Local symmetries of the Lagrangian imply conserved currents Updated 2024-12-23 +Created 1970-01-01
TODO. I think this is the key point. Notably, symmetry implies charge conservation.
More precisely, each generator of the corresponding Lie algebra leads to one separate conserved current, such that a single symmetry can lead to multiple conserved currents.
This is basically the local symmetry version of Noether's theorem.
Then to maintain charge conservation, we have to maintain local symmetry, which in turn means we have to add a gauge field as shown at Video "Deriving the qED Lagrangian by Dietterich Labs (2018)".
Forces can then be seen as kind of a side effect of this.
Bibliography:
- photonics101.com/relativistic-electrodynamics/gauge-invariance-action-charge-conservation#show-solution has a good explanation of the Gauge transformation. TODO how does that relate to symmetry?
- physics.stackexchange.com/questions/57901/noether-theorem-gauge-symmetry-and-conservation-of-charge
Or is real word data necessary, e.g. with robots?
Fundamental question related to Ciro's 2D reinforcement learning games.
Bibliography:
- youtu.be/i0UyKsAEaNI?t=120 How to Build AGI? Ilya Sutskever interview by Lex Fridman (2020)
Host: Ben Krasnow.
Deals with materials, chemistry, microscopy, electronics.
Uber practical, well described setups deep science stuff, he is awesome and has been at Google since 2014: www.linkedin.com/in/ben-krasnow-6796a94/
Ben studied at University of California, Santa Barbara.
cat-v.org/ by Rob Pike, co-creator of Go, looong time Unixer, and some kind of leader of a 9p resurrection cult. That one's spicy. E.g.: harmful.cat-v.org/, Ciro's version: good and evil.
Full name Carl Mark Force IV, the fourth! As mentioned at www.vice.com/en/article/vv7dgj/great-moments-in-shaun-bridges-a-corrupt-silk-road-investigator (this made Ciro Santilli laugh quite hard:
Carl Mark Force IV - the other corrupt cop charged alongside Bridges - is pretty hard to beat, just name-wise.
It is quite comical that two separate towns were founded one next to the other right in the middle of nowhere. And that both have so slightly weird names.
The images you have to have in mind are:
Yes, Sheldon he has separate American and British English versions of pages!!!
For example, Kross bicycle (2017) had a Schwalbe tyre with markings:When inflated, the tires were about 3.5cm wide as measured with a ruler.
42-622 (28 x 1.60, 700x40C)
And the Mavic A319 rim had markings:
622x19C
In this:
- ISO (Etrto): 42-622. So:
- 42 is the inner rim width. The actual inflated tire is going to be even wider.
- 622 is the bead seat diameter. The actual inflated tire is going to be even wider.
- imperial: 28 x 1.60
- French: 700x40C:
- meaning of the "C" asked at: bicycles.stackexchange.com/questions/16190/what-does-the-c-in-bicycle-tire-size-mean
- www.sheldonbrown.com/tire-sizing.html#french says A is larger than B which is larger than C, and C means 622 mm
- meaning of the "C" asked at: bicycles.stackexchange.com/questions/16190/what-does-the-c-in-bicycle-tire-size-mean
Ciro once told a friend that his ideal life would be to "just chill out and eat his bread in peace" (while also learning and teaching the sciences). Quote "Omar Khayyam's chill out quote" comes to mind. See also: Ciro Santilli's cheapness.
where:
- : matrix in the old basis
- : matrix in the new basis
- : change of basis matrix
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