The Universe Shouldn't Decohere That Fast — And Doesn't

Cosmic decoherence — Quantum-Geometric Correspondence series

A formula that blows up the cosmos

Our framework makes a concrete prediction for how gravity destroys quantum superpositions. For a mass M split across a distance d, the decoherence rate is set by the gravitational self-energy:

$\Gamma = \frac{G\,(\Delta m)^2}{\hbar\, d}$

Plug in a laboratory dust grain and you get a nanosecond. Plug in the observable universe — take the mass difference as everything we can see, and the distance as the Hubble radius — and you get something absurd:

$\Gamma \sim 10^{103}\ \mathrm{Hz}$

That is one hundred and twenty-one orders of magnitude above the causal bound set by the expansion of the universe itself. If the formula were literally true at cosmic scales, spacetime would decohere so violently that the cosmos as we know it could not exist.

That is not a prediction. It is an internal contradiction — and resolving it taught us something important about where the laboratory formula is allowed to travel.

The bug was flat spacetime

The lab formula assumes a flat background: the field that carries which-path information can roam freely to arbitrarily long wavelengths. That is an excellent approximation when the separation is a millimetre and the cosmic horizon sits tens of billions of light-years away.

It is a terrible approximation when the separation is the horizon.

On an expanding de Sitter universe — the geometry that actually describes our late cosmos — long-wavelength modes freeze. Once a fluctuation's wavelength stretches beyond the Hubble radius, it stops oscillating and stops driving decoherence. The catastrophe that produced 10¹⁰³ Hz was an artifact of using the wrong propagator at the wrong scale.

Recomputing with the modes appropriate to an expanding universe yields a correction factor:

$\Gamma_{\mathrm{dS}} = \frac{G\,(\Delta m)^2}{\hbar\, d}\, g\!\left(\frac{Hd}{c}\right)$

where

$g(x) = 1 - \frac{2}{\pi}\,\mathrm{Si}(x)$

and Si is the sine integral. For a laboratory experiment the argument is absurdly small, so g = 1 to dozens of digits — the flat-space formula is recovered exactly where it belongs. At the Hubble radius, g ≈ 0.398: finite and causal.

Granularity, not total mass

Even with that factor, feeding in the total mass of the universe would still give a huge rate. The second piece of the resolution is quantum-cosmological: what decoheres is not "the universe as one giant superposition of all its mass," but the elementary graininess of the cosmic wavefunction.

That graininess is set by the thermal mass associated with the cosmic horizon. Summed over the holographic count of horizon modes, the cosmic rate collapses to something remarkably simple:

$\Gamma_{\mathrm{total}} \approx \frac{H}{10\pi} \approx 7 \times 10^{-20}\ \mathrm{Hz}$

That is slower than the expansion of the universe. The cosmos is allowed to exist.

What this locks — and what it doesn't

The result is not a free parameter. The same number that appears in the form factor also locks the MOND acceleration scale — the mysterious acceleration that shows up in galaxy rotation curves — to this cosmic rate at a parameter-free ratio of about 5.03. Every cosmological input cancels.

So the fix is not a patch. It is a structural consequence of doing the calculation on the background the universe actually has.

Honesty still matters. The result rests on the expanding-universe recomputation, the identification of branch graininess with the thermal mass scale, and the framework's first-order rate in Newton's constant — which is itself still a conjecture as a full operator equation, though solid in expectation values and solvable models. An order-one uncertainty in the graininess remains; we do not pretend otherwise.

What we do claim is that the 10¹⁰³ Hz disaster is gone, and that its disappearance was diagnostic: the laboratory formula is a controlled limit of a cosmic result, not a universal law to be extrapolated blindly to the horizon.

The moral

Every theory that reaches for cosmology from a laboratory formula risks this kind of blow-up. The useful response is not to abandon the formula, and not to invent an arbitrary cutoff. It is to ask: where did the approximation fail?

Here the answer was concrete. Flat-space gravitons at horizon separations were the bug. Expanding-universe modes and holographic graininess were the fix. The universe decoheres — but at roughly one tick per ten Hubble times, not once per 10⁻¹⁰³ seconds.

Nature, it turns out, was never in danger. Our formula was.

Related: The Horizon Clock, Three Axioms, One Decoherence Rate.