality offers a potential pathway toward resolution by challenging the conventional treatment of vacuum energy. In this framework, spacetime isn’t a smooth backdrop but a dynamically emerging structure built from discrete quantum constituents; this fundamentally alters how vacuum energy contributions are calculated, potentially taming the otherwise infinite divergences that plague theoretical models. Achieving a complete theory of quantum gravity necessitates grappling with this fragmentation, as it directly impacts the nature of spacetime at the Planck scale and, consequently, the very fabric of the universe – resolving inconsistencies between quantum mechanics and general relativity requires acknowledging that reality, at its most fundamental level, isn’t continuous, but granular and profoundly fragmented.

Many conventional approaches to quantum gravity begin with the problematic assumption of a pre-existing spacetime framework, effectively treating space and time as a static backdrop against which quantum events unfold. This foundational premise creates a significant obstacle because it prevents a genuine description of how spacetime itself emerges from more fundamental quantum constituents. By presupposing spacetime, these methods struggle to address the universe’s earliest moments, where spacetime would have been dynamic and potentially non-existent, and fail to naturally incorporate the principles of general relativity at the quantum level. Consequently, the very nature of gravity, intrinsically linked to the geometry of spacetime, remains elusive, hindering progress toward a complete and consistent theory that unifies quantum mechanics and gravity.

Symmetry as the Foundation of Reality

The SU(∞)-QGR model postulates that the universe’s fundamental quantum state is governed by the infinite-dimensional special unitary group, SU(∞). This symmetry group serves as the mathematical basis for the emergence of spacetime, differing from conventional approaches which treat spacetime as a pre-existing background. The selection of SU(∞) is motivated by its capacity to describe a complete set of quantum states without requiring external parameters defining a spacetime manifold. Instead, the structure we perceive as spacetime is considered a derived property resulting from the dynamics governed by this symmetry. The SU(∞) group’s infinite dimensionality allows for a potentially infinite number of degrees of freedom to define the emergent spacetime, accommodating complexities observed in cosmological scales.

The SU(∞)-QGR model posits that the fundamental constituents of the universe’s quantum state are described by the generators of the infinite-dimensional SU(∞) symmetry group. These generators, mathematically represented as J_i where i ranges from 1 to infinity, function as the primary variables defining the quantum state, effectively bypassing the necessity for a pre-existing spacetime manifold. Instead of defining quantum properties within a spacetime, the model utilizes these generators to construct the state itself, with the resulting dynamics then giving rise to the observed spacetime structure. Each generator corresponds to a degree of freedom, and their commutation relations dictate the fundamental interactions and correlations within the quantum state, establishing a framework where spacetime is a derived property rather than a foundational assumption.

Within the SU(∞)-QGR model, quantum state evolution is not treated as occurring in a pre-existing spacetime, but rather as the fundamental mechanism generating spacetime itself. This departs from conventional quantum mechanics and general relativity, which assume a fixed spacetime background. The dynamics of the SU(∞) symmetry group dictate how the quantum state evolves, and this evolution manifests as the emergence of geometric properties – length, area, and volume – that are then interpreted as spacetime. Consequently, the model posits that spacetime is not a fundamental entity but an emergent property arising from the underlying quantum state and its associated symmetries, effectively reversing the conventional relationship between quantum phenomena and spacetime structure.

The Diffeo-Surface, within the SU(∞)-QGR model, functions as the parameter space defining all possible configurations of the emergent spacetime geometry. It is mathematically constructed from the SU(∞) generators and represents the space of all possible diffeomorphisms – smooth, invertible transformations – that can be applied to the emergent spatial structure. Each point on the Diffeo-Surface corresponds to a specific geometric configuration, effectively encoding the shape and connectivity of the emergent spacetime. The dynamics of the SU(∞) symmetry group then define how the system evolves across this surface, resulting in the observed changes in spacetime geometry; thus, the Diffeo-Surface isn’t in spacetime, but provides the foundation for its structure and evolution.

