From Quantum Foam to Spacetime: A New Emergent Gravity?

Author: Denis Avetisyan

This review explores how quantum field theory might give rise to classical gravity, investigating the role of Planck constants in shaping spacetime itself.

The Akama-Diakonov-Wetterich theory links symmetry breaking phases to transitions between quantum mechanics and emergent gravity through dimensional analysis of the quantum vacuum.

The conventional separation between quantum field theory, quantum mechanics, and classical mechanics presents a foundational challenge in physics. This work, ‘Quantum and Classical mechanics vs QFT’, extends the Akama-Diakonov-Wetterich theory to explore emergent gravity, positing that Planck constants- $\hbar$ and $\hbar c$ -may constitute elements of the spacetime metric itself. The authors demonstrate how symmetry breaking mechanisms, or conversely emergent symmetry, can link pre-geometric quantum fields to the emergence of both quantum mechanics and classical physics through dimensional analysis, effectively treating $1/\hbar$ as an order parameter. Could this framework ultimately reconcile gravity with the quantum realm and redefine the relationship between fundamental physical laws?

The Illusion of Gravity: A Crisis in Fundamental Physics

The persistent challenge in modern physics lies in the incompatibility between general relativity and quantum mechanics. General relativity, which brilliantly describes gravity as the curvature of spacetime, operates on a smooth, continuous framework. Conversely, quantum mechanics governs the universe at the smallest scales, characterized by discrete, probabilistic behavior. Attempts to combine these theories – particularly when considering extreme conditions like black holes or the very early universe – consistently yield nonsensical results, such as infinite probabilities or undefined physical quantities. This fundamental discord suggests a flaw in current understandings of gravity, prompting exploration into alternative frameworks where gravity isn’t a fundamental force, but rather an emergent property arising from more basic quantum interactions. The resulting theoretical inconsistencies aren’t merely mathematical curiosities; they represent a profound crisis in the foundations of physics, demanding a radical rethinking of the nature of spacetime and gravity itself.

The Akama-Diakonov-Wetterich (ADW) theory challenges the conventional understanding of gravity, proposing it isn’t a force of the universe, but a consequence of it. This radical perspective suggests gravity emerges from the collective behavior of underlying quantum fields, much like temperature arises from the average kinetic energy of molecules. Instead of gravitons mediating a force between masses, ADW posits that gravity manifests as a long-wavelength approximation of more fundamental interactions at the quantum level. The theory introduces a deformation of spacetime at extremely small scales, effectively ‘smearing out’ the singularity predicted by general relativity and offering a potential pathway towards a consistent theory of quantum gravity. By treating gravity as an emergent phenomenon, ADW aims to bypass the problematic infinities and inconsistencies that plague attempts to directly quantize gravity, potentially uniting general relativity with the principles of quantum mechanics.

The notion of gravity as an emergent phenomenon challenges the conventional understanding of this fundamental force. Rather than being a fundamental interaction itself, the Akama-Diakonov-Wetterich (ADW) theory proposes gravity arises from the collective behavior of underlying quantum fields – a process akin to temperature emerging from the collective motion of molecules. This perspective offers a potential resolution to the longstanding inconsistencies between general relativity and quantum mechanics; by treating gravity as a secondary effect, the theory circumvents the need to quantize gravity directly, a process that leads to intractable mathematical problems. Instead, the quantum properties are inherent in the underlying fields, with gravity manifesting as a large-scale approximation of their complex interactions, potentially offering a pathway toward a unified theory where all forces are understood as emergent properties of a more fundamental quantum reality.

The Quantum Vacuum: A Structured Foundation for Spacetime

The ADW theory postulates that the quantum vacuum is not empty space, but rather a ‘Fermionic Crystalline Medium’ – a structured, non-perturbative state of fermions. This medium is characterized by a high degree of symmetry in its ground state. Spontaneous symmetry breaking within this medium is a foundational element of the theory, representing a transition from a highly symmetric initial state to a lower-symmetry state. This process does not involve an external force altering the system, but arises from inherent instabilities within the Fermionic Crystalline Medium itself. The resulting broken symmetry is crucial, as it provides the mechanism by which fundamental properties, such as mass and spacetime structure, emerge from the vacuum state.

Spontaneous symmetry breaking within the ADW theory’s Fermionic Crystalline Medium results in the emergence of tetrads, which are proposed as the fundamental constituents of spacetime. This process is analogous to phase transitions observed in condensed matter physics, where a system transitions from a symmetrical high-energy state to a lower-energy state with reduced symmetry. The resulting tetrads are not pre-existing entities but rather collective excitations arising from the broken symmetry, effectively defining the local metric and geometric structure of spacetime. These emergent tetrads provide a discrete, pre-geometric foundation upon which continuous spacetime geometry can be built, differing from traditional approaches that begin with a pre-defined continuous spacetime manifold.

