Predicting rotation velocities of stars

In a previous discussion on a new gravitational equation, we presented a method for calculating the rotation speeds of stars. This Kolmogorov equation articulates that the velocity of stars decreases as their distance from the gravitational center increases, thus providing an explanation consistent with Newton's Inverse Square Law. However, it also suggests that a star's historical data—including its age, temperature, and its movement relative to the galaxy's center—must be factored into velocity predictions. The Kolmogorov equation captures the impact of minute time increments on stellar velocities. Furthermore, it integrates historical data by considering prediction errors for stars situated closer to the galaxy's center.

Insights into galaxies

The limited qualifications in astrophysics and the lack of advanced computational resources have hindered access to stellar data in galaxies. The analysis described herein has been conducted using an Excel spreadsheet on a standard personal computer. The main objective of this work is to provide empirical support for further exploration of the concepts presented in earlier articles.

Data from the SPARC database, which comprises 3,660 stars across 175 galaxies, is publicly available. The data utilized in the Excel analysis includes:

• An estimate of the galaxy's age
• Velocities of the bulge, disk, and gas masses
• Distances from the galaxy's center
• The constant expansion rate of the universe at 72 km/second/megaparsec.

As will be elaborated, the Excel analysis focused on stars that are at least 2 kiloparsecs (kpc) from the galaxy's center, with results derived from 2,665 stars in 161 galaxies.

Adjusting for age and temperature

The data analysis revealed that the gas mass in the galaxy requires distinct treatment compared to the masses of stars in the bulge and disk. This finding aligns with the hypothesis that certain gas types can serve as mediums for encoding information. When hydrogen gas is extremely hot near the galaxy's center, it becomes ionized and unsuitable for this purpose. In contrast, hydrogen gas cools as it moves outward, enabling it to encode information.

The Kolmogorov formula for predicting a star's velocity (excluding the gravitational constant) is expressed as follows:

v² ~ {(m_b + m_d + m_g) + [(m_g * k_a) * (1 + k_d)]} / d

where: - v = star's velocity - m_b = mass of stars in the bulge within radius d - m_d = mass of stars in the disk within radius d - m_g = mass of gas within radius d - d = distance from the center of the galaxy - k_a = adjustment factor based on average age and temperature - k_d = adjustment factor for the average increase in distance due to cosmic expansion, calculated as 0.074 for every billion years.

When k_d equals 0, the Kolmogorov formula aligns with Newton's inverse square law. The values for k_a were assessed by analyzing the mean error and standard deviation across all stars, with the optimal adjustment factor approximated at 2.7.

Stars located within 2 kpc of the galaxy's center were deemed to have an adjustment factor of 0 and excluded from the analysis, as the differences in predictions between the two equations would converge. As discussed in Article 30, gas nearer the center is too hot for instantiating information, thus k_a is set to 0 for these stars.

The individual value of k_a is contingent on a star's age and temperature, which are not easily available. The formula outlining how k_a may vary with age and temperature is:

([13.7/A]*[4/T])/([{d/d}*{4/T}]+1)²

where A is the age of the star, T is the temperature, and d is adjusted for cosmic expansion.

According to astrophysicists, fusion of hydrogen initiates when a star's core temperature reaches approximately 10 million K, with its final temperature being significantly influenced by its mass. Massive stars can exceed 10,000 K from an initial average of around 4,000 K, resulting in a lower k_a as temperatures rise.

Reducing prediction error for star velocities

The simulation results indicate that for galaxies with stars orbiting 2 kpc or further from the center, the root mean square error (RMSE) for velocity predictions using Newton’s inverse square law is -19% for 2,665 stars in 161 galaxies, with a standard deviation of 28%. Conversely, the Kolmogorov equation yields an RMSE of -17% and a standard deviation of 25%. This suggests that incorporating hydrogen gas's ability to encode information into the velocity prediction formula leads to a decrease in average prediction error, hinting that dark matter might be associated with informational mass.

The Kolmogorov equation accounts for small time variations, similar to differential equations in calculus. Over extended periods, modifications to the equation may be necessary. As explored in Article 1, one approach to modeling significant time changes is to adjust the equation to reflect errors in predicting the velocity of neighboring stars, where the error size corresponds to the cumulative differences over time between predicted and actual velocities.

When both Newton's and Kolmogorov equations incorporate the velocity of neighboring stars, notable reductions in mean prediction errors and standard deviations are observed. Some adjustments to the Kolmogorov equation have been made to account for a star’s historical data; specifically, k_a has been altered from 2.7 to 0.3, though variations around this value do not significantly impact predictive performance.

The equations are expressed as follows:

P_r = N_r — (N_{r-1} - A_{r-1})

and

P_r = K_r — (K_{r-1} - A_{r-1})

where: - P_r = predicted velocity of a star at radius r - N_r = velocity predicted using only stellar masses (Newton's equation) at radius r - K_r = velocity predicted using both masses and information (Kolmogorov equation) at radius r - A_{r-1} = measured velocity of the nearest star at radius r-1.

