arXiv:gr-qc/0508052gr-qc
In an expanding universe, what doesn't expand?
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
Abstract
The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general expansion, but a much more subtle question is whether bound systems expand partially. In this paper, a very definitive answer is given for a very simple system: a classical "atom" bound by electrical attraction. With a mathemical description appropriate for undergraduate physics majors, we show that this bound system either completely follows the cosmological expansion, or -- after initial transients -- completely ignores it. This "all or nothing" behavior can be understood with techniques of junior-level mechanics. Lastly, the simple description is shown to be a justifiable approximation of the relativistically correct formulation of the problem.
And since the even the whole groups of galaxies are gravitationally bound, it seems that the galaxies, including our own galaxy, are not "stretching" but remain the same size. And, based on the same principle, everything inside of them also, including us. So back to the cupcake…
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