What if atoms are shrinking?

Nothing we could measure would change. Light from distant galaxies arrives stretched toward red, and that fits two descriptions: space grew while the light travelled, or atoms were bigger long ago and have shrunk since. Physicist Christof Wetterich argued in 2013 that both describe the same physics, because every measurement compares a distance with the size of atoms. 2 14

There is a condition. The swap only works if every particle mass and the strength of gravity change together, in step; a version where only atoms shrink would break measured limits. 2 This page starts with a bedroom floor, then looks at what really stretches in an expanding universe, what Hubble measured in 1929, how an atom's size can change, and why we still say space grows.

Measure your room in footsteps

Walk across your bedroom heel to toe and count: ten steps from wall to wall. The next morning you walk it again and get twelve. Either the room grew or your feet shrank, and the count alone can't say which. A room 20% longer and feet a sixth shorter both give twelve.

The reason is simple. A count of footsteps is a ratio: room length divided by foot length. Your foot is both the ruler and a part of you. Cosmology has the same structure. Wetterich puts it in one line: "Only dimensionless ratios as the distance between galaxies divided by the atom radius are observable." 2

From the bedroom to the sky

Here is the mapping. 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. 2 9

What telescopes record is light. Light from faraway galaxies arrives with its waves stretched: each wavelength is longer, shifted toward red. This is called redshift. 14 In the usual description, the light waves are stretched by the stretching of the space they travel through. 14 The farther the galaxy, the larger the shift. 12

Now flip the description. Suppose that when a distant galaxy sent its light, electrons and protons were lighter than they are today. Lighter particles make larger atoms, and their light comes out at lower frequencies, which means redder light. 2 7 Wetterich writes that this effect "could replace the redshift due to expanding distances." 2

So the extra red has two readings. In one, the room grew. In the other, the feet shrank. Both say the same thing about the only quantity we can check: the gap between galaxies grew compared with the size of atoms. 2

Does space stretch atoms?

A common picture of the expanding universe treats it as a uniform stretching of space that would affect atoms and stars as well as the separation of galaxies. Physicists Price and Romano open their 2012 paper in the American Journal of Physics by naming exactly that picture. 4

They tested it on a simple model atom held together by electric attraction. The result was all or nothing: the system either follows the cosmological expansion completely, or, after initial transients, ignores it completely. There is no stretching a little. 4 For a real atom the comparison is lopsided. The atom's own timescale is about 10⁻¹⁶ seconds, the expansion's is about 4 × 10¹⁷ seconds, and the authors conclude that atoms "are in no danger of being disrupted by cosmological expansion." 4

Larger systems behave the same way. A 1998 study by Cooperstock, Faraoni and Vollick found the effect of the expansion insignificant for a planetary orbit and on galactic and galaxy-cluster scales. 5 Insignificant is the word they use; it is not the same as zero.

For groups of galaxies there is a measurable boundary. Pavlidou and Tomaras describe the turnaround radius as "the non-expanding shell furthest away from the center of a bound structure." Every group of galaxies they examined lies within the limit, even within errors. 9 Inside that shell the group holds together. Outside it, the gaps grow.

Our neighbour galaxy, Andromeda, shows this directly. It is not moving away from the Milky Way: measurements of its motion give a radial velocity of about 109 km/s toward us. 13 In the footstep picture, your feet stay the same size and only the room grows. 4 9

What Hubble actually measured

In 1929 Hubble published a relation between the distances of galaxies and their radial velocities, worked out from the redshift of their light. 1 12 He was careful with the wording: he referred to the redshift as giving an "apparent velocity." 12 The slope he quoted came out at 530 and 500 km/s per megaparsec. 12

Today's values are much smaller: 67.4 ± 0.5 km/s/Mpc from the Planck Collaboration's 2018 results, and 73.04 ± 1.04 km/s/Mpc from the SH0ES team's Cepheid and supernova sample. 6 8 Kirshner explains the gap: Hubble's 1929 distances were too small by a factor of 7, yet his conclusion about cosmic expansion held up. 12

Every velocity on that plot was worked out from the colour of light. That matters for the shrinking-atoms idea, because the colour is the measurement and the velocity is an interpretation. 12 2

Even within the expanding picture, physicists argue about the best way to describe redshift. Davis and Lineweaver ruled out the special-relativistic Doppler interpretation, the idea of galaxies moving through static space, at a confidence level of 23 sigma. 10 Bunn and Hogg argue that in general relativity, the most natural interpretation of redshift is still a Doppler shift. 11

How an atom's size can change

In the Bohr model of hydrogen, the radius of the atom is a₀ = 4πε₀ħ²/(mₑe²). The electron's mass, mₑ, sits in the denominator. 7 15 The measured value is 5.29177210544 × 10⁻¹¹ m. 7

Follow the formula with a thought experiment, keeping every other constant the same. If the electron were twice as heavy, the atom would be half as wide. If it were three times as heavy, the atom would be a third as wide. 7 15 A heavier electron also spreads the energy levels apart, so the atom's light shifts to higher frequency. 2 15 Run that backwards in time: lighter electrons in the past mean bigger atoms and redder light. 2

The Bohr model is a simplified picture of the atom. We use it here because it shows the link between mass and size in one line. 15

