Chapter 1: The Origins of Dark Matter Theory

The concept of dark matter originated from observations that galaxy clusters rotate around each other at rates that exceed predictions made by Newton’s inverse square law. In the 1930s, Fritz Zwicky noted this anomaly, leading astronomers to speculate about the existence of hidden matter to explain these rapid rotations.

In the 1970s, Vera Rubin further advanced this idea when she observed that stars in numerous galaxies exhibited velocities surpassing their estimated escape velocities. This suggested that stars should drift away from the center of their galaxies, reinforcing the hypothesis of unseen matter.

The confirmation of hidden matter in galaxies came through measurements of light from distant galaxies, which was distorted when other galaxies lay between them and Earth. This phenomenon, known as gravitational lensing, demonstrated that the actual path of light was longer than expected based on the known mass of visible galaxies. This divergence is attributed to the presence of dark matter.

Dark matter is now integral to our understanding of the universe's evolution. For instance, theories suggest that the universe's structure formed from smaller scales first, with dark matter acting as a "scaffold" for normal matter, which later took the shape of galaxies and clusters.

Despite the strong theoretical backing for dark matter, there has yet to be any detection of dark matter particles.

Chapter 2: The Rotation Curves of Galaxies

The spiral galaxy Messier 33 exemplifies the discrepancies between predicted and observed star rotation curves. These curves vary significantly among galaxies; some show a positive slope, while others are flat or negative.

However, skepticism about dark matter exists within the scientific community. Some astrophysicists advocate for MOND theory, which modifies Newton's gravitational equations over large distances.

A notable statistical relationship concerning dark matter has not been thoroughly examined by mainstream cosmologists. This analysis poses substantial challenges to the current understanding of dark matter. By utilizing public data from the SPARC database, which includes the velocities of 3,360 stars across 175 galaxies, researchers can compute the necessary amount of dark matter to reconcile the discrepancies between expected and observed velocities.

For stars located 2 kiloparsecs (kpc) or more from a galaxy's center, the average deviation between predicted and observed velocities is -19%, with a standard deviation of 28%. However, when applying a revised equation, the average discrepancy becomes -2%, with a standard deviation of 5%.

The uncertainty in measuring star velocities and estimating their radial distances can significantly influence the calculated discrepancies. The predicted velocity equation is as follows:

V? ~ √(M?/r) ………………………………… (1)

Where V? represents the velocity at radius r, M? is the mass of the galaxy within radius r, and r is the radius of the galaxy.

The adjusted equation is:

V? ~ √([M? — {dev(r-1)*M(r-1)}]/r) …………. (2)

In this context, dev(r-1) refers to the deviation in velocity for the nearest inner star, while M(r-1) denotes the mass of the galaxy associated with that star.

This analysis indicates that the velocities of stars can be accurately predicted using Newton's equations after accounting for deviations linked to nearby stars. While this outcome may superficially align with the dark matter hypothesis, physicist Sabine Hossenfelder has argued that Renzo’s rule implies that dark matter should eliminate any correlation between the luminosity of baryonic matter and the galaxy's rotation curve.

“For every feature in the curve for visible emission like a wiggle or a bump, there is also a feature in the rotation curve. That’s an observational fact, but it makes absolutely no sense for dark matter if you think that most of the matter in galaxies is dark matter. The dark matter should remove any correlation between luminosity and rotation curves.” (time 6:21)

The video titled "No Dark Matter? New Research Suggests That Our Universe Has No..." examines these findings and their implications for our understanding of dark matter.

Chapter 3: Reevaluating Dark Matter Hypothesis

The dark matter hypothesis does not clarify how dark matter is distributed within galaxies. Thus, the observation that a star's velocity is influenced by the dark matter linked to a nearby star cannot be easily disproven.

This article series proposes a hypothesis that offers a scientific rationale for the observed statistical relationships, which can potentially be tested. In this proposal, there is no prior distinction made between various galaxy types. All stars situated beyond a radius of 1.95 kpc from a galaxy's center are included in the analysis, without assumptions regarding dark matter distribution.

The central question posed is: Are astrophysicists overlooking the fact that the dark matter hypothesis may not be easily testable?