There is something in modern physics that works well enough not to be questioned, yet when examined closely begins to reveal a tension that is difficult to resolve, and it appears most clearly when we look at how galaxies rotate. If you take a spiral galaxy and measure the velocity of its stars, the result does not match what you would expect by applying the same laws that describe the solar system with remarkable precision, where bodies farther away move more slowly. In galaxies, however, stars at the edge rotate at almost the same speed as those closer to the center, as if the entire disk were coupled and turning as a single structure.
From the standpoint of classical physics, those stars should be flung outward, and yet they are not, which has led for decades to a solution that has now become familiar, dark matter, a form of mass we do not see but that would account for what is missing. The problem is that, after more than half a century of searching, it has not been directly detected, and although alternatives such as MOND adjust Newton’s law in certain regimes and describe the data surprisingly well, they do so without a deeper derivation that explains why they should work.
My starting point was not to introduce a new entity or modify a law, but to shift attention toward something that usually remains implicit in the formulation itself, the relationship. Most of physics is built on an essentially binary structure, something here, something there, and an interaction between them, but we rarely treat the bond itself as having its own consistency. This works as long as the interaction can be described as instantaneous, but it begins to fall short when the system depends on how it reached its current state.
At that point, a simple intuition appears with far-reaching consequences, the relationship is not merely a channel through which something happens, it is a structure that can persist, deform and accumulate history. In many areas of physics this is already familiar, materials that do not return exactly to their original state after repeated cycles, systems whose response depends on the path they have followed, phenomena grouped under the idea of hysteresis, where the present cannot be explained solely by current conditions but also by the trajectory.
From there, the question changes. It is no longer whether mass is missing or whether Newton’s law fails in certain regimes, but whether we are describing gravity as if the relationship were instantaneous when it might not be. This is not to say that gravity “remembers” in a metaphorical sense, but that the relationship gravity expresses between matter may have a persistence we are not modeling.
To capture this possibility, I introduce a variable, C(r), which does not represent additional matter or an arbitrary modification of the law, but the accumulated history of the bond at each scale. Each time matter in a galaxy completes an orbit, it does not simply move, the relationship is reiterated, and that repetition leaves a trace that does not dissipate instantaneously. That trace does not belong to matter itself nor is it an independent field in the usual sense, it is the persistence of the relationship over time.
When that persistence is negligible, the dynamics reduce exactly to Newton’s, which indicates that we are not replacing the law but extending its domain. When it begins to accumulate, the relationship ceases to be purely instantaneous and a dependence on the path emerges, which translates into an effective modification of the field, so that the same position can correspond to different states depending on the system’s history. What we call hysteresis in other contexts appears here as a direct consequence of the fact that the relationship carries memory.
What matters is that this construction does not remain at a qualitative level. When applied to real data, the model reproduces the vast majority of observed galaxies without introducing additional matter, with a level of precision that is unusual for this kind of approach. In an initial test on the SPARC catalogue, 23 out of 25 galaxies are described with very small deviations using parameters fixed in a single system, suggesting that this is not a local fit but a structure that persists across scales.
Up to this point, it could still look like a model that simply works. The real question is where it comes from.
The answer does not come from gravity, but from the physics of turbulence, specifically from Kolmogorov’s work on how energy is distributed in a fluid. The interstellar gas in a galactic disk is not static, it is turbulent, and that turbulence leaves a measurable geometric imprint in the structure of neutral hydrogen. When the exponents described by that theory are taken and connected with the way the relationship can accumulate history in the system, the value does not need to be fitted, it emerges naturally, with a difference on the order of a few tenths of a percent compared to the observed one.
What matters is not the precision, but the independence, the number does not come from the gravitational model but from a different branch of physics, and that closure, where the deviation is on the order of 0.3%, turns what might appear as a fit into a consequence.
With this structure, the model is able to reproduce most of the galaxies in the SPARC catalogue without introducing dark matter, using a reduced set of parameters fixed in a single system, and it also allows for additional predictions, such as the fact that galaxies whose gas does not follow Kolmogorov turbulence should show deviations in that parameter, something that is beginning to appear in available data. It is not a definitive confirmation, but it is not compatible with a trivial coincidence either.
The most unexpected result appears when this formulation is expressed in a language compatible with general relativity, where the same exponent that governs the persistence of the relationship in galaxies reappears when analyzing how the field couples across scales, and when that calculation is carried out, the fraction of energy associated with that term in the cosmological regime turns out to be approximately 70%, which is precisely the value attributed to dark energy in the standard model. Here it is not introduced as a free parameter, but emerges from the same structure that explains galaxy rotation curves, connecting domains that are usually treated separately, from fluid dynamics to the expansion of the universe.
The model is not closed, and it is important to state its limits clearly. It does not reproduce the smallest galaxies well, it needs to be tested against larger datasets and requires independent validation, and the cosmological predictions it generates will be confronted with observations in the coming years, which will ultimately confirm or falsify it. There is also a particularly demanding prediction, if the persistence of the relationship depends on the structure of the medium, then local correlations should appear between what we call dark energy and the conditions of the gas in each environment, something that does not arise in any standard theory and that, if observed, would have deep implications.
Beyond this point, any extension must be understood as speculation in the strict sense, even if it follows the internal logic of the model, such as the possibility of interpreting quantum entanglement as a limit in which the relationship does not dissipate, or of understanding the weakness of gravity not as an intrinsic property but as the result of a process that requires time to accumulate, or even of rethinking the problem of its quantization if what we are trying to treat as just another interaction is in fact the condition under which interactions are structured across scales.
If one takes this idea to its conclusion, the shift is not so much in the equations as in what they are describing. What emerges is not a new force, nor even a modification of existing ones, but a layer that is usually left implicit, that of the bond as an entity that is not exhausted in the instant. In that sense, what we call gravity might not be an interaction in the usual sense, but the way in which this relational structure is expressed across scales, making visible a history that would otherwise remain implicit.
This is not a philosophical addition, it is the direct consequence of introducing a variable that does not describe objects but relationships, and once that variable becomes part of the dynamics, the system no longer depends only on what exists at each instant, but also on how it arrived there. In that sense, the universe would not simply evolve under instantaneous rules, it would accumulate its own history.
The full preprint, including derivations and data, is available here
https://doi.org/10.5281/zenodo.19705771
José Javier Meizoso Fernández
April 2026