from garden/karlicoss/study/tostudy.md by @karlicoss
Table of Contents
[20200119]
John Carlos Baez on Twitter: "Entropy is the amount of information you don't have about the random details of a system: what you'd need to describe those details. It takes 500 zettabytes to fully describe a gram of liquid water, but a manageable amount per molecule! (1/n) https://t.co/cDg7ZFpLt3" / Twitter[20200217]
Nikita Lisitsa on Twitter: "Simulating Hamiltonian mechanics instead of MetropolisHastings algorithm: https://t.co/cVZiaTGP7u" / Twitter[20200801]
Viktor T. Toth  Spinors in three dimensions[20200623]
Quantum vs. classical  Dee Mon. Былое и думы — LiveJournal[20200715]
Understanding quaternions and the Dirac belt trick (2010)[20190126]
general topology  What is a topological space good for?  Mathematics Stack Exchange [[topology]][20190223]
III Advanced Quantum Field Theory  QFT in one dimension (i.e. QM) [[qft]]
visualising QFT [[viz]] [[qft]]
[20190211]
A new way of visualising quantum fields  IOPscience [[qft]] [[viz]]
[20190211]
software  Where can I find visualizations of quantum field theory equations?  Physics Stack Exchange [[qft]] [[viz]] [20190211]
Proton quarks empty mass calculation GIF : askscience [[qft]][20190211]
Derek Leinweber [[viz]] [[qcd]] hmm, no one seems to have visualised klein gordon, even numerically? [[quantum]] [[viz]]
[20190211]
(8) Empty Space is NOT Empty  YouTube [[qft]] [[viz]]

[20190224]
Is it true that the Schrödinger equation only applies to spin1/2 particles?  Physics Stack Exchange [20190210]
(6) Quantum Spin  Visualizing the physics and mathematics  YouTube [[spin]] [[viz]]
[20190223]
III Advanced Quantum Field Theory  QFT in zero dimensions [[qft]] [[study]] 
[20190223]
Lagrangian formalism for fields  Scholarpedia [[lagrangian]] [[spinor]] 
Tensors [[tensor]]
[20190424]
need to make sure I understand it and archive[20190223]
Tensor Calculus [[tensor]][20190223]
Tensor derivative (continuum mechanics)  Wikipedia[20190223]
Partial derivative of tensor with respect to tensor  Mathematics Stack Exchange[20190223]
partial differentiation of a variable w.r.t. its time derivative  Mathematics Stack Exchange[20190223]
Tensors_{Poor}_{Man.pdf}

[20190211]
AharonovBohm Experiment [[quantum]] [[study]] 
[20190223]
Einstein–Hilbert action  Wikipedia  SO3 vs SU2 https://labcit.ligo.caltech.edu/~ethrane/Resources/seminar/Ch2.Spinors.pdf [[reprtheory]]
[20190319]
Quantum computing for the very curious [[qft]][20190320]
What is the point of complex fields in classical field theory?  Physics Stack Exchange [[qft]]
[20190215]
electromagnetism  Are electron fields and photon fields part of the same field in QED?  Physics Stack Exchange [[qft]] 
[20190312]
Cambridge Notes [[math]] [[physics]] [20190312]
III Quantum Field Theory  Spinors[20190328]
Simulation of Lattice QuantumChromodynamics and Other Lattice Models : TechWeb : Boston University [[viz]] [[qft]] Tweet from Borja Sotomayor (@borjasotomayor), at Apr 2, 12:21 [[art]]
[20190424]
angular momentum  An electron has no known internal structure, does that imply it has an unknown one?  Physics Stack Exchange [[spin]]
chirality and helicity
[20190424]
polarization  What is polarisation, spin, helicity, chirality and parity?  Physics Stack Exchange[20190424]
polarization  What is polarisation, spin, helicity, chirality and parity?  Physics Stack Exchange[20190424]
What should be the intuitive explanation of wave equation?  Physics Stack Exchange[20190208]
polarisation and helicity some derivations [[gauge]]
 read rosetta stone again [[study]]
[20190605]
Gauge invariance  Scholarpedia
[20190620]
Jacopo Bertolotti on Twitter: "I am not satisfied yet, but this is my spin rotating around the xaxis, with the color representing the phase term common to both components of the spinor (which shows that you need two rounds to go back to the original state). I will work more on it in the next days.… https://t.co/ji4cYUNRu8" [[spinor]] [[viz]]  Tweet from George Corney (@Haxiomic), at Oct 3, 00:08 [[sim]] [[qft]]

[20191114]
John Carlos Baez on Twitter: "Murray GellMann won the Nobel prize for discovering "quarks":" protons, neutrons, and other baryons are made of 3 quarks, while pions, kaons and other mesons are made of a quark and an antiquark. But he got some help from his tennis partner! (1/n) https://t.co/YHGDNpvfZX" / Twitter  Tweet from Nikita Lisitsa (@lisyarus), at Nov 22, 14:40
 Tweet from Dr Martin Kleppmann (@martinkl), at Nov 15, 15:49
[20200511]
Mel Andrews 𓃻 on Twitter: "Explain mean field theory to philosophers in one sentence GO!" / Twitter[20200511]
(1) jestem króliczkiem on Twitter: "@litgenstein I was hoping to work on some interactive Python notebooks based on this: https://t.co/yUd0TyTmQZ Will finally have some time to try it out soon!" / Twitter [[toblog]][20200525]
Valentin Fadeev on Twitter: "Hamiltonian or Lagrangian? Why choose when you can have the best of both (provided you have some cyclic coordinates). Enter Routhian. From L&L "Mechanics" §41. https://t.co/AcuXAxR4hf" / Twitter[20200623]
Nikita Lisitsa on Twitter: "Digging through "Introduction to Quantum Field Theory for Mathematicians" by Sourav Chatterjee. The first book with a title like this I've found that seems to actually do the job." / Twitter [[study]][20200709]
Simulating physical reality with a quantum computer [[totweet]][20200716]
(1) John Carlos Baez on Twitter: "A wonderful thing: any differentiable function from the complex numbers to the complex numbers preserves angles  except where its derivative is zero. So it's a conformal mapping! The complex numbers capture the geometry of angles in 2 dimensions. (4/n) https://t.co/NQBOMOFibR" / Twitter Qft rigorous book [[qft]]
[20200718]
How can electrons be “topological”?  Gravity and Levity
[20200809]
Phase plane analysis: examples [[toblog]] [20201120]
Quantum Field Theory visualized  YouTube[20201020]
Dirac — Greg Egan[20200831]
I made an animation showing how a ring of N classical (left) or quantum (right) harmonic oscillators reproduces the physics of fields when N becomes large! (More details in comments) /r/Physics Tweet from Nikita Lisitsa (@lisyarus), at Jul 17, 15:52
 https://www.google.com/url?q=https://www.math.tecnico.ulisboa.pt/~jnatar/MG03/Marsden/ms_book_ch7.pdf&sa=U&ved=2ahUKEwinuLe39freAhWLLMAKHUKTBFkQFjACegQIHBAB&usg=AOvVaw0VdF3GJLsrDR7x48z6XgBq
 Tweet from Valentin Fadeev (@ValFadeev), at Oct 9, 01:21 dirac equation
[20191009]
Три книги  Dee Mon. Былое и думы — LiveJournal thinking about schrodinger's cat experiment [[study]] [[think]] [[toblog]]
[20200811]
Higgs mechanism  Wikipedia weinstein says yangmills equations are simpler? [[study]]
[20200915]
Higgs fermions and bosons[20201022]
Nyquist frequency  Wikipedia[20200704]
Gluon  Wikipedia Tweet from @wickrotate
 Excellent article, need to reread and process [[study]]
[20200713]
Klein–Gordon equation  Wikipedia[20200713]
Why don’t photons interact with the Higgs field?  Physics Stack Exchange[20200713]
On the Higgs Mechanism[20200713]
On the Higgs Mechanism[20200714]
mathpages.com/home/kmath654/kmath654.htm [[readagain]][20200718]
Klein–Gordon equation  Wikipedia[20200720]
dirac gif[20200724]
ShtetlOptimized » Blog Archive » Rosser’s Theorem via Turing machines[20200801]
Viktor T. Toth  Quaternions and the Dirac equation[20200801]
Spinor Info – About physics and other things Tweet from michael_{nielsen} (@michael_{nielsen}), at Oct 18, 20:59
 Tweet from John Carlos Baez (@johncarlosbaez), at Nov 29, 18:54
 Tweet from John Carlos Baez (@johncarlosbaez), at Nov 29, 19:21
 [
[20200501]
Gauge Symmetry The Physics Travel Guide  ax
[20200624]
File:Metals and insulators, quantum difference from band structure.ogv  Wikipedia[20200703]
america hater sarahzrf on Twitter: "@lisyarus …so conservation of energy is {H, H} = 0 when the hamiltonian is the same as energy, which i seem to recall being the case exactly when consrevation of energy is true 👀" / Twitter Tweet from @gregeganSF
[20200323]
Black Holes Are Not Empty Voids. A Black Hole at the Heart! /r/Physics The hydrogen atom is the simplest atom, and you ought to be able to understand it if you understand atoms at all [[study]]
[20200526]
Novel insight reveals topological tangle in unexpected corner of the universe[20200618]
John Carlos Baez on Twitter: "I love condensed matter physics! I hadn't even known dielectrons were a thing: normally electrons repel. But in a sodiumammonia solution, electrons pair up with opposite spins. Here's a new simulation of a dielectron, lasting 2.75 picoseconds: (2/n) https://t.co/onDLm8yP4S" / Twitter[20200615]
Quote of the day: Physics · Andrew's Blog[20200414]
Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful—Stephen Wolfram Writings Tweet from @lisyarus Quantum Chemistry Done Wrong
 SICM https://news.ycombinator.com/item?id=23155017

[20201018]
Dan Girshovich  Foundations Journal Club. [[social]] [[study]] [[physics]] [20190805]
books http://math.ucr.edu/home/baez/books.html
Unruh effect
[20190902]
The Unruh Effect  Space Time  YouTube[20190902]
Эффект Унру — Википедия[20190902]
Unruh effect  Wikipedia[20190902]
What causes the Unruh effect? : askscience[20190902]
Can someone explain the Unruh effect/radiation to me? How are virtual particles forced into existence if they are nothing but convenient mathematical models and don't actually exist? : askscience Эффект Унру — Заметки о теоретической физике
[20200719]
Talk:Photon/Photons and Mass Debate3  Wikipedia[20200719]
quantum mechanics  Einstein's box  unclear about Bohr's retort  Physics Stack Exchange[20200719]
energy  Explain how (or if) a box full of photons would weigh more due to massless photons  Physics Stack Exchange from Lisitsa: алгебры клиффорда и спинорные группы [[towatch]]
[20190414]
CFDPython/14_{Step}_{11.ipynb} at master · barbagroup/CFDPython [[ipython]][20190125]
Schrödinger Equation https://physkcstravelguide.com/equations/schroedinger_equation#tab__faq
[20190123]
Everything about Representation theory of finite groups : math [[reprtheory]][20190506]
These representations are unique up to a change of basis (equivalent to a similarity transform), so this means each possible eigenvalue of the Hamiltonian 'belongs' to a certain representation of the group of the Schrodinger Equation.[20190506]
Also remember that each eigenvalue has its own representation, so different eigenvalues of the same Hamiltonian can have different degeneracy.[20190123]
Normally, if the degeneracy cannot be explained by symmetry then it is known as an 'accidental' degeneracy, but Fock showed that there is actually a set of operations in 4D which exploits the symmetry. The hydrogen potential has the group O(4), and you should be able to understand most of the language in the introduction here.
[20190114]
(2) Quantum Tunneling  Complex Plot  YouTube [[quantum]] [[viz]] Nikita Lisitsa on Twitter: ""When a classical physics problem is described by a variety, some magic happens. The process of quantization becomes completely systematic—and surprisingly simple." @johncarlosbaez Would you be so kind to provide any reference on this?"
 ¬¬(Dan Piponi) on Twitter: "What I find confusing is that I learnt QFT two different ways: (1) pretending univariate wavefunction is classical and quantizing again & (2) considering multivariate wavefunctions. Not obvious these get you to the same place.… https://t.co/uaw1AZIEDz" [[qft]]

[20190407]
Field Play [[viz]]  На пути к теории всего https://nplus1.ru/material/2018/02/02/justlookingforsomeaction
[20190317]
Quantum electrodynamics  Wikipedia [[qed]] I first saw this kind of explanation in Steve Vickers' Topology via Logic, which is an excellent little book [[study]] [[topology]]
 revise cs/math/physics stuff [[habit]] [[spacedrep]]
[20181223]
Integral manipulations · Issue #5396 · sympy/sympy The Born Rule Has Been Derived From Simple Physical Principles  Quanta Magazine
 Easier than harmonic oscillator: repulsive potential? Admits both trajectories
 start following one of scott aaronsons posts about motivation for square probability rule and play with equations [[quantum]] [[viz]]
[20190126]
A Neighborhood of Infinity: What's all this E8 stuff about then? Part 1. [[reprtheory]][20190211]
A Journey to The Manifold SU(2): Differentiation, Spheres and Fiber Bundles [[study]][20190110]
www.math.lsa.umich.edu/~idolga/lecturenotes.html [[math]] [[physics]] [[lagrangian]]
[20190123]
Charts on SO(3)  Wikipedia [20190123]
3D rotation group  Wikipedia[20190124]
How is a Lie Algebra able to describe a Group? – Jakob Schwichtenberg [[lie]][20190123]
Group Theory and Physics  S. Sternberg  Google Books[20190201]
List of Fundamental Groups of Common Spaces  Mathonline[20181124]
Seminar: Fall 2008 [[baez]] Nikita Lisitsa on Twitter: "The rep.theory book by Fulton & Harris demonstrates the idea of restricting to an abelian subgroup (which is fundamental for Lie groups) using S₃ as an example (rather than, say, SL(n)) and it is beautifully simple and understandable."

[20181110]
User ACuriousMind  Physics Stack Exchange [20190123]
quantum mechanics  Spin operators in QM  Physics Stack Exchange [[spin]][20190126]
* To semidecide this, just start generating every possible proof.[20190126]
* Suppose the property N[D[_{x}_]D](_{y}_) = (_{x}_ ≠ y) is semidecidable for each x[20190223]
homework and exercises  Functional Derivative of action  Physics Stack Exchange[20190223]
resource recommendations  What is a complete book for introductory quantum field theory?  Physics Stack Exchange
[20190226]
Is there a reason why a relativistic quantum theory of a single fermion exists, but of a single scalar not?  Physics Stack Exchange [20190210]
general topology  Triangulation of torus  understanding why  Mathematics Stack Exchange [[topology]][20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience[20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience[20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience[20190210]
general topology  Why aren’t continuous functions defined the other way around?  Mathematics Stack Exchange [[topology]][20190223]
From Griffiths to Peskin: a lit review for beginners  An American Physics Student in England[20190222]
general relativity  Why do we select the metric tensor for raising and lowering indices?  Physics Stack Exchange https://math.stackexchange.com/questions/36683/mathandmusictheorybooks [[musictheory]]
 The Reference Frame: Why are there spinors? [[spinor]]
[20190222]
Book_{Chapter}_{Lagrangian.pdf}[20190223]
lec33.dvi  lec33.pdf[20190223]
radiation.dvi  radiation.pdf
Yoneda [[yoneda]]
[20180731]
Soham Chowdhury on Twitter: "Vakil (in his book, or perhaps on MO) likens the Yoneda lemma to a particle accelerator, in that if you know how a particle reacts to being smashed into by other particles, you know everything about it… https://t.co/jtdQupZoGH"[20180731]
From the Yoneda lemma to categorical physics[20180808]
🇪🇸🇵🇹_{jack} on Twitter: Yoneda[20180808]
Understanding Yoneda  Bartosz Milewski's Programming Cafe[20180808]
The Yoneda Lemma — Math3ma
[20190223]
Introduction to the Modern Theory of Dynamical Systems  Anatole Katok, Boris Hasselblatt  Google Books [[lagrangian]][20190304]
A Python utility for analyzing a given solution to the Einstein field equations. /r/Python[20190319]
Gödel metric  Wikipedia[20190331]
quantum mechanics  Relation between radio waves and photons generated by a classical current  Physics Stack Exchange[20190223]
I've been making a gravity simulator using RustSDL2! Source is in the comments, hope you enjoy it! /r/rust [[sim]] Higgs
[20190424]
at.algebraic topology  How to demonstrate (SO(3)) is not simply connected?  MathOverflow[20190424]
Real projective plane  Wikipedia[20190424]
mass  Why is the (S_{z} =0) state forbidden for photons?  Physics Stack Exchange[20190424]
mass  Why is the (S_{z} =0) state forbidden for photons?  Physics Stack Exchange[20190426]
Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics  YouTube [[viz]][20190117]
Quantum Diaries[20190117]
Quantum Diaries[20190210]
classification theorem [[topology]] renormalisation group flow
 group of physicists and mathematicians is studying a geometric object called an “amplituhedron” that has the potential to further simplify calculations of particle interactions.
