What if atoms are shrinking?

Course outline

Every lesson as plain text, if you'd rather read than click.

1. 1.Bigger room, or smaller feet?BABY MODE

   You count your bedroom heel to toe: 10 steps. Next morning it's 12. What changed? The count can't tell. A room 20% longer and feet a sixth shorter both give twelve. A count of feet is a ratio: room divided by foot.

   Now swap in the sky. The room is the gap between groups of galaxies. Your feet are atoms, the pieces every ruler, clock and eye is made of. The count is what telescopes record: light from faraway galaxies arrives with its waves stretched, shifted toward red. That's redshift.

   The usual story: space stretched while the light travelled, and the light stretched with it. The flipped story: long ago electrons and protons were lighter, atoms were bigger, and their light came out redder from the start. The 2013 paper behind the idea says this effect "could replace the redshift due to expanding distances."

   Why can't a telescope simply measure the distance to a galaxy and settle it? Because a distance is always counted in something made of atoms. In Wetterich's words: "Only dimensionless ratios as the distance between galaxies divided by the atom radius are observable." The growing ratio fits growing gaps or shrinking atoms.

2. 2.What doesn't stretchBIG BABY MODE

   Space between galaxy groups is stretching. Does an atom stretch with it, even a little? Not at all. Bound systems are all or nothing, and an atom's forces win by a huge margin.

   Price and Romano (2012) tested a simple model atom held together by electric pull. It either follows the expansion completely or ignores it completely: there's no stretching a little. For a real atom, the atom's timescale is about 10⁻¹⁶ s and the expansion's about 4 × 10¹⁷ s, so atoms "are in no danger of being disrupted by cosmological expansion."

   Bigger things hold too. For a planet's orbit, a galaxy or a galaxy cluster, a 1998 study found the expansion's effect insignificant. Each bound group of galaxies has a turnaround radius, the outermost shell that isn't expanding. Our neighbour Andromeda is even coming toward us, at about 109 km/s. Only the gaps between bound groups grow.

3. 3.How an atom could shrinkBIG BABY MODE

   In the Bohr model, an atom's radius is a₀ = 4πε₀ħ²/(mₑe²). The electron's mass sits in the denominator: a heavier electron gives a smaller atom. Today's measured value is 5.29 × 10⁻¹¹ m. It's a simplified model, but it shows the link between mass and size in one line.

   Change the electron's mass

   1. Rule: radius ∝ 1 / electron mass (all other constants kept the same).
   2. Double the mass: radius × 1/2. The atom is half as wide.
   3. Run it backwards in time: if electrons were lighter when a galaxy sent its light, atoms were bigger and the light came out redder.

   How fast would atoms have to shrink to copy today's expansion? About 7% every billion years at today's rate. That's our estimate, not a number from the paper: with space holding still, atoms shrink at the Hubble rate. 67.4 to 73.04 km/s per megaparsec works out to 6.7% to 7.5% per billion years. Long ago, it would have been faster.

4. 4.Same physics, easier mathBIG BABY MODE

   Where the footsteps picture breaks: in your room you could hold your foot against a shoe. In the universe there's no shoe; every ruler is made of atoms. And a lazy version fails. If particles got heavier while gravity stayed the same, measured limits would be broken. In the working version every particle mass and the Planck mass grow together, and gravity weakens in step.

   If both pictures fit the same sky, why do we say space grows? Because the math is easiest there. Wetterich calls the shrinking picture complementary, "not as opposing" expansion, and writes that observations are "typically most easily done in the Einstein frame," where gravity and particle masses stay fixed. Same universe, less to track.

   One part can be tested. Wetterich's full model adds a field, the cosmon, behind inflation and dark energy. Its simplest version predicted r = 0.13 for early gravitational waves; the 2021 limit is r < 0.036. By our comparison, that version misses the limit. The paper notes modified versions can predict a smaller r.