New articles - OurBigBook.com

Ciro Santilli 37 Updated 2025-07-16

As of the 20th century, this can be described well as "the phenomena described by Maxwell's equations".

Back through its history however, that was not at all clear. This highlights how big of an achievement Maxwell's equations are.

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Ciro Santilli's mother by

Ciro Santilli 37 Updated 2025-07-16

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Maxwell's equations by

Ciro Santilli 37 Updated 2025-07-16

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Unified all previous electro-magnetism theories into one equation.

Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.

The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.

The equations are a system of partial differential equation.

The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:

$E_{x} (t, x, y, z)$ , $E_{y} (t, x, y, z)$ , $E_{z} (t, x, y, z)$ : directions of the electric field $E : R^{4} \to R^{3}$
$B_{x} (t, x, y, z)$ , $B_{y} (t, x, y, z)$ , $B_{z} (t, x, y, z)$ : directions of the magnetic field $B : R^{4} \to R^{3}$

and two known input functions:

$ρ : R^{3} t o R$ : density of charges in space
$J : R^{3} \to R^{3}$ : current vector in space. This represents the strength of moving charges in space.

Due to the conservation of charge however, those input functions have the following restriction:

\frac{\partial ρ}{\partial t} + \nabla \cdot J = 0

(1)

Equation 1.

Charge conservation

Also consider the following cases:

if a spherical charge is moving, then this of course means that $ρ$ is changing with time, and at the same time that a current exists
in an ideal infinite cylindrical wire however, we can have constant $ρ$ in the wire, but there can still be a current because those charges are moving
Such infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.

The goal of finding

E

and

B

is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.

Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:

d i v E = \frac{ρ}{ε _{0}}

(2)

Equation 2.

Gauss' law

d i v B = 0

(3)

Equation 3.

Gauss's law for magnetism

\nabla \times E = - \frac{\partial B}{\partial t}

(4)

Equation 4.

Faraday's law

\nabla \times B = μ_{0} (J + ε_{0} \frac{\partial E}{\partial t})

(5)

Equation 5.

Ampere's circuital law

You should also review the intuitive interpretation of divergence and curl.

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Four-current by

Ciro Santilli 37 Updated 2025-07-16

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Magnetic field by

Ciro Santilli 37 Updated 2025-07-16

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Charge conservation by

Ciro Santilli 37 Updated 2025-07-16

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Magnetic vector potential by

Ciro Santilli 37 Updated 2025-07-16

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Optical fiber engineer by

Ciro Santilli 37 Updated 2025-07-16

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Lorentz transform consequence: everyone sees the same speed of light by

Ciro Santilli 37 Updated 2025-07-16

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OK, so let's verify the main desired consequence of the Lorentz transformation: that everyone observes the same speed of light.

Observers will measure the speed of light by calculating how long it takes the light going towards

+ x

cross a rod of length

L = x_{2} - x_{1}

laid in the x axis at position

X 1

TODO image.

Each observer will observe two events:

$(t_{1}, x_{1}, y_{1}, z_{1})$ : the light touches the left side of the rod
$(t_{2}, x_{2}, y_{2}, z_{2})$ : the light touches the right side of the rod

Supposing that the standing observer measures the speed of light as

c

and that light hits the left side of the rod at time

T 1

, then he observes the coordinates:

t_{1} x_{1} t_{2} x_{2} = T 1 = X 1 = \frac{L}{c} = X 1 + L

(1)

Now, if we transform for the moving observer:

t_{1}^{'} x_{1}^{'} t_{2}^{'} x_{2}^{'} = γ (t_{1} - \frac{v x _{1}}{c ^{2}}) = γ (x_{1} - v t_{1}) = γ (t_{2} - \frac{v x _{2}}{c ^{2}}) = γ (x_{2} - v t_{2})

(2)

and so the moving observer measures the speed of light as:

c^{'} = \frac{x _{2}^{'} - x _{1}^{'}}{t _{2}^{'} - t _{1}^{'}} = \frac{( x _{2} - v t _{2} ) - ( x _{1} - v t _{1} )}{( t _{2} - \frac{v x _{2}}{c ^{2}} ) - ( t _{1} - \frac{v x _{1}}{c ^{2}} )} = \frac{( x _{2} - x _{1} ) - v ( t _{2} - t _{1} )}{( t _{2} - t _{1} ) - \frac{v}{c ^{2}} ( x _{2} - x _{1} )} = \frac{\frac{x _{2} - x _{1}}{t _{2} - t _{1}} - v}{1 - \frac{v}{c ^{2}} \frac{x _{2} - x _{1}}{t _{2} - t _{1}}} = \frac{c - v}{1 - \frac{v}{c ^{2}} c} = \frac{c - v}{\frac{c - v}{c}} = c

(3)

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Four-gradient by

Ciro Santilli 37 Updated 2025-07-16

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A 4D gradient with some small special relativity specifics added in (the light of speed and sign change for the time).