 Slowly start learning IPA? Use spaced repetition
 Sight reading on computer keyboard [[piano]]
 Why is the phase picked up during identical particle exchange a topological invariant?  Physics Stack Exchange
 The Difference Between 3/4 & 6/8 Time (with examples)  School of Composition [[music]]
[20190510]
"Higher Homotopy Groups Are Spooky: Enter the world of 3dimensional holes in 2dimensional objects". A blog post by Evelyn Lamb. /r/math[20190325]
(2) Dirac equation: Zitterbewegung in two dimensions  YouTube[20190601]
Topological Quantum Computer  Professor John Preskill, Caltech  YouTube [[qcomp]][20181223]
Quantum Python: Animating the Schrodinger Equation  Pythonic Perambulations [[viz]] [[python]] [[matplotlib]][20190208]
Spare me the math: the Lamb Shift  Gravity and Levity [[quantum]] Tweet from Igal Tabachnik (@hmemcpy), at Oct 21, 20:23 Category Theory for Programmers by @BartoszMilewski is now complete, and available for purchase in hardcover! [[cattheory]]
 Todo visualise that??? [[viz]]
[20190117]
Looking inside the standard model: Electromagnetism, photons, and symmetry[20190123]
what happens when computer: structural regular expressions [[study]] [[project]][20190510]
Problems with the Standard Model Higgs  Azimuth[20190612]
Serious What's the most USEFUL course I can take online for FREE? /r/AskReddit Tweet from Eric Aleman (@EricAleman_), at Jun 13, 10:28
 What happens if we don't postulate speed of light limit?
 Tweet from Smart Biology (@SmartBiology3D), at Jun 24, 15:17

[20190423]
fast.ai · Making neural nets uncool again [[ai]] [20190211]
The Picture Book of Quantum Mechanics: Siegmund Brandt, Hans Dieter Dahmen: 9781461439509: Amazon.com: Books [[quantum]][20181115]
The Geometry of Physics: An Introduction: Amazon.co.uk: Theodore Frankel: 9781107602601: Books Tweet from Nikita Lisitsa (@lisyarus), at Jul 11, 22:23
 Tweet from Некстджен и Усиление (@turbojedi), at Jul 18, 11:16 [[ml]]
[20190115]
Kevin Boone's Web site[20190620]
Amir on Twitter: "Итого, чтобы собрать программируемый транзисторный микропроцессор, нужно уметь проектировать 1) ISA – см. MIPS 2) микроархитектуру – см Harris&Harris 3) RTL  верилог 4) цифровую технику  см курс Панчула… https://t.co/MqVes4WlZu" Tweet from niall tl (@nialltl), at Aug 1, 13:02
 Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Jul 31, 17:07
[20190802]
〈 Berger  Dillon 〉 (@InertialObservr) / Twitter[20181224]
convention  Obtaining the (\frac{1}{2\pi}) factor in the Fourier transform  Mathematics Stack Exchange[20181224]
ho.history overview  The (2\pi) in the definition of the Fourier transform  MathOverflow[20190612]
Quantum Diaries https://www.quantumdiaries.org/2011/06/19/helicitychiralitymassandthehiggs/ [[readagain]] [[stm]][20190727]
Michael Nielsen[20190504]
Cadabra manual: Sphere https://cadabra.science/notebooks/sphere.html[20190510]
Geometric Quantization (Part 1)  Azimuth[20190723]
resource recommendations  Gentle introduction to the Formalism of Quantum Zeno Effect  Physics Stack Exchange Tweet from michael_{nielsen} (@michael_{nielsen}), at Apr 15, 19:22 This is true  a set of ideas introduced by economists to study the distribution of wealth also turn out to govern the behaviour of quantum entanglement. Pretty wild! Here's the paper: https://t.co/Wf9iGL59JO https://t.co/wXXbIP697I
[20190618]
Jacopo Bertolotti on Twitter: ""I quickly learned to hate spinors. They’re nonintuitive, far more complicated than they have any right to be, and come either with two components or four, both versions being equally hard to comprehend." A Child’s Guide to Spinors William O. Straub"[20190803]
(6) Abhishek Singharoy on Twitter: "The first study of an entire cell organelle in allatom details. https://t.co/R2t6YdyiAu I am told it'll take the field either 30 years back or 30 years forward. Please help me decide :)" / Twitter Tweet from John Carlos Baez (@johncarlosbaez), at Aug 11, 05:50 I've been thinking about this sum for a while. I finally had an idea, which you can see here:
 Tweet from John Carlos Baez (@johncarlosbaez), at Aug 14, 11:28
[20190811]
(3) michael_{nielsen} on Twitter: "Amazing Twitter thread, giving an overview of work on quantum computer architectures. Lots of intuitionbuilding tidbits, broad principles, and detailed references. Summarized here: https://t.co/VDzUrfCpA8 https://t.co/i30oRFruw2" / Twitter Something Deeply Hidden  Not Even Wrong
 Нейронауки для всех. Методы: транскраниальная магнитная стимуляция  Neuronovosti
 Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Aug 18, 07:06
[20190818]
(1) Daniel Litt on Twitter: "The fundamental group of SO(3) is Z/2Z! https://t.co/MnJS0YnNrJ" / Twitter[20190819]
(1) Daniel Piker on Twitter: "New 'Live Soap' component for interactive formfinding of minimal surfaces with topology changes https://t.co/YuARGfXlSO" / Twitter
[20190628]
Anki decks by LW users  LessWrong 2.0  Tweet from Nikita Lisitsa (@lisyarus), at Aug 26, 18:32
 Tweet from Dmitrii Kovanikov (@ChShersh), at Aug 27, 13:51
 Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Aug 30, 18:28
[20190621]
Finding a potential function for conservative vector fields  Math Insight[20190621]
Finding a potential function for conservative vector fields  Math Insight
[20190906]
David Pfau on Twitter: "Thrilled to be able to share what I've been working on for the last year  solving the fundamental equations of quantum mechanics with deep learning! https://t.co/pzp0Xhsxbu" / Twitter [20190629]
Particle filter  Wikipedia[20190727]
explained.ai [[ai]] Tweet from isis agora lovecruft (@isislovecruft), at Sep 22, 00:47
 The Yoneda Perspective
[20190929]
John Carlos Baez on Twitter: "@sigfpe There are theorems about this stuff. A simple example is the lowest eigenvalue of d²/dx² + x² + λx⁴ as a function of λ. You can formally compute the Taylor series of this function, which diverges, and Borel sum it, and get the right answer for λ>0." / Twitter[20190524]
Going Critical — Melting Asphalt [[sim]][20120810]
An argument against call/cc /r/programming[20120810]
An argument against call/cc /r/programming[20190704]
Understandable RayTracing in 256 lines of bare C++ /r/cpp[20190828]
ELI5 The Wigner's Friend Thought Experiment /r/explainlikeimfive [[quantum]] Tweet from michael_{nielsen} (@michael_{nielsen}), at Nov 4, 01:38
 Tweet from Nikita Lisitsa (@lisyarus), at Mar 20, 09:27 An excellent read  "The stability of matter: from atoms to stars" https://t.co/qFktkarHAk [[study]] [[read]]
[20191202]
The Hardware of a Quantum Computer  edX[20190105]
Are we expecting to have a symmetry breaking of the electromagnetic force in the future? /r/Physics[20190105]
Are we expecting to have a symmetry breaking of the electromagnetic force in the future? /r/Physics[20190105]
What exactly is explicit symmetry breaking? And what are some examples? /r/Physics[20190123]
Can Representation Theory be Explained Using Basic Abstract and Linear Algebra? /r/math Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Dec 14, 23:57
 Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Dec 15, 00:02
[20190718]
Quantum Leaps, Long Assumed to Be Instantaneous, Take Time  Quanta Magazine /r/Physics Try TLA
[20191220]
1/(1  1/(1  1/(1  Dan Piponi))) on Twitter: "The padics are like science fiction in mathematics. They are alternative universes alongside the familiar realm of the reals. And there are objects that transcend the barriers between these worlds but manifest a little differently in each one." / Twitter[20191224]
〈 Berger 🎄 Dillon 〉 on Twitter: "Putting it all together, we get the leading order Feynman diagram that led to the discovery of the Higgs Boson. 👀 https://t.co/w9ug4yfJc1" / Twitter[20191220]
What Makes the Hardest Equations in Physics So Difficult? (2018)  Hacker News[20191228]
Simulating physical reality with a quantum computer Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Jan 4, 19:35
[20190804]
the Synthetic Biology Open Language (SBOL)  a language for genetic design Tweet from John Carlos Baez (@johncarlosbaez), at Jan 17, 17:34 Planck
[20200227]
bollu.github.io  code + contents of my website, and programming life[20200306]
Spin, Statistics, CPT and All That Jazz[20200324]
Are quantum fields in any way similar to classical fields? /r/askscience That being said, a lot of research asking very fundamental questions about QM is happening, and it does not necessarily involve large colliders Tweet from Valentin Fadeev (@ValFadeev), at Jan 13, 11:03
 Tweet from @nntaleb
 New spaces in mathematics and physics https://ncatlab.org/nlab/show/New+Spaces+for+Mathematics+and+Physics
[20200507]
Physicists Criticize Stephen Wolfram’s ‘Theory of Everything’  Hacker News[20191213]
Simone Sturniolo on Twitter: "@InertialObservr @__{ice9} @tequehead That we observe a single eigenvalue isn't what interpretations are about. Interpretations try to explain WHY we do. Which is the whole problem." / Twitter[20191207]
Mathematical formulation of the Standard Model  Wikipedia[20191207]
Mathematical formulation of the Standard Model  Wikipedia[20191208]
newtonian mechanics  Antigravity in an infinite lattice of point masses  Physics Stack Exchange[20191208]
electrostatics  Paradox with Gauss' law when space is uniformly charged everywhere  Physics Stack Exchange[20191209]
AVƎ on Twitter: "If you're interested in the animated anatomy studies; Here's a 1 minute tute on how to make your own (You'll only need Zbrush) : https://t.co/RMlLZKSLH0 They've definitely helped me improve my understanding, hope they help you :) https://t.co/pXZew0PP9k" / Twitter[20191209]
AVƎ on Twitter: "2/6  Anatomy studies. Arm supination/pronation and flex.[20191210]
1/(1  1/(1  1/(1  Dan Piponi))) on Twitter: "An explanation of dimensional regularisation, one of the more bizarre sounding ideas in physics, applied to classical electrodynamics. Should make it accessible to a wider audience https://t.co/3Dj0eG3Brv (Spot the 1/ε subtraction, related to my recent "moral truth" example.)" / Twitter[20200511]
\mathcal{L} on Twitter: "Are there any good QFT visualizations that facilitate genuine understanding and don’t mislead?" / Twitter EPR is arguably the most controversial paper Einstein ever published,
 Tweet from Path Integral Salesman (@litgenstein), at Dec 31, 01:53
[20200413]
Your statement is 100% correct but misses the entire point  Lobsters [[security]] Tweet from @johncarlosbaez: In 1907 Einstein tried to combine special relativity with gravity  and very soon he realized gravity would make clocks tick slower, and would bend light
[20200115]
Path Integral Salesman on Twitter: "I’ve been reading a lot of old conference proceedings. Here are some from the 1927 Solvay Conference attended by Einstein, Planck, Pauli, Born, Lorentz, Schrödinger, etc. https://t.co/1mD4Fdk4GS Responding to Einstein, Bohr says: “I do not know what quantum mechanics is.” https://t.co/ybyKjp6EHK" / Twitter[20191225]
(1) John Carlos Baez on Twitter: "For more, see Hubert Goenner's article "On the history of unified field theories". Part I: https://t.co/vapByPYAi4 Part II: https://t.co/YBIqX120Gg" / Twitter [[qft]] Physics stuff
[20191202]
Paul Dirac: The Mozart of Science (2008)  Hacker News Tweet from George Corney (@Haxiomic), at Oct 1, 21:59 The author Wyatt Flanders makes incredible things! Here's his website https://t.co/RYAHVDDAM8 [[sim]] [[qft]]
[20191225]
(1) John Carlos Baez on Twitter: "Einstein worked obsessively on unified field theories until his death in 1955. He lost touch with his colleagues' discoveries in particle physics. He had an assistant try to teach him quantum field theory, but lost interest in a month. But there's more to this story… (6/n) https://t.co/f4C9e7iAHx" / Twitter Perhaps most spectacularly of all, in 2020, Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP*=RE. Here MIP* means the class of problems solvable using multiprover interactive proof systems with quantumly entangled provers (and classical polynomialtime verifiers), while RE means Recursively Enumerable: a class that includes not only all the computable problems, but even the infamous halting problem (!). To say it more simply, entangled provers can convince a polynomialtime verifier that an arbitrary Turing machine halts.
 key ceremonies [[study]] [[security]]
[20200709]
(1) 14 Subatomic Stories: Where Einstein failed quantum gravity  YouTube[20200714]
Maissam Barkeshli on Twitter: "1/ The study of topological quantum matter has been one of the most popular and exciting developments in physics in the last 15 years, although there has been a steady stream of amazing developments for the last 50 years." / Twitter[20200227]
bollu.github.io  code + contents of my website, and programming life Tweet from @johncarlosbaez
[20200709]
Спиральность частицы — Википедия[20200715]
Understanding quaternions and the Dirac belt trick (2010)  Hacker News Tweet from Statebox  ステートボックス (@statebox), at Dec 18, 18:38
[20200809]
Amazon.com: Lectures On Phase Transitions And The Renormalization Group (Frontiers in Physics) (9780201554090): Goldenfeld, Nigel: Books[20200819]
Michael Nielsen on Twitter: "Somehow, the combination: quasiparticles + statistics + universality / RG + equilibrium is just mindbogglingly rich." / Twitter[20200811]
Neutrino oscillation  Wikipedia[20200811]
quantum field theory  How does the Higgs mechanism work?  Physics Stack Exchange[20200811]
HiggsLectureNote.pdf  HiggsLectureNote.pdf[20200812]
How can SU(2) group has 3 dimensional representation?  Mathematics Stack Exchange [[reprtheory]] Tweet from @akivaw
[20200819]
Fundamental Forces
[20200819]
Brian Skinner on Twitter: "@michael_{nielsen} @sigfpe I like this example. Generally bosonic systems store heat/entropy much more easily than fermionic systems. In a boson system, all the particles can store heat, while in a fermionic system only the ones near the Fermi surface can." / Twitter [20200819]
Maissam Barkeshli on Twitter: "@michael_{nielsen} But we do live in a superconductor in a sense! The Higgs boson has condensed, which is the origin of mass, similar to how photons acquire mass in electronic superconductors. The idea of technicolor in particle physics is that the Higgs may be a pair of more fundamental fermions" / Twitter[20200820]
Vijay Mocherla on Twitter: "@michael_{nielsen} Check out the notes by David Tong from Cambridge. Ch3 of statistical physics notes is the shortest comprehensive summary of BEC I can think off. https://t.co/ED0PrMXvBK" / Twitter[20200821]
arXiv:0910.4855v1 [hepph] 26 Oct 2009  0910.4855.pdf[20200823]
special relativity  Why don't we construct a spin 1/4 spinor?  Physics Stack Exchange X Thus, in a given direction, the momentum has a maximum possible magnitude. The space of allowable momenta is called the Brillouin zone, and its shape depends on the arrangement of atoms in the crystal.
[20200811]
PPlect17.pdf lecture 17 – the Higgs Boson[20200813]
lomb2ndEd.pdf Lomb: Polyglot  How I Learn Languages[20200801]
Viktor T. Toth  KaluzaKlein theory Tweet from John Carlos Baez (@johncarlosbaez), at Sep 9, 08:09
[20190921]
ShtetlOptimized » 2013 » March The zone Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Oct 16, 08:49
 Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Aug 19, 14:45
 Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Aug 19, 14:51
 Tweet from John Carlos Baez (@johncarlosbaez), at Oct 16, 16:46
[20190824]
Greg Egan on Twitter: "[1/4]
Welcome to HopfWorld! Every point on the surface of our own world has been replaced by a circle, creating a threedimensional sphere in four dimensions. If you take a rotating slice through that 3sphere (as shown in the second image), this is what the slice looks like: https://t.co/Rn12So6iKf" / Twitter[20191009]
Три книги  Dee Mon. Былое и думы — LiveJournal GR tensor – it's the only way to construct it? (from Physics from Symmetry book) [[study]]
[20160925]
gravitational waves[20130215]
fusion[20200219]
wigner's friend experiment is different from shrodinger's cat in that the entangled observer (the friend) is conscious [[quantum]][20200826]
Van der Waals force  Wikipedia[20200705]
Feynman diagram  Wikipedia[20200713]
MathPages: Physics[20200711]
Cracking a Black Hole Paradox  Sixty Symbols  YouTube [[study]][20200714]
Reflections on Relativity [[read]] [[study]][20200718]
fine_{structure.pdf}[20200718]
The Lamb Shift
[20200718]
The Hydrogen 21cm Line [20200720]
Visualizing quaternions  3blue1brown + Ben Eater[20200720]
Wavefunction Visualizer[20200720]
Ask Ethan #36: The Amazing Spinning Electron  by Ethan Siegel  Starts With A Bang!  Medium[20200730]
algebraic geometer BLM on Twitter: "@KSHartnett @stevenstrogatz @QuantaMagazine Sad that there was no room for one of the main storylines, the love/hate relationship/competition between symplectic and complex geometry." / Twitter[20200731]
Алгебры Клиффорда, часть 1  VK Tweet from michael_{nielsen} (@michael_{nielsen}), at Aug 5, 22:37
 Classically, a scalar field is a collection of an infinity of oscillator normal modes. It suffices to consider a 1+1dimensional spacetime ℝ×S1, in which the spatial direction is compactified to a circle of circumference 2π, rendering the momenta discrete.
