Why Gravity Attracts: The Redshift Ratchet Mechanism

For over a century, we’ve known how gravity works. Einstein showed us it’s the curvature of spacetime. But why does mass always attract rather than repel? Why don’t we see regions of “anti-gravity” in nature? A new formulation reveals an unexpectedly simple answer: gravity’s attractive nature emerges from an asymmetric feedback loop between energy flux and gravitational redshift.

The Flux Law: How Energy Writes Time

In the time-first formulation of general relativity, we elevate the lapse function N = e^Φ to primary status, where Φ represents the temporal potential. The key evolution equation is:

∂_t Φ(t,r) = -4πG r T_tr(t,r)

This flux law states something profound: only actual energy flux (T_tr ≠ 0) can change the local flow of time. When energy crosses a spherical shell at radius r, it permanently alters the temporal geometry at that location. Once the flux stops, the temporal profile freezes, creating what we might call a “temporal scar.”

The Redshift Ratchet: Why Infall Wins

Here’s where the mechanism becomes clear. In a static gravitational field, energy flux obeys a conservation law along radial paths:

T_tr(r) ∝ 1/(r² N(r))

Since N(r) = e^Φ(r) < 1 inside a gravitational well, this creates a fundamental asymmetry:

Infalling energy (T_tr > 0): - Gets progressively blueshifted as r decreases - Local flux density grows as 1/N(r) - Creates stronger ∂_t Φ at smaller radii - Result: Runaway deepening of the temporal well

Outflowing energy (T_tr < 0): - Gets progressively redshifted as r increases
- Local flux density suppressed by N(r) factor - Creates weaker |∂_t Φ| that barely affects the profile - Result: Can flatten existing curvature but cannot invert it

The same 1/r² geometric focusing affects both directions, but the N^(-1) factor creates the bias: blueshift amplifies infall’s ability to etch the temporal potential, while redshift cripples outflow’s ability to reverse it.

A Concrete Example

Consider a thin shell of mass ΔM = M_☉ falling through radius R = 5r_s (about 15 km for a solar mass). The temporal change is:

ΔΦ = -GM/R = -0.10

This creates a 9.5% instantaneous slowdown of local clocks as the shell passes. The same mass flowing outward would need to fight against its own redshift, making the reversal progressively less efficient at each radius.

Why No Anti-Gravity?

Three constraints select the converging solution:

1. Asymptotic flatness: Φ → 0 as r → ∞
2. Positive energy: T_μν u^μ u^ν ≥ 0 implies M ≥ 0
3. Constraint structure: These conditions uniquely give e^(2Φ) = 1 - 2GM/r

A static “anti-gravity” profile would require negative mass, violating energy conditions. Dynamically, the redshift ratchet ensures positive energy creates converging patterns. Even Hawking radiation, while carrying away mass, only flattens the profile - it cannot invert it to create repulsion.

Observable Consequences

This mechanism predicts testable signatures:

1. Delay drift in strong lensing: Source variability should produce correlated, sign-locked drifts in multiple image time delays. For a galaxy lens, we estimate ~0.9 μs drift for 10^(-12) fractional mass changes.

2. Temporal memory: Energy transients leave permanent offsets in Φ, analogous to gravitational wave memory but in the temporal sector.

3. Asymmetric variability response: Equal-energy inflow/outflow episodes have unequal effects once local redshift factors are included.

The Physical Picture

Mass isn’t actively “pulling” anything. Instead:

1. Historical energy flows (during formation) created patterns in temporal geometry
2. Infalling energy blueshifted itself into runaway collapse, etching deep temporal wells
3. These patterns froze when the flux ceased, leaving “temporal scars”
4. Objects now follow geodesics through this frozen temporal landscape
5. All geodesics through a converging temporal pattern lead toward the center

Gravity is the fossil record of ancient energy flows, preserved in the geometry of time itself.

Relation to Standard GR

This isn’t new physics. It’s Einstein’s theory in different variables. The Raychaudhuri equation’s focusing theorem appears here as the redshift ratchet. The novelty is explanatory: by isolating time as the dynamical field and making the flux-redshift feedback explicit, we see why positive energy creates attraction rather than simply calculating that it does.

Conclusion

The attractive nature of gravity emerges from a simple feedback asymmetry: energy flux writes temporal geometry, but gravitational redshift biases the writing process to favor convergence over divergence. This transforms gravity from a mysterious universal attraction into a comprehensible consequence of how energy interacts with its own temporal effects. The universe’s gravitational landscape is, quite literally, the accumulated temporal scars of every energy flow that ever occurred.

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Paper reference: "Gravity as Temporal Geometry VIII: Why Gravity Attracts" - https://doi.org/10.5281/zenodo.16942936