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Organism model by

Ciro Santilli 37 Updated 2025-07-16

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Single electron double slit experiment by

Ciro Santilli 37 Updated 2025-07-16

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Video 1.

Electron Interference by the Italian National Research Council (1976)

Source.

Institutional video about the 1974 single electron experiment by Merli, Missiroli, Pozzi from the University of Bologna.

Uses an electron biprism as in electron holography inside a transmission electron microscope.

Shows them manually making the biprism by drawing a fine glass wire and coating it with gold.

Then actually show the result live on a television screen, where you see the interference patterns only at higher electron currents, and then on photographic film.

This was elected "the most beautiful experiment" by readers of Physics World in 2002.

Accompanying website: l-esperimento-piu-bello-della-fisica.bo.imm.cnr.it/english/index.html.

Italian title: "Interferenza di elettroni". Goddammit, those Italian cinematographers can make even physics look exciting!

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just IMAGINE if... by

Ciro Santilli 37 Updated 2025-07-16

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www.reading.ac.uk/just-imagine-if/

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Relativistic energy by

Ciro Santilli 37 Updated 2025-07-16

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OurBigBook CLI by

Ciro Santilli 37 Updated 2025-07-16

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Official Command-line interface to convert a directory of OurBigBook Markup files into a static website. See also: cirosantilli.com/ourbigbook/ourbigbook-cli

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OurBigBook.com / Crowdfunding by

Ciro Santilli 37 Updated 2025-07-16

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See: Section "Sponsor Ciro Santilli's work on OurBigBook.com".

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OurBigBook.com / Funding by

Ciro Santilli 37 Updated 2025-07-16

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Ciro is looking for:

university teachers who might be interested in trying it out as described at Section "Action plan", especially those who already use open licenses for their lecture notes
funding possibilities for this project, including donations as mentioned at Section "Sponsor Ciro Santilli's work on OurBigBook.com" and contracts

The initial incentive for the creators is to make them famous and allow them to get more fulfilling jobs more easily, although Ciro also wants to add money transfer mechanisms to it later on.

We can't rely on teachers writing materials, because they simply don't have enough incentive: publication count is all that matters to their careers. The students however, are desperate to prove themselves to the world, and becoming famous for amazing educational content is something that some of them might want to spend their times on, besides grinding for useless grade.

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Saylor Academy by

Ciro Santilli 37 Updated 2025-07-16

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This is an interesting initiative which has some similarities to Ciro Santilli's OurBigBook project.

The fatal flaw of the initiative in Ciro Santilli's opinion is the lack of user-generated content. We will never get there without UGC and algorithms, never.

Also as of 2021, it mostly useless business courses: learn.saylor.org unfortunately.

But it has several redeeming factors which Ciro Santilli aproves of:

exam as a service-like
they have a GitHub: github.com/saylordotorgo

Licensing appears to be a mixed mess between the dreaded CC BY-NC-SA and the good CC BY, e.g.:

The founder Michael J. Saylor looks a bit crooked, Rich people who create charitable prizes are often crooked comes to mind. But maybe he's just weird.

Video 1.

Michael Saylor interview by Lex Fridman (2022)

Source.

At the timestamp:

When I go, all my assets will flow into a foundation, and the foundation's mission is to make education free for everybody forever.

What statement... maybe he's actually not crooked, maybe it was just an accounting mistake... God, why.

If only Ciro Santilli knew how to contact him and convince him that his current approach is innefective and that Ciro has something better! Michael, please Google into this page some day, Ciro Santilli needs funding for OurBigBook.com. A hopeless Tweet at: twitter.com/cirosantilli/status/1548350114623660035. Also tried to hit his saylor@strategy.com.

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CIA 2010 covert communication websites / Non .com .net TLDs by

Ciro Santilli 37 Updated 2025-07-16

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.com and .net are very dominant. Here we list other choices made:

.info: has a few hits:
- archived comms:
  - beyondthefringe.info
- unarchived comms:
  - crickettoday.info
- unarchived:
  - talkingpointnews.info
  - theventurenews.info
  - worldconcerns.info
Did a full Wayback Machine CDX scanning on .info after:
```
grep -e news -e noticias -e nouvelles -e world -e global
```
That makes about 10k domains, so it's about the right size.
.org: has a least one hit, see: Are there .org hits?
.biz:
- unarchived comms:
  - atthemovies.biz

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How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it / Equipment used by

Ciro Santilli 37 Updated 2025-07-16

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 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!

Video 1.

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-calculus
Articles 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/derivative
Video 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:
- 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
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.
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 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.
Internal cross file references done right:
Infinitely deep tables of contents:
Figure 6.
Dynamic article tree with infinitely deep table of contents
.
Live URL: ourbigbook.com/cirosantilli/chordate
Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade

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

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 Pinned article: Introduction to the OurBigBook Project