[20191019]
statistical mechanics  Is there any proof for the 2nd law of thermodynamics?  Physics Stack Exchange Tweet from David Holz (@DavidSHolz), at Nov 7, 21:36
[20191107]
Bartosz Milewski on Twitter: "@johncarlosbaez @sigfpe I even adapted his notation to profunctors. https://t.co/f7p0BErEip" / Twitter[20191110]
michael_{nielsen} on Twitter: "@predzemshara The IPCC report is surprisingly good  try assessment report 5. There are, of course, many many books. I enjoyed Daniel Schrag's EdX class, though it focuses more on the earthsystem aspect, and only gradually moves onto humancaused climate stuff." / Twitter [[climate]] Georgi–Glashow model  Wikipedia
[20200602]
(1) Sean Carroll on Twitter: "The Biggest Ideas in the Universe: idea #11 is Renormalization. We deal with "infinities" in quantum field theory by admitting that we don't understand arbitrarily high energies, and constructing "effective" theories instead. https://t.co/kZ8pnYJ5nA" / Twitter[20200619]
Breakthrough in inverse Laplace transform procedures  Hacker News[20200619]
Breakthrough in inverse Laplace transform procedures  Hacker News[20200626]
MathStory  Hilberts Problems(1).pdf[20200630]
(2) Introduction to Energy Band Theory  Material Science  YouTube [[study]][20200703]
D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i on Twitter: "@johncarlosbaez @sarah_{zrf} Yeah, symplectic integrators are the way to go. They often conserve notquiteenergy which is the wrong thing to conserve but it still stops things getting out of hand." / Twitter Tweet from @johncarlosbaez
[20200314]
Dave Burke on Twitter: "RNA looks like DNA except the T is replaced with a U. The RNA moves out into the cell and is used to build proteins it specifies. This DNA>RNA>protein sequence is called the central dogma of molecular biology." / Twitter[20200314]
Dave Burke on Twitter: "Every cell in your body contains your full DNA or genome (3 bn base pairs). But each cell doesn't use all of the instructions, e.g. a skin cell shouldn't make an iris. This is where gene expression comes in. DNA in the nucleus is first copied to short strands of RNA." / Twitter Geom algebra Vs vector
 Structure and Interpretation of Classical Mechanics  Wikipedia
 Tweet from @litgenstein
[20200428]
(1) The Holographic Universe Explained  YouTube [[physics]][20200429]
Tensors Explained Intuitively: Covariant, Contravariant, Rank  YouTube[20200429]
Tensors Explained Intuitively: Covariant, Contravariant, Rank  YouTube[20200430]
A theory of everything  Garrett Lisi  YouTube [[qft]] Tweet from @johncarlosbaez
[20200520]
Subatomic Stories: Antimatter  YouTube [[study]] Tweet from @litgenstein [[study]]
[20200612]
Joe Rogan Experience #1203  Eric Weinstein  YouTube [[study]] Tweet from @johncarlosbaez
 conductivity stuff [[physics]]
[20200623]
Majorana fermion  Wikipedia Tweet from John Carlos Baez (@johncarlosbaez), at May 10, 16:05
[20190214]
Why The Schrodinger Equation Fails at Relativity : Physics[20190126]
Locally constant function  Wikipedia
[20190126]
Math3ma [[cattheory]]  books [[study]] [[electronics]]
[20190211]
Life on the lattice [[qft]] [[qcd]][20190211]
[heplat/0506036] Lattice QCD for Novices [[qcd]]
[20190123]
pushout in nLab [[cattheory]] [20190126]
logic  How can a formal system ever be nonobviously unsound?  Mathematics Stack Exchange [[logic]][20190308]
(2) Slut_{jack} on Twitter: "Q: wat is Functor F A: you can add F to both ends a > b F a > F b Q: FullyFaithful F? A: rm F from both ends F a > F b a > b Q: L left adjoint to R? A: Pulling L right turns it to R A: Pulling R left turns it to L L a > b a > R b L a > b" / Twitter Nontransitive dice  Wikipedia
 Tweet from Jibran Haider (@jibranhaider), at Jan 2, 09:11 [[numeric]]
[20180610]
Hacker's guide to Neural Networks [[nn]][20180610]
How a Kalman filter works, in pictures  Bzarg[20181129]
myPhysicsLab Single Spring [[viz]][20181213]
Derivatives and dissections of data types  Lambda the Ultimate Really interesting and informative site about physical simulations and mechanics, and the maths behind it.👍👍👍 [[viz]] [[sim]]
 Tweet from John Carlos Baez (@johncarlosbaez), at Mar 23, 17:08 sheaf
 Linear algebra done right
[20190304]
plot of sin(z)/(z  mouse position) in the complex plane /r/math [[viz]] Tweet from John Carlos Baez (@johncarlosbaez), at Apr 10, 03:21 [[cattheory]] [[baez]]
 Tweet from ¬¬(Dan Piponi) (@sigfpe), at Apr 10, 22:05 [[cattheory]]
 Таким образом, любой, даже самый маленький электрический заряд черной дыры полностью меняет тип сингулярности в ее центре.
[20190424]
Fundamental polygon  Wikipedia[20180916]
The 5/8 Theorem  Azimuth[20190210]
klein bottle [[topology]][20190210]
armstrong p.138 van jampen theorem for simplicial complexes [[topology]] Tweet from John Carlos Baez (@johncarlosbaez), at May 12, 17:51 [[baez]]
 Fundamental Design Issues of Gradle Build System
 Tweet from Nikita Lisitsa (@lisyarus), at May 28, 15:10
 Tweet from Roman Elizarov (@relizarov), at May 20, 22:48
[20190318]
Product Spaces [[topology]][20171106]
https://www.reddit.com/r/AskElectronics/wiki/education [[electronics]] Физик оправдал принцип космической цензуры https://nplus1.ru/news/2019/06/19/censorship
 Visual complex analysis
[20190628]
John Carlos Baez on Twitter: "Fong and Spivak's book on applied category theory is coming out! I'm getting my copy in the mail soon! (cont)… "[20181129]
Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60): V. I. Arnold, A. Weinstein, K. Vogtmann: 9780387968902: Amazon.com: Books [[math]] [[physics]] короче очень советую, если ты хочешь немного инсайтов в статистикумлдатасаенс без хуйни https://medium.com/@kozyrkov Cassie Kozyrkov – Medium
 Tweet from Jamie Portsmouth (@jamportz), at Jan 3, 09:14 [[physics]] [[viz]]
 Sam Walters ☕️ on Twitter: "My Einstein paper is posted on arXiv. (It resulted from my MathPhysics Symposium talk.) https://t.co/b7qp6baxIJ… "
 Tweet from Derek Lowe (@Dereklowe), at Oct 11, 15:03 [[study]]
[20190407]
A Proposal for Proquints: Identifiers that are Readable, Spellable, and Pronounceable[20191109]
Formalizing expresiveness of line editors /r/dependent_{types} Tweet from Nikita Lisitsa (@lisyarus), at Nov 27, 08:41
 щас посмотрел видос пиздос, типа Планк не верил в фотоны (да и чуть ли не в атомы) до 20х годов
[20200522]
Physicists of reddits, what's the most Intetesting stuff you've studied so far?? /r/Physics[20200707]
A Concurrency Cost Hierarchy  Performance Matters https://arbital.com/p/bayes_rule_proportional/?pathId=36904
 Tweet from Eric Lengyel (@EricLengyel), at Jul 29, 11:11
[20190804]
Sameorigin policy  Wikipedia https://en.wikipedia.org/wiki/Sameorigin_policy[20190805]
Об Байеса  2: plakhov — LiveJournal[20190806]
reddit: the front page of the internet Tweet from @preskill
 Tweet from John Carlos Baez (@johncarlosbaez), at Aug 14, 03:29
[20191124]
Breit–Wheeler process  Wikipedia[20200414]
(1) We certainly do have formal derivations of Lorentz covariance and the Einste…  Hacker News
Drill
 S(N) is { det = 1 } U(N) is { M*M = 1 } [[drill]] [[reprtheory]]
[20190314]
lorenzian vs riemannian manifold {spacetime vs space} [[drill]][20190123]
exponentiating the observable results in representations [[reprtheory]] [[drill]][20190823]
Cook–Levin theorem  Wikipedia [[drill]] {Zu veil geld} too much money [[drill]]
[20190622]
universe is { 13.7 billion } years old [[drill]] Margoluslevitin theorem: limit on QC . Processing rate is or order {10 ** 33} op/s per joule. Or, system needs time about {h / E} to flip the state to orthogonal [[drill]]
[20200707]
Upgrading the Particle Physics Toolkit: The Future Circular Collider  Harry Cliff, John Womersley  YouTube [[study]] [[drill]]
 hmm, quantum fields seem to be very poorly visualised. I wonder if I can do better with something very simple [[viz]] [[qft]]
[20191101]
John Carlos Baez on Twitter: "Take the real numbers. Throw in some square roots of +1 and some square roots of 1, all anticommuting. You get a Clifford algebra. Clifford algebras are important in geometry and physics  we need them to understand spin! They also display some amazing patterns. (1/n) https://t.co/IlnbpTbBqN" / Twitter[20191001]
John Carlos Baez on Twitter: "@gregeganSF @monsoon0 @wtgowers @LauraDeming Okay, you've managed to cancel out any potential "insult" with an overload of praise. It was this paper: https://t.co/vlxpqR8G1w The stabilization hypothesis, homotopy hypothesis, cobordism hypothesis and tangle hypothesis are in here. No theorems, amusingly." / Twitter[20191030]
Jesper Cockx  Rewriting type theory /r/agda[20191112]
Sofia 🧹 on Twitter: "Follow up, matrix multiplication is essentially the unique solution to the following problem: given dot :: (j > a) > (j > b) > c derive mmul :: (i > j > a) > (j > k > b) > (i > k > c) the solution is: mmul as bs i k = dot (as i) (flip bs k)" / Twitter[20191112]
Nikita Lisitsa on Twitter: "Hence we are forced to include this bizarre state into consideration. Are we missing some more states? Surely we are. This all boils down to representations of the SO(3) group and how those behave under tensor product  this is known as ClebschGordan decomposition. (8/8)" / Twitter Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Nov 30, 19:14
 Tweet from michael_{nielsen} (@michael_{nielsen}), at Nov 30, 18:57
 Tweet from Quanta Magazine (@QuantaMagazine), at Dec 5, 19:02
 Tweet from michael_{nielsen} (@michael_{nielsen}), at Dec 6, 03:04
 Tweet from Juan Carlos ∞ (@PonceCampuzano), at Jan 8, 17:04
[20191230]
Path Integral Salesman on Twitter: "If you want to study physics but your life just does not permit you the time or energy to do maths rigorously (or, at least, however rigorously we physicists do maths), check out these 3 friendly texts: https://t.co/G62SmoXuPc https://t.co/uFCqVj4Exs https://t.co/1QhwJVOKBI https://t.co/ZWhDtvFyju" / Twitter[20200103]
vacuum[20191227]
mathematical_{offering.pdf}[20191227]
notes10.pdf[20191227]
404 Not Found[20191227]
404 Not Found[20191231]
Klein–Gordon equation  Wikipedia[20191231]
Schrödinger field  Wikipedia Tweet from @johncarlosbaez
 Tweet from @johncarlosbaez
 Tweet from @litgenstein
[20200307]
reference request  Atlaslike websites on specific areas of mathematics  MathOverflow[20200307]
Phil Lynch on Twitter: "My copy of the Bible finally arrived https://t.co/8XomO2d887" / Twitter[20200308]
On the shoulders of the giants  Hacker News Tweet from @johncarlosbaez
[20200319]
John Carlos Baez on Twitter: "@seanmcarroll The CRC Handbook of Chemistry and Physics. Imagine how much work it took to collect all that knowledge…" / Twitter
[20190129]
John Baez on Research Tactics  Machine Intelligence Research Institute [[research]] [[learning]] 
[20190521]
How I learn and practice music with anki /r/Anki [[music]] [[spacedrep]] 
[20190213]
The Frustrating Success of Our Best Theory of Physics – The Third Triumvirate [[relativity]] [[physics]]  https://vk.com/wall9471321_26902 Фундаментально ли время во Вселенной

[20200716]
Topology Illustrated  Mathematics Is A Science [20201203]
The fundamental Group of the Torus is abelian  YouTube[20201220]
Twostate quantum system  Wikipedia
[20201220]
Twostates_{03.tex}  Twostates_{03.pdf} [[quantum]] [[study]] [20201220]
The Feynman Lectures on Physics Vol. III Ch. 9: The Ammonia Maser[20150111]
Тензор энергииимпульса NATO phonetic alphabet  Wikipedia https://en.m.wikipedia.org/wiki/NATO_phonetic_alphabet [[study]]
 symplectic.ipynb [[symplectic]] [[tostudy]]
 Tweet from @gravity_{levity}
 Tweet from @nplusodin
 Tweet from @Dereklowe
 
 Tweet from @mekarpeles [[chinese]]
[20190805]
Metamorphisms  Bartosz Milewski's Programming Cafe https://bartoszmilewski.com/2019/01/03/metamorphisms/ Tweet from Nick Sharp (@nmwsharp), at Jul 24, 13:25
 
[20210122]
ECAP10 Joscha Bach on AI singularity.pdf[20210126]
Syllabus for Classics of Computer Science [[tostudy]] [[hci]][20190818]
kitspace/awesomeelectronics: A curated list of awesome resources for electronic engineers and hobbyists https://github.com/kitspace/awesomeelectronics[20190117]
Maldacena: The symmetry and simplicity of thelaws of physics and the Higgs boson https://arxiv.org/pdf/1410.6753.pdf[20190921]
A visual introduction to machine learning http://www.r2d3.us/visualintrotomachinelearningpart1/ [[ml]][20200724]
ShtetlOptimized » Blog Archive » The Busy Beaver Frontier [[toread]][20210317]
Can We Understand The Standard Model?  Azimuth [[towatch]] [[toread]][20210317]
Mathematics in the 21st Century  Azimuth [[towatch]][20210418]
Black Dwarf Supernovae  Azimuth
[20200119]
John Carlos Baez on Twitter: "Entropy is the amount of information you don't have about the random details of a system: what you'd need to describe those details. It takes 500 zettabytes to fully describe a gram of liquid water, but a manageable amount per molecule! (1/n) https://t.co/cDg7ZFpLt3" / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1218927345836285952
Entropy is the amount of information you don't have about the random details of a system: what you'd need to describe those details.
It takes 500 zettabytes to fully describe a gram of liquid water, but a manageable amount per molecule!
[20200217]
Nikita Lisitsa on Twitter: "Simulating Hamiltonian mechanics instead of MetropolisHastings algorithm: https://t.co/cVZiaTGP7u" / Twitter
pull tweet">https://twitter.com/lisyarus/status/1229487593684901889
Simulating Hamiltonian mechanics instead of MetropolisHastings algorithm:
[20200801]
Viktor T. Toth  Spinors in three dimensions
So what are spinors for anyway? Quantities that transform like a spinor appear in quantum mechanics: the coefficients in the Diracequation form a spinor, for instance, because when you rewrite the equation under a change of coordinates, in order for it to remain invariant, the Diraccoefficients must transform as spinors do.
ok, this is a very clear spinor explanation
[20200623]
Quantum vs. classical  Dee Mon. Былое и думы — LiveJournal
Потому, кстати, диаграммы с большим числом промежуточных узлов вносят очень малый вклад  там заряд в энной степени, и если он изначально мал, в энной степени выходит совсем мало. Кроме сильного взаимодействия, там он не так мал.
