Why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics? Updated 2025-04-05 +Created 1970-01-01
Physicists love to talk about that stuff, but no one ever has the guts to explain it into enough detail to show its beauty!!!
Perhaps the wisest thing is to just focus entirely on the part to start with, which is the quantum electrodynamics one, which is the simplest and most useful and historically first one to come around.
Perhaps the best explanation is that if you assume those internal symmetries, then you can systematically make "obvious" educated guesses at the interacting part of the Standard Model Lagrangian, which is the fundamental part of the Standard Model. See e.g.:
- derivation of the quantum electrodynamics Lagrangian
- Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 7 "Interaction Theory" derives all three of quantum electrodynamics, weak interaction and quantum chromodynamics Lagrangian from each of the symmetries!
One bit underlying reason is: Noether's theorem.
Notably, axelmaas.blogspot.com/2010/08/global-and-local-symmetries.html gives a good overview:so it seems that that's why they are so key: local symmetries map to the forces themselves!!!
A local symmetry transformation is much more complicated to visualize. Take a rectangular grid of the billiard balls from the last post, say ten times ten. Each ball is spherical symmetric, and thus invariant under a rotation. The system now has a global and a local symmetry. A global symmetry transformation would rotate each ball by the same amount in the same direction, leaving the system unchanged. A local symmetry transformation would rotate each ball about a different amount and around a different axis, still leaving the system to the eye unchanged. The system has also an additional global symmetry. Moving the whole grid to the left or to the right leaves the grid unchanged. However, no such local symmetry exists: Moving only one ball will destroy the grid's structure.Such global and local symmetries play an important role in physics. The global symmetries are found to be associated with properties of particles, e. g., whether they are matter or antimatter, whether they carry electric charge, and so on. Local symmetries are found to be associated with forces. In fact, all the fundamental forces of nature are associated with very special local symmetries. For example, the weak force is actually associated in a very intricate way with local rotations of a four-dimensional sphere. The reason is that, invisible to the eye, everything charged under the weak force can be characterized by a arrow pointing from the center to the surface of such a four-dimensional sphere. This arrow can be rotated in a certain way and at every individual point, without changing anything which can be measured. It is thus a local symmetry. This will become more clearer over time, as at the moment of first encounter this appears to be very strange indeed.
axelmaas.blogspot.com/2010/09/symmetries-of-standard-model.html then goes over all symmetries of the Standard Model uber quickly, including the global ones.
Philosophically, machine learning can be seen as a form of lossy compression.
And if we make it too lossless, then we are basically overfitting.
Organization developing superconducting quantum computer Updated 2025-04-05 +Created 1970-01-01
This is how electronic circuits are normally prototyped!
Once you validate them like this, the next step is usually to move on to printed circuit boards for more reliable production setups.
Breadboards are a thing of beauty and wonder.
Point-to-point constructions on woden boards
. Source. Predecessors to breadboards from where the name came. A thing of beauty, so vintage. You could actually write stuff on those with a pencil!Our Final Invention - Artificial General Intelligence by Sciencephile the AI (2023)
Source. AGI via simulation section.Ciro Santilli defines an "AI game" as:
a game that is used to train AI, in particular one that was designed with this use case in mind, and usually with the intent of achieving AGI, i.e. the game has to somehow represent a digital world with enough analogy to the real world so that the AGI algorithms developed there could also work on the real world
Most games played by AI historically so far as of 2020 have been AI for games designed for humans: Human game used for AI training.
Ciro Santilli took a stab at an AI game: Ciro's 2D reinforcement learning games, but he didn't sink too much/enough into that project.
A closely related and often overlapping category of simulations are artificial life simulations.
Bibliography:
A concise to describe a specific permutation.
A permutation group can then be described in terms of the generating set of a group of specific elements given in cycle notation.
E.g. en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Permutation_groups mentions that the Mathieu group is generated by three elements:which feels quite compact for a simple group with 95040 elements, doesn't it!
- (0123456789a)
- (0b)(1a)(25)(37)(48)(69)
- (26a7)(3945)
Simulates vintage hardware synthesizers, and includes some pretty complex ones!
Aims to show an UI that looks exactly like the synthesizers in question.
This is a really good piece of software. You can search on YouTube how some classic synths, work, and the immediately start playing them!
The more familiar transitions we are familiar with like liquid water into solid water happen at constant temperature.
However, other types of phase transitions we are less familiar in our daily lives happen across a continuum of such "state variables", notably:
- superfluidity and its related manifestation, superconductivity
- ferromagnetism
Thought experiment that illustrates the path integral formulation of quantum field theory.
Mentioned for example in quantum field theory in a nutshell by Anthony Zee (2010) page 8.
The best Romance of the Three Kingdoms adaptation of all time? Mind blowing.
There seems to exist a version with full Chinese + English subtitles: www.youtube.com/watch?v=0_r3eWfTMDs&list=PLdAMXqGeRsOkXzuocRkBPhe5RhZ6RotGH&index=2
www.youtube.com/watch?v=e8VWVvHjskM&list=PLIj4BzSwQ-_ueXTO7EBmShk1b3lEqc5b_ official CCTV电视剧 (CCTV TV Series Channel) upload without Chinese + English subtitles.
Title sequence of the Romance of the Three Kingdoms (1994 TV series)
. Source. From this you can understand that the number os extras is off the charts! There are unlisted articles, also show them or only show them.