The first really good quantum mechanics theory made compatible with special relativity was the Dirac equation.
TODO: does it use full blown QED, or just something intermediate?
TODO understand better, mentioned e.g. at Subtle is the Lord by Abraham Pais (1982) page 20, and is something that Einstein worked on.
I've finally had enough of Nvidia breaking my Ubuntu 21.10 suspend, so I investigated some more and found a workaround on the NVIDIA forums: stackoverflow.com/questions/58233482/next-js-setting-up-eslint-for-nextjs/70519682#70519682.
Thanks enormously to heroic user humblebee, and once again, Nvidia, fuck you.
The Kennelly–Heaviside layer, also known as the E layer of the ionosphere, is a region in the Earth's upper atmosphere that is characterized by a high concentration of ionized particles. This layer is located approximately 30 to 100 kilometers (18 to 62 miles) above the Earth's surface and plays a significant role in radio wave propagation.
Predicted by the Dirac equation.
We've likely known since forever that photons are created: just turn on a light and see gazillion of them come out!
Photon creation is easy because photons are massless, so there is not minimum energy to create them.
The creation of other particles is much rarer however, and took longer to be discovered, one notable milestone being the discovery of the positron.
In the case of the electron, we need to start with at least enough energy for the mass of the electron positron pair. This requires a photon with wavelength in the picometer range, which is not common in the thermal radiation of daily life.
Klein-Gordon equation by Ciro Santilli 40 Updated 2025-07-16
A relativistic version of the Schrödinger equation.
Correctly describes spin 0 particles.
The most memorable version of the equation can be written as shown at Section "Klein-Gordon equation in Einstein notation" with Einstein notation and Planck units:
Has some issues which are solved by the Dirac equation:
The Klein-Gordon equation directly uses a more naive relativistic energy guess of squared.
But since this is quantum mechanics, we feel like making into the "momentum operator", just like in the Schrödinger equation.
But we don't really know how to apply the momentum operator twice, because it is a gradient, so the first application goes from a scalar field to the vector field, and the second one...
So we just cheat and try to use the laplace operator instead because there's some squares on it:
But then, we have to avoid taking the square root to reach a first derivative in time, because we don't know how to take the square root of that operator expression.
So the Klein-Gordon equation just takes the approach of using this squared Hamiltonian instead.
Since it is a Hamiltonian, and comparing it to the Schrödinger equation which looks like:
taking the Hamiltonian twice leads to:
We can contrast this with the Dirac equation, which instead attempts to explicitly construct an operator which squared coincides with the relativistic formula: derivation of the Dirac equation.
Originally done with (neutral) silver atoms in 1921, but even clearer theoretically was the hydrogen reproduction in 1927 by T. E. Phipps and J. B. Taylor.
Video 1.
The Stern-Gerlach Experiment by Educational Services, Inc (1967)
Source. Featuring MIT Professor Jerrold R. Zacharias. Amazing experimental setup demonstration, he takes apart much of the experiment to show what's going on.
Spintronics by Ciro Santilli 40 Updated 2025-07-16
Video 1.
Introduction to Spintronics by Aurélien Manchon (2020)
Source.
Video 1.
What is spintronics and how is it useful? by SciToons (2019)
Source. Gives a good 1 minute explanation of tunnel magnetoresistance.
Spin-transfer torque by Ciro Santilli 40 Updated 2025-07-16
Video 1.
Introduction to Spintronics by Aurélien Manchon (2020) spin-transfer torque section
. Source.
Describes how how spin-transfer torque was used in magnetoresistive RAM
Anyon by Ciro Santilli 40 Updated 2025-07-16
The name actually comes from "any". Amazing.
Can only exist in 2D surfaces, not 3D, where fermions and bosons are the only options.
All known anyons are quasiparticles.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
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