[20200715]
Understanding quaternions and the Dirac belt trick (2010)
https://arxiv.org/abs/1001.1778
[20190126]
general topology  What is a topological space good for?  Mathematics Stack Exchange [[topology]]
https://math.stackexchange.com/questions/1795583/whatisatopologicalspacegoodfor/1795995
Given topological spaces X,YX,Y, the product topology on X×YX×Y is the smallest topology which makes the projections continuous. (this also holds for infinite products)
Given a topological space XX and a subset AA, the induced topology on AA is the smallest topology which makes the inclusion continuous.
Given a topological space XX and an equivalence relation ∼∼ on XX, the quotient topology on X/∼X/∼ is the biggest topology which makes the projection continuous.
The topology induced by a metric on XX is the smallest topology which makes dd a continuous functions.
[20190223]
III Advanced Quantum Field Theory  QFT in one dimension (i.e. QM) [[qft]]
https://dec41.user.srcf.net/h/III_L/advanced_quantum_field_theory/2_4
visualising QFT [[viz]] [[qft]]
[20190211]
A new way of visualising quantum fields  IOPscience [[qft]] [[viz]]
https://iopscience.iop.org/article/10.1088/13616404/aaa032
[20190211]
software  Where can I find visualizations of quantum field theory equations?  Physics Stack Exchange [[qft]] [[viz]]
[20190211]
shit… so apparently it's pretty much impossible to visualise due to high number of states…
[20190211]
Proton quarks empty mass calculation GIF : askscience [[qft]]
https://www.reddit.com/r/askscience/comments/gyqaz/proton_quarks_empty_mass_calculation_gif/
The only way we've figured out for handling these calculations is to do them numerically, on a lattice. (In the computer program, we discretize space and time instead of having them be continuous.) Even with this, the calculations are notoriously hard to implement, but some of them turn out good results. That animation is the result of one of those.
right, so lattice QCD will result in something fruitful presumably
[20190211]
Derek Leinweber [[viz]] [[qcd]]
http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel/
hmm, no one seems to have visualised klein gordon, even numerically? [[quantum]] [[viz]]
[20190211]
(8) Empty Space is NOT Empty  YouTube [[qft]] [[viz]]
https://www.youtube.com/watch?v=J3xLuZNKhlY&feature=youtu.be
visualisation of vacuum for a proton sized box
[20190224]
Is it true that the Schrödinger equation only applies to spin1/2 particles?  Physics Stack Exchange
If we pretend the wave function is a classical field (which happens all the time during the "second quantization" procedure), then it turns out to describe a spin0 field. See Brian Hatfield's Quantum Field Theory of Point Particles and Strings, specifically chapter 2  on "Second Quantization".
But wait, there's more! If we consider other nonrelativistic fields and attempt quantizing, e.g. the Newton Cartan theory of gravity, we also get spin0 boson! For this result (specific to quantizing Newtonian gravity), see:
Joy Christian's "Exactly Soluble Sector of Quantum Gravity"
[20190506]
mm. can't say I really understand it..
The "vanilla" Schrodinger's equation (from nonrelativistic QM) does not describe a spin1/2 particle.
The plain, old Schrodinger's equation describes a nonrelativistic spin0 field.
[20190506]
for those interested in more on this, geocalc.clas.asu.edu/pdf/Consistency.pdf argues that "Schrodinger theory is identical to the Pauli theory when the electron is in an eigenstate of the spin"
[20190210]
(6) Quantum Spin  Visualizing the physics and mathematics  YouTube [[spin]] [[viz]]
https://www.youtube.com/watch?v=3k5IWlVdMbo&list=WL&t=0s&index=81
Eugene Khutoryansky
really good spin visualisations. ok, so spin is a unit quaternion, ok
[20190223]
III Advanced Quantum Field Theory  QFT in zero dimensions [[qft]] [[study]]
https://dec41.user.srcf.net/h/III_L/advanced_quantum_field_theory/1
[20190312]
really nice looking book!
[20190223]
Lagrangian formalism for fields  Scholarpedia [[lagrangian]] [[spinor]]
http://www.scholarpedia.org/article/Lagrangian_formalism_for_fields
[20190424]
pretty good motivation for the shape of lagrangian and examples with different kinds of fields
Tensors [[tensor]]
[20190424]
need to make sure I understand it and archive
[20190223]
Tensor Calculus [[tensor]]
https://ion.uwinnipeg.ca/~vincent/4500.6001/Cosmology/TensorCalculus.htm
This problem arises because of the very definition of the derivative. Differentiation involves comparing a quantity evaluated at two neighbouring points,
To define a tensor derivative we shall introduce a quantity called an affine connection and use it to define covariant differentiation.
[20190223]
Tensor derivative (continuum mechanics)  Wikipedia
https://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics)#Derivative_{of}_{the}_{inverse}_{of}_{a}_{second}order_{tensor}
[20190223]
Partial derivative of tensor with respect to tensor  Mathematics Stack Exchange
https://math.stackexchange.com/questions/2803090/partialderivativeoftensorwithrespecttotensor
[20190223]
partial differentiation of a variable w.r.t. its time derivative  Mathematics Stack Exchange
[20190223]
Tensors_{Poor}_{Man.pdf}
https://web2.ph.utexas.edu/~jcfeng/notes/Tensors_Poor_Man.pdf
some ok explanations for covariant derivatives ans some index notation
[20190211]
AharonovBohm Experiment [[quantum]] [[study]]
 State "START" from
[20190420]
https://physicstravelguide.com/experiments/aharonovbohm#tab__abstract
Functions that are not single valued can only exist in spaces that are not simply connected, or those that do not have trivial first homotopy group. We see that the manifold of the vacuum is thus the key to understanding the new physical result, and the topological defect gives us the intuition
[20190222]
Euler–Lagrange equation  Wikipedia [[lagrangian]]
https://en.wikipedia.org/wiki/Euler%E2%80%93Lagrange_equation
Derivation of onedimensional Euler–Lagrange equation
Derivation of onedimensional Euler–Lagrange equation – this section is actually the one that makes sense of it
[20190222]
basically
we have J = int F(x, f, f'). for any variaiton v, g_{e} = f + e v. So, F_{e} = F(x, g_{e}, g'_{e}) and J_{e} = int F(x, g_{e}, g'_{e})
next, total derivative: dJ_{e}/de = int dF_{e}/de dx
dF_{e}/de = dx/de pF_{e}/px + dg_{e}/de pF_{e}/pg_{e} + dg'_{e}/de pF_{e}/pg'_{e}
but dx/de = 0; dg_{e}/de = v and dg'_{e}/de = v'
in general we can't just replace pF_{e}/pg_{e} with pF/pf!!! but, we can use the fact that we are computing derivative at zero, and at zero g_{e} is equal to f.
so, we get dJ/dee=0 = int v(x) dF/df + v'(x) dF/df' = 0
use integration by parts to eliminate higher order derivatives of the variation
[20190223]
Einstein–Hilbert action  Wikipedia
https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action
[20190312]
some nice calculations involving tensor chain rule [[tensor]]
SO3 vs SU2 https://labcit.ligo.caltech.edu/~ethrane/Resources/seminar/Ch2.Spinors.pdf [[reprtheory]]
SU2 – threesphere; purely algebraically x^{2} + y^{2} + u^{2} + v^{2}
SO3 – more tricky
each rotation is described by unit vector n (two spherical angles) and rotation angle gamma (from 0 to pi)
we have a degeneracy (n, pi) = (n, pi)
these angles are ALSO a surface of a three sphere; but if we have a degeneracy, opposite points are identified
[20190319]
Quantum computing for the very curious [[qft]]
The standard model is an example of a particular type of quantum mechanical theory called a quantum field theory. John Preskill and his collaborators have written a series of papersFor a review of progress see: John Preskill, Simulating quantum field theory with a quantum computer (2018). explaining how to use quantum computers to efficiently simulate quantum field theories. Those papers don’t yet simulate the full standard model, but they do make considerable progress. It remains an exciting open problem, albeit a problem where much encouraging progress has been made.
[20190320]
What is the point of complex fields in classical field theory?  Physics Stack Exchange [[qft]]
Two real scalar fields ϕ1ϕ1 and ϕ2ϕ2 satisfying an SO(2)SO(2) symmetry and one complex scalar field ψψ are equivalent. However, the latter is more convenient because the particles made by ψψ and ψ†ψ† are each others' antiparticles. In the real case, the fields that have this property are ϕ1±iϕ2ϕ1±iϕ2, so once you change basis from ϕ1ϕ1 and ϕ2ϕ2 to ϕ1±iϕ2ϕ1±iϕ2 you've reinvented the complex scalar field.
This is explained nicely starting from p.53 in Sidney Coleman's QFT notes.
[20190215]
electromagnetism  Are electron fields and photon fields part of the same field in QED?  Physics Stack Exchange [[qft]]
In our modern understanding, every electron is thought to be a localized excitation of the electron (or Dirac) (spinor) field Ψ(xμ)Ψ(xμ), while every photon is considered to be an excitation of the photon (vector) field Aν(xμ)Aν(xμ), which is the quantum fieldtheoretic counterpart of the classical fourpotential.
[20190506]
The 'covariant derivative' Dμ≡∂μ+ieAμ encodes the interaction between the two fields Aμ and Ψ, and the 'strength' of the interaction is given by e, the charge of the electron.
[20190506]
hmm that sort of makes sense, because covariant derivatives gives the connection for fiber bundle, which is related to the gauges and that stuff??
[20190312]
Cambridge Notes [[math]] [[physics]]
https://dec41.user.srcf.net/notes/
[20190612]
some nicery rendered stuff
[20190312]
III Quantum Field Theory  Spinors
https://dec41.user.srcf.net/h/III_M/quantum_field_theory/4_1
read all these course notes over again
[20190328]
Simulation of Lattice QuantumChromodynamics and Other Lattice Models : TechWeb : Boston University [[viz]] [[qft]]
https://www.bu.edu/tech/support/research/visualization/gallery/latticeqcd09/
Tweet from Borja Sotomayor (@borjasotomayor), at Apr 2, 12:21 [[art]]
A liberal arts curriculum (like the one at @UChicagoCollege) makes you a more wellrounded individual, and builds a lot of crosscutting skills like good writing, critical thinking, building a good argument, etc. I didn't really appreciate that when I was younger.
pull tweet">https://twitter.com/borjasotomayor/status/1113038716929560578
[20190612]
huh. liberal arts means whole set of sciences, not just 'art'
[20190612]
do some of these? https://www.coursera.org/browse/artsandhumanities
[20190612]
graphic design could be interesting, 'modern art & ideas'; creative writing?
[20190424]
angular momentum  An electron has no known internal structure, does that imply it has an unknown one?  Physics Stack Exchange [[spin]]
Spin is a purely quantum mechanical phenomenon, it cannot be understood with classical physics alone, and every analogy will break down. It has also, intrinsically, nothing to do with any kind of internal structure.
(Nonrelativistic) spin arises simply because quantum things must transform in some representation of the rotation group SO(3)SO(3) in order for the operators of angular momentum to act upon them (and because we need to explain the degree of freedom observed in, e.g., the SternGerlach experiment. Since the states in the QM space of states are only determined up to rays, we seek a projective representation upon the space, and this means that we actually represent the covering group SU(2)SU(2). The SU(2)SU(2) representations are labeled by a number s∈N∨s∈N+12s∈N∨s∈N+12, which we call spin. Whether the thing we are looking at is "composite" or "fundamental" has no impact on the general form of this argument.
chirality and helicity
[20190424]
polarization  What is polarisation, spin, helicity, chirality and parity?  Physics Stack Exchange
Spin is determined from the representation of the Lorentz group the quantum field transforms in. The projective finitedimensional representations of the Lorentz group are labeled by two halfintegers (s1,s2)(s1,s2). The spin of a field is the sum s=s1+s2s=s1+s2. For example, a scalar transforms in (0,0)(0,0), a vector field in (12,12)(12,12), a Dirac spinor in (12,0)⊕(0,12)(12,0)⊕(0,12), and those have spin 00, 11 and 1212, respectively.
[20190424]
polarization  What is polarisation, spin, helicity, chirality and parity?  Physics Stack Exchange
What is polarisation, spin, helicity, chirality and parity?
good answer from acurious mind
[20190424]
What should be the intuitive explanation of wave equation?  Physics Stack Exchange
Observe that
(v2∂2∂x2−∂2∂t2)y=0
(v2∂2∂x2−∂2∂t2)y=0
can be factored as (which is what you probably mean by "squaring" in the question)
(v∂∂x+∂∂t)(v∂∂x−∂∂t)y=0
(v∂∂x+∂∂t)(v∂∂x−∂∂t)y=0
hmm…. wonder if that might help with solving wave equation in sympy
[20190208]
polarisation and helicity some derivations [[gauge]]
https://www.ippp.dur.ac.uk/~krauss/Lectures/QuarksLeptons/QED/QEDLagrangian_4.html
read rosetta stone again [[study]]
[20190605]
Gauge invariance  Scholarpedia
http://www.scholarpedia.org/article/Gauge_invariance
[20190620]
Jacopo Bertolotti on Twitter: "I am not satisfied yet, but this is my spin rotating around the xaxis, with the color representing the phase term common to both components of the spinor (which shows that you need two rounds to go back to the original state). I will work more on it in the next days.… https://t.co/ji4cYUNRu8" [[spinor]] [[viz]]
pull tweet">https://twitter.com/j_bertolotti/status/1141724827599941633
I am not satisfied yet, but this is my spin rotating around the xaxis, with the color representing the phase term common to both components of the spinor (which shows that you need two rounds to go back to the original state). I will work more on it in the next days.
[20190809]
also baez got a discussion in comments, so might help with my understaning! [[baez]]
Tweet from George Corney (@Haxiomic), at Oct 3, 00:08 [[sim]] [[qft]]
This realtime simulation of field equations coupling gravity, electromagnetism and chromodynamics is the coolest damn thing <3<3, by wyatt on shadertoy https://t.co/KSiohs52r7 https://t.co/Zg55xtkfOF
pull tweet">https://twitter.com/Haxiomic/status/1179112422503833601
[20191114]
John Carlos Baez on Twitter: "Murray GellMann won the Nobel prize for discovering "quarks":" protons, neutrons, and other baryons are made of 3 quarks, while pions, kaons and other mesons are made of a quark and an antiquark. But he got some help from his tennis partner! (1/n) https://t.co/YHGDNpvfZX" / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1195047685922807808
Murray GellMann won the Nobel prize for discovering "quarks":" protons, neutrons, and other baryons are made of 3 quarks, while pions, kaons and other mesons are made of a quark and an antiquark. But he got some help from his tennis partner!
[20191123]
https://en.wikipedia.org/wiki/Eightfold_way_(physics) [[study]]
Tweet from Nikita Lisitsa (@lisyarus), at Nov 22, 14:40
Went through the first 20 pages of this and already learned a lot. Seems to be an excellent overview & roadmap for learning QFT, Feynman diagrams, Standard Model, etc.
pull tweet">https://twitter.com/lisyarus/status/1197887639980068864
Tweet from Dr Martin Kleppmann (@martinkl), at Nov 15, 15:49
Fascinating quantum mechanics experiment: measurements are subjective to observers, suggesting that there is no objective reality at a quantum level https://t.co/mCF3jGiTk0
pull tweet">https://twitter.com/martinkl/status/1195302299465326592
[20191123]
Experimental test of local observer independence  Science Advances [[quantum]]
https://advances.sciencemag.org/content/5/9/eaaw9832
eh, still didn't quite get what are the mscroscopic consequences of that?
[20200511]
pull tweet">Mel Andrews 𓃻 on Twitter: "Explain mean field theory to philosophers in one sentence GO!" / Twitter
Nathaniel Virgo
@NathanielVirgo
Level 2:
Replying to
@bayesianboy
1/ Every part of a system interacts with its immediate surrounding parts, which interact with their surrounding parts, and so on. A mean field approximation consists of replacing this complex spatial structure by an assumption that every part of the system interacts with
11:20 PM · May 10, 2020·Twitter Web App
7
Likes
jestem króliczkiem
Tweet your reply
Nathaniel Virgo
@NathanielVirgo
·
9h
Level 3:
2/ the *average* of all other parts of the system, regardless of their spatial location or network structure. For deep and surprising reasons, this sometimes gives not just approximately the right answer, but *exactly* the right answer, at least in an infinite limit.
[20200511]
pull tweet">(1) jestem króliczkiem on Twitter: "@litgenstein I was hoping to work on some interactive Python notebooks based on this: https://t.co/yUd0TyTmQZ Will finally have some time to try it out soon!" / Twitter [[toblog]]
I was hoping to work on some interactive Python notebooks based on this: https://dec41.user.srcf.net/h/III_L/advanced_quantum_field_theory/ 1
Will finally have some time to try it out soon!
