Ciro Santilli @cirosantilli 34

Key for quantum mechanics, see: mathematical formulation of quantum mechanics, the most important example by far being $L^2$.

The discovery of the photon was one of the major initiators of quantum mechanics.

Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???

This was a key development for people to eventually notice that the electron is also a wave.

This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).

This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.

In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.

The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.

This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.

It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.

Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:

Bibliography:

Free borrow on the Internet Archive: archive.org/details/inwardboundofmat0000pais/page/88/mode/2up

The book unfortunately does not cover the history of quantum mechanics very, the author specifically says that this will not be covered, the focus is more on particles/forces. But there are still some mentions.

$L^p$ is:

And then this is why quantum mechanics basically lives in $L^2$: not being complete makes no sense physically, it would mean that you can get closer and closer to states that don't exist!

TODO intuition

Follows the "certified teacher only" approach which is in Ciro Santilli's opinion a fatal flaw of most elearning systems out there, OurBigBook.com won't suffer from that!

But that is a very, very good project.

All notes appear to have been extracted from existing notes, as noted on the bottom of each page.

Appears to have mixed licenses. E.g.:

TODO how does it work exactly? Do they ask for permission from authors in every case, including when the content has open license? Or when it has open license, do they just do it? In some cases, the notes have no license, so they must have asked.

TODO what is the source code that authors write? LaTeX or something else? LaTeX feels extremely likely given that it is what most original materials were already written in.

They are attempting a "model up this entire university" thing: phys.libretexts.org/Courses which is good. E.g. they have a bunch of "quantum mechanics ones under: phys.libretexts.org/Bookshelves/Quantum_Mechanics

Appears to be UC Davies-based mostly.

They claim to use this closed source backend: www.nice.com/resources/cxone-expert-knowledge-management? Seriously? For a publicly funded project with low-tech requirements?? It is mind blowing.

Some issues:

OK let's database it:

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.

Combination of electromagnetism and general relativity. Unlike combining quantum mechanics and general relativity, this combination was easier.

TODO any experiments of interest at all?

In the standard formulation of Maxwell's equations, the electric current is a convient but magic input.

Would it be possible to use Maxwell's equations to solve a system of pointlike particles such as electrons instead?

The following suggest no, or only for certain subcases less general than Maxwell's equations:This is the type of thing where the probability aspect of quantum mechanics seems it could "help".

The first quantum mechanics theories developed.

Their most popular formulation has been the Schrödinger equation.

If Ciro Santilli were to write a book about quantum mechanics as of 2020 (before OurBigBook.com went live), he would upload an OurBigBook Markup website to GitHub Pages.

But there is one major problem with that: the entry barrier for new contributors is very large.

If they submit a pull request, Ciro has to review it, otherwise, no one will ever see it.

Our amazing website would allow the reader to add his own example of, say, The uncertainty principle, whenever they wants, under the appropriate section.

Then, people who want to learn more about it, would click on the "defined tag" by the article, and our amazing analytics would point them to the best such articles.

Many subjects have changed very little in the last hundred years, and so it is mind-blowing that people have to pay for books that teach them!

If computers are bicycles for the mind, Ciro wants this website to be the Ferrari of the mind.

Since Ciro Santilli was young, he has been bewildered by the natural sciences and mathematics due to his bad memory.

The beauty of those subjects has always felt like intense sunlight in a fresh morning to Ciro. Sometimes it gets covered by clouds and obscured by less important things, but it always comes back again and again, weaker or stronger with its warmth, guiding Ciro's life path.

As a result, he has always suffered a lot at school: his grades were good, but he wasn't really learning those beautiful things that he wanted to learn!

School, instead of helping him, was just wasting his time with superficial knowledge.

First, before university, school organization had only one goal: put you into the best universities, to make a poster out of you and get publicity, so that more parents will be willing to pay them money to put their kids into good university.

Ciro once asked a chemistry teacher some "deeper question" after course was over, related to the superficial vision of the topic they were learning to get grades in university entry exams. The teacher replied something like:Ciro feels that this was one of the greatest compliments he has ever received in his life. This teacher, understood him. Funny how some things stick, while all the rest fades.