The characteristics of the emergent tetrads within the ADW theory are directly dictated by the pattern of spontaneous symmetry breaking occurring in the Fermionic Crystalline Medium. This means the specific way in which the initial symmetry is broken defines the resulting properties of the tetrads, including their dimensionality and interaction strengths. Critically, these tetrads manifest as ‘Elasticity Tetrads’ which describe the local elasticity of the quantum vacuum; the symmetry-breaking pattern determines the components and relationships within these elasticity tetrads, effectively establishing the fundamental structure of spacetime as it emerges from the vacuum’s underlying fermionic condensate. Variations in the symmetry-breaking pattern therefore lead to variations in the properties of the emergent spacetime geometry.

Rewriting the Constants: Emergence and Renormalization

The ADW (Asymptotic Dynamical Wave) framework proposes that $\hbar$ , commonly known as the Planck constant, is not a pre-existing fundamental constant of nature. Instead, it emerges as an order parameter during a symmetry breaking process inherent in the formation of spacetime. This means that $\hbar$ ’s value isn’t fixed a priori, but rather is determined by the dynamics of this symmetry breaking and the resulting structure of spacetime. Consequently, the observed value of $\hbar$ reflects the specific state of the emergent spacetime, and deviations from this value might be expected under different conditions or in different regions of spacetime where the symmetry breaking process differs.

Analysis within the ADW framework indicates that $\hbar$ and $c$ are not fundamental constants existing prior to spacetime, but rather components arising within the emergent Minkowski metric. Specifically, the pre-geometric phase, preceding the symmetry breaking process, lacks explicit values for these constants; their magnitudes are determined as a consequence of the emergent spacetime structure. This means $\hbar$ and $c$ are calculated from the underlying dynamics of the framework, rather than being input parameters, and are intrinsically linked to the geometry of the resulting spacetime.

The ADW framework’s treatment of fundamental constants as emergent properties has significant implications for renormalization procedures in quantum gravity. Conventional renormalization aims to remove divergences arising from calculations involving infinite quantities, often by introducing counterterms; however, these procedures can lead to a loss of predictability and require arbitrary parameter adjustments. By positing that $ℏ$ and $c$ are not fundamental but arise from symmetry breaking in a pre-geometric phase, the ADW approach suggests divergences may stem from applying renormalization to parameters that are themselves emergent and scale-dependent. This allows for the possibility of a renormalization scheme grounded in the underlying, pre-geometric dynamics, potentially avoiding the need for arbitrary counterterms and offering a pathway towards finite, predictive calculations in quantum gravity. The normalization condition $\intd³r |Ψ|² = 1$ serves as a critical constraint within this emergent framework, guiding the renormalization process and ensuring physical quantities remain well-defined.

Within the ADW framework, established techniques of Dimensional Analysis and Renormalization are utilized to calculate physical observables originating from an emergent spacetime. These calculations are not performed with pre-defined constants, but rather derive them as a consequence of the symmetry breaking process. Crucially, the framework grounds these calculations in the normalization condition $\intd³r |Ψ|² = 1$ , which ensures probabilistic interpretation of the wave function Ψ and provides a foundational constraint for determining the values of emergent physical quantities. This approach links the calculation of observables directly to the underlying geometry and allows for a consistent treatment of quantities within the emergent spacetime paradigm.

Modeling the Fabric: Spacetime from Emergent Dynamics

The Arnowitt-Deser-Misner (ADM) formalism, a cornerstone of general relativity, finds a novel application within the Asymptotic Dynamics Whole (ADW) theory, allowing for the construction of spacetime solutions not as fundamental entities, but as emergent phenomena. Traditionally, the ADW framework posits that spacetime arises from a more fundamental, underlying structure; applying the ADW formalism enables researchers to mathematically describe this emergence. By treating the familiar Einstein field equations as descriptions of these emergent properties-rather than as the primary laws governing reality-the ADW theory, in conjunction with ADM, offers a fresh perspective on gravitational dynamics. This approach facilitates the exploration of solutions that may bypass traditional limitations, potentially revealing insights into the nature of gravity and the very fabric of spacetime itself, treating geometrical properties as collective behaviors of the underlying dynamics.

Within the ADW theory, the Einstein-Cartan action-an extension of general relativity incorporating the concept of torsion-emerges as a natural consequence of the framework. This action describes gravity not solely through spacetime curvature, but also through its twisting, represented mathematically by the torsion tensor $T^{\mu}_{\nu\lambda}$ . Crucially, the inclusion of torsion offers a potential pathway to resolving the problematic singularities predicted by classical general relativity, such as those found at the center of black holes or at the Big Bang. These singularities, points of infinite density and curvature, are widely believed to signal a breakdown of the theory; torsion introduces a degree of freedom that effectively ‘softens’ spacetime at extreme conditions, preventing the formation of such infinitely dense points. This suggests that what appear as singularities within standard general relativity may, in reality, be regions of incredibly high, but finite, curvature described by the Einstein-Cartan action, offering a more complete and physically realistic picture of gravity at its most extreme.