[20200525]
pull tweet">Valentin Fadeev on Twitter: "Hamiltonian or Lagrangian? Why choose when you can have the best of both (provided you have some cyclic coordinates). Enter Routhian. From L&L "Mechanics" §41. https://t.co/AcuXAxR4hf" / Twitter
Valentin Fadeev
@ValFadeev
Level 1:
Hamiltonian or Lagrangian? Why choose when you can have the best of both (provided you have some cyclic coordinates). Enter Routhian. From L&L "Mechanics" §41.
[20200623]
pull tweet">Nikita Lisitsa on Twitter: "Digging through "Introduction to Quantum Field Theory for Mathematicians" by Sourav Chatterjee. The first book with a title like this I've found that seems to actually do the job." / Twitter [[study]]
Digging through "Introduction to Quantum Field Theory for Mathematicians" by Sourav Chatterjee. The first book with a title like this I've found that seems to actually do the job.
[20200709]
Simulating physical reality with a quantum computer [[totweet]]
useful for my tweet thread for physical impl of quantum computations
[20200716]
pull tweet">(1) John Carlos Baez on Twitter: "A wonderful thing: any differentiable function from the complex numbers to the complex numbers preserves angles  except where its derivative is zero. So it's a conformal mapping! The complex numbers capture the geometry of angles in 2 dimensions. (4/n) https://t.co/NQBOMOFibR" / Twitter
A wonderful thing: any differentiable function from the complex numbers to the complex numbers preserves angles  except where its derivative is zero. So it's a conformal mapping!
The complex numbers capture the geometry of angles in 2 dimensions.
Qft rigorous book [[qft]]
(from hn)
Ballentine's book is a modern textbook that relies on that (as opposed to Shankar which you mentioned)
[20200718]
How can electrons be “topological”?  Gravity and Levity
[20200809]
Phase plane analysis: examples [[toblog]]
[20201220]
useful for they see me flowin they hatin
[20201120]
Quantum Field Theory visualized  YouTube
[20201020]
Dirac — Greg Egan
nice illustration of spinor states
[20200831]
I made an animation showing how a ring of N classical (left) or quantum (right) harmonic oscillators reproduces the physics of fields when N becomes large! (More details in comments) /r/Physics
Tweet from Nikita Lisitsa (@lisyarus), at Jul 17, 15:52
"... there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists."
Lamb, Antiphoton  quite an interesting read
pull tweet">https://twitter.com/lisyarus/status/1151504899907162112
https://www.google.com/url?q=https://www.math.tecnico.ulisboa.pt/~jnatar/MG03/Marsden/ms_book_ch7.pdf&sa=U&ved=2ahUKEwinuLe39freAhWLLMAKHUKTBFkQFjACegQIHBAB&usg=AOvVaw0VdF3GJLsrDR7x48z6XgBq
Tweet from Valentin Fadeev (@ValFadeev), at Oct 9, 01:21 dirac equation
Let's talk about the Dirac equation. What interesting physics can we extract from it using relatively simple manipulations? And why does it matter outside of highenergy world? Let's confine ourselves to the timeindependent case, and write it in components. (a long thread<<EOF) https://t.co/foe5zQmzpi
https://twitter.com/ValFadeev/status/1181726341844148224
[20191009]
Три книги  Dee Mon. Былое и думы — LiveJournal
https://thedeemon.livejournal.com/140306.html
КлейнГордон и Дирак логически вылезают из метрики пва Минковского. Ну и чуток постулирования, как и оное пространство с его метрикой. И с СТО математически КМ давно подружили, на этом вся КТП стоит. А вот как эти формулы понимать, что они говорят содержательно о мире  это вопрос интерпретаций. И тут не все одинаково хорошо справляются.
Про разложение в КТП есть такое, там при критическом анализе у математиков волосы дыбом встают, ряды частенько не сходятся. Но както получается у физиков на это наплевать и получать практически подтверждаемые результаты. :)
Но это не относится к вопросу интерпретации, это к вопросу вычислений.
thinking about schrodinger's cat experiment [[study]] [[think]] [[toblog]]
conscious actions arent' unitary
radioactive atom – necessarily interacts with the environment by entangling?
so let's say the atom starts stable (state 0> ) and the cat is alive: 0> A>
how does this end up in p_{a} 0> A> + p_{d} 1> D> after a certain time interval??? needs to be some kind of evolution?
it depends on the definition of D> and I guess here quantum immortality comes into play
actually I guess somehow the idea is that 1> A> is transformed into 1> D> somehow. This is def weird and something is missing
[20200721]
ah, ok, so transformation from A> to A> + D> is ok, it's unitary?
[20200811]
Higgs mechanism  Wikipedia
Fermions, such as the leptons and quarks in the Standard Model, can also acquire mass as a result of their interaction with the Higgs field, but not in the same way as the gauge bosons.
weinstein says yangmills equations are simpler? [[study]]
[20200915]
Higgs fermions and bosons
In this model, the particles acquire mass through spontaneous symmetry breaking; the W and Z as a result of a local gauge symmetry and the fermions, such as the muon, as a result of Yukawa couplings to the Higgs field – a novel type of interaction among fundamental particles that is not derived from a symmetry principle
[20201022]
Nyquist frequency  Wikipedia
[20200704]
Gluon  Wikipedia
It is often said that the stable strongly interacting particles (such as the proton and the neutron, i.e. hadrons) observed in nature are "colorless", but more precisely they are in a "color singlet" state, which is mathematically analogous to a spin singlet state.[7] Such states allow interaction with other color singlets, but not with other color states; because longrange gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.[7]
Tweet from @wickrotate
pull tweet">https://twitter.com/wickrotate/status/1280624828026740737
@wickrotate: @AsplingEric Try this https://t.co/A8Yk5kYMN6
Excellent article, need to reread and process [[study]]
[20200713]
On the Higgs Mechanism
[20200713]
On the Higgs Mechanism
However, there is one remaining case to consider. Suppose there exists a field ψi with nonzero Ki and with a nonzero selfinteraction coefficient kii. Such a field, in isolation, satisfies the equation
[20200713]
On the Higgs Mechanism
The particles have an effective mass only because of the existence of one special field, called the Higgs field, whose governing equation has a negative Ki and positive kii.
[20200713]
Selfenergy  Wikipedia
The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass.
[20200713]
Selfenergy  Wikipedia
The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of the Ward identity. The Wboson and the Zboson get their masses through the Higgs mechanism; they do undergo mass renormalization through the renormalization of the electroweak theory.
[20200713]
On the Higgs Mechanism
Consequently, whenever some quantity of energy is contained and prevented from propagating (macroscopically) at the speed c, the configuration has rest mass.
[20200713]
On the Higgs Mechanism
For example, a photon bouncing around inside a box with mirrored internal walls is microscopically massless and propagates at c as it travels from wall to wall, but the photon’s energy contained within the box contributes to the rest mass of the stationary box. Likewise the mass of an atom is not just the sum of the microscopic rest masses of the constituent elementary particles, it also has contributions from the bound kinetic energies of those particles, as well as the binding energies.
[20200713]
On the Higgs Mechanism
Thus it would be more accurate to say that all rest mass arises from mechanisms that constrain configurations of energy, preventing them from propagating (at least macroscopically) at the speed of light, which implies that they are (at least macroscopically) stationary in some inertial frame. The Higgs interaction is just one such mechanism, albeit one that operates on perhaps the most fundamental level.
[20200713]
Klein–Gordon equation  Wikipedia
Since the Higgs boson is a spinzero particle, it is the first observed ostensibly elementary particle to be described by the Klein–Gordon equation
[20200713]
Why don’t photons interact with the Higgs field?  Physics Stack Exchange
[20200713]
On the Higgs Mechanism
Even if we were previously unacquainted with the Dirac equation, these considerations might have led us to suspect that most elementary quantum fields have multiple components that would individually be massless and propagate at c, but that are mutually coupled together in a bound configuration of energy that possesses a rest frame.
[20200713]
On the Higgs Mechanism
Likewise the mass of an electron (for example) can be associated with the coupling between the two 2spinor components of Dirac’s model.
[20200714]
mathpages.com/home/kmath654/kmath654.htm [[readagain]]
[20200718]
Klein–Gordon equation  Wikipedia
The analogous limit of a quantum KleinGordon field is complicated by the noncommutativity of the field operator. In the limit v << c, the creation and annihilation operators decouple and behave as independent quantum Schrödinger fields.
[20200720]
dirac gif
[[https://www.gregegan.net/images/DiracAnimation.gif][DiracAnimation.gif (GIF Image, 500 × 330 pixels)]]
[20200724]
ShtetlOptimized » Blog Archive » Rosser’s Theorem via Turing machines
Why didn’t Gödel simply talk about soundness? Because unlike consistency or ωconsistency, soundness is a “metatheoretic” concept that’s impossible to formalize in F. So, if he used soundness, then the First Incompleteness Theorem couldn’t even be stated, let alone proved, in F itself, and that in turn would create problems for the proof of his Second Incompleteness Theorem.
[20200801]
Viktor T. Toth  Quaternions and the Dirac equation
One way to make this work is to have αi that satisfy the equation, αiαj+αjαi=ηij+ηji, where ηij is the Minkowskimetric.
[20200801]
Spinor Info – About physics and other things
Tweet from michael_{nielsen} (@michael_{nielsen}), at Oct 18, 20:59
Terrific paper by @johncarlosbaez and Ted Emory, explaining the meaning of the Einstein field equations for general relativity: https://t.co/drNd6NsAfE https://t.co/65fMVQR2tH
pull tweet">https://twitter.com/michael_nielsen/status/1185284280542322688
Tweet from John Carlos Baez (@johncarlosbaez), at Nov 29, 18:54
What's "free energy"? I don't mean energy you get for free. I mean the concept from physics: roughly, energy that you can use to do work.
More precisely, free energy is energy that you can use to do work at constant temperature. But why the fine print?
pull tweet">https://twitter.com/johncarlosbaez/status/1200473111029698560
Tweet from John Carlos Baez (@johncarlosbaez), at Nov 29, 19:21
But what's really going on here! In which situations does "free energy" make sense?
It's very general. We can define free energy whenever we have a finite set X with a probability distribution p and realvalued function E on it, and a number T called "temperature".
pull tweet">https://twitter.com/johncarlosbaez/status/1200480005119078400
[20200501]
[Gauge Symmetry The Physics Travel Guide
The best laymen explanation can be found in The symmetry and simplicity of the laws of physics and the Higgs boson by Juan Maldacena
ax
No, Quanta is fine  you're making a subtle error, which is in fact common even in graduate textbooks.
There are two distinct things going on here: formally "swapping" the arguments in the wavefunction, and physically moving the particles around. A priori, there is no reason the phase shifts from these two actions should be related.
You're focusing on the swap, but it's not interesting: your argument that the swap phase squares to 1 applies to both 2D and 3D equally well. When people talk about anyons, they're talking about the phase from moving the particles. That has more options in 2D because the paths one can take when moving particles around can have a greater range of topologies (https://en.wikipedia.org/wiki/Braid_group).
The reason that textbooks mix these things up is because in relativistic quantum field theories these two phases are always the same, by virtue of the spinstatistics theorem. But the anyons of condensed matter are nonrelativistic.
[20200624]
File:Metals and insulators, quantum difference from band structure.ogv  Wikipedia
[20200703]
pull tweet">america hater sarahzrf on Twitter: "@lisyarus …so conservation of energy is {H, H} = 0 when the hamiltonian is the same as energy, which i seem to recall being the case exactly when consrevation of energy is true 👀" / Twitter
...so conservation of energy is {H, H} = 0 when the hamiltonian is the same as energy, which i seem to recall being the case exactly when consrevation of energy is true
Tweet from @gregeganSF
https://twitter.com/gregeganSF/status/1307163276837441536
@gregeganSF: U(1) is the circle S^1 with points that add modulo 2π.
Its universal cover is the real line, (R,+).
Both have the same Lie algebra, so … apparently some physicists refer to the latter as “a noncompact U(1)”.
This is why they can’t have nice things.
https://t.co/PbmBsaVXAs
[20200323]
Black Holes Are Not Empty Voids. A Black Hole at the Heart! /r/Physics
The hydrogen atom is the simplest atom, and you ought to be able to understand it if you understand atoms at all [[study]]
todo
from ip A Math Puzzle Worthy of Freeman Dyson  Quanta Magazine
[20200526]
Novel insight reveals topological tangle in unexpected corner of the universe
[20200618]
pull tweet">John Carlos Baez on Twitter: "I love condensed matter physics! I hadn't even known dielectrons were a thing: normally electrons repel. But in a sodiumammonia solution, electrons pair up with opposite spins. Here's a new simulation of a dielectron, lasting 2.75 picoseconds: (2/n) https://t.co/onDLm8yP4S" / Twitter
I love condensed matter physics! I hadn't even known dielectrons were a thing: normally electrons repel. But in a sodiumammonia solution, electrons pair up with opposite spins.
[20200615]
Quote of the day: Physics · Andrew's Blog
If one wants to summarize our knowledge of physics in the briefest possible terms, there are three really fundamental observations: (i) Spacetime is a pseudoRiemannian manifold M, endowed with a metric tensor and goverened by geometrical laws. (ii) Over M is a vector bundle X with a nonabelian gauge group G. (iii) Fermions are sections of (S~+⊗VR)⊕(S~−⊗VR~). R and R~ are not isomorphic; their failure to be isomorphic explains why the light fermions are light and presumably has its origins in a representation difference Δ
in some underlying theory. All of this must be supplemented with the understanding that the geometrical laws obeyed by the metric tensor, the gauge fields, and the fermions are to be interpreted in quantum mechanical terms.
Edward Witten, “Physics and Geometry”, 1986
[20200414]
Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful—Stephen Wolfram Writings
Tweet from @lisyarus Quantum Chemistry Done Wrong
pull tweet">https://twitter.com/lisyarus/status/1251429402526846976
@lisyarus: Finished it: "Quantum Chemistry Done Wrong", by me,  a book about using numpy & scipy to solve some tiny quantumchemical systems. github.com/lisyarus/chembook/r…
SICM https://news.ycombinator.com/item?id=23155017
I posted this because it was recommended to me several times in [0], together with several other "computational approaches to Physics" books, and thought it would be interesting to HN users. If you're looking for more books like this, the whole Twitter thread is worth a read. It's full of good recommendations.
[0] https://twitter.com/dennybritz/status/1260137814982787073
[20201018]
Dan Girshovich  Foundations Journal Club. [[social]] [[study]] [[physics]]
I’ve been organizing the Foundations Journal Club, which meets online every few weeks. If you’d like to be included, shoot me an email.
[20201127]
eh, no rss
[20190805]
books http://math.ucr.edu/home/baez/books.html
Unruh effect
[20190902]
The Unruh Effect  Space Time  YouTube
https://www.youtube.com/watch?v=7cj6oiFDEXc&list=WL&index=3&t=0s
ok, interesting. basically the idea is that observer
with constant acceleration would generate an event horizon behind them
(the bigger acceleration the closer), because certain photos won't reach them ever.
Even temporary acceleration creates temporary Rindler horizons.
Then, it's similar to hawking radiation and for an accelerating observer it would create particles.
[20190902]
Эффект Унру — Википедия
https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%A3%D0%BD%D1%80%D1%83
Эффект Унру позволяет дать грубое объяснение излучения Хокинга, но не может считаться полным его аналогом.[4] При равноускоренном движении позади ускоряющегося тела тоже возникает горизонт событий, но разница в граничных условиях задач даёт различные решения для этих эффектов. В частности, подход, основанный на расчёте ограниченных интегралов по путям, даёт следующую картину для эффекта Унру: «тепловая атмосфера» ускоренного наблюдателя состоит из виртуальных частиц, но если такая виртуальная частица поглощается ускоренным наблюдателем, то соответствующая античастица становится реальной и доступна для детектирования инерциальным наблюдателем.[4] В этом случае ускоренный наблюдатель теряет часть своей энергии. В случае эффекта Хокинга для чёрной дыры, сформировавшейся в результате гравитационного коллапса, картина другая: появляющиеся в результате эффекта частицы «тепловой атмосферы» являются реальными. Эти частицы, уходящие на бесконечность, могут наблюдаться и поглощаться удаленным наблюдателем, однако, независимо от их поглощения, эти частицы уносят массу (энергию) чёрной дыры.[4]
[20190902]
Unruh effect  Wikipedia
https://en.wikipedia.org/wiki/Unruh_effect
The free field needs to be decomposed into positive and negative frequency components before defining the creation and annihilation operators. This can only be done in spacetimes with a timelike Killing vector field. This decomposition happens to be different in Cartesian and Rindler coordinates (although the two are related by a Bogoliubov transformation). This explains why the "particle numbers", which are defined in terms of the creation and annihilation operators, are different in both coordinat
[20190902]
What causes the Unruh effect? : askscience
https://www.reddit.com/r/askscience/comments/4s653u/what_causes_the_unruh_effect/
Because the accelerating and inertial observer can "see" different portions of spacetime (the accelerating observer sees only a wedge of spacetime bounded by a Rindler horizon). Therefore they are not bound to agree on what the state of minimum energy (the ground aka the vacuum) is, because inertial dude has access to a larger system.
