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From observing the universe, we know that space expands.
I see what that means on cosmic scales.

But what does it mean on smaller scales?

If I have a graduated beaker of 2 liter, and 1 liter of water in it, what should I expect to happen?

As nothing obvious happens, I assume that changes may be small enough to not be visible. But what would I see if the change would be large enough to see it?

Assuming the water does not evaporate, is the level of water in the beaker lowering because the beaker expands?

Would something different happen if the beaker would be very large? If I had a galaxy-sized beaker that does not collapse?*

*let's assume the water somehow does not become a black hole, and is accelerated to the bottom of the beaker

Volker Siegel
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Space only expands inbetween gravitationally bound systems. Have a look at the swiss cheese model. The spacetime of a star or galaxy (though non-rotating) is glued to the spacetime of an expanding universe. The boundary of the bubble is growing in such a way that the volume of the bubble multiplied by the surrounding energy density matches the mass of the star or galaxy. Inside the bubble the universe is not expanding.

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$$\frac{4\pi}{3}R^3(t)\rho(t)=M,$$

where $M$ is the Schwarzschild mass of the star or galaxy, $\rho(t)$ is the homogeneous energy density of the expanding universe and $R(t)$ is the radius of the bubble, inside which cosmological expansion doesn't take place.

And of course, your bag of milk is contained well inside a graviational system. And certainly, similar considerations apply to systems bound by electromagnetic forces, ie. fluids, solids. They should not be ripped apart by the spacetime expansion, even if they were in intergalactic places of the universe.

p6majo
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  • Does gravitation have a limited reach? – Volker Siegel Mar 07 '20 at 14:19
  • Geometrically, there are two different solution of Einstein's field equations. Inside the bubble, there is a spacetime that is created by a static central object, outside the bubble, there is the spacetime of an expanding universe. Usually, both spacetimes cover all of the space, but they can be nicely combined into a model, where you have stars and and expanding universe at the same time. – p6majo Mar 07 '20 at 14:39