The ADW theory offers a novel pathway to understand the cosmological constant, not as a fundamental constant of nature, but as an intrinsic property arising from the structure of spacetime itself. Within this framework, spacetime isn’t a pre-existing stage upon which the universe unfolds, but rather an emergent phenomenon built from more fundamental constituents. Consequently, the energy density associated with this emergent spacetime – effectively the cosmological constant, denoted by Λ – is determined by the dynamics and interactions of these constituents. This perspective sidesteps the traditional difficulties in reconciling the observed value of Λ with quantum field theory predictions, which typically yield values many orders of magnitude larger. By treating the cosmological constant as a geometric property of emergent spacetime, the ADW theory opens up possibilities for modeling dark energy and exploring its influence on the universe’s expansion without invoking exotic forms of matter or fine-tuning of fundamental parameters.

Beyond the Standard Model: Charting Alternative Pathways

Extending the foundational principles of the Asymptotic De Sitter Worldline (ADW) theory, the ‘GUT Scheme’ and its counterpart, the ‘Anti-GUT Scheme’, propose distinct mechanisms for how fundamental symmetries break down and ultimately give rise to the spacetime geometry observed in the universe. These schemes diverge in their approach to symmetry breaking, with the ‘GUT Scheme’ favoring patterns reminiscent of Grand Unified Theories in particle physics, while the ‘Anti-GUT Scheme’ explores alternative, less conventional pathways. Crucially, both schemes posit that spacetime itself isn’t a pre-existing entity, but emerges from these symmetry-breaking processes, potentially resolving long-standing conflicts between quantum mechanics and general relativity. The resulting emergent spacetimes differ in their properties – including curvature and dimensionality – offering a wider range of theoretical possibilities for understanding the universe’s earliest moments and its ultimate fate.

The pursuit of a complete understanding of gravity extends beyond conventional approaches through explorations of alternative schemes like the ‘GUT Scheme’ and ‘Anti-GUT Scheme’. These models posit that gravity isn’t a fundamental force, but an emergent phenomenon arising from more basic interactions at a deeper level of reality. By altering the patterns through which symmetries break down – the processes that define the forces and particles of the universe – these schemes propose radically different pathways for gravity to manifest. Some models suggest gravity could be linked to the strong nuclear force, while others explore connections to previously unknown interactions, potentially resolving long-standing conflicts between general relativity and quantum mechanics. This diversity of approaches offers the exciting possibility of uncovering a more holistic picture of the universe, where gravity isn’t an isolated entity but an integral component of a unified framework governing all physical phenomena.

The pursuit of a complete theory uniting gravity with quantum mechanics necessitates a deepened investigation into alternative frameworks like the ‘GUT Scheme’ and ‘Anti-GUT Scheme’. Realizing the full potential of emergent gravity-the idea that gravity isn’t a fundamental force, but arises from underlying microscopic degrees of freedom-demands more than theoretical development. Advanced computational techniques, including sophisticated simulations and data analysis methods, are crucial for navigating the complex mathematical landscapes these schemes present. These tools will allow researchers to test the validity of emergent gravity’s predictions, explore the parameter space of possible spacetime structures, and ultimately determine if these alternative schemes offer a pathway toward resolving the long-standing incompatibility between general relativity and quantum field theory, potentially revealing the universe’s fundamental building blocks and interactions.

The exploration within this paper, detailing the Akama-Diakonov-Wetterich theory and the potential emergence of gravity, reveals a fascinating truth: models are, at their heart, reflections of the human tendency to impose order on chaos. It’s a comforting illusion, really. As Sergey Sobolev once observed, “The most difficult thing is the decision to act, the rest is merely technique.” This rings true because the very act of constructing a framework-whether it concerns Planck constants or dimensional analysis-is a decision born not solely of logic, but of a deeply ingrained need to simplify, to categorize, and to believe in a predictable universe. The shifts between quantum field theory and quantum mechanics, driven by symmetry breaking, are simply rounding errors between our desire for elegance and the messy reality of existence.

What Lies Ahead?

The pursuit of emergent gravity, as illustrated by explorations within the Akama-Diakonov-Wetterich framework, consistently circles back to a fundamental discomfort with scale. The mathematics function adequately, yet the insistence on linking Planck constants directly to the metric components feels less like discovery and more like a sophisticated renaming of the problem. It is a predictable human tendency – to perceive order where only correlation exists. Even with perfect information, people choose what confirms their belief.

Future work will inevitably focus on refining the symmetry breaking phases, attempting to map transitions between quantum field theory and quantum mechanics with ever-increasing precision. However, a more fruitful avenue might lie in accepting the inherent limitations of dimensional analysis. The universe doesn’t care about human-defined units; forcing it to conform risks obscuring deeper, more subtle relationships. Most decisions aim to avoid regret, not maximize gain, and the same holds true for theoretical physics.

Ultimately, the true test will not be whether these models predict experimental results – all models predict something – but whether they offer a genuinely different way of thinking about spacetime. A shift in perspective, not simply a refinement of calculations, is needed to escape the well-worn grooves of expectation. The quantum vacuum remains, as always, a convenient place to hide what one does not understand.

Original article: https://arxiv.org/pdf/2602.21243.pdf

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