[20190902]
Can someone explain the Unruh effect/radiation to me? How are virtual particles forced into existence if they are nothing but convenient mathematical models and don't actually exist? : askscience
From "Spacetime and Geometry, an Introduction to General Relativity" by Sean Carroll, chapter 9, pg. 412:
If the Rindler observer is to detect background particles, she must carry a detectorsome sort of apparatus coupled to the particles being detected. But if a detector is being maintained at constant acceleration, energy is not conserved; we need to do work constantly on the detector to keep it accelerating. From the point of view of the Minkowski observer, the Rindler detector emits as well as absorbs particles; once the coupling is introduced, the possibility of emission is unavoidable. When the detector registers a particle, the inertial observer would say that it had emitted a particle and felt a radiationreaction force in response. Ultimately, then, the energy needed to excite the Rindler detector does not come from the background energymomentum tensor, but from the energy we put into the detector to keep it accelerating.
So from "our" perspective as inertial observers, the accelerating observer is detecting particles due to a sort of backemf countering whatever is accelerating her. The accelerating observer interprets this as her passing through a thermal spectrum of particles instead.
Эффект Унру — Заметки о теоретической физике
https://susy.written.ru/2011/02/28/Unruh_effect
[20200719]
Talk:Photon/Photons and Mass Debate3  Wikipedia
Weight/mass of single photon in a box bouncing up and down
[20200719]
quantum mechanics  Einstein's box  unclear about Bohr's retort  Physics Stack Exchange
[20200719]
energy  Explain how (or if) a box full of photons would weigh more due to massless photons  Physics Stack Exchange
from Lisitsa: алгебры клиффорда и спинорные группы [[towatch]]
pull tweet">https://twitter.com/lisyarus/status/1186739246650052614
https://www.lektorium.tv/course/22937
@johncarlosbaez @zariskitopology @silvascientist I now realized that I do know an excellent source, but sadly it is on video and only in Russian
[20190414]
CFDPython/14_{Step}_{11.ipynb} at master · barbagroup/CFDPython [[ipython]]
https://github.com/barbagroup/CFDPython/blob/master/lessons/14_Step_11.ipynb
go throught and make sure I understand how I compute things…
[20190125]
Schrödinger Equation https://physkcstravelguide.com/equations/schroedinger_equation#tab__faq
Schrodinger's equation can be derived using symmetry arguments. Specifically, you write out the commutation relations that exist between the generators of the Galilei group and then choose the position representation. What you find is that the generator of time translations has the same form that is usually ascribed to the Hamiltonian. Details can be found, for example, in the third chapter of Ballentine's "Quantum Mechanics: A Modern Development"
Schrödingers equation can be derived by using Galilei invariance: "I encourage everyone to learn the derivation of Schrödinger's equation straight from the representation theory of the Galilei group! It's cool. (I think it appears in the books by Mackey and Jauch listed here.)" http://math.ucr.edu/home/baez/symmetries.html > Page 209 in Josef M. Jauch, Foundations of Quantum Mechanics page V (I.e. chapter 125)
[20190123]
Everything about Representation theory of finite groups : math [[reprtheory]]
Then RH psi = R E psi, which means H (R psi) = E (R psi), so (R psi) is a new eigenfunction which has the same energy as the original. We can continue with all operations in the group to find all the degenerate wavefunctions corresponding to the eigenvalue E
[20190506]
These representations are unique up to a change of basis (equivalent to a similarity transform), so this means each possible eigenvalue of the Hamiltonian 'belongs' to a certain representation of the group of the Schrodinger Equation.
[20190506]
Also remember that each eigenvalue has its own representation, so different eigenvalues of the same Hamiltonian can have different degeneracy.
[20190123]
Normally, if the degeneracy cannot be explained by symmetry then it is known as an 'accidental' degeneracy, but Fock showed that there is actually a set of operations in 4D which exploits the symmetry. The hydrogen potential has the group O(4), and you should be able to understand most of the language in the introduction here.
[20190114]
(2) Quantum Tunneling  Complex Plot  YouTube [[quantum]] [[viz]]
https://www.youtube.com/watch?v=BI7dbp3uIdY
Nikita Lisitsa on Twitter: ""When a classical physics problem is described by a variety, some magic happens. The process of quantization becomes completely systematic—and surprisingly simple." @johncarlosbaez Would you be so kind to provide any reference on this?"
pull tweet">https://twitter.com/lisyarus/status/1101210066059964418
[20190506]
http://math.ucr.edu/home/baez/gq/
¬¬(Dan Piponi) on Twitter: "What I find confusing is that I learnt QFT two different ways: (1) pretending univariate wavefunction is classical and quantizing again & (2) considering multivariate wavefunctions. Not obvious these get you to the same place.… https://t.co/uaw1AZIEDz" [[qft]]
pull tweet">https://twitter.com/sigfpe/status/1101554393126584320
What I find confusing is that I learnt QFT two different ways: (1) pretending univariate wavefunction is classical and quantizing again & (2) considering multivariate wavefunctions. Not obvious these get you to the same place.
[20190413]
pull tweet">https://twitter.com/johncarlosbaez/status/1101541977105981440 Furthermore unitary time evolution in a Hilbert space is a fine classical dynamics. So, we can quantize a classical system, get a Hilbert space, and treat that as a classical system and quantize it again. This is a nice way to get Fock space
hmm….
[20190407]
Field Play [[viz]]
[20190424]
nice vizualisation for 2D vector fields, allows to change integration parameters etc
На пути к теории всего https://nplus1.ru/material/2018/02/02/justlookingforsomeaction
Самым простым таким инвариантом является детерминант метрики. Тем не менее, если мы включим в действие только его, мы не получим дифференциальное уравнение, поскольку это выражение не содержит производных метрики. А если уравнение не является дифференциальным, оно не может описывать ситуации, в которых метрика меняется со временем. Поэтому нам нужно добавить к действию простейший инвариант, который содержит производные gμν. Таким инвариантом является так называемый скаляр Риччи R,
[20190317]
Quantum electrodynamics  Wikipedia [[qed]]
https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathematics
I first saw this kind of explanation in Steve Vickers' Topology via Logic, which is an excellent little book [[study]] [[topology]]
revise cs/math/physics stuff [[habit]] [[spacedrep]]
def need more systematic way of rehearsing
[20181223]
Integral manipulations · Issue #5396 · sympy/sympy
https://github.com/sympy/sympy/issues/5396
The Born Rule Has Been Derived From Simple Physical Principles  Quanta Magazine
The Born rule itself, he said, is thus an example of Wheeler’s “law without law.”
Easier than harmonic oscillator: repulsive potential? Admits both trajectories
start following one of scott aaronsons posts about motivation for square probability rule and play with equations [[quantum]] [[viz]]
[20190126]
A Neighborhood of Infinity: What's all this E8 stuff about then? Part 1. [[reprtheory]]
http://blog.sigfpe.com/2007/11/whatsallthise8stuffaboutthenpart.html
[20190211]
A Journey to The Manifold SU(2): Differentiation, Spheres and Fiber Bundles [[study]]
https://www.physicsforums.com/insights/journeymanifoldsu2mathbbcpart/
really read this through and try to understand all the definitions. e.g. coordinate charts etc
[20190110]
www.math.lsa.umich.edu/~idolga/lecturenotes.html [[math]] [[physics]] [[lagrangian]]
http://www.math.lsa.umich.edu/~idolga/lecturenotes.html
shit.. some interesting mathematical details about metric from the very beginning
[20190123]
Charts on SO(3)  Wikipedia
 State "STRT" from
[20190424]
https://en.wikipedia.org/wiki/Charts_on_SO(3)#The_{hypersphere}_{of}_{rotations}
[20190424]
shit.
Problems of this sort are inevitable, since SO(3) is diffeomorphic to real projective space P3(R), which is a quotient of S3 by identifying antipodal points
S^{3} is a 4 dim sphere! hmm. although perhaps it's same thing as 3ball with opposite points identified?
another thought: if you have a disk with opposite points identified – which topology does it have?? it's not same as torus right?
[20190123]
3D rotation group  Wikipedia
https://en.wikipedia.org/wiki/3D_rotation_group
Consider the solid ball in R3 of radius π (that is, all points of R3 of distance π or less from the origin). Given the above, for every point in this ball there is a rotation, with axis through the point and the origin, and rotation angle equal to the distance of the point from the origin. The identity rotation corresponds to the point at the center of the ball. Rotation through angles between 0 and −π correspond to the point on the same axis and distance from the origin but on the opposite side of the origin. The one remaining issue is that the two rotations through π and through −π are the same. So we identify (or "glue together") antipodal points on the surface of the ball. After this identification, we arrive at a topological space homeomorphic to the rotation group.
[20190124]
How is a Lie Algebra able to describe a Group? – Jakob Schwichtenberg [[lie]]
http://jakobschwichtenberg.com/liealgebraabledescribegroup/
well, ok, so the point we can associal lie algebra elements with lie groups elements via exponentiation
[20190123]
Group Theory and Physics  S. Sternberg  Google Books
[20190201]
List of Fundamental Groups of Common Spaces  Mathonline
http://mathonline.wikidot.com/listoffundamentalgroupsofcommonspaces
[20181124]
Seminar: Fall 2008 [[baez]]
http://math.ucr.edu/home/baez/qgfall2008/
Nikita Lisitsa on Twitter: "The rep.theory book by Fulton & Harris demonstrates the idea of restricting to an abelian subgroup (which is fundamental for Lie groups) using S₃ as an example (rather than, say, SL(n)) and it is beautifully simple and understandable."
pull tweet">https://twitter.com/lisyarus/status/1101517866250186752
[20181110]
User ACuriousMind  Physics Stack Exchange
 State "STRT" from
[20190424]
https://physics.stackexchange.com/users/50583/acuriousmind
[20190424]
https://physics.stackexchange.com/users/50583/acuriousmind?tab=questions&sort=votes
[20190123]
quantum mechanics  Spin operators in QM  Physics Stack Exchange [[spin]]
https://physics.stackexchange.com/questions/295412/spinoperatorsinqm
to be precise, in quantum mechanics we are interested in projective representations because physically, two vectors that differ by a phase are indistinguishable.
[20190126]
* To semidecide this, just start generating every possible proof.
https://perl.plover.com/classes/datatopology/samples/slide007.html
Gödel's first incompleteness theorem:
This property is semidecidable, but not decidable.
[20190126]
* Suppose the property N[D[_{x}_]D](_{y}_) = (_{x}_ ≠ y) is semidecidable for each x
https://perl.plover.com/classes/datatopology/samples/slide020.html
Suppose the property Nx(y) = (x ≠ y) is semidecidable for each x
Then the set { x } is closed for each x
Then the space is Hausdorff
[20190223]
homework and exercises  Functional Derivative of action  Physics Stack Exchange
https://physics.stackexchange.com/questions/229200/functionalderivativeofaction
[20190223]
resource recommendations  What is a complete book for introductory quantum field theory?  Physics Stack Exchange
Mark Srednicki, Quantum Field Theory. I really like the organisation and design of the book, which consists of around a hundred of short and essentially selfcontained chapters that introduce a single topic, discuss it in the necessary level of detail, and move on to the next topic.
[20190226]
Is there a reason why a relativistic quantum theory of a single fermion exists, but of a single scalar not?  Physics Stack Exchange
[20190506]
eh, can't say I understood any of arguments
[20190210]
general topology  Triangulation of torus  understanding why  Mathematics Stack Exchange [[topology]]
https://math.stackexchange.com/questions/1772650/triangulationoftorusunderstandingwhy
In a triangulation (specifically, a simplicial complex), the three vertices of a triangle are distinct.
right, maybe for computational and efficiency purposes it would be ok to generate pseudo triangulations
[20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience
Although the action S may not generally have a meaningful interpretation, there is an alternative formulation of the ELequations which gives an equation that gives the value of S directly but not the function that achieves the minimum value of S. This equation is called the HamiltonJacobi equation, and is also a very widely studied equation, particularly in the context of conservation laws and symplectic geometry. The standard method of solving the HJequation is by the method of characteristics. The characteristic equations are precisely the Hamiltonian equations also learned in a typical mechanics course.
[20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience
At this point you can look in any standard text to see what happens next. The gold standard in calculus of variations is the text by Gelfand & Fomin (I strongly recommend this text, and it's also very cheap). The punchline here is twofold.
The minimum value of S is guaranteed to exist under certain conditions on L. (Most of the standard theorems require some sort of convexity condition on L.)
Under the same conditions, the minimum value of S (and which functions achieve that minimum) can be found by solving the associated EulerLagrange equations, which is a set of coupled, nonlinear partial differential equations. (The ELequations are found by using L.)
[20190214]
What is a Lagrangian? What is the action? Why does the principle of least (stationary) action work? : askscience
This study started in the 1930s (?), and Douglas discovered necessary and sufficient conditions for a Lagrangian to exist. These conditions, which you would think should be called the Douglas conditions, are called the Helmholtz conditions. (Douglas was a mathematician who won a Fields Medal for his work in the calculus of variations, specifically in the theory of minimal surfaces (think: soap films).) These conditions though are not at all easy to verify though. The conditions are of the form "Lagrangian exists if there is a nonsingular matrix G such that (1), (2), and (3)". The first condition is purely algebraic, the second condition is that a certain ODE for the components of G have a solution, and the third condition is that a certain system of coupled PDE's for the components of G have a solution. The third condition is the one that is not at all easy to verify.
[20190210]
general topology  Why aren’t continuous functions defined the other way around?  Mathematics Stack Exchange [[topology]]
[20190223]
From Griffiths to Peskin: a lit review for beginners  An American Physics Student in England
https://fliptomato.wordpress.com/2006/12/30/fromgriffithstopeskinalitreviewforbeginners/
[20190222]
general relativity  Why do we select the metric tensor for raising and lowering indices?  Physics Stack Exchange
If your manifold is guaranteed to carry other nondegenerate 2tensors, then you may use those as well to raise and lower indices (though the meaning is different from that of raising and lowering with the metric). This is the case, for instance, if your manifold is symplectic (i.e. carries a closed, nondegenerate 2form ωω).
https://math.stackexchange.com/questions/36683/mathandmusictheorybooks [[musictheory]]
 State "STRT" from "TODO"
[20190221]
The Reference Frame: Why are there spinors? [[spinor]]
https://motls.blogspot.com/2012/04/whyaretherespinors.html
jeez, this guy is a graphomaniac…
[20190222]
Book_{Chapter}_{Lagrangian.pdf}
chromeextension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdf_{viewer.html}?r=http://www.physicsquest.org/Book_Chapter_Lagrangian.pdf
whoa. that's something interesitng
[20190223]
lec33.dvi  lec33.pdf
chromeextension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdf_{viewer.html}?r=http://www.tapir.caltech.edu/~chirata/ph236/201112/lec33.pdf
ok, this is kind of on the right track
[20190223]
radiation.dvi  radiation.pdf
chromeextension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdf_{viewer.html}?r=http://www.iphc.cnrs.fr/IMG/pdf/radiation.pdf
ok, at least here they are treating variations with asymptotic terms…
Yoneda [[yoneda]]
[20180731]
Soham Chowdhury on Twitter: "Vakil (in his book, or perhaps on MO) likens the Yoneda lemma to a particle accelerator, in that if you know how a particle reacts to being smashed into by other particles, you know everything about it… https://t.co/jtdQupZoGH"
pull tweet">https://twitter.com/mrkgrnao/status/979353398225993728
Vakil (in his book, or perhaps on MO) likens the Yoneda lemma to a particle accelerator, in that if you know how a particle reacts to being smashed into by other particles, you know everything about it
[20180731]
From the Yoneda lemma to categorical physics
https://www.classe.cornell.edu/spr/199909/msg0017972.html
[20180808]
🇪🇸🇵🇹_{jack} on Twitter: Yoneda
pull tweet">https://twitter.com/Iceland_jack/status/1018229009786826752
[20180808]
Understanding Yoneda  Bartosz Milewski's Programming Cafe
https://bartoszmilewski.com/2013/05/15/understandingyoneda/
[20180808]
The Yoneda Lemma — Math3ma
http://www.math3ma.com/mathema/2017/9/14/theyonedalemma
[20190223]
Introduction to the Modern Theory of Dynamical Systems  Anatole Katok, Boris Hasselblatt  Google Books [[lagrangian]]
https://books.google.co.uk/books?id=9nL7ZX8Djp4C&pg=PA367&lpg=PA367&dq=%22euler+lagrange%22+solutions+%22global+minimum%22&source=bl&ots=oUmdX3lEHJ&sig=lWeYTxDvVFemkLadlfSg7rgc8_8&hl=en&sa=X&ved=2ahUKEwjF4c7ukoDfAhU9SxUIHatDDmYQ6AEwD3oECA8QAQ#v=onepage&q=%22euler%20lagrange%22%20solutions%20%22global%20minimum%22&f=false
sufficiently long segments cease to be the minimum..
