Beyond Dark Matter: A Quantum Link to Galactic Rotation

Author: Denis Avetisyan

New research proposes a connection between quantum fluctuations and the observed discrepancies in galactic rotation curves, offering a potential explanation for Modified Newtonian Dynamics (MOND).

This review explores how second-order moment fluctuations in accelerated frames, induced by deSitter spacetime, may provide a quantum mechanical basis for MOND’s modified inertial behavior.

The persistent discrepancy between observed galactic rotation curves and predictions from standard gravity remains a fundamental challenge in astrophysics. This paper, ‘Local Short-Time Acceleration and deSitter Spacetime induced Extra Spectral Broadening: a Simple Interpretation of Modified Inertial in MOND’, proposes a quantum mechanical interpretation of Modified Newtonian Dynamics (MOND) rooted in the broadening of particle spectra induced by local, short-time acceleration and deSitter spacetime. Specifically, we demonstrate that this effect-a generalization of the Unruh effect reliant on second-order moment fluctuations-offers a framework for understanding both galactic dynamics and the accelerating expansion of the universe. Could this novel connection between quantum fluctuations and modified inertia offer insights into the foundations of quantum gravity and the nature of dark matter?

The Persistent Riddle of Galactic Motion

The enduring puzzle of galactic rotation curves poses a significant hurdle for conventional cosmological models. Observations consistently reveal that stars at the outer edges of galaxies orbit much faster than predicted by Newtonian gravity, given the visible matter present. This discrepancy implies either the existence of substantial amounts of unseen ‘dark matter’ exerting gravitational influence, or a fundamental misunderstanding of how gravity behaves on galactic scales. The need to postulate this non-luminous matter, comprising roughly 85% of the universe’s mass, isn’t simply an additive detail; it fundamentally challenges the completeness of the Standard Model of particle physics and necessitates a re-evaluation of the underlying assumptions governing gravitational interactions. The persistent reliance on dark matter as an explanation, while currently the prevailing theory, continues to drive exploration of alternative gravitational frameworks and motivates increasingly precise astronomical observations designed to either detect this elusive substance directly or further refine our understanding of its gravitational effects.

Galactic dynamics, as revealed through empirical relationships like the Tully-Fisher and Faber-Jackson relations, consistently challenge predictions derived from standard gravitational models. The Tully-Fisher relation, connecting a spiral galaxy’s luminosity to its rotational velocity, and the Faber-Jackson relation, linking elliptical galaxy luminosity to its velocity dispersion, both indicate that galaxies rotate and move faster than expected given their visible mass. These observations suggest either a significant underestimation of galactic mass, necessitating the concept of dark matter, or a fundamental misunderstanding of gravitational interactions at galactic scales. Specifically, the observed flat rotation curves of spiral galaxies – where rotational velocity remains constant with increasing distance from the galactic center – are particularly difficult to reconcile with Newtonian predictions, which anticipate a decline in velocity with distance. These discrepancies aren’t merely statistical anomalies; they represent a systemic deviation between theoretical expectations and observed reality, fueling ongoing research into alternative explanations for galactic behavior.

The persistent anomalies in galactic rotation curves and the need for substantial dark matter have spurred investigation into Modified Newtonian Dynamics (MOND) as a potential alternative. Rather than positing the existence of unseen matter to account for these discrepancies, MOND proposes a fundamental alteration to the laws of gravity at extremely low accelerations. A key prediction of MOND is the existence of a characteristic acceleration scale, denoted $a_0$ , below which Newtonian gravity breaks down and a different gravitational regime takes hold. Intriguingly, this acceleration scale is not merely a parameter confined to galactic dynamics; mounting evidence suggests a connection between $a_0$ and the cosmological constant, a value describing the expansion rate of the universe. This unexpected link implies a deep and potentially fundamental relationship between the behavior of galaxies and the large-scale structure and evolution of the cosmos, prompting researchers to explore a unified framework governing gravitational phenomena across vastly different scales.

Seeking Relativistic Grounding for MOND

Bimetric Modified Newtonian Dynamics (MOND) theories propose a relativistic framework by introducing two spacetime metrics: one that governs the dynamics of standard matter and another that defines the gravitational interaction. This approach attempts to reconcile MOND’s observed galactic rotation curves with the principles of general relativity by postulating that gravity is mediated through this second, distinct geometry. The core concept involves a mapping between the two metrics, allowing for a variable gravitational constant effectively dependent on acceleration. This differs from standard general relativity which utilizes a single spacetime metric to describe both matter distribution and gravitational effects, and aims to provide a self-consistent relativistic formulation of MOND without violating local Lorentz invariance.

