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These are the key mathematical ideas to understand!!
There are actually a few formulations out there. By far the dominant one as of 2020 has been the Schrödinger picture, which contrasts notably with the Heisenberg picture.
Another well known one is the de Broglie-Bohm theory, which is deterministic, but non-local.
The first quantum mechanics theories developed.
Their most popular formulation has been the Schrödinger equation.
The first really good quantum mechanics theory made compatible with special relativity was the Dirac equation.
And then came quantum electrodynamics to improve it: Dirac equation vs quantum electrodynamics.
TODO: does it use full blown QED, or just something intermediate?
www.youtube.com/watch?v=NtnsHtYYKf0 "Mercury and Relativity - Periodic Table of Videos" by Periodic Videos (2013). Doesn't give the key juicy details/intuition. Also mentioned on Wikipedia: en.wikipedia.org/wiki/Relativistic_quantum_chemistry#Mercury
Quantum field theory lecture by Tobias Osborne (2017) mentions that quantization is a guess.
Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.
Examples:
- www.youtube.com/watch?v=tt8gVXDsh7Q "Interference in quantum mechanics" by Looking Glass Universe (2015) shows how a left-right spin measurement has a defined value for a superposed half up half down state, but not for a pure up state.TODO can this be conducted? As mentioned in the video, this is closely linked to the fact that you can describe the wave function in multiple different bases (up/down or left/right), which is also at the root of the uncertainty principle.
- Video "Quantum Mechanics 9b - Photon Spin and Schrodinger's Cat II by ViaScience (2013)" gives a similar photon version
- it seems that the single particle double slit experiment can also be thought of as in terms of a superposition of "the particle goes through the right" and "the particle goes through the right", although it is a bit harder to thing about as it is not a discrete process
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.Quantum is getting hot in 2019, and even Ciro Santilli got a bit excited: quantum computing could be the next big thing.
No useful algorithm has been economically accelerated by quantum yet as of 2019, only useless ones, but the bets are on, big time.
To get a feeling of this, just have a look at the insane number of startups that are already developing quantum algorithms for hardware that doesn't/barely exists! quantumcomputingreport.com/players/privatestartup (archive). Some feared we might be in a bubble: Are we in a quantum computing bubble?
To get a basic idea of what programming a quantum computer looks like start by reading: Section "Quantum computing is just matrix multiplication".
Some people have their doubts, and that is not unreasonable, it might truly not work out. We could be on the verge of an AI winter of quantum computing. But Ciro Santilli feels that it is genuinely impossible to tell as of 2020 if something will work out or not. We really just have to try it out and see. There must have been skeptics before every single next big thing.
Man-in-the-middle attack
quantumcomputing.stackexchange.com/questions/142/advantage-of-quantum-key-distribution-over-post-quantum-cryptography/25727#25727 Advantage of quantum key distribution over post-quantum cryptography has Ciro Santilli's comparison to classical encryption.
Long story short:
- QKD allows you to generate shared keys without public-key cryptography. You can then use thses shared keys
- QKD requires authentication on a classical channel, exactly like a classical public-key cryptography forward secrecy would. The simplest way to do this is a with a pre-shared key, just like in classical public key cryptography. If that key is compromised at any point, your future messages can get man-in-the-middle'd, exactly like in classical cryptography.
QKD uses quantum mechanics stuff to allow sharing unsnoopable keys: you can detect any snooping and abort communication. Unsnoopability is guaranteed by the known laws of physics, up only to engineering imperfections.
Furthermore, it allows this key distribution without having to physically take a box by car somewhere: once the channel is established, e.g. optical fiber, you can just keep generating perfect keys from it. Otherwise it would be pointless, as you could just drive your one-time pad key every time.
However, the keys likely have a limited rate of generation, so you can't just one-time pad the entire message, except for small text messages. What you would then do is to use the shared key with symmetric encryption.
Therefore, this setup usually ultimately relies on the idea that we believe that symmetric encryption is safer than , even though there aren't mathematical safety proofs of either as of 2020.
Best ones:
- Change in your couch
- Put ketchup on fries
In Ciro Santilli's view, the following three artists form a Holy Trinity of popular Brazilian music:
Elis Regina is not far though.
Ciro remembers quite clearly when he was riding the car with his parents when he pre teen, and he could not understand why they seemed so obsessed with The Trinity et al. Ciro in particular remembers listening to Video "Refazenda by Gilberto Gil (1975)". They had picked it up of course from the 70's and 80's when they were younger.
Young Ciro would also always confuse who was whom from the three of them.
Then Ciro got older, and he understood, they are mind blowing. You do have to look back in time a bit though, lots of lukewarm stuff on later periods. The military dictatorship in Brazil was good for music.
Mostly interpreter of songs written by others. But she's just too amazing, many of her interpretations are better than the original.
God, even Ciro Santilli is slightly shocked by her death, which happened before he was born, can you imagine it at the time? She was MPB's golden girl...
Atrás da Porta performed by Elis Regina
. Source. Composed by Francis Hime and Chico Buarque.Águas de março performed by Elis Regina
. Source. From the 1972 eponymous album. Composed by Antônio Carlos Jobim.There are no stable isotopes.
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 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . 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. 
- 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