[20190304]
A Python utility for analyzing a given solution to the Einstein field equations. /r/Python
I wanted to share with the community an open source python package I had been developing since November. It is called Spacetime Engine.
[github.com/spacetimeengineer/spacetimeengine](https://github.com/spacetimeengineer/spacetimeengine)
My name is Michael. I am a physicist who works as an engineer. My story is that in October 2018 I was preparing to submit my first physics publication, which reviewed a particular cosmological model that I had been working with for some time. I was at the point where I had completed all of my research and was fully prepared. The only problem was that at the time I felt concerned that I may have made some mistakes which went unnoticed, so I decided to write a computer algebra software to check the veracity of my solutions so that I could feel confident in my results. After using this new utility, I realized I had made some fairly significant errors in my approach, and so the software apparently did it’s job. At first I was quite frustrated because I had put a significant amount of time into this solution, but I realized I had a new ability to correct my own errors and expand upon what I already knew. I was now able to study any solution, and not just the ones that interested me. In fact, anyone could study any solution to the Einstein field equations if they wanted to by using this software. For this reason I realized the research I wanted to publish was not yet ready to be submitted, but the software became the real publication. I then decided to polish, package, and publish the code into a form that was accessible, informative, and educational. If you are a student new to general relativity, a gravity researcher actively working with solutions to the Einstein field equations, or an engineer who is interested in importing some of the functionality, then this package should come in handy. I was not able to publish my physics research, unfortunately, but I felt that this project served as a good alternative, and perhaps had more potential value. If you have technical questions, use the Github tools to communicate with me. You can install the package with
[20190319]
Gödel metric  Wikipedia
https://en.wikipedia.org/wiki/G%C3%B6del_metric
[20190331]
quantum mechanics  Relation between radio waves and photons generated by a classical current  Physics Stack Exchange
[20190223]
I've been making a gravity simulator using RustSDL2! Source is in the comments, hope you enjoy it! /r/rust [[sim]]
Higgs
[20190211]
Higgs Mechanism
https://physicstravelguide.com/advanced_notions/symmetry_breaking/higgs_mechanism#tab__faq
“In summary, the Higgs mechanism accounts for about 1 per cent of the mass of ordinary matter, and for only 0.2 per cent of the mass of the universe. This is not nearly enough to justify the claim of explaining the origin of mass”.
[20190211]
Higgs Mechanism
(Breaking of gauge symmetry is a bad thing, because the renormalizability, i.e. the removing of the infinities that popup in most quantum field theory calculations, depends on the existence of gauge symmetry
[20190211]
Demystifying the Higgs mechanism – Jakob Schwichtenberg
http://jakobschwichtenberg.com/higgsintuitively/
[20190424]
I thunk I should postpone reading about the Higgs etc until I start properly understanding photons at least.
[20190424]
at.algebraic topology  How to demonstrate (SO(3)) is not simply connected?  MathOverflow
https://mathoverflow.net/questions/22975/howtodemonstrateso3isnotsimplyconnected
here are two kinds of loops on the unit ball with antipodal identifications in the boundary: either it's also a loop in the ball (without identifications) or else it starts and ends at antipodal points. The example curve in the question is of the latter kind. It seems intuitive that any continuous deformation of this curve which remains closed has to still connect antipodal points, since you cannot move the ends closer to each other  which is what you'd have to do in order to get a contractible loop  while keeping it a closed curve.
hm, good point, I have to move both points on the sphere?
[20190424]
Real projective plane  Wikipedia
https://en.wikipedia.org/wiki/Real_projective_plane
The projective sphere[edit]
Consider a sphere, and let the great circles of the sphere be "lines", and let pairs of antipodal points be "points". It is easy to check that this system obeys the axioms required of a projective plane:
any pair of distinct great circles meet at a pair of antipodal points; and
any two distinct pairs of antipodal points lie on a single great circle.
[20190424]
mass  Why is the (S_{z} =0) state forbidden for photons?  Physics Stack Exchange
physics.stackexchange.com/q/73911 . For photon we use helicity, not spin, because massless representations of the Poincare group can't be characterized by the spin. – user8817 Aug 31 '13 at 17:27
[20190424]
mass  Why is the (S_{z} =0) state forbidden for photons?  Physics Stack Exchange
Massless particles with spin do not have a "Sz=0Sz=0" state because they actually do not have spin like massive particles do. They have helicity, which is the value of the projection of the spin operator onto the momentum operator. The reason for this is the representation theory of the group of spacetime symmetry, the Poincaré group.
[20190426]
Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics  YouTube [[viz]]
https://www.youtube.com/watch?v=FoR3hq5b5yE
at 9:11 interesting visual explanation why the force is not decreasing for strong nuclear force
[20190117]
Quantum Diaries
https://www.quantumdiaries.org/2014/12/01/standardmodelintroduction/
In fact, electric charge is a combination of hyper and isospin charges.
[20190117]
Quantum Diaries
https://www.quantumdiaries.org/2014/12/01/standardmodelintroduction/
Mass and Electroweak Symmetry Breaking: In the early universe, all elementary fermions and gauge bosons were massless. At some point, everything underwent a phase transition that broke the hypercharge and isospin conservation laws. During this phase transition, quarks and charged leptons acquired mass
[20190210]
classification theorem [[topology]]
compact closed surfaces are spheres with handles and klein bottles (remove a disk, attach the mobius strip, which has a circular surface)
renormalisation group flow
group of physicists and mathematicians is studying a geometric object called an “amplituhedron” that has the potential to further simplify calculations of particle interactions.
todo
from ip How Feynman Diagrams Revolutionized Physics  Quanta Magazine
Slowly start learning IPA? Use spaced repetition
Sight reading on computer keyboard [[piano]]
[20190519]
could at least do it in pairs
Why is the phase picked up during identical particle exchange a topological invariant?  Physics Stack Exchange
The Difference Between 3/4 & 6/8 Time (with examples)  School of Composition [[music]]
https://www.schoolofcomposition.com/whatisthedifferencebetween34and68time/
[20190510]
"Higher Homotopy Groups Are Spooky: Enter the world of 3dimensional holes in 2dimensional objects". A blog post by Evelyn Lamb. /r/math
[20190325]
(2) Dirac equation: Zitterbewegung in two dimensions  YouTube
https://www.youtube.com/watch?v=uJjOiNehZ3c
[20190601]
Topological Quantum Computer  Professor John Preskill, Caltech  YouTube [[qcomp]]
https://www.youtube.com/watch?v=igPXzKjqrNg
[20181223]
Quantum Python: Animating the Schrodinger Equation  Pythonic Perambulations [[viz]] [[python]] [[matplotlib]]
https://jakevdp.github.io/blog/2012/09/05/quantumpython/
[20190208]
Spare me the math: the Lamb Shift  Gravity and Levity [[quantum]]
https://gravityandlevity.wordpress.com/2013/04/24/thelambshift/
some supposedly simple argument about Lamb shift… still need to follow more carefully. maybe, visualise?
Tweet from Igal Tabachnik (@hmemcpy), at Oct 21, 20:23 Category Theory for Programmers by @BartoszMilewski is now complete, and available for purchase in hardcover! [[cattheory]]
Category Theory for Programmers by @BartoszMilewski is now complete, and available for purchase in hardcover!
As always, the PDF is free, and available online!
Hardcover: https://t.co/2nsnzq1dFu
PDF: https://t.co/UzrVSy9IyV https://t.co/H5w8E0G9Uu
pull tweet">https://twitter.com/hmemcpy/status/1054089875526504452
Todo visualise that??? [[viz]]
Right at the critical point, something very cool happens: the system transforms in a simple way under scaling! What does this mean? Well, if you get some water right at the critical point, it looks "opalescent" like a moonstone. If you stare at it carefully, you'll see a bunch of liquid water droplets of all different sizes floating around in steam. However, if you look closely at any of these droplets, you see they are full of bubbles of steam, and if you look closely at the steam, you see it's full of little droplets of liquid! It's like a random fractal: no matter how closely you look, you see the same thing. You can't tell if you're looking at water droplets in steam or bubbles of steam in water, and there is no distinguished length scale... at least until you get down to the scale of atoms, that is.
from renormalization http://math.ucr.edu/home/baez/renormalization.html
[20190117]
Looking inside the standard model: Electromagnetism, photons, and symmetry
https://axelmaas.blogspot.com/2010/10/electromagnetismphotonsandsymmetry.html
Now, the relation between the four convenient numbers and the two important ones is quite in analogy to this case, and is therefore also a U(1) symmetry. That is how the symmetry becomes associated with electromagnetism. This tells us that if we change the four numbers by, so to say, moving them around on the circle, we do not change the two numbers describing the photon (or the six describing the electric and magnetic field). Only when we move away from the circumference, the two (and six) numbers change.
[20190123]
what happens when computer: structural regular expressions [[study]] [[project]]
https://what.happens.when.computer/20160830/structuralres/
As Ron Minnich once said:
You want to make your way in the CS field? Simple. Calculate rough time of amnesia (hell, 10 years is plenty, probably 10 months is plenty), go to the dusty archives, dig out something fun, and go for it. It's worked for many people, and it can work for you.
[20190510]
Problems with the Standard Model Higgs  Azimuth
https://johncarlosbaez.wordpress.com/2019/02/25/problemswiththestandardmodelhiggs/
[20190612]
Serious What's the most USEFUL course I can take online for FREE? /r/AskReddit
A basic first aid course.
Tweet from Eric Aleman (@EricAleman_), at Jun 13, 10:28
@patrickc Principles of Electrodynamics by Melvin Schwartz has the clearest derivation
pull tweet">https://twitter.com/EricAleman_/status/1139102125039005696
What happens if we don't postulate speed of light limit?
[20190620]
https://physics.stackexchange.com/questions/160759/einsteinsfirstpostulateimpliesthesecond ok so basically we need some speed in lorentz transformations, that's how we end up with c
Tweet from Smart Biology (@SmartBiology3D), at Jun 24, 15:17
The Bacterial Flagellum is powered by the flow of protons across the cell membrane and driven by a rotating protein engine. It is an enormous protein megacomplex that can reach incredibly high RPMs. #biology #cellbiology #flagellum #education #biologyanimation https://t.co/nWqX9bF9J5
pull tweet">https://twitter.com/SmartBiology3D/status/1142837932388167685
[20190423]
fast.ai · Making neural nets uncool again [[ai]]
[20190715]
has practical deep learning for coders course
[20190211]
The Picture Book of Quantum Mechanics: Siegmund Brandt, Hans Dieter Dahmen: 9781461439509: Amazon.com: Books [[quantum]]
 State "START" from
[20190227]
https://www.amazon.com/PictureBookQuantumMechanics/dp/1461439507
[20181115]
The Geometry of Physics: An Introduction: Amazon.co.uk: Theodore Frankel: 9781107602601: Books
https://www.amazon.co.uk/GeometryPhysicsIntroductionTheodoreFrankel/dp/1107602602
Tweet from Nikita Lisitsa (@lisyarus), at Jul 11, 22:23
Representation theory of the group with 2 elements at work
pull tweet">https://twitter.com/lisyarus/status/1149413911722151937
Tweet from Некстджен и Усиление (@turbojedi), at Jul 18, 11:16 [[ml]]
То есть это всё было не слишком смешной шуткой ровно до момента, когда оказалось, что это и правда неплохо работает, причём даже не на специализированной модели. https://t.co/rVvPF4P5N2
pull tweet">https://twitter.com/turbojedi/status/1151797865532014592
[20190115]
Kevin Boone's Web site
http://www.kevinboone.net/separation_variables.html
basically the point is that separation of variables is disguised chain rule – make sense
[20190620]
Amir on Twitter: "Итого, чтобы собрать программируемый транзисторный микропроцессор, нужно уметь проектировать 1) ISA – см. MIPS 2) микроархитектуру – см Harris&Harris 3) RTL  верилог 4) цифровую технику  см курс Панчула… https://t.co/MqVes4WlZu"
pull tweet">https://twitter.com/disruptnhandlr/status/1141788486938349578
Итого, чтобы собрать программируемый транзисторный микропроцессор, нужно уметь проектировать 1) ISA – см. MIPS 2) микроархитектуру – см Harris&Harris 3) RTL  верилог 4) цифровую технику  см курс Панчула
Tweet from niall tl (@nialltl), at Aug 1, 13:02
🌊 i've written a big reference for implementing the Material Point Method: https://t.co/UopvaXxotV
included: an MITlicensed, incremental, commented implementation of MLSMPM for softbodies and fluids: https://t.co/q26gakgHD1
pull tweet">https://twitter.com/nialltl/status/1122885806241263616
Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Jul 31, 17:07
The concept of "spontaneous symmetry breaking" (SSB) is vital to understanding the Higgs
👉 SSB is when the equations of motion satisfy a certain symmetry, but its lowestenergy vacuum solutions do not
• For the Higgs, SSB is triggered entirely by the Higgs potential (below) https://t.co/e3vNaLRHy7
pull tweet">https://twitter.com/InertialObservr/status/1156595791378571265
[20190802]
〈 Berger  Dillon 〉 (@InertialObservr) / Twitter
https://twitter.com/InertialObservr
SSB is when the equations of motion satisfy a certain symmetry, but its lowestenergy vacuum solutions do not
[20181224]
convention  Obtaining the (\frac{1}{2\pi}) factor in the Fourier transform  Mathematics Stack Exchange
[20181224]
ho.history overview  The (2\pi) in the definition of the Fourier transform  MathOverflow
https://mathoverflow.net/questions/265299/the2piinthedefinitionofthefouriertransform
[20190612]
Quantum Diaries https://www.quantumdiaries.org/2011/06/19/helicitychiralitymassandthehiggs/ [[readagain]] [[stm]]
omg, that's a really super intuitive explanation of chirality, helicity, interactions with Higgs and I think explains the representations as well.
[20190727]
Michael Nielsen
Geometric complexity: Understanding quantum computing as free fall in a curved geometry. And some preliminary investigations into how that curved geometry works.
[20190504]
Cadabra manual: Sphere https://cadabra.science/notebooks/sphere.html
This notebook computes the curvature of a 2sphere by computing connection coefficients and the Riemann tensor components.
[20190510]
Geometric Quantization (Part 1)  Azimuth
https://johncarlosbaez.wordpress.com/2018/12/01/geometricquantizationpart1/
[20190723]
resource recommendations  Gentle introduction to the Formalism of Quantum Zeno Effect  Physics Stack Exchange
My first, introductory, quantum course was (partially) from Griffiths introduction to quantum mechanics. We went through the whole book and, I recall a section introducing the quantum Zeno effect. They did a nice series expansion of the decay probability fir a state transition and showed for measurements very close together you can increase (or possibly decrease) the lifetime of a state. Very simple introductory explanation. –
Tweet from michael_{nielsen} (@michael_{nielsen}), at Apr 15, 19:22 This is true  a set of ideas introduced by economists to study the distribution of wealth also turn out to govern the behaviour of quantum entanglement. Pretty wild! Here's the paper: https://t.co/Wf9iGL59JO https://t.co/wXXbIP697I
pull tweet">https://twitter.com/michael_nielsen/status/1117855694936371201
[20190618]
Jacopo Bertolotti on Twitter: ""I quickly learned to hate spinors. They’re nonintuitive, far more complicated than they have any right to be, and come either with two components or four, both versions being equally hard to comprehend." A Child’s Guide to Spinors William O. Straub"
pull tweet">https://twitter.com/j_bertolotti/status/1140611372214038528
thread where Baez answers some questions about spinors
[20190803]
(6) Abhishek Singharoy on Twitter: "The first study of an entire cell organelle in allatom details. https://t.co/R2t6YdyiAu I am told it'll take the field either 30 years back or 30 years forward. Please help me decide :)" / Twitter
pull tweet">https://twitter.com/abhisekhsingha1/status/1157302336219312128
Abhishek Singharoy
@abhisekhsingha1
The first study of an entire cell organelle in allatom details. (link: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3365009) papers.ssrn.com/sol3/papers.cf…
I am told it'll take the field either 30 years back or 30 years forward. Please help me decide :)
Tweet from John Carlos Baez (@johncarlosbaez), at Aug 11, 05:50 I've been thinking about this sum for a while. I finally had an idea, which you can see here:
It lets you calculate the entropy of a bunch of classical harmonic oscillators if *all you know* is their maximum allowed energy  not how many there are! https://t.co/OV5MAvxobY
pull tweet">https://twitter.com/johncarlosbaez/status/1160413211843104768
Tweet from John Carlos Baez (@johncarlosbaez), at Aug 14, 11:28
@arula_artwork @RAnachro To understand colimits you just need to understand colimits; all these things you list are special cases of those. But it's good to start by understanding some special cases.