From Quantum Rules to Classical Geometry

The SU(∞)-QGR model posits that classical spacetime emerges as an effective metric derived from the fundamental quantum state through spontaneous symmetry breaking. Initially, the system exists in a highly symmetric state described by the SU(∞) group. This symmetry is then broken, leading to the identification of specific degrees of freedom that define the emergent geometric structure. The resulting effective metric, g_{\mu\nu}, is not a fundamental entity but rather a collective property arising from the organization of the underlying quantum state. This process establishes a correspondence between the Hilbert space of the quantum system and the manifold representing classical spacetime, effectively translating quantum information into geometric properties.

The SU(∞)-QGR model posits that the geometry of emergent spacetime is directly determined by the Affine Separation between quantum states. This separation, calculated as d = ||\psi_1 - \psi_2||, functions as a fundamental measure of distance within the emergent spacetime. Specifically, the Affine Separation quantifies the difference between two quantum states, \psi_1 and \psi_2, in an infinite-dimensional Hilbert space, and this difference is mapped onto the geometric separation of points in the classical spacetime manifold. Consequently, the relationships between quantum states, as defined by their Affine Separation, dictate the geometric properties-including distances and spatial relationships-observed in the emergent classical reality.

The SU(∞)-QGR model departs from traditional approaches to quantum gravity by employing the Yang-Mills field, typically used to describe fundamental forces in particle physics, to model gravitational dynamics. This formulation treats gravity not as a consequence of spacetime curvature, but as a manifestation of the Yang-Mills field acting on the quantum state. Specifically, the model leverages the non-Abelian nature of the Yang-Mills field – characterized by self-interacting gauge bosons – to define interactions between quantum states, effectively generating gravitational forces. This approach avoids the issues of non-renormalizability often encountered in perturbative quantum gravity by reformulating gravity as a gauge theory, and allows for the potential unification of gravity with other fundamental forces. The field strength tensor F_{\mu\nu} of this Yang-Mills field directly contributes to the effective metric defining the emergent spacetime geometry.

Investigations within the SU(∞)-QGR model reveal a quantifiable relationship between the Quantum Speed Limit (QSL) and the emergence of classical spacetime geometry. Specifically, the rate at which quantum states can evolve – as defined by the QSL \frac{d}{dt} |\psi(t)\rangle \leq \frac{2}{\hbar} ||H - E_0|| |\psi(t)\rangle – directly constrains the rate of change in the emergent spacetime metric. Analysis shows that deviations from the minimum QSL are correlated with curvature in the derived geometry; faster evolution of quantum states corresponds to greater spacetime curvature. This implies that the geometric properties of the emergent classical spacetime are not independent of the underlying quantum dynamics, but are fundamentally dictated by the limitations imposed on the evolution of the quantum state, effectively linking quantum information processing to the structure of spacetime.

The Universe’s Energy Budget and its Underlying Rules

The SU(∞)-QGR model uniquely integrates the Energy-Momentum Tensor into the very fabric of spacetime emergence. Unlike traditional approaches that treat spacetime as a pre-existing background, this model posits that spacetime arises from the complex interplay of quantum states. The Energy-Momentum Tensor, which mathematically describes the density and flux of energy and momentum, isn’t simply placed within spacetime; rather, it’s fundamental to its creation. This integration allows for a dynamic spacetime where the distribution of energy and momentum directly influences the geometry, potentially resolving inconsistencies between general relativity and quantum field theory. By treating these physical quantities as intrinsic to the emergent process, the model provides a framework for understanding how gravity itself arises from the underlying quantum structure, offering a potential pathway to a complete theory of quantum gravity and a more nuanced understanding of the universe’s large-scale structure.

The SU(∞)-QGR model addresses a longstanding challenge in cosmology: the cosmological constant problem. Theoretical calculations of the vacuum energy – the energy inherent in empty space – predict values vastly exceeding those observed through measurements of the universe’s expansion rate. This discrepancy, often cited as one of the most significant puzzles in modern physics, stems from the difficulty in accurately quantifying vacuum fluctuations. The model proposes a mechanism where the infinite-dimensional symmetry group inherent in the theory naturally regulates these fluctuations, effectively “taming” the vacuum energy. By connecting the energy-momentum tensor to the emergent spacetime geometry, the SU(∞)-QGR framework offers a pathway towards a self-regulating vacuum energy density, potentially bringing theoretical predictions into alignment with observational data and offering a more complete understanding of the universe’s accelerating expansion. This approach suggests the cosmological constant isn’t necessarily a fixed parameter, but rather a dynamic property arising from the underlying quantum structure of spacetime.

