Formal name: "plantae".
Published by Werner Heisenberg in 1925-07-25 as quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), it offered the first general formulation of quantum mechanics.
It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.
It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.
QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) mentions however that relativistic quantum mechanics broke that analogy, because some 2x2 matrix had a different form, TODO find that again.
Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.
Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
- Compton scattering, also suggests that photons carry momentum
- photoelectric effect
- single photon production and detection experiments
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.
The main ones as of 2020 are:
- Mentor Graphics, which was bought by Siemens in 2017
- Cadence Design Systems
- Synopsys
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.
No mention of education specifically on website. But at www.washingtonpost.com/wp-srv/liveonline/00/business/saylor0621.htm from Michael J. Saylor they did show interest, so adding to this Educational charitable organization list anyways.
Are particles bounced by the first wall in the double slit experiment? by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16It would be amazing to answer this with single particle double slit experiment measurements!
This is an extremely widely used technique as of 2020 and much earlier.
If allows you to amplify "any" sequence of choice (TODO length limitations) between a start and end sequences of interest which you synthesize.
If the sequence of interest is present, it gets amplified exponentially, and you end up with a bunch of DNA at the end.
You can then measure the DNA concentration based on simple light refraction methods to see if there is a lot of DNA or not in the post-processed sample.
Even Ciro Santilli had some contact with it at: Section "How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it", see: PCR!
One common problem that happens with PCR if you don't design your primers right is: en.wikipedia.org/wiki/Primer_dimer
Sometime it fails: www.reddit.com/r/molecularbiology/comments/1kouomw/when_your_pcr_fails_again_and_you_start/and a comment:
Nothing humbles you faster than a bandless gel. One minute you’re a scientist, the next you’re just a pipette-wielding wizard casting spells that don’t work. Meanwhile, physicists are out there acting like gravity always behaves. Smash that upvote if your reagents have ever gaslit you.
PCR = Pray, Cry, Repeat
Bibliography:
- www.youtube.com/watch?v=Fu1BGGeyqHQ&list=PL54DF0652B30D99A4&index=63 "K6. The Pauli Equation" by doctorphys
Cody'sLab had a nice 5 video series on making it at home! But the United States Government asked him to take it down as suggested at Video "What's Been Going On With Cody'sLab? by Cody'sLab (2019)" at youtu.be/x1mv0vwb08Y?t=84.
The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose by Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16Let's show that this definition is equivalent to the orthogonal group is the group of all matrices that preserve the dot product.
Note that:and for that to be true for all possible and then we must have:i.e. the matrix inverse is equal to the transpose.
These matricese are called the orthogonal matrices.
TODO is there any more intuitive way to think about this?
The canonical undecidable problem.
Synthesizing the DNA itself is not the only problem however.
You then have to get that DNA into a working living form state so that normal cell processes can continue:
Multicellular questions:
Apparently achieved for the first time in 2021: www.jcvi.org/research/first-self-replicating-synthetic-bacterial-cell by the J. Craig Venter Institute.
This one strikes the right balance between restriction and permissions. NC and ND are simply too restrictive.
TODO where does the SA boundary end? E.g.:
- software: opensource.stackexchange.com/questions/173/what-do-i-need-to-share-if-i-include-cc-by-sa-artwork-in-my-software/11323#11323
- video game:
- website: graphicdesign.stackexchange.com/questions/68805/using-cc-by-sa-3-0-images-in-website-does-share-alike-affect-my-websites-lice/145124#145124
- book: academia.stackexchange.com/questions/48375/using-images-with-cc-by-sa-license-in-slides-or-a-thesis
- music in a podcast: opensource.stackexchange.com/questions/7022/using-cc-by-sa-music-in-a-podcast
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