Not so dark with Alena Tensor: Math framework could explain dark matter without invisible particles

Alena Tensor is a relatively new mathematical approach that allows for arbitrary curving and straightening of analyzed spacetimes. As it turns out, generalizing this model to all known fields and fully describing matter, spontaneously gives rise to the phenomena known from research on dark matter and dark energy.

A recently published paper in Physica Scripta shows that Alena Tensor allows for the description of the dark sector, proposing a new and intriguing solution to the dark matter problem, ensures the existence of gravitational waves consistent with GR predictions, and enables the description of quantum vortices that might behave similarly to elementary particles, while maintaining structural consistency with the Yukawa and Higgs mechanisms.

Will Alena Tensor help unravel the mysteries of modern physics?

One method of description—many perspectives

At the heart of the approach is a deceptively simple question: what if the same physical system could be described consistently in curved spacetime, flat spacetime, classical mechanics and quantum theory with the help of one method? That is what the Alena Tensor is meant to help with.

In the new paper, I extended the solutions beyond simple “dust” matter described previously, to more general matter distributions, including how matter rotates, pushes against itself, and interacts through all known fundamental forces.

This matters, because real physical systems are not made of idealized point masses. Galaxies rotate. Matter flows. Energy is transported. Internal stresses and vortical motion can appear. The paper shows that when these effects are fully incorporated into Alena Tensor, they may mimic the gravitational influence usually assigned to dark matter halos.

Dark matter without dark particles?

In standard cosmology, galaxies are thought to sit inside large halos of invisible dark matter, whose gravity keeps stars orbiting faster than visible matter alone would allow. The Alena Tensor framework offers another route.

Imagine a spinning figure skater: as she extends her arms, her rotational speed changes. Angular momentum flows outward through her body, not because of added mass, but because of the way rotation redistributes energy through the organized system. In a galaxy, something analogous may happen at a vastly larger scale. As stars and gas rotate, angular momentum is continuously transported outward through the disk.

The Alena Tensor framework shows that this transport process itself contributes to the gravitational field: the faster and more organized the rotation, the stronger this effect. No invisible particles are required.

I have tested this approach against more than one hundred galaxies and compared it to the MOND model, which also tries to explain the mystery of dark matter. It appears that, in this preliminary approximation, Alena Tensor produces better results (or comparable) than MOND in 80% of cases, allowing for further accuracy improvement.

That, of course, does not yet settle the dark matter problem. Fitting galaxy rotation curves is only one drop in the ocean of tests needed: from galaxy clusters, gravitational lensing to large-scale structure formations. But it means that Alena Tensor produces equations that can be confronted with data and successfully passes first tests.

Theories become interesting when they risk being wrong. An inclination-dependent lensing signature predicted by Alena Tensor for galaxies, would be a clear observational target and a potentially sharp distinction from more conventional halo models.

Dark energy as a property of the fields themselves

The paper also offers a reinterpretation of dark energy. Instead of treating the cosmological constant as an unexplained extra term added to Einstein’s equations, it emerges here from field equations as field invariant. In this picture, dark energy becomes less like an arbitrary patch and more like a built-in property of the system’s field structure.

Whether that idea can reproduce the full observed behavior of cosmic expansion and cosmological perturbations remains an open question. My claim is not that all cosmology is solved, but that the framework offers a new geometric and dynamical interpretation worth exploring. It is also shown that the mathematics behind it gives dark energy a deeper meaning.

From galaxies to quantum vortices

It turns out that the same equations that describe galaxies can be used in the quantum version to describe quantum vortices, including a coupling between spin and vorticity.

The paper demonstrated, for example, that mass in such a system can emerge spontaneously as a result of a certain balance between the phase structure and spin-vorticity coupling. Even more interestingly, this leads to analogs of equations known from the Yukawa and Higgs mechanisms and the framework reproduces the already known Mashhoon effect, linking the rotational sector to measurable quantum behavior.

This does not mean, of course, that a complete picture of the particles has been obtained, but this leads to the suggestion that stable quantum vortices resulting from Alena Tensor, could help model certain structural features of elementary particles.

Is Alena Tensor a theory of everything?

Science does not advance by bold claims alone. It advances by replication, criticism, failed attempts, improved models and hard comparisons with data.

The Alena Tensor has so far shown itself to be just a useful research tool: it connects general relativity, continuum mechanics and quantum descriptions into one mathematical framework, while generating many consistent results. That is already a significant achievement for a three-year-old research direction. However, it is far from the maturity of e.g. String Theory, which we have been studying for over 50 years.

The most important tests are still ahead. Can Alena Tensor explain gravitational lensing in clusters? Can it survive cosmological structure-growth constraints? Can its quantum sector be developed into something predictive? Can other researchers reproduce the fits and extend them independently? Until that happens, skepticism is a scientific duty.

Still, there is something exciting here. The physics community has spent decades searching for invisible substances to explain visible anomalies. The Alena Tensor points toward a different possibility: maybe some of what we call “dark” is not hidden matter at all, but hidden structure in the way matter, motion and spacetime work together.

That would not make the universe simple. But it might make it a little less dark.

This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.

Piotr Ogonowski, Lecturer at Kozminski University, Warsaw, Poland.

Experienced lecturer, author of a series of lectures and trainings, researcher, author of publications in physics and management. In 2010, he was selected as one of the four experts consulting planned changes in the rules for co-financing innovative projects from EU funds in Poland. In the years 2018–2022 he was a member of the expert group in auxiliary body at the Chancellery of the Prime Minister of Poland.