Another interesting anecdote is how Ciro Santilli's mother recalls that she always found out about exams in the same way: when the phone started ringing as Ciro's friends started asking for help with the subjects just before the exam. Sometimes it was already too hopelessly late, but Ciro almost always tried. Nothing shows how much better you are than someone than teaching them.

Then, after entering university, although things got way better because were are able to learn things that are borderline useful.

Ciro still felt a strong emotion of nostalgia when after university his mother asked if she could throw away his high school books, and Ciro started tearing them all down for recycling. Such is life.

University teachers were still to a large extent researchers who didn't want to, know how to and above all have enough time and institutional freedom to teach things properly and make you see their beauty, some good relate articles:

The very fact that you had very little choice of what to learn so that a large group can get a "Diploma", makes it impossible for people to deeply learn what the really want.

This is especially true because Ciro was in Brazil, a third world country, where the opportunities are comparatively extremely limited to the first world.

Also extremely frustrating is how you might have to wait for years to get to the subject you really want. For example, on a physics course, quantum mechanics is normally only taught on the third year! While there is value to knowing the pre-requisites, holding people back for years is just too sad, and Ciro much prefers backward design. And just like the university entry exams, this creates an entry barrier situation where you might in the end find that "hey, that's not what I wanted to learn after all", see also: students must have a flexible choice of what to learn.

We've created a system where people just wait, and wait, and wait, never really doing what they really want. They wait through school to get into university. They wait through university to get to masters. They wait through masters to get to PhD. They wait through PhD to become a PI. And for the minuscule fraction of those that make it, they become fund proposal writers. And if you make any wrong choice along the, it's all over, you can't continue anymore, the cost would be too great. So you just become software engineer or a consultant. Is this the society that we really want?

And all of this is considering that he was very lucky to not be in a poor family, and was already in some of the best educational institutions locally available already, and had comparatively awesome teachers, without which he wouldn't be where he is today if he hadn't had such advantages in the first place.

But no matter how awesome one teacher is, no single person can overcome a system so large and broken. Without technological innovation that is.

The key problem all along the way is the Society's/Government's belief that everyone has to learn the same things, and that grades in exams mean anything.

Ciro believes however, that exams are useless, and that there are only two meaningful metrics:

Even if you wanted to really learn natural sciences and had the time available, it is just too hard to find good resources to properly learn it. Even attending university courses are hit and miss between amazing and mediocre teachers.

If you go into a large book shop, the science section is tiny, and useless popular science books dominate it without precise experiment descriptions. And then, the only few "serious" books are a huge list of formulas without any experimental motivation.

And if you are lucky to have access to an university library that has open doors, most books are likely to be old and boring as well. Googling for PDFs from university courses is the best bet.

Around 2012 however, he finally saw the light, and started his path to Ciro Santilli's Open Source Enlightenment. University was not needed anymore. He could learn whatever he wanted. A vision was born.

To make things worse, for a long time he was tired of seeing poor people begging on the streets every day and not doing anything about it. He thought:which like everything else is likely derived subconsciously from something else, here Schindler's list possibly adapted quote from the Talmud:

So, by the time he left University, instead of pursuing a PhD in theoretical Mathematics or Physics just for the beauty of it as he had once considered, he had new plans.

We needed a new educational system. One that would allow people to fulfill their potential and desires, and truly improve society as a result, both in rich and poor countries.

And he found out that programming and applied mathematics could also be fun, so he might as well have some fun while doing this! ;-)

So he started Booktree in 2014, a GitLab fork, worked on it for an year, noticed the approach was dumb, and a few years later started building this new version. The repo github.com/booktree/booktree is a small snapshot of Ciro's 2014 brain on the area, there were quite a few similar projects at the time, and most have died.

Ciro is basically a librarian at heart, and wants to be the next:

Used a lot in quantum mechanics, where the equations are really hard to solve. There's even a dedicated wiki page for it: en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics). Notably, Feynman diagrams are a way to represent perturbation calculations in quantum field theory.

Let's gather some of the best results we come across here:

An "alternative" formulation of quantum mechanics that does not involve operators.