7 November 2026 · Day 3

Sharpening the prediction: one number per black hole

Day 2 gave us our first prediction beyond Einstein: faint echoes after a black hole merger, roughly 0.1 to 0.3 seconds apart. But that range is fuzzy — and a fuzzy prediction is easy to wriggle out of. Today we make it sharp.

The rule

Here is the key: the gap between echoes grows in step with the size of the black hole, and the size is set by its mass. So a heavier black hole rings slower, with longer gaps between its echoes. A lighter one rings faster, with shorter gaps.

Putting numbers on it

For a black hole about 60 times the mass of the Sun — like the one LIGO first saw in 2015 — we expect echoes roughly every 0.2 seconds.

Double the mass, to about 120 Suns, and the gap doubles to about 0.4 seconds. Halve the mass, to about 30 Suns, and it halves to about 0.1 seconds. The rule is simple and strict: the gap is proportional to the mass.

Why this is a stronger flag

This is much harder to wriggle out of than Day 2. Every time LIGO records a merger, it already measures the final black hole’s mass. Our theory then says: the echoes must come at the one spacing that matches that mass. Not a range — one number, fixed in advance.

So the test becomes clean. Line up many mergers of different masses. If the echo gaps grow in step with the masses, exactly as the rule says, that is strong support. If the gaps are random, or there are no echoes at all, the pixel idea fails. The universe gets to decide.