System of linear equations Updated 2025-07-16
University education level Updated 2025-07-16
University of Sussex Updated 2025-07-16
Facebook Updated 2025-07-16
Quantum electrodynamics Updated 2025-07-16
Theory that describes electrons and photons really well, and as Feynman puts it "accounts very precisely for all physical phenomena we have ever observed, except for gravity and nuclear physics" ("including the laughter of the crowd" ;-)).
While Ciro acknowledges that QED is intrinsically challenging due to the wide range or requirements (quantum mechanics, special relativity and electromagnetism), Ciro feels that there is a glaring gap in this moneyless market for a learning material that follows the Middle Way as mentioned at: the missing link between basic and advanced. Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) is one of the best attempts so far, but it falls a bit too close to the superficial side of things, if only Feynman hadn't assumed that the audience doesn't know any mathematics...
The funny thing is that when Ciro Santilli's mother retired, learning it (or as she put it: "how photons and electrons interact") was also one of her retirement plans. She is a pharmacist by training, and doesn't know much mathematics, and her English was somewhat limited. Oh, she also wanted to learn how photosynthesis works (possibly not fully understood by science as that time, 2020). Ambitious old lady!!!
Combines special relativity with more classical quantum mechanics, but further generalizing the Dirac equation, which also does that: Dirac equation vs quantum electrodynamics. The name "relativistic" likely doesn't need to appear on the title of QED because Maxwell's equations require special relativity, so just having "electro-" in the title is enough.
Before QED, the most advanced theory was that of the Dirac equation, which was already relativistic but TODO what was missing there exactly?
As summarized at: youtube.com/watch?v=_AZdvtf6hPU?t=305 Quantum Field Theory lecture at the African Summer Theory Institute 1 of 4 by Anthony Zee (2004):
- classical mechanics describes large and slow objects
- special relativity describes large and fast objects (they are getting close to the speed of light, so we have to consider relativity)
- classical quantum mechanics describes small and slow objects.
- QED describes objects that are both small and fast
That video also mentions the interesting idea that:Therefore, for small timescales, energy can vary a lot. But mass is equivalent to energy. Therefore, for small time scale, particles can appear and disappear wildly.
- in special relativity, we have the mass-energy equivalence
- in quantum mechanics, thinking along the time-energy uncertainty principle,
QED is the first quantum field theory fully developed. That framework was later extended to also include the weak interaction and strong interaction. As a result, it is perhaps easier to just Google for "Quantum Field Theory" if you want to learn QED, since QFT is more general and has more resources available generally.
Like in more general quantum field theory, there is on field for each particle type. In quantum field theory, there are only two fields to worry about:
- photon field
- electromagnetism field
Lecture 01 | Overview of Quantum Field Theory by Markus Luty (2013)
Source. This takes quite a direct approach, one cool thing he says is how we have to be careful with adding special relativity to the Schrödinger equation to avoid faster-than-light information. Statistical physics Updated 2025-07-16
Quantum computing scholarship Updated 2025-07-16
Plutonium Updated 2025-07-16
What a material:
- only exists in trace amounts in nature,but it can be produced at kilogram scale in breeder reactors
- it is only intentionally produced for one application, and one application only basically: nuclear weapons
Plausible deniability of email password handover Updated 2025-07-16
You need a secondary password that when used leads to an empty inbox with a setting set where message are deleted after 2 days.
This way, if the attacker sends a test email, it will still show up, but being empty is also plausible.
PlanetMath Updated 2025-07-16
Joe Corneli, of of the contributors, mentions this in a cool-sounding "Peeragogy" context at metameso.org/~joe/:
I earned my doctorate at The Open University in Milton Keynes, with a thesis focused on peer produced support for peer learning in the mathematics domain. The main case study was planetmath.org; the ideas also informed the development of “Peeragogy”.
Plancherel theorem Updated 2025-07-16
Some sources say that this is just the part that says that the norm of a function is the same as the norm of its Fourier transform.
The comment at math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725#1235725 may be of interest, it says that the bijection statement is an easy consequence from the norm one, thus the confusion.
TODO does it require it to be in as well? Wikipedia en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.
Pipa piece Updated 2025-07-16
Pinto bean Updated 2025-07-16
Edit: after buying it, not 100% sure. This one felt smaller than what Ciro had in Brazil, borlotti beans might be closer. Pinto beans are smaller, and creamier, and have softer peel, possibly produced less natural gas.
2021-04: second try.
2021-03: did for first time, started with same procedure as borlotti beans 2021-03. Maybe 1h30 is too much. Outcome was still very good.
Physics research institute Updated 2025-07-16
Physics Letters A Updated 2025-07-16
Pernosco Updated 2025-07-16
Proprietary extension to Mozilla rr by rr lead coder Robert O'Callahan et. al, started in 2016 after he quit Mozilla.
TODO what does it add to
rr? Peptidoglycan Updated 2025-07-16
Forms the bacterial cell wall.
From the Wikipedia image we can see clearly the polymer structure formed: it is a mesh with:
- sugar covalent bond chains in one direction. These have two types of monosaccharide, NAM and NAG
- peptide chains on the other, and only coming off from NAM
Peptidoglycan polymer structure
. Source. Peano existence theorem Updated 2025-07-16
Path to AGI Updated 2025-07-16
There are two main ways to try and reach AGI:Which one of them to take is of of the most important technological questions of humanity according to Ciro Santilli
- AI training robot: expensive, slow, but realistic world
- AI training game: faster, less expensive, but possibly non-realistic-enough realistic
There is also an intermediate area of research/engineering where people try to first simulate the robot and its world realistically, use the simulation for training, and then transfer the simulated training to real robots, see e.g.: realistic robotics simulation.
Path integral formulation Updated 2025-07-16
This one might actually be understandable! It is what Richard Feynman starts to explain at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The difficulty is then proving that the total probability remains at 1, and maybe causality is hard too.
The path integral formulation can be seen as a generalization of the double-slit experiment to infinitely many slits.
Feynman first stared working it out for non-relativistic quantum mechanics, with the relativistic goal in mind, and only later on he attained the relativistic goal.
TODO why intuitively did he take that approach? Likely is makes it easier to add special relativity.
This approach more directly suggests the idea that quantum particles take all possible paths.
There are unlisted articles, also show them or only show them.
