🔭 astrophysics

Rotational Nonlocal Model for Large-Scale Galaxy Rotation Coherence Based on Proposed Nonlocal Coherence Mechanism

Motivated by observational reports of large-scale galaxy rotation coherence, this paper proposes a speculative rotational nonlocal model based on early-universe phase synchronization to offer an alternative explanation for enhanced galactic rotational velocities typically attributed to dark matter.

Original authors: Michiaki Kobayashi, Nozomi Kobayashi

Published 2026-07-06

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Michiaki Kobayashi, Nozomi Kobayashi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: A Cosmic "Wireless Connection"

Imagine you have two identical clocks in different rooms. Usually, if you wind them up, they might tick at slightly different speeds because of tiny differences in the air or the table they sit on. But what if, without any wires connecting them, they suddenly started ticking in perfect unison, no matter how far apart they were?

This paper proposes a similar idea for the universe. The authors, Michiaki and Nozomi Kobayashi, suggest that distant galaxies might be "synced up" with each other through a hidden, invisible connection they call Nonlocal Coherence.

The Problem: Galaxies That Spin Too Fast

Astronomers have noticed two strange things:

Galaxy Alignment: Galaxies far apart seem to be spinning in the same direction, like a crowd of people all turning their heads the same way at a concert, even though they are miles apart.
The "Dark Matter" Mystery: Galaxies spin much faster than they should. According to standard physics (like the rules that keep planets orbiting the Sun), the outer edges of a galaxy should fly off because they aren't spinning fast enough to stay in orbit. To explain this, scientists usually say there is invisible "Dark Matter" holding them together.

The authors ask: What if the galaxies aren't just held together by invisible mass, but are actually "dancing" together because they are connected?

The Theory: The "Vibrating String" Analogy

To explain how this connection works, the authors look at something much smaller: atoms vibrating in a solid object (like a crystal).

The Normal Way (Local): Usually, when you shake one end of a rope, the wave travels to the other end at a specific speed. This is how sound travels. The authors call this "local coherence."
The Special Way (Nonlocal): The authors propose that under very specific conditions (which they call "optical mode" vibrations), the "information" about the movement travels instantly. It's as if the rope is so perfectly connected that when you shake one end, the other end moves at the exact same instant, regardless of distance.

They call this the Nonlocal Coherence Mechanism (NLCM). They tested this idea with computer simulations of vibrating atoms and found that, mathematically, this "instant connection" is possible.

Scaling Up: From Atoms to Galaxies

The paper argues that if this "instant vibration" can happen in a tiny crystal, maybe a similar version happens in the massive structures of the universe.

The Analogy: Imagine the universe is a giant, cosmic drum. When the universe was born (the Big Bang), it was shaken violently. The authors suggest this created a "phase" or a rhythm that got locked into the fabric of space.
The Result: Just like two dancers holding hands and spinning together, distant galaxies might be "holding hands" through this invisible cosmic rhythm. They don't need to touch or send signals to each other; they are just part of the same synchronized wave.

What This Means for Galaxy Rotation

The authors suggest that because these galaxies are "entangled" in this special way, they spin faster than normal.

The "Dark Matter" Connection: In standard physics, we need extra invisible mass (Dark Matter) to explain why galaxies spin so fast. The authors propose that the "extra speed" isn't from extra mass, but from this nonlocal connection. The galaxies are spinning faster because they are part of a synchronized, large-scale dance that adds extra energy to their rotation.
The Math: They created a new formula that adds this "nonlocal spin" to the normal rules of gravity. When they plug this into their model, the resulting curve looks very similar to the curves astronomers actually see in real galaxies.

Important Caveats (What the Paper Actually Says)

The authors are very careful to state that this is speculative.

They are not saying they have proven Dark Matter doesn't exist.
They are not saying this is a finished theory.
They are proposing a new way to think about the problem. They suggest that instead of looking for invisible mass, we should look for these "long-range connections" that might have been set up during the birth of the universe.

Summary

Think of the universe not as a collection of lonely islands, but as a giant, synchronized orchestra. The authors suggest that distant galaxies are playing the same note at the same time because they are connected by a fundamental "rhythm" of the universe, not because they are physically touching or because of invisible glue. This "rhythm" might explain why galaxies spin so fast and why they seem to align with each other across vast distances.

Technical Summary: Rotational Nonlocal Model for Large-Scale Galaxy Rotation Coherence

Problem Statement
Recent observational studies have identified large-scale coherence phenomena in the universe that challenge standard cosmological assumptions. Specifically, observations by Hutsemékers et al. (2014) revealed alignments of quasar polarization axes with large-scale structures over gigaparsec scales. Subsequently, Lee et al. (2019) and Shamir (2025) reported coherent behaviors in galaxy rotations across several megaparsecs, while Tudorache et al. (2025) identified a 15-Mpc rotating galaxy filament. These findings suggest a long-range synchronization of galactic rotations and spin axes that cannot be explained by local interactions or standard gravitational dynamics alone. Furthermore, the persistence of these macroscopic alignments contradicts the expectation that quantum entanglement would decohere under environmental perturbations. The paper addresses the need for a theoretical framework that explains these large-scale rotational coherences and the associated anomalous rotation velocities (often attributed to dark matter) without assuming rigid rotation or direct long-range forces.