The comparative statistics for 2,665 stars reveal that these equations accurately predict star velocities with minimal standard deviations. However, the standard errors for estimated star velocities in the SPARC database may exceed 5%. Further adjustments for age and temperature are necessary for accurate predictions, but such data is lacking in the SPARC database. While Kolmogorov's predictions are not statistically distinct from those of Newton, they offer a theoretical rationale for including neighboring star velocity errors in the equation, elucidating the importance of a star's movement history within a galaxy.

The notion that the spatial fabric could encapsulate historical information aligns with Loop Quantum Gravity's view on gravity. Carlo Rovelli articulates that:

> Space is a spin network whose nodes represent its elementary grains, and whose links describe their proximity relations. Space-time is generated by processes in which these spin networks transform into one another, described by sums over spinfoams. A spinfoam represents a history of a spin network, creating a granular space-time where the nodes of the graph combine and separate.

Impact of torsion on stellar velocity predictions

The Kolmogorov equation (adjusted for torsion) is predicated on the concept that space itself is twisted (torsion). As detailed in Article 22, Dr. Nikolai Kozyrev posited that time possesses an energy that induces a spiraling motion in the fabric of space, which is responsible for celestial rotation. He theorized that this spiraling motion mirrors the Golden Spiral in Sacred Geometry.

Article 24 discusses how interstellar hydrogen comprises particles with varying spin states, potentially causing spatial curvature to twist over time.

According to the website www.rigobertomuniz.com:

> The great sages of ancient India claimed that the phenomenon of precession causes the equinoctial points of our Sun to take 24,000 years for a complete circuit around the Zodiac. Modern science estimates the precession rate at 50.1" yearly or 1° in 72 years. At this rate, it would take approximately 25,920 years for the Vernal Equinox to complete one full cycle around the Zodiac. Yet, there is no definitive proof that this precession rate remains constant, as the ancients suggested variations in speed at different cycle stages.

Using a cycle of 24,000 years alongside the Golden Ratio of 1.618, a single year in the Golden Spiral equates to 0.002% of the cycle, i.e., 1.618 = (1.00002)^24,000. The average distance between stars in the Milky Way varies, typically ranging from 2.2 to 3.5 light-years. Given that one parsec equals 3.25 light-years, a stellar unit could be defined as 1 parsec.

The spatial distances between neighboring stars fluctuate due to cosmic expansion and their rotation around the galaxy's center. This rotational movement might parallel the dynamics of the Golden Spiral, where one stellar unit correlates to one year in a Golden Spiral cycle.

The average distance between stars located beyond 1.99 kiloparsecs in the STARC database is slightly over 1 kpc or 1,000 stellar units. The 2.1% prediction error within the Kolmogorov equation could partly result from neglecting torsion's influence on stellar velocity. For instance, if a 1 stellar unit distance increment raises the predicted velocity by 0.002%, then a 1 kpc increase could elevate the velocity by 2%. By proportionately adjusting all predicted velocities in the Kolmogorov equation by 2% for each kpc, the mean prediction error can be decreased to -0.2%.

This reduction in the mean prediction error does not involve dark matter. Based on SPARC data, if dark matter exists, its quantity would be the difference between the necessary mass for the observed velocity and the total measured masses of the bulge, disk, and gas. For stars more than 1.99 kpc from the galaxy's center, dark matter would average 1.27 times the baryonic matter, with a standard deviation of 189%. Nonetheless, this calculation indicates that 26% of stars exhibit negative dark matter, meaning some stars possess velocities lower than those predicted by Newton's inverse square law. Additionally, 18% of stars have less dark matter than that found in the neighboring star closer to the galaxy's center. These observations contradict the conventional understanding of dark matter, suggesting that its definition must be revised to align with the Kolmogorov equation. This raises the question: why create a new type of matter if existing explanations suffice for stellar velocities?

Galactic collisions

As elaborated in later articles, the mechanisms through which a star's historical information is communicated may relate to hydrogen atom spins. For instance, molecular density with negative spins might affect spatial curvature. Given that information possesses mass, the perceived dark matter associated with a star could stem from the spins of hydrogen atoms, which may 'flip' based on the need for more or less matter.

Astrophysicists propose that most galaxies have undergone at least one collision with another galaxy. The cumulative history of star movements influenced by such collisions could be reflected in the prediction errors of the adjusted Kolmogorov equations.

Einstein's analogy for gravity compares space to a rubber sheet that deforms under mass. Conversely, the imagery suggested by the Kolmogorov equation likens space to a memory foam mattress, where each section retains the memory of previous loads.

Does dark matter shape galaxies?

This empirical investigation posits that dark matter may correlate with information. The discrepancies between the anticipated velocities of stars from Newton's inverse square law and their actual velocities are not the sole reason dark matter features in the Lambda Cold Dark Matter (?CDM) model for our universe's evolution. As discussed in Article 24, astrophysicists maintain that dark matter provides the foundational structure for the shape and development of galaxies. The informational perspective on dark matter merits further exploration by astrophysicists studying cosmic evolution.

The central inquiry of this article is:

Should information be recognized as possessing mass?

For a comprehensive view of all articles in this series, please visit https://readmedium.com/orbiting-stars-and-origin-of-our-universe-338906930f51.

To acquire a copy of the book ‘Orbiting Stars,’ which includes the original drafts of these articles, please check https://www.amazon.com.