Quantum entanglement is often called spooky/surprising/unintuitive, but they key question is to understand why.
To understand that, you have to understand why it is fundamentally impossible for the entangled particle pair be in a predefined state according to experiments done e.g. where one is deterministically yes and the other deterministically down.
In other words, why local hidden-variable theory is not valid.
How to generate entangled particles:
- particle decay, notably pair production
- for photons, notably: spontaneous parametric down-conversion, e.g.: www.youtube.com/watch?v=tn1sEaw1K2k "Shanni Prutchi Construction of an Entangled Photon Source" by HACKADAY (2015). Estimatd price: 5000 USD.
Contains the clearest Bell test experiment description seen so far.
It clearly describes the photon-based 22.5, 45 degree/85%/15% probability photon polarization experiment and its result conceptually.
It does not mention spontaneous parametric down-conversion but that's what they likely hint at.
Done in Collaboration with 3Blue1Brown.
Question asking further clarification on why the 100/85/50 thing is surprising: physics.stackexchange.com/questions/357039/why-is-the-quantum-venn-diagram-paradox-considered-a-paradox/597982#597982
Quantum Mechanics: Animation explaining quantum physics by Physics Videos by Eugene Khutoryansky (2013)
Source. Usual Eugene, good animations, and not too precise explanations :-) youtu.be/iVpXrbZ4bnU?t=922 describes a conceptual spin entangled electron-positron pair production Stern-Gerlach experiment as a Bell test experiments. The 85% is mentioned, but not explained at all.Quantum Entanglement Lab by Scientific American (2013)
Source. The hosts interview Professor Enrique Galvez of Colgate University who shows briefly the optical table setup without great details, and then moves to a whiteboard explanation. Treats the audience as stupid, doesn't say the keywords spontaneous parametric down-conversion and Bell's theorem which they clearly allude to. You can even them showing a two second footage of the professor explaining the rotation experiments and the data for it, but that's all you get.Power, Sex, Suicide by Nick Lane (2006) paints a colorful picture of the man!
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.
How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it Sequencing by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16- Dilbert
- Severance 2022
- tvtropes.org/pmwiki/pmwiki.php/Main/SoulCrushingDeskJob
- en.wikipedia.org/wiki/Bullshit_Jobs
- Falling Down 1993
Where derivation == "intuitive routes", since a "law of physics" cannot be derived, only observed right or wrong.
TODO also comment on why are complex numbers used in the Schrodinger equation?.
Some approaches:
- en.wikipedia.org/w/index.php?title=Schr%C3%B6dinger_equation&oldid=964460597#Derivation: holy crap, this just goes all in into a Lie group approach, nice
- Richard Feynman's derivation of the Schrodinger equation:
- physics.stackexchange.com/questions/263990/feynmans-derivation-of-the-schrödinger-equation
- www.youtube.com/watch?v=xQ1d0M19LsM "Class Y. Feynman's Derivation of the Schrödinger Equation" by doctorphys (2020)
- www.youtube.com/watch?v=zC_gYfAqjZY&list=PL54DF0652B30D99A4&index=53 "I5. Derivation of the Schrödinger Equation" by doctorphys
Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.
I.e.: they are both:
- solutions to the time-independent Schrödinger equation for the quantum harmonic oscillator
- a complete basis of that space
The study of the proteome.
With X-ray crystallography by David Chilton Phillips. The second protein to be resolved fter after myoglobin, and the first enzyme.
Published at: Structure of Hen Egg-White Lysozyme: A Three-dimensional Fourier Synthesis at 2 Å Resolution (1965). The work was done while at the Davy Faraday Research Laboratory of the Royal Institution.
Phillips also published a lower resolution (6angstrom) of the enzyme-inhibitor complexes at about the same time: Structure of Some Crystalline Lysozyme-Inhibitor Complexes Determined by X-Ray Analysis At 6 Å Resolution (1965). The point of doing this is that it points out the active site of the enzyme.
This is basically what became the dominant formulation as of 2020 (and much earlier), and so we just call it the "mathematical formulation of quantum mechanics".
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!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. Web editor. You can also edit articles on the Web editor without installing anything locally.Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact