Ciro Santilli @cirosantilli 37

Split in energy levels due to interaction between electron up or down spin and the electron orbitals.

Numerically explained by the Dirac equation when solving it for the hydrogen atom, and it is one of the main triumphs of the theory.

NIST database for spectral line: physics.nist.gov/PhysRefData/ASD/lines_form.html

Let's do a sanity check.

Searching for "H" for hydrogen leads to: physics.nist.gov/cgi-bin/ASD/lines1.pl?spectra=H&limits_type=0&low_w=&upp_w=&unit=1&submit=Retrieve+Data&de=0&format=0&line_out=0&en_unit=0&output=0&bibrefs=1&page_size=15&show_obs_wl=1&show_calc_wl=1&unc_out=1&order_out=0&max_low_enrg=&show_av=2&max_upp_enrg=&tsb_value=0&min_str=&A_out=0&intens_out=on&max_str=&allowed_out=1&forbid_out=1&min_accur=&min_intens=&conf_out=on&term_out=on&enrg_out=on&J_out=on

From there we can see for example the 1 to 2 lines:

We see that the table is sorted from lower from level first and then by upper level second.

So it is good to see that we are in the same 121nm ballpark as mentioned at hydrogen spectral line.

TODO why I can't see 2s to 2p transitions there to get the fine structure?

Same motivation as Galilean invariance, but relativistic version of that: we want the laws of physics to have the same form on all inertial frames, so we really want to write them in a way that is Lorentz covariant.

This is just the relativistic version of that which takes the Lorentz transformation into account instead of just the old Galilean transformation.

There are several choices of electromagnetic four-potential that lead to the same physics.

E.g. thinking about the electric potential alone, you could set the zero anywhere, and everything would remain be the same.

The Lorentz gauge is just one such choice. It is however a very popular one, because it is also manifestly Lorentz invariant.

Bibliography:

This section is about games initially designed for humans, but which ended up being used in AI development as well, e.g.:

As of 2020's and earlier, humans were far far behind. As of 2020s and earlier, even an average personal computers without a GPU, the hallmark of deep learning beats every human.

Chess is just too easy!

Isothermal means "at fixed temperature".

This is to contrast with the more well established polymerase chain reaction, which requires heating and cooling the sample several times.

The obvious advantage of isothermal methods is that their machinery can be simpler and cheaper, and the process can happen faster, since you don't have to do through heating and cooling cycles.