Methodology
The authors propose a conceptual framework extending a previously established "Nonlocal Coherence Mechanism" (NLCM) from microscopic lattice vibrations to macroscopic astrophysical systems.

Theoretical Foundation (NLCM): The study builds on a mechanism derived from optical-mode lattice vibrations in fracture-induced shock-wave states. In this regime, at a wave number $k=0$ , the phase velocity becomes effectively infinite, and the wavelength becomes infinite. Unlike acoustic modes (which obey local coherence and the CHSH inequality), optical modes under these specific conditions violate the CHSH inequality, suggesting nonlocal coherence and entanglement that is robust against decoherence.
Dimensional Extension:
- One-Dimensional Case: The authors review simulations showing that under $k=0$ , optical lattice vibrations exhibit instantaneous synchronization between distant points, modeled as superposed positive and negative phonons (analogous to qubits) that do not interfere destructively.
- Two-Dimensional Rotational Model: The core methodological contribution is the extension of this 1D nonlocal theory to two dimensions. By combining displacement equations for $x$ and $y$ directions with equal amplitudes and specific phase relationships, the authors derive a mathematical formulation (Eq. 7) where the wave packet exhibits a rotating character.
Astrophysical Application: The authors hypothesize that galaxies and quasars formed during the Big Bang or cosmic inflation may have retained this macroscopic entanglement. They apply the 2D nonlocal theory to galaxy rotation curves, positing that the total angular frequency ( $\omega$ ) is a superposition of the Keplerian frequency ( $\omega_K$ ) and a nonlocal frequency ( $\omega_{NL}$ ) derived from the NLCM.

Key Contributions

Rotational Nonlocal Model: The paper introduces a specific "Rotational Nonlocal Model" where macroscopic entities (galaxies) are theorized to undergo synchronized rotation due to nonlocal phase coherence originating from early-universe dynamical processes.
Macroscopic Entanglement Hypothesis: The authors distinguish their proposed "macroscopic entanglement" from standard quantum entanglement. They argue that while quantum entanglement decoheres upon observation, the macroscopic entanglement derived from optical-mode lattice vibrations remains stable under perturbations, making it a viable candidate for explaining persistent galactic alignments.
Alternative to Dark Matter: The model offers a phenomenological explanation for the "flat" rotation curves of galaxies. By introducing a nonlocal frequency component ( $\omega_{NL}$ ), the model suggests that the observed enhanced rotational velocities are a result of nonlocal gravitational fields rather than the presence of unseen dark matter mass.
Mathematical Formulation: The paper provides specific equations (Eqs. 5–10) linking the nonlocal phase coherence to galactic circular velocity ( $V$ ), showing how $V$ deviates from Kepler's law ( $V \propto 1/\sqrt{r}$ ) at large radii due to the additive nonlocal term.

Results

Simulation of Waveforms: Theoretical simulations (Figs. 2–4) demonstrate that under $k=0$ conditions, optical modes exhibit synchronized oscillations between distant points that are independent of time and space separation, unlike acoustic modes.
Rotational Dynamics: The 2D extension (Fig. 6) confirms that the superposition of orthogonal nonlocal waves results in a coherent rotational motion.
Rotation Curve Analysis: The derived rotation curve (Fig. 7) illustrates that while the Keplerian component dominates at small radii, the nonlocal component ( $\omega_{NL}$ ) becomes significant at larger radii (e.g., $r > 15$ kpc), causing the total rotation frequency to exceed the natural Keplerian frequency. This mathematically reproduces the enhanced velocities observed in galactic rotation curves without invoking dark matter halos.
Alignment Consistency: The model provides a theoretical basis for the observed alignment of quasar spin axes and galaxy rotations with cosmic filaments, interpreting these as manifestations of the same underlying nonlocal synchronization.

Significance and Claims
The authors explicitly state that this work is speculative and intended as a "conceptual basis" rather than a complete astrophysical description.

Interpretative Framework: The primary significance lies in offering a new perspective on large-scale coherence phenomena, suggesting that they may originate from phase-coherent processes established during the early universe (Big Bang/Inflation) rather than local dynamical evolution.
Connection to General Relativity: The paper notes that the proposed model aligns with suggestions that effective theories of General Relativity must include nonlocal parameters to account for galaxy rotation curves.
Future Direction: The authors claim that if the hypothesis holds, the NLCM could explain the parallel alignment of quasar spin axes with large-scale structures and the coherence of distant galaxy rotations. They emphasize that the predictive statements regarding the widespread recognition of NLCM are prospective research directions, not established facts.

In summary, the paper proposes that the large-scale coherence of galaxy rotations and quasar alignments is a macroscopic manifestation of nonlocal phase coherence, analogous to optical-mode lattice vibrations, which modifies galactic rotation curves and potentially obviates the need for dark matter in these specific contexts.