The announcement in May was significant: MOND had been deemed invalid, largely due to findings from the Cassini spacecraft. As I was about to publish my paper that linked MOND to a five-dimensional extension of Einstein's theory, I wondered if my efforts were in vain. However, there may be more to consider.

Modified Newtonian Dynamics (MOND) was initially proposed to address the unexpected rapid rotation of stars in the outskirts of galaxies, which seemed disproportionate to their visible mass.

Take the Milky Way, for example. It has a dense concentration of stars at its center, tapering off toward the edges. If the mass distribution followed the Newtonian model, one would expect outer stars to rotate slower, akin to planets in our Solar System where mass is centered. Yet, observations reveal that stars in galaxies do not conform to this expectation.

To account for the anomaly, astrophysicists introduced the idea of dark matter, an unseen substance that uniformly fills galaxies. This uniformity maintains a consistent mass density, ensuring that stars feel a similar gravitational pull regardless of their distance from the center.

While this dark matter model provided some insights, it has its shortcomings.

Why didn’t scientists abandon Newtonian gravity entirely? Altering gravitational theory could yield significant repercussions. The laws of gravity work effectively within our Solar System; any new theory must reconcile its performance at both galactic and solar scales.

Moreover, compelling evidence for dark matter emerged as scientists examined the universe on larger scales. According to Einstein's general relativity, matter can bend light, similar to how light refracts when passing from air to water, creating optical illusions like a pencil appearing broken when placed in a glass of water.

Galaxies appeared to warp light around them, indicating they possessed far more mass than what was visible. This effect was also observed in galaxy clusters, where the distribution of visible matter did not align with gravitational effects.

Observations at the cosmic scale suggested that dark matter was necessary for the universe to have evolved as it has. The evidence was present in the Cosmic Microwave Background (CMB) radiation, the earliest light detectable.

While some attempted to explain these observations using alternate gravity theories, the challenge remained with galaxies. Dark matter theories did not provide satisfactory explanations at these scales, whereas MOND managed to elucidate some of these galaxy dynamics more effectively.

MOND posits that gravitational pull changes in very weak fields. For instance, stars in galaxies experience such minimal gravitational force that their orbits span hundreds of millions of years across vast distances. MOND offers a formula that transitions from Newtonian to MONDian gravity in weak gravitational scenarios, resulting in a nearly constant gravitational pull with distance, allowing galaxies to rotate similarly to a spinning tire rather than a solar system.

Originally, MOND was viewed as a modification of dynamics, interpreted primarily as a change in gravitational experience. This notion is encapsulated in AQUAL (A QUAdratic Lagrangian), a mathematical framework for discussing forces. Various relativistic adaptations of AQUAL aim to account for light bending around galaxies as though they harbor significant dark matter.

Until recently, MOND withstood scrutiny. In 2006, gravitational lensing from the Bullet Cluster appeared to provide strong evidence for dark matter, leading many to declare MOND obsolete. However, counterarguments surfaced, suggesting that the Bullet Cluster does not fit neatly within existing cosmological models, permitting MOND to remain a contender.

When CMB data hinted at further support for dark matter, researchers demonstrated the ability to reproduce key CMB features using MOND.

The crucial insight many researchers identified in resolving the debate between dark matter and MOND was the importance of examining smaller scales.

Recent studies of "wide binary" systems—star systems where two stars orbit at a significant distance—indicated varying implications for MOND's validity, with results depending on the datasets employed.

What about the Solar System?

MOND was crafted to ensure its effects would not disrupt planetary orbit predictions. However, it does not entirely negate its influence when gravitational accelerations are high; rather, its impact diminishes.

Until recently, accurate positional data for planetary orbits were insufficient to draw definitive conclusions about MOND's relevance in the Solar System. The Cassini probe, launched to study Saturn in 1996, has provided exceptional orbital data, allowing us to test MOND’s predictions.

This data indicates no deviation from Newtonian gravity within the Solar System. The complete absence of MONDian effects here seems at odds with MOND formulations that successfully account for galaxy rotation. Essentially, it is challenging to have a MOND framework that explains galaxy behavior while being entirely absent in our Solar System.

For MOND to be valid for galaxies, it must alter gravity behavior at specific accelerations and apply only to certain scales, such as galaxies, while exempting solar systems.

While MOND lacks such scaling, Modified Gravity (MOG) does possess this feature, suggesting it remains a viable avenue for my forthcoming research on five-dimensional gravity.

MOG differs significantly from MOND, being more intricate but also offering a relativistic framework that aligns with the Scalar-Tensor-Vector representation akin to the Tensor-Vector-Scalar theory derived from five-dimensional gravity.

Developed by John Moffat of the Perimeter Institute in Waterloo, Canada, MOG—also known as Scalar-Tensor-Vector gravity (or STeVe)—has not garnered the same attention as MOND but features intriguing characteristics.

One notable aspect is its Yukawa-like modification to gravitational force, which arises when the force carrier particle possesses mass, resulting in a limited effective range. This introduces a length scale to the force.

The Yukawa force is repulsive, counteracting gravitational force over short distances while vanishing over longer ranges. Consequently, at galactic scales where dark matter appears significant, gravity is stronger than predicted by Newtonian physics.

MOG can create the illusion of matter existing in regions where it is not present, a crucial element for explaining galaxy clusters where light bending reveals gravitational discrepancies between luminous matter and actual gravitational presence.

For instance, the green lines in the lensing map represent the distribution of matter inferred from lensing, contrasting with the luminous matter distribution in the Bullet Cluster.

Critics of MOG describe it as a "non-local" theory, asserting that only such a framework could explain the disparity between the center of mass and center of luminosity without invoking dark matter. In reality, MOG modifies the lensing equations themselves, dynamically scaling the Newtonian mass based on spatial location. This variation means that mass increases from the cluster's center, resulting in more pronounced bending at the edges.

Thus, the notion of non-locality arises from viewing the cluster as a singular object rather than a multitude of gravitating entities, each exhibiting variable gravitational behavior based on interactions.

Therefore, the situation is not a binary choice between non-local gravity or unseen matter. MOG presents a third pathway, suggesting that gravitational behavior varies based on proximity and the number of interacting bodies.

Similar dynamics occur in atomic nuclei, where electromagnetic forces dominate at a distance, but the strong force prevails when atoms are in close proximity, leading to entirely different interactions. Such variations are not typically labeled as "non-local."

MOG effectively explains weak lensing in colliding clusters, such as the Bullet Cluster. Before a collision, lensing is centrally aligned, while post-collision, it shifts outward due to the uneven matter distribution.

Currently, MOG can account for observations of the Bullet Cluster without needing dark matter—a feat MOND has yet to achieve. It also addresses cosmological scenarios devoid of dark matter. However, the primary drawback of MOG lies in its complexity and non-linearity, presenting challenges for effective modeling.