In An Expanding Universe, What Doesn't Expand?

I just recently discovered this paper, and am still reading it. But I think if you have access to AJP, you might want to get a copy and read this too.

The paper addressed[1] the question that I've heard before. If our universe is expanding, does that mean that the atom is also getting larger?

Abstract:  The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects such as 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 definitive answer is given for a very simple system: a classical “atom” bound by electrical attraction. With a mathematical 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 using analysis techniques used in junior-level mechanics. We also demonstrate that this simple description is a justifiable approximation of the relativistically correct formulation of the problem.

But what was equally interesting is the impetus for the authors to write this paper.

This paper is the result of a question posed by high school student Deepak Ramchand Mahbubani, Jr. at the University of Texas at Brownsville’s “21st Century Astronomy Ambassador’s Program,” and by the lack of a clear answer at the right level.

See kids? You ask an interestingly-enough question to the right person, you'll end up being cited by name in a physics paper!

So what's the answer to the question? It appears that if we adopt the realistic parameters, the atoms does not participate in the expansion.

We end with a practical consideration. Our quantification of the relative strengths of atomic and expansion forces is given in terms of a characteristic time Tatom for the motion of electrons in atoms, and a cosmological expansion time Texp (e.g., the Hubble time). Our analyses show that atomic forces are initially stronger if Tatom=Texp is less than order unity. Because Tatom ~10^ 16 s and Texp ~ 4x10^17 s, we see that atoms are in no danger of being disrupted by cosmological expansion.

In other words, you can't blame the expansion of the universe for your expanding waistline.

Damn it!

Zz.

[1] R. Price and J. Romano, Am. J. Phys v.80, p.376 (2012)