The Mystery That Shouldn’t Exist
In the early 20th century, astronomers believed they had the universe mostly figured out.
Gravity, as described by Newton and refined by Einstein, was elegant and precise. It explained everything from falling apples to the motion of planets.
Then, something strange happened.
In the 1930s, Swiss astronomer Fritz Zwicky studied galaxies inside the Coma Cluster.
He found that the galaxies were moving far too fast to be held together by the visible matter alone. By all known laws of gravity, the cluster should have flown apart.
The same puzzle reappeared in the 1970s, when Vera Rubin measured the rotation speeds of spiral galaxies. Instead of slowing down at large distances — as Newton’s law predicts — the stars on the outskirts kept orbiting just as fast as those near the center.
It was as if each galaxy were surrounded by an invisible halo of extra mass — a hidden substance exerting gravitational pull but emitting no light. This invisible ingredient was named dark matter.
Fig. 1: Left: a galaxy with dark matter, Right: a galaxy with pure newtonian gravityComparison of rotating disc galaxies. The imaginary galaxy on the left is orbiting rapidly due to the presence of large amounts of Timeflow gradients around the central regions. On the other hand the galaxy at the right, which is in the distant Universe, and seen as it was about ten billion years ago, is rotating more slowly in its outer parts as dark matter is more diffuse.
MOND: A Radical Alternative
MOND: A Radical Alternative
While most physicists embarked on the search for the dark matter particle, some were skeptical. In 1983, Israeli physicist Mordehai Milgrom proposed a radical alternative called MOND (Modified Newtonian Dynamics).
Milgrom noticed that the discrepancy wasn't related to the size of the galaxy, but to the acceleration experienced by the stars. The laws of gravity seemed to work perfectly in high-acceleration environments (like our solar system). But whenever the gravitational acceleration dropped below a very specific, incredibly small value—termed a0—the standard laws failed.
MOND proposed that below this critical acceleration threshold, gravity becomes stronger than Newton or Einstein predicted. This simple modification explained the flat rotation curves perfectly, without needing any dark matter.
Despite its empirical success in predicting galactic dynamics—often better than dark matter models—MOND remained on the fringe. It was a descriptive rule, a mathematical fix without a physical foundation. It explained what was happening, but not why. Why should gravity care about a critical acceleration scale?
Hum of Time
In Timeflow Gravity, everything — matter, space, energy — arises from a single physical field: the Timeflow field. It’s a continuous, oscillating medium that carries information at the constant speed of light.
Each point in this field vibrates at a certain frequency (ω) and with a corresponding amplitude (A). Together, they define the local rate of time and the scale of space.
Even in the absence of matter or radiation, this field doesn’t stand still. It oscillates with a vacuum frequency, ω₀ — the background rhythm of the universe’s “empty” spacetime. This is the ground state of Timeflow — the minimal oscillation needed to sustain the constant speed of light, c = ω/A.
You can think of this vacuum oscillation as a quantum hum of time itself. Every atom, photon, and gravitational field is just a local modulation of this background rhythm.
Self-Reinforcing Voids
In normal physics, fields like electromagnetism are linear: doubling the source doubles the response. But the Timeflow field is inherently non-linear, because Timeflow controls its own rate of change.
In mathematical terms, the field’s own energy density — which depends on ω and A — feeds back into its evolution. As the local frequency increases (higher energy density), the field’s “stiffness” or resistance to deformation also changes. This feedback makes the relationship between energy density and curvature non-linear.
At high energy densities (inside stars, near galactic centers), the field behaves almost linearly — recovering Newtonian and Einsteinian gravity. But in low-density environments, the field becomes much more flexible: a small change in energy density causes a larger response in curvature. This transition is the origin of the MOND-like regime.The vacuum frequency ω0 defines the boundary between the linear and non-linear regimes.
When the local oscillation frequency of Timeflow falls below this background rhythm, the field’s behaviour changes. It begins to amplify gravitational effects — not because there’s extra mass, but because Timeflow becomes self-reinforcing.
In this state, small perturbations in the Timeflow field spread more efficiently, creating extended gravitational coherence around galaxies. This coherence is what we observe as the dark matter halo.
Thus, the apparent extra gravity appears precisely in regions where the local frequency ω approaches or drops below the vacuum frequency ω0. At that threshold, the field transitions from a stiff, linear regime to a fluid, collective one — where the flow of time becomes non-local and self-coupled.
Is Dark Matters?
The "dark matter" effect appears in the outskirts of galaxies, where the density of matter is extremely low and the gravitational acceleration drops below the critical scale (a<a0). In this regime, the local gravitational field is so weak that the thermodynamic properties of the Timeflow itself become dominant.
This is where the Law of Entropy Equilibrium asserts itself non-linearly. In the weak-field regime, the relationship between the source matter and the field's response must change to maintain the fundamental symmetry (ω/A=Constant) and satisfy the Law of Entropy Equilibrium.
The field undergoes a kind of "phase transition." To maintain its equilibrium state against the background vacuum frequency (ω0), the Timeflow Field amplifies the gravitational effect of the existing matter.
The spacetime medium becomes more responsive. For a given small input of energy (the visible matter), the resulting increase in Amplitude (A, spatial contraction) and Frequency (ω, time dilation) is significantly larger than the standard linear prediction.
This amplified distortion of the Timeflow Field creates steeper gradients in time and space. Steeper gradients mean stronger gravity.
The "dark matter" phenomenon is this amplified thermodynamic response. It is the signature of the Timeflow Field actively adapting to the dilution of energy to enforce its most fundamental laws—the balance of order and chaos, constrained by the absolute invariance of the speed of light.