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Why space expansion affects matter?
Why does space expansion not expand matter?

As we know, the universe is expanding, galaxies are away from each other. But what about atoms? Do they also in expanding?

What's more, Bohr radius is $$a_0=\frac{\hbar}{m_e c \alpha}$$, if it is increasing, does it means

$m_e$ is decreasing due to the density of Higgs field is getting thinner.

or

$c$ is decreasing

or

$\hbar$ is increasing?

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No, the size of the atoms isn't changing as the Universe keeps on expanding. The Bohr radius will always be the same fraction of a nanometer or the same fraction of a wavelength of some light (of a certain spectral line).

Because the Universe is expanding and the size is growing, it literally means that there's "more room" and one can squeeze an increasing number of atoms in the "same" volume, i.e. into the tetrahedron with vertices located at centers of 4 galaxies.

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  • $\begingroup$ This isn't the answer I expected. So galaxies are growing with the scale factor of the universe, and stars, poodles and hamburgers too. Also bacteria and a ring molecule of ~100 carbon atoms around empty space. But then the electrons flying around a carbon nucleus are not getting further away from it with the scale factor of the universe? That's where it stops? $\endgroup$
    – Dzamo Norton
    Commented Mar 8, 2017 at 18:13
  • $\begingroup$ No, @DzamoNorton , your misunderstanding is much deeper than that. Galaxies, Solar System, poodles, hamburgers, and all such bound things are not growing at all when the Universe is expanding. Only the distance between objects (different galaxies) that are not bound with each other is growing as the Universe expands. $\endgroup$
    – Luboš Motl
    Commented Mar 9, 2017 at 6:35
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    $\begingroup$ CMB is not bound in any sense. CMB is a collection of free, non-interacting photons moving through the Universe. As the linear sizes in the Universe expand $k$ times, so do the wavelengths of the CBM photons, and their energy is therefore going down as $1/k$, on top of density like $1/k^3$. - It's meaningless to ask how "a rock on a parabollic orbit" scales. The only question that makes sense to be answered is the precise trajectory on which the rock moves. But the "place" of the rock isn't "static" in any sense, so it makes no sense to describe it as a static "object" that is just scaling. $\endgroup$
    – Luboš Motl
    Commented Mar 9, 2017 at 10:37
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    $\begingroup$ Radiation, like everything, is sourcing gravitational field but it is in no way a bound system. The net "force" acting on a photon is zero. By its nonzero stress-energy tensor, uniform content of the Universe like CMB or dark energy is just modifying the rate by which the expansion of the Universe accelerates. This question is whether things expand proportionally to the size of the expanding Universe. The bound states don't, the free ones - like CMB - do. I can't understand what you find so hard that you have already asked 4 identical questions. $\endgroup$
    – Luboš Motl
    Commented Mar 9, 2017 at 10:48
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    $\begingroup$ I think that technically, atoms are slightly larger than they would be without the expansion; the expansion pulls the electrons away from the nucleus. The force the electron feels pulling into the nucleus is decreased, increasing the radius. But the effect is tiny, and not cumulative. $\endgroup$
    – Acccumulation
    Commented May 24, 2019 at 17:00

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