The accelerating expansion of the universe, a phenomenon currently attributed to dark energy, finds a potential explanation within the SU(∞)-QGR model through its connection of quantum fluctuations to vacuum energy density. This framework posits that the very fabric of space isn’t empty, but rather teeming with transient quantum fluctuations – virtual particles popping into and out of existence. These fluctuations, while typically considered negligible, contribute to an inherent energy density of the vacuum itself. The model demonstrates that the collective effect of these fluctuations can generate a repulsive gravitational force, counteracting the attractive force of matter and driving the observed accelerated expansion. Consequently, the cosmological constant, representing the energy density of empty space, isn’t a fixed parameter but an emergent property arising from the dynamics of quantum fluctuations, offering a potential resolution to the long-standing discrepancy between theoretical predictions and empirical observations of the universe’s expansion rate.

Investigations within the SU(∞)-QGR model reveal a critical role for ultraviolet (UV) modes in shaping the quantum vacuum. Calculations demonstrate these high-frequency modes exhibit a disproportionately large contribution to the overlap of quantum states, effectively amplifying local interactions at the Planck scale. This heightened interaction directly impacts the vacuum energy density, suggesting a dynamic relationship between quantum fluctuations and the cosmological constant. Furthermore, the concept of coherence reduction provides a quantifiable measure of decoherence – the loss of quantum coherence – and simultaneously elucidates how discernible features emerge within the overall global quantum state, hinting at a mechanism for the universe’s structure arising from fundamental quantum principles.

The pursuit of quantum gravity, as demonstrated in this exploration of SU(∞)-QGR, reveals a fascinating truth about how humans attempt to model reality. The fragmentation of Hilbert space, central to the paper’s argument regarding energy-momentum and dark energy, isn’t merely a mathematical construct; it’s a reflection of the inherent limitations of any complete description. This approach, seeking to understand spacetime’s emergence from quantum structure, highlights that models are built upon assumptions, interpretations, and, ultimately, human biases. As Paul Feyerabend observed, “Anything goes.” This isn’t nihilism, but rather an acknowledgement that there is no single, objective truth waiting to be discovered, only a multitude of perspectives, each with its own strengths and weaknesses. All behavior is a negotiation between fear and hope.

Where Do We Go From Here?

This exploration of SU(∞)-QGR, with its linking of Hilbert space fragmentation to cosmological phenomena, feels less like an arrival and more like a carefully constructed holding pattern. Every hypothesis, after all, is an attempt to make uncertainty feel safe. The proposal offers a compelling, if complex, architecture for understanding dark energy not as a property of spacetime, but as a consequence of its quantum underpinnings. But the model’s predictive power remains largely unaddressed; the translation of these elegant structures into testable, falsifiable claims is the obvious next hurdle.

The insistence on non-commutative geometry and the detailed accounting of energy-momentum tensors suggest a deep commitment to mathematical consistency. Yet, it is worth remembering that inflation is just collective anxiety about the future, and that even the most rigorous formalism is built on assumptions about what constitutes ‘reality’ at the Planck scale. Future work might benefit from a more direct engagement with the psychological biases inherent in model building-the desire for symmetry, the aversion to paradox, the need for a neat narrative.

Ultimately, the real challenge isn’t simply to refine the equations, but to confront the uncomfortable possibility that our current tools-mathematics, logic, even the very notion of objective observation-may be fundamentally inadequate to grasp the true nature of quantum gravity. The fragmentation of Hilbert space, so central to this framework, might well be a metaphor for the fragmentation of our knowledge itself.

Original article: https://arxiv.org/pdf/2604.10519.pdf

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

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2026-04-14 10:29