Thank you.

This is not a stupid question:

> Do you mean that Manhattan (and the Earth-Moon system, etc.) literally are not expanding even one smidgen, or do you mean that at that scale the expansion is just too small to (notice|measure|care about)?

More the former.

In General Relativity, we have several exact solutions of the Einstein Field Equations, which basically means we have a lot of standard spacetime metrics. The Schwarzschild metric for a central spherically symmetrical non-rotating mass is one. The Kerr metric, which is essentially an axisymmetric deformation of Schwarzschild is another. There are related metrics which incorporate gravitationally collapsing matter into a spacetime like these.

Many such solutions are asymptotically flat. Very roughly, the inverse square law for gravity means that at a large distance you can ignore the gravitation of a central mass (which grows more and more pointlike in gravitational behaviour with increasing distance). Eventually you're in an area where the gravitational contribution can be ignored. In the language of General Relativity you are in effectively flat spacetime. The function of distance goes asymptotically to flat. There are obvious analogies with electromagnetism: distant stars are dim and pointlike, and really distant ones can be clumped together in larger structures with their clumped-together light curves being an example of an aggregated observable. (Indeed even at the level of a single star we are aggregating lots of tiny events into one spectrum equipped with emission and absorption lines, both for close-up stars and for distant ones).

We have some procedures available that let us stitch together asymptotically flat spacetimes with a "thin shell" mathematical boundary used to translate values from one side of the stitching to another. We can thus build up our solar system as a hierarchical stitching-together of Kerr-like metrics (one for each rotating body) each of which can "meet" another at some relatively flat-space point.

We can even stitch in Kerr-like metrics into a broader spacetime. The swiss cheese cosmology approach does this, and that technique traces back to the 1930s: https://en.wikipedia.org/wiki/Einstein%E2%80%93de_Sitter_uni...
(it has of course been refined over the decades).

Careful observation of our solar system supports this hierarchical stitching method reasonably well, but only if the far regions away from bodies are asymptotically flat. If we generate almost any amount of metric expansion -- much less than \Lambda -- to the otherwise asymptotically flat areas around the Earth, the moon's orbit changes dramatically. Likewise, if we change it within our solar system, things look very different in fairly short order. The same so far holds remarkably well for larger structures that are gravitationally bound, up to galaxy clusters.

A couple of decades ago, there were good astrophysical-observation reasons to think the hierarchical "stitching" process was broken enough that either an inhomogeneous metric would be needed from the start (throwing away lots of useful symmetries). These have faded with subsequent observation.

There is still some small wiggle room that allows for things like fifth-force screening to be taken seriously, however one has to do headstands to keep Manhattan (or Earth-Moon or Earth-Sun) from expanding measurably.

Measurability here is very tight. Laser lunar ranging, very long baseline interferometry, and even GPS and friends keep tightening the bounds on how much expansion the "true" metric Earth sources can allow compared to its approximate Kerr metric.

This is why I think it is safer to say that it's not expanding at all, rather than that we will find expansion if we look closer and closer.

As a sibling comment has noted, there are also constraints from particle physics and chemistry. Those constraints also arise in astrophysical systems like megamasers, planetary nebulae, stellar deflagrations, supernovae, binary+ millisecond pulsars, and so forth. The wiggle room for a suppression rather than extinction of cosmological expansion keeps tightening, and the constraints are from a diversity of lines of evidence.

However, it is reasonable to qualify the "it's not expanding" with "all our measurements to date are consistent with exactly no expansion in the solar system, and we have lots of rather different types of measurements all saying the same thing". I'm not sure that's as helpful for understanding the physical neighbourhood around here, or in galaxies and star systems generally, though.

> I'd always interpreted "expansion" as being space itself expanding, and thought that it happened at all scales

Observations are consistent with expansion happening only in really good extragalactic (extra-galaxy-cluster, even) vacuum.

This is really easy to explain with a non-accelerating expanding universe.

The mechanism for the (actually accelerated!) expansion is not known, but is usually what is meant by "dark energy".

This is a highly conventional take on the matter. I'm not offering up any sort of pet hypotheses, and I generally avoid doing so anywhere like HN as explaining the standard theory is more interesting (even to me) anyway.

Here is Ethan Siegel making similar points in somewhat different ways, with the benefit of editing and images: https://www.forbes.com/sites/startswithabang/2019/02/19/this...

> even weirder

Yep!

The sky is full of weird stuff that can be seen. Check out the "variable universe" -- astronomers like https://asas-sn.osu.edu/atlas/visualizations#star-map-panel keep finding bizarro things to think about even far away (in a theory-space sense) from the dark matter / dark energy sectors, that may test theories about those sectors.

You'd expect that as visible matter gets weirder, the invisible stuff must get weirder still in proportion. Oddly, that is not really the case.