The Soussa-Woodard No-Go Theorem establishes a fundamental instability within relativistic Modified Newtonian Dynamics (MOND) theories constructed using a single metric. This theorem demonstrates that any attempt to formulate a relativistic MOND theory based on a simple modification of the metric, aiming to reproduce the MONDian dynamics at low accelerations, necessarily introduces ghosts – particles with negative kinetic energy. These ghosts violate unitarity, leading to an exponentially growing instability and rendering the theory physically unacceptable. The instability arises from the specific requirements for recovering Newtonian dynamics in the non-relativistic limit, coupled with the need to maintain Lorentz invariance in the relativistic regime, effectively precluding viable, metric-based relativistic MOND formulations.

Modified Gravity theories, aiming to directly alter the foundations of gravitational physics to account for observations currently attributed to dark matter, encounter difficulties mirroring those faced by relativistic MOND formulations. These challenges primarily involve maintaining consistency with established general relativity in the strong-field regime and avoiding instabilities. However, a numerical coincidence has emerged: the MOND acceleration constant, $a_0$ , exhibits a close relationship to the cosmological constant, Λ. Specifically, the approximation $a_0 \approx 2a_{bg} = \frac{1}{2\sqrt{3}}\Lambda$ -where $a_{bg}$ represents the background acceleration-suggests a possible connection between the dynamics requiring dark matter explanation at galactic scales and the accelerating expansion of the universe, potentially offering a pathway towards a more unified and self-consistent gravitational framework.

Beyond the Field: Reimagining Inertial Effects

Modified Inertial (MI) approaches to Modified Newtonian Dynamics (MOND) deviate from standard MOND formulations by directly altering the fundamental laws governing particle motion rather than introducing a modified gravitational field. These approaches typically involve either a modification of Newton’s second law, $F = ma$ , or adjustments to the kinematic description of free particles. Unlike tensor-vector-scalar (TeVeS) theories which modify gravity itself, MI frameworks propose alterations to inertial effects, potentially impacting the observed dynamics without requiring new gravitational fields. This allows for a different pathway to reproduce MOND’s predictions regarding galactic rotation curves and other phenomena, providing an alternative theoretical landscape for exploring the nature of dark matter and dark energy. The modifications can manifest as an effective inertial mass that depends on environmental factors, effectively mimicking the influence of unseen matter.

Theoretical support for modified inertial frameworks stems from the Quantum Equivalence Principle, which posits an inherent connection between gravity and quantum mechanics, and the analysis of second-order moment fluctuations in quantum systems. These fluctuations, arising from the uncertainty inherent in quantum measurements, manifest as stochastic variations in inertial mass. Specifically, models leverage the correlation between these fluctuations and the observed galactic rotation curves, suggesting that the anomalous acceleration experienced by objects in these environments isn’t due to dark matter, but rather to a quantum-induced modification of inertia. The mathematical formulation often involves relating the strength of these fluctuations to the external gravitational field, expressed through $δm/m \propto a_0^2/a^2$ , where $δm$ is the inertial mass variation, $m$ is the rest mass, $a_0$ is a fundamental acceleration scale, and $a$ is the observed acceleration. This framework offers a potential link between quantum phenomena and the large-scale structure of the universe, bypassing the need for non-baryonic dark matter.

Theoretical connections between Modified Inertial frameworks, the Unruh Effect, and de Sitter spacetime suggest a role for acceleration and cosmological expansion in modifying inertial behavior. Specifically, these models propose a link to observed spectral line broadening, positing that transient, short-time acceleration conditions – characterized by $δs << 1/a$ , where δs represents the duration of acceleration and a is the acceleration – allow for perturbative analysis of the modified dynamics. This condition enables the approximation of non-inertial effects as small perturbations to standard inertial behavior, facilitating mathematical tractability and enabling quantitative predictions regarding the observed broadening of spectral lines.

