Why 21 cm is our Universe's "magic length"

For those who feel weird about the whole "forbidden transitions being only possible with quantum tunneling" thing and want an alternative interpretation:

It's only true that the transitions are forbidden under a given simplified model of the atom. It is very much possible to calculate the transition probabilities under a more realistic model, and the previously "forbidden" transitions are now just regular transitions that occur with lower probability.

In this case, the simplified model is that of the electric dipole approximation, where the atom is taken to be an electric dipole (reasonable when the wavelength of light emitted during an atomic transition is much larger than the size of the atom).This means it interacts with electromagnetic radiation only through electric dipole interactions, which implies that energy transitions must change orbital angular momentum, hence the 21cm transition is "forbidden". However, in reality, the atom is not truly an electric dipole, and so the 21cm transition is possible by the magnetic dipole interaction, just with low probability. (This low probability is due to the relative strength of the magnetic interaction compared to the electric interaction).

This 21-centimeter transition was chosen by the designers of the Pioneer plaques (https://en.wikipedia.org/wiki/Pioneer_plaque) to explain to any alien readers how big we are. At top left is a cartoon of two hydrogen nuclei in opposite spin orientations, and a ruler in between them marked "1". Over on the far right you can see another ruler that measures the height of the female figure, marked with binary numeral "8" ("|---") to indicate that she is approximately 8×21 = 168 cm tall.

Amazing article! It seems incredibly to weird to hear about transitions causing photons at 21cm wavelength; I guess I'm only used to seeing (no pun intended) much shorter wavelengths at hundreds of nanometers.

Loved this article! I initially was confused by how this transition would work with the conservation of angular momentum (since the electron would be flipping from spin ±½ to the opposite one). But then remembered that photons are spin 1 particles, so the math works out. Neat.

The 21cm wavelength is also the wavelength that was proposed for potential SETI radio communication, I guess because of its distinctiveness. Of course modern SETI searches look at a wide range of frequencies.

Precisely 21cm or a precise amount that is approximately 21cm?

It’s neat to see theory that allows us to practically see further into the past.

I find it disturbing/puzzling that there is this fundamental physical behaviour like emission of light with wavelength of _exactly_ 21cm -- assuming one centimeter wasn't based on any such property but was just a "random" unit measure that stayed with us historically and through sheer volume of use (in U.S. inches filled the same niche; still do). I mean what are the odds that the wavelength is _exactly_ (the word used in the article) 21cm?

In Contact the alien beacon arrives at 4.4623 GHz. Pi times the Hydrogen line...

From the article:

Of course, there’s another possibility that takes us far beyond astronomy when it comes to making use of this important length: creating and measuring enough spin-aligned hydrogen atoms in the lab to detect this spin-flip transition directly, in a controlled fashion. The transition takes about ~10 million years to “flip” on average, which means we’d need around a quadrillion (1015) prepared atoms, kept still and cooled to cryogenic temperatures, to measure not only the emission line, but the width of it. If there are phenomena that cause an intrinsic line-broadening, such as a primordial gravitational wave signal, such an experiment would, quite remarkably, be able to uncover its existence and magnitude.

Isn't that basically an H-maser? Not something found every day on eBay, but not really all that exotic either. Every VLBI site has one or more.

Given a suitable state selection mechanism, which is what masers rely on, I don't see why it would be necessary to flip the states "manually" through ionization or any other mechanism. Keeping the state-selected atoms away from the container walls is the real trick.

> precisely 21 cm

Imprecise use of "precise" in the strapline. According to https://en.wikipedia.org/wiki/Hydrogen_line the best measurement of it so far is 21.106114054160 +/- 0.000000000030 cm

I had a CS professor that used to hold up a length of string roughly that length and talk about how that is how far a bit of data can travel at the speed of light during a clock cycle or something. Honestly don't remember the point he was trying to make.

[stub for offtopicness]

[come on you guys]

I posted this thread to o3 and found the results interesting. https://chatgpt.com/share/680aad8d-ce54-800c-8973-df4258bbe1...