The 2013 paper behind the idea

Christof Wetterich posted the paper as a preprint in March 2013. It appeared in December 2013 in Physics of the Dark Universe under the title "Universe without expansion." 2 When Nature's news story reported it in July 2013, the paper had not yet been peer-reviewed. 3 17

The central idea is a change of variables. Wetterich writes that the units in which geometric distances are measured can be changed by a field-dependent redefinition of the metric, and that this choice "does not matter for physical observables." 2 He calls this freedom "field relativity," comparing it to the freedom to choose different coordinate systems in general relativity. 2 He also notes that the general setting, with particle masses and the Planck mass varying together, goes back to his own work from 1988. What is new in the 2013 paper is the simple picture of a universe that shrinks during the radiation and matter eras. 2

This detail is easy to miss. In the frame Wetterich mainly uses, space does not hold still: it shrinks during those eras, and atoms shrink even faster, so the ratio still grows. He also points out a choice in which the universe "is static at present, shrinking in the past and expanding in the future." 2 The version on this page, with space holding still and atoms shrinking, is one of these equivalent choices.

Wetterich states his position plainly: "Our model should be interpreted as a new complementary picture of cosmology, not as opposing the more standard picture of an expanding universe." And: "The different pictures are equivalent, describing the same physics." 2

How fast would atoms shrink?

In the description where space holds still today, the ratio of galaxy distance to atom size grows at the rate the universe expands, so atoms shrink at that rate. 2 The 2013 paper does not give a percentage. The figure below is our estimate from the measured Hubble constant.

1. Take the Planck value, 67.4 km/s per megaparsec. A megaparsec is 3.0857 × 10¹⁹ km, so the rate is 2.18 × 10⁻¹⁸ per second. 6
2. A billion years is 3.156 × 10¹⁶ seconds. Multiply: 0.069, or about 6.9% per billion years at today's rate.
3. With the SH0ES value, 73.04, the same steps give about 7.5%. 8 Counting the full billion years instead of the instant rate gives 6.7% to 7.2%.

So at today's pace, atoms would shrink about 7% every billion years. The expansion rate was higher in the past, so in this description atoms shrank faster long ago. 6

Where the footsteps picture breaks

In your bedroom you would catch the trick in seconds: hold your foot next to a shoe or a floor tile. Out in the universe there is no shoe. Every ruler, clock and eye is made of atoms, so there is nothing outside the ratio to compare against. 2

The clue arrives by a different route. Light from a distant galaxy left long ago, so it carries the step size of atoms from that time. Your feet can't send you a note from yesterday; old light can. 2 14

There is a second, deeper limit. If only the particles got heavier while gravity stayed the same, the ratio between particle masses and the Planck mass, which sets the strength of gravity, would drift over time. Wetterich writes that this would violate "the strict observational bounds." 2 In his model, the Planck mass and every particle mass increase together, so all bounds on the time variation of fundamental constants and on apparent violations of the equivalence principle are obeyed. 2 As the masses grow, the effective strength of gravity falls roughly as the inverse square of the field that sets them. 2 Our derivation from those two scalings: the product of gravity's strength and the square of a particle's mass stays constant, so the pull between two particles, compared with everything else, comes out the same. 2

That is why the lazy version, where atoms shrink and nothing else changes, would be caught. The working version changes everything in step. 2

So why do we say space grows?

Nature's news story of 16 July 2013 ran the headline "Cosmologist claims Universe may not be expanding." 3 It is easy to read that as a proof that the universe isn't expanding. The paper says something gentler: the shrinking picture is complementary, and both pictures describe the same physics. 2 One cosmologist quoted in the story, Hongsheng Zhao of the University of St Andrews, called it "this alternative representation" and said the treatment "seems rigorous enough to be entertained." 17

A second analogy helps here. You sit on a train at a station, and the train on the next track starts to slide. For a moment you can't tell which one is moving; the view through the window is the same either way. The two trains are the two descriptions, and the window is the telescope. Wetterich's own comparison is with choosing coordinates. 2

This analogy breaks too. On a real train you can look at the platform or feel the jolt, and one train really is moving. In cosmology there is no platform, and neither description is an illusion. 2

So why describe the universe as expanding at all? Because the arithmetic is easier there. Wetterich writes that "the discussion of observations is typically most easily done in the Einstein frame," the standard description, "since one has no longer to pay attention to a varying gravitational constant and varying particle masses." 2 Same universe, less to keep track of.

The part that can be tested

Choosing between the two descriptions can't be tested, because they make the same predictions. 2 Wetterich's full model, though, adds more than the change of description. It includes a field he calls the cosmon, similar to the Higgs field, whose potential drives inflation in the early universe and today's dark energy. He writes that its properties can be tested through dynamical dark energy and the density fluctuations left over from inflation. 2

Its simplest version predicted a spectral index of n = 0.97 and a tensor-to-scalar ratio of r = 0.13, a measure of how strong gravitational waves from the earliest era should be. Wetterich himself wrote that r = 0.13 "may be considered borderline." 2 In 2021 the BICEP/Keck collaboration set a limit of r < 0.036 at 95% confidence. 16 By our comparison, that limit is less than a third of the simplest version's prediction, so that version misses it. The paper notes that modified versions can give a smaller r; we did not check where those stand today. 2 16