Emergent Time

I’ve spent weeks chasing a single number: 2π.

MOND — the alternative to dark matter — fits galaxy rotation curves remarkably well once you accept one free constant, the acceleration scale a₀ ≈ 1.2×10⁻¹⁰ m/s². Nobody has a first-principles reason for that number. But it sits suspiciously close to cH₀ (light speed times the Hubble constant) divided by 2π — the “MOND coincidence.” That coincidence is the seed of my side project: an “emergent time” framework built on the idea that low-acceleration gravity traces back to the thermodynamics of the cosmological horizon.

Most of the work has been numerical: simulating a quantum field on an expanding (McVittie) spacetime and watching for where particle creation peaks, repeating that across four orders of magnitude in mass to check the result is universal, then checking the resulting formula against 120 real galaxies from the SPARC rotation-curve catalog. The encouraging part: several independent routes — Gibbons-Hawking horizon temperature, Bohr-Sommerfeld quantization at the horizon, a QFT resonance near ω ≈ 2πH — all land on the same 2π. And the correction clearly matters: plain cH alone predicts barely 22% of the galaxy masses SPARC actually shows.

Then, this month (July 2026), I turned adversarial on myself: pre-registered falsification tests against my own paper’s specific claims, no re-tuning allowed after seeing results. It was humbling. A “motion budget” claim failed outright against real high-redshift galaxies. A “flow” picture of gravitational time dilation turned out to be mathematically identical to standard GR — true, but useless as a test. And a claimed GR-distinguishing prediction about epoch-dependent time dilation traced back to a… ehh… sign error… in my own derivation; corrected, it predicts nothing new.

Real signal in the 2π, real damage from testing my own claims against it. Both feel like progress.