The Relational Universe: Gravity as Emergent Information

The conventional understanding of gravity as a fundamental force is challenged by the Quantum Reference Frame (QRF) concept, which posits that gravity isn’t an inherent property of spacetime itself, but emerges from the relational process of observation. This perspective suggests that gravity arises not from how objects interact with a fixed spacetime background, but from how different observers, each with their own quantum reference frame, measure and perceive spacetime intervals. Each observer effectively constructs their own spacetime geometry based on their unique state of motion and measurement apparatus, and discrepancies between these geometries manifest as what is perceived as gravity. Consequently, gravity isn’t absolute, but relative – an effect of comparing measurements made within different quantum reference frames. This framework implies that the gravitational “force” is essentially a statement about information transfer and correlations between observers, rather than a direct interaction mediated by a force-carrying particle.

Describing gravity as arising from observer-dependent measurements necessitates a sophisticated mathematical framework, prominently featuring General Coordinate Transformations and Ricci Flow. General Coordinate Transformations allow physicists to analyze how spacetime measurements change based on the observer’s chosen frame of reference, effectively demonstrating that gravitational effects aren’t absolute but relational. Ricci Flow, a geometric evolution equation, then provides a means to smooth out irregularities in spacetime, revealing an underlying structure independent of specific coordinate choices-analogous to how polishing a rough surface reveals its true form. This approach isn’t merely a mathematical trick; it suggests that gravity isn’t a force in spacetime, but rather a consequence of how spacetime is defined by observers, potentially linking quantum phenomena and the geometry of the universe through the lens of relational measurements and evolving geometric structures.

The subtle fluctuations within quantum reference frames, which underpin the very fabric of spacetime perception, are increasingly understood through the analysis of spectral data. Techniques like the Gabor Transform allow researchers to dissect these fluctuations, revealing inherent uncertainties in how observers define gravitational effects. This approach yields surprising connections to large-scale astrophysical phenomena; for instance, the velocity dispersion – a measure of the random motions of stars – within elliptical galaxies demonstrates a compelling relationship to the galaxy’s mass ( $M$ ) and the background acceleration ( $abg$ ) of its environment, specifically following the proportionality $σ⁴ ~ GMabg$ . This connection suggests that gravitational effects aren’t simply inherent properties of mass, but are also intimately linked to the observer’s frame of reference and the larger cosmological context, hinting at a deeper, observer-dependent nature of gravity itself.

The pursuit of reconciling observed phenomena with theoretical frameworks, as demonstrated in this paper’s exploration of MOND, inevitably introduces approximations. These simplifications, while offering immediate explanatory power, carry inherent future costs-a principle echoing throughout all complex systems. As Leonardo da Vinci observed, “Simplicity is the ultimate sophistication.” This echoes the core concept of the article: attempting to explain galactic rotation curves through quantum mechanical principles necessitates a careful balance between model complexity and predictive accuracy. Each layer of abstraction, while streamlining calculations, potentially obscures underlying mechanisms, creating a ‘technical debt’ within the theoretical structure. The study’s focus on second-order moment fluctuations, and its link to DeSitter spacetime, represents a move toward greater sophistication, but also introduces new avenues for potential future refinement.

The Horizon Beckons

The assertion that MOND’s anomalies stem from fluctuations within accelerated frames-a linkage to the Unruh effect and, by extension, a quantum gravity phenomenology-is not, itself, novel. What distinguishes this work is the specific focus on second-order moment fluctuations as the measurable signature. However, this approach merely shifts the locus of inquiry. The question is no longer if gravity requires modification, but whether this particular quantum mechanical interpretation will withstand the inevitable scrutiny of increasingly precise spectroscopic data. Every delay in definitive confirmation is, of course, the price of understanding-a necessary accumulation of evidence before embracing a paradigm shift.

The true challenge lies in bridging the gap between these locally observed spectral distortions and the cosmological implications of a DeSitter spacetime. To claim a connection to the larger structure of the universe without a robust predictive framework is to build architecture without history-fragile and ephemeral. Future work must therefore prioritize the development of testable predictions regarding the spatial distribution of these fluctuations, and their potential influence on galactic dynamics beyond simple rotation curves.

Ultimately, the significance of this approach may not reside in solving MOND, but in providing a new lens through which to examine the fundamental relationship between quantum mechanics and gravity. Systems decay; the objective is not immortality, but graceful aging. To map the mechanisms of this decay-to understand how gravity deviates from classical expectations-is a worthwhile endeavor, regardless of the ultimate outcome.

Original article: https://arxiv.org/pdf/2602.14515.pdf

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

The Persistent Riddle of Galactic Motion

Seeking Relativistic Grounding for MOND

Beyond the Field: Reimagining Inertial Effects

The Relational Universe: Gravity as Emergent Information

The Horizon Beckons

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