Space-Time Approach to Quantum Electrodynamic by Richard Feynman (1949) by 
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01The first key paper to his approach to quantum electrodynamics apparently.
Published on Physical Review 76.769.
In the Galilean transformation, there are two separate invariants that two inertial frame of reference always agree on between two separate events:
- time
- length, given by the Pythagorean theorem
However, in special relativity, neither of those are invariant separately, since space and time are mixed up together.
Note that this distance can be zero for two events separated.
They were superseded by transistor radios, which were much more reliable, portable and could amplify the signal received.
How a Crystal radio Works by RimstarOrg
. Source. 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.
Rank of an elliptic curve over the rational numbers by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01Mordell's theorem guarantees that the rank (number of elements in the generating set of the group) is always well defined for an elliptic curve over the rational numbers. But as of 2023 there is no known algorithm which calculates the rank of any curve!
It is not even known if there are elliptic curves of every rank or not: Largest known ranks of an elliptic curve over the rational numbers, and it has proven extremely hard to find new ones over time.
TODO list of known values and algorithms? The Birch and Swinnerton-Dyer conjecture would immediately provide a stupid algorithm for it.
- something about finding a unitary representation of the poincare group
These often come pre-soldered on devboards, e.g. and allow for easy access to GPIO pins. E.g. they're present on the Raspberry Pi 2.
Why would someone ever sell a devboard without them pre-soldered!
6x1 pin header
. Source. 
Underside of a Raspberry Pi 2
. Source. At the top of this image we can clearly see how the usually pre-soldered pin header connectors go through the PCB and are soldered on both sides.- Stern-Gerlach experiment
- fine structure split in energy levels
- anomalous Zeeman effect
- of a more statistical nature, but therefore also macroscopic and more dramatically observable:
- ferromagnetism
- Bose-Einstein statistics vs Fermi-Dirac statistics. A notable example is the difference in superfluid transition temperature between superfluid helium-3 and superfluid helium-4.
Pinned article: ourbigbook/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