Chat programs that don't have a proper web-only operation and force you to have a mobile phone, e.g. WhatsApp.
Heck, even Signal, which is supposed to be super secure and good for your privacy, forces you to disclose your freaking cell phone to all contacts! lifehacker.com/how-to-use-signal-without-revealing-your-private-phone-1818996580
It seems impossible to avoid the signaling server. With signaling server:
Ciro Santilli's email can be found by cloning one of his repositories on GitHub. It is also given at: Section "How to contact Ciro Santilli".
Their reference markup is incredibly overengineered, convoluted, and underdocumented, it is unbelivable!
Use the reference:
This is a fact.{{sfn|Schweber|1994|p=487}}Define the reference:
===Sources===
{{refbegin|2|indent=yes}}
*{{Cite book|author-link=Silvan S. Schweber |title=QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga|last=Schweber|first=Silvan S.|location=Princeton|publisher=University Press|year=1994 |isbn=978-0-691-03327-3 |url=https://archive.org/details/qedmenwhomadeitd0000schw/page/492 |url-access=registration}}
{{refend}}sfn is magic and matches the the author last name and date from the Cite, it is documented at: en.wikipedia.org/wiki/Template:SfnUnforutunately, if there are multiple duplicate
Cites inline in the article, it will complain that there are multiple definitions, and you have to first factor out the article by replacing all those existing Cite with sfn, and keeping just one Cite at the bottom. What a pain...You can also link to a specific page of the book, e.g. if it is a book is on Internet Archive Open Library with:
{{sfn|Murray|1997|p=[https://archive.org/details/supermenstory00murr/page/86 86]}}For multiple pages should use
pp= instead of p=. Does not seem to make much difference on the rendered output besides showing p. vs pp., but so be it:{{sfn|Murray|1997|pp=[https://archive.org/details/supermenstory00murr/page/86 86-87]}}Equation 1.
Lorentz force
. A little suspicious that it bears the name of Lorentz, who is famous for special relativity, isn't it? See: Maxwell's equations require special relativity.
For numerical algorithms and to get a more low level understanding of the equations, we can expand all terms to the simpler and more explicit form:
Is implied by Gauss' law if Maxwell's equations: physics.stackexchange.com/questions/44418/are-the-maxwells-equations-enough-to-derive-the-law-of-coulomb
The "static" part is important: if this law were true for moving charges, we would be able to transmit information instantly at infinite distances. This is basically where the idea of field comes in.
Coulomb's Law experiment with torsion balance with a mirror on the balance to amplify rotations by uclaphysics (2010)
Source. Understanding Electromagnetic Radiation! by Learn Engineering (2019)
Source. Shows animations of a dipole antenna which illustrates well how radiation is emitted from moving charges and travels at the speed of light. Existence and uniqueness of solutions to Maxwell's equations by 
Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16
Hall effect experimental diagram
. Source. The Hall effect refers to the produced voltage , AKA on this setup.
An intuitive video is:
The key formula for it is:where:
- : current on x direction, which we can control by changing the voltage
- : strength of transversal magnetic field applied
- : charge carrier density, a property of the material used
- : height of the plate
- : electron charge
Applications:
- the direction of the effect proves that electric currents in common electrical conductors are made up of negative charged particles
- measure magnetic fields, TODO vs other methods
Other more precise non-classical versions:
A different and more elegant way to express Maxwell's equations by using the:instead of the:
Experimental verification of the Maxwell-Boltzmann distribution by Ciro Santilli 40 Updated 2025-07-16
Ciro Santilli 40 Updated 2025-07-16Most applications of the Maxwell-Boltzmann distribution confirm the theory, but don't give a very direct proof of its curve.
Here we will try to gather some that do.
S page 146.
For this sub-case, we can define the Lie algebra of a Lie group as the set of all matrices such that for all :If we fix a given and vary , we obtain a subgroup of . This type of subgroup is known as a one parameter subgroup.
The immediate question is then if every element of can be reached in a unique way (i.e. is the exponential map a bijection). By looking at the matrix logarithm however we conclude that this is not the case for real matrices, but it is for complex matrices.
TODO example it can be seen that the Lie algebra is not closed matrix multiplication, even though the corresponding group is by definition. But it is closed under the Lie bracket operation.
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