You've already met "coproducts", which in the category of sets are just disjoint unions. 1/2
pull tweet">https://twitter.com/johncarlosbaez/status/1161585331600150529
[20190811]
(3) michael_{nielsen} on Twitter: "Amazing Twitter thread, giving an overview of work on quantum computer architectures. Lots of intuitionbuilding tidbits, broad principles, and detailed references. Summarized here: https://t.co/VDzUrfCpA8 https://t.co/i30oRFruw2" / Twitter
pull tweet">https://twitter.com/michael_nielsen/status/1160319447900545024
Something Deeply Hidden  Not Even Wrong
I found Carroll’s clear explanations especially useful on topics where I disagree with him, since reading him clarified for me several different issues. I wrote recently here about one of them. I’ve always been confused about whether I fall in the “Copenhagen/standard textbook interpretation” camp or “Everett” camp, a
Нейронауки для всех. Методы: транскраниальная магнитная стимуляция  Neuronovosti
Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Aug 18, 07:06
BTW do you know Penrose's celestial sphere work? That's where I first came across Möbius transformations as conformal maps of spheres. https://t.co/vN0lOD0lW7
pull tweet">https://twitter.com/sigfpe/status/1162969025867124736
[20190818]
(1) Daniel Litt on Twitter: "The fundamental group of SO(3) is Z/2Z! https://t.co/MnJS0YnNrJ" / Twitter
pull tweet">https://twitter.com/littmath/status/1162723903204220930
The fundamental group of SO(3) is Z/2Z!
[20190819]
(1) Daniel Piker on Twitter: "New 'Live Soap' component for interactive formfinding of minimal surfaces with topology changes https://t.co/YuARGfXlSO" / Twitter
pull tweet">https://twitter.com/KangarooPhysics/status/1135989061976563715
New 'Live Soap' component for interactive formfinding of minimal surfaces with topology changes
[20190628]
Anki decks by LW users  LessWrong 2.0
https://www.lesswrong.com/posts/Kbp8riSbpKv8jie8o/ankidecksbylwusers
[20190825]
mm, I guess only music is interesting for me?
Tweet from Nikita Lisitsa (@lisyarus), at Aug 26, 18:32
I've recently learnt the technique called "imaginary time evolution" that can be used to obtain e.g. ground states of quantum systems and I want to share a tiny thread on how it works. The usual evolution operator is exp(itH/h). (1/n)
pull tweet">https://twitter.com/lisyarus/status/1166025743106809858
Tweet from Dmitrii Kovanikov (@ChShersh), at Aug 27, 13:51
Just finished reading this article. Interesting usage of Free monads in #haskell. Now, the next blog post would be really nice:
1. Take one small but reallife problem
2. Solve it with different approaches
3. Explain each approach
4. Compare them and present the pros and cons https://t.co/FBQyAbNFXz
pull tweet">https://twitter.com/ChShersh/status/1166317343561175042
Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Aug 30, 18:28
How was the Higgs Boson discovered? (1/n)
👉The main process which led to its discovery is its decay into 2 photons: ℎ → γ + γ
👉This process is occurs at "loop level" mediated by the top and bottom quarks 𝑡 & 𝑏
👉The higgs lifetime is 1.56×10⁻²² s https://t.co/A4swAukBBY
pull tweet">https://twitter.com/InertialObservr/status/1139242278755553280
[20190621]
Finding a potential function for conservative vector fields  Math Insight
https://mathinsight.org/conservative_vector_field_find_potential
[20190621]
Finding a potential function for conservative vector fields  Math Insight
https://mathinsight.org/conservative_vector_field_find_potential
[20190906]
David Pfau on Twitter: "Thrilled to be able to share what I've been working on for the last year  solving the fundamental equations of quantum mechanics with deep learning! https://t.co/pzp0Xhsxbu" / Twitter
pull tweet">https://twitter.com/pfau/status/1169981588412817409
David Pfau
@pfau
Thrilled to be able to share what I've been working on for the last year  solving the fundamental equations of quantum mechanics with deep learning!
[20190906]
David Pfau on Twitter: "Thrilled to be able to share what I've been working on for the last year  solving the fundamental equations of quantum mechanics with deep learning! https://t.co/pzp0Xhsxbu" / Twitter
pull tweet">https://twitter.com/pfau/status/1169981588412817409
We've developed a new neural network architecture that can represent wavefunctions for systems of fermions  the kind of particles that make up most matter  and show that it is much more accurate than conventional approximate wavefunctions.
[20190906]
David Pfau (@pfau) / Twitter
study brains and intelligence. Anarchist biocosmist. So far I have not found the science, but the numbers keep on circling me. http://davidpfau.com
[20190629]
Particle filter  Wikipedia
https://en.wikipedia.org/wiki/Particle_filter
[20190727]
explained.ai [[ai]]
Tweet from isis agora lovecruft (@isislovecruft), at Sep 22, 00:47
it’s like pointing at a fucking Zener diode and saying, “quantum supremacy” simply because quantum electromagnetic domain wall tunnelling happens at random, followed by a nonjustification of “well your iphone can’t do that”
pull tweet">https://twitter.com/isislovecruft/status/1175557098375004160
The Yoneda Perspective
https://www.math3ma.com/blog/theyonedaperspective
[20190929]
John Carlos Baez on Twitter: "@sigfpe There are theorems about this stuff. A simple example is the lowest eigenvalue of d²/dx² + x² + λx⁴ as a function of λ. You can formally compute the Taylor series of this function, which diverges, and Borel sum it, and get the right answer for λ>0." / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1178330369449328641
There are theorems about this stuff. A simple example is the lowest eigenvalue of d²/dx² + x² + λx⁴ as a function of λ. You can formally compute the Taylor series of this function, which diverges, and Borel sum it, and get the right answer for λ>0.
[20190524]
Going Critical — Melting Asphalt [[sim]]
https://meltingasphalt.com/interactive/goingcritical/
[20120810]
An argument against call/cc /r/programming
I was reading this thinking "heck yeah... but I hope they're aware of delimited continuations". Then I look at the site address... *rolleyes* It's Oleg  I use *his* delimcc.
[20120810]
An argument against call/cc /r/programming
[20190704]
Understandable RayTracing in 256 lines of bare C++ /r/cpp
[20190828]
ELI5 The Wigner's Friend Thought Experiment /r/explainlikeimfive [[quantum]]
To understand Wigner's Friend, you must first understand Schrödinger's cat; so if you don't, search ELI5 for explanations of that first.
So the Wigner's Friend experiment is basically like the Schrödinger's cat experiment, except it involves 2 people and a cat, instead of just one person and a cat. Wigner leaves the laboratory, then Wigner's friend performs the Schrödinger's cat experiment. Wigner then comes back, to find out whether or not the cat died.
In Schrödinger's cat experiment, we say that the cat is in a super position of being both alive and dead. The question is, in Wigner's Friend experiment, do we also say that the friend is in a superposition of being happy and sad (on the assumption that the friend would be happy if the cat is alive, and sad if the cat is dead).
Thought experiments are generally not created with the intent of "messing with people". They are often formulate to raise a point. In this case, Wigner wanted to raise the point that quantum physics, as he understood it, placed some sort of special importance on the concept of "consciousness". Wigner claims that it's not meaningful for someone to be in a superposition of being happy and sad, and so he claims that the action that "triggers" the collapse of the superposition is the friend's consciousness, and not Wigner returning to the lab to "observe" whether the friend is happy or sad.
That said, some people believe it IS possible for a person to be in a superposition of happy and sad, and so they claim that Wigner's experiment doesn't actually show that consciousness is important after all.
Tweet from michael_{nielsen} (@michael_{nielsen}), at Nov 4, 01:38
Well, I goofed. Energy conservation in GR turns out to be subtle, and it's certainly not right to flatly say energy is conserved. Quite a few people pointed this out. Here's a couple of samples, at different levels of explanation: https://t.co/1TpCKKiCPy
pull tweet">https://twitter.com/michael_nielsen/status/1191167713789399041
Tweet from Nikita Lisitsa (@lisyarus), at Mar 20, 09:27 An excellent read  "The stability of matter: from atoms to stars" https://t.co/qFktkarHAk [[study]] [[read]]
pull tweet">https://twitter.com/lisyarus/status/1108299018969464832
https://projecteuclid.org/download/pdf_1/euclid.bams/1183555452
[20191202]
The Hardware of a Quantum Computer  edX
https://www.edx.org/course/hardwareofquantumcomputer
[20190105]
Are we expecting to have a symmetry breaking of the electromagnetic force in the future? /r/Physics
One can think of superconductivity as a breakdown of electromagnetism gauge symmetry. In other words, the "photon" acquires a mass in a superconductor. This is the description for instance given by Weinberg in his book "Quantum Field Theory" if you want to take a look. The order parameter is related to the attractive strength of electrons in the condensation of Cooper pairs.
However that does not apply to the universe as a whole. A material piece of superconductor does break Lorentz invariance in a sense (the material occupies a finite amount of space so it is not invariant under translations).
[20190105]
Are we expecting to have a symmetry breaking of the electromagnetic force in the future? /r/Physics
Just as an FYI, electromagnetic gauge symmetry is not *really* broken in a superconductor. The BCS wavefunction is still fully gauge invariant. [This paper here](https://arxiv.org/abs/condmat/0503400) gives a good discussion, but the basic point is that superconductivity comes about due to global U(1) symmetry breaking, and that a gauge symmetry can never *really* be broken in a physical system because it is not a physical symmetry  only a symmetry of description.
[20190105]
What exactly is explicit symmetry breaking? And what are some examples? /r/Physics
If you understand SSB, you’re probably familiar with the Mexican hat potential. Let’s say I have a system where the potential energy function V(**r**) = U(r), where U(r) is a typical Mexican hat potential. The potential energy function has rotational symmetry, but the ground state of the system doesn’t. That’s a spontaneous symmetry breaking.
Now imagine my potential is V(**r**) = U(r) + kx^(2).
Now my potential has explicit dependence on x. This is an explicit breaking of rotational symmetry. The symmetry is broken in the Hamiltonian and the ground state of the system.
[20190123]
Can Representation Theory be Explained Using Basic Abstract and Linear Algebra? /r/math
I highly recommend [this book](http://www.amazon.com/RepresentationsCharactersGroupsSecondGordon/dp/052100392X) for an introduction to representation theory over the complex numbers. It's one of my favorite math books as far as presentation and writing style are concerned.
For an example of something that can be proved about groups using representation theory there's the [Burnside theorem](http://en.wikipedia.org/wiki/Burnside_theorem). For about 60 years the only known proof was using representation theory. Nowadays we know how to prove it without representation theory but the proof is **much** more difficult. It seems that using representation theory is the "right" or "natural" way to prove this theorem.
In combinatorics there is a theorem concerning conjugates of regular [partitions](http://en.wikipedia.org/wiki/Partition_%28number_theory%29) and the Mullineux map; I have it written down in my office but I can't remember it off the top of my head. Anyway the theorem is proven using the representation theory of S_n (group of permutations on n letters). To date there is no known combinatorial proof.
Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Dec 14, 23:57
...but only at low frequencies or we couldn't see the sun or receive radio waves above a certain frequency. So we can model the atmosphere as a thin shell between two spheres, from ground to maybe 50km up. We can solve Maxwell's equation to find out what kind of waves...
pull tweet">https://twitter.com/sigfpe/status/1206000218027610112
Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Dec 15, 00:02
You can guess the lowest frequency resonance simply by computing the time it takes for an EM wave to get around the earth:
(speed of light)/(circumference of earth)=7.5Hz
(Hope I did that right).
pull tweet">https://twitter.com/sigfpe/status/1206001431691419648
[20190718]
Quantum Leaps, Long Assumed to Be Instantaneous, Take Time  Quanta Magazine /r/Physics
The experiment is great, but it needs to be emphasized that it does not overturn _anything_ we know about quantum mechanics. It is a cool experimental technique, not a theoretical revolution.
Instant quantum jumps simply don't exist outside of badquality popsci; they are a basic misconception. This experiment, like many others, implies this naive popsci picture is wrong, but every physicist already knew that. The fact that quantum states evolve continuously (rather than jumping) is basic QM 101 material in every textbook.
Despite that, I'm seeing tons of buzz about how this has upended all of quantum mechanics. It really doesn't.
Try TLA
pull tweet">https://twitter.com/hillelogram/status/1207382046890496002
[20191220]
1/(1  1/(1  1/(1  Dan Piponi))) on Twitter: "The padics are like science fiction in mathematics. They are alternative universes alongside the familiar realm of the reals. And there are objects that transcend the barriers between these worlds but manifest a little differently in each one." / Twitter
pull tweet">https://twitter.com/sigfpe/status/1208051225255538688
1/(1  1/(1  1/(1  Dan Piponi)))
@sigfpe
The padics are like science fiction in mathematics. They are alternative universes alongside the familiar realm of the reals. And there are objects that transcend the barriers between these worlds but manifest a little differently in each one.
[20191224]
〈 Berger 🎄 Dillon 〉 on Twitter: "Putting it all together, we get the leading order Feynman diagram that led to the discovery of the Higgs Boson. 👀 https://t.co/w9ug4yfJc1" / Twitter
pull tweet">https://twitter.com/InertialObservr/status/1139315877080207360
〈 Berger 
🎄
 Dillon 〉
@InertialObservr
Putting it all together, we get the leading order Feynman diagram that led to the discovery of the Higgs Boson.
[20191220]
What Makes the Hardest Equations in Physics So Difficult? (2018)  Hacker News
https://news.ycombinator.com/item?id=21832980
[20191228]
Simulating physical reality with a quantum computer
https://ahelwer.ca/post/20191221quantumchemistry/
Tweet from 〈 Berger  Dillon 〉 (@InertialObservr), at Jan 4, 19:35
I'm starting a channel on Discord for Quantum Field Theory/Particle Physics discussion
(1) Ask questions at *any level* of the topic (stay on topic)
(2) Mods do our best to answer (others welcome to answer)
Current mods: me & @litgenstein
pull tweet">https://twitter.com/InertialObservr/status/1213543568754634752
[20190804]
the Synthetic Biology Open Language (SBOL)  a language for genetic design
Tweet from John Carlos Baez (@johncarlosbaez), at Jan 17, 17:34 Planck
For more on this, read Helge Kragh's great article "Max Planck: the reluctant revolutionary":
It seems he was not trying to revolutionize physics. He was trying to understand the data.
pull tweet">https://twitter.com/johncarlosbaez/status/1218225086202703873
[20200227]
bollu.github.io  code + contents of my website, and programming life
https://bollu.github.io/#stuffilearntin2019
Gravitation by Misner Thorne and Wheeler This is an imposing book. I first read through the entire thing (Well, the parts I thought I needed), to be able to get a vague sense of what they’re going for. They’re rigorous in a very curious way: It has a bunch of great physics perspectives of looking at things, and that was invaluable to me. Their view of forms as “slot machines” is also fun. In general, I found myself repeatedly consulting this book for the “true physical” meaning of a thing, such as curvature, parallel transport, the equation of a geodesic, and whatnot.
[20200306]
Spin, Statistics, CPT and All That Jazz
http://math.ucr.edu/home/baez/spin_stat.html
[20200324]
Are quantum fields in any way similar to classical fields? /r/askscience
In the canonical picture, quantum fields are operatorvalued fields (distributions, to be more precise). The Hilbert space on which they act is spanned by number states. Each number state consists of a given number of particles with given momenta and other quantum numbers (spin, color etc.). In fact the \*free\* fields behave like a set of harmonic oscillators for each momentum/spin/color/etc. Of course not every state is a number state, but they provide a basis by which you can express any state by linear combination.
In this picture, the fields are just operators that create and destroy particles, but the particle content is in the abstract quantum state.
The path integral picture is closer to the classical interpretation, but the relationship to particles is a bit more difficult to see. Basically, there is the path integral/partition functional, which consists of a sum over all possible classical field configurations weighted by the value of the action on the given field configuration. Thus all possible field configurations contribute to the amplitudes and expectation values. In the classical limit, only those configurations contribute for which the action is stationary, eg. those that satisfy the classical equations of motion.
TL;DR: In the canonical approach, fields are just tools. In the path integral approach, physical processes happen by summing over classical fields, even those that do not solve the (classical) equations of motion.
That being said, a lot of research asking very fundamental questions about QM is happening, and it does not necessarily involve large colliders Tweet from Valentin Fadeev (@ValFadeev), at Jan 13, 11:03
pull tweet">https://twitter.com/ValFadeev/status/1216677220023963648
Tweet from @nntaleb
pull tweet">https://twitter.com/nntaleb/status/1250286202877440007
@nntaleb: Witness here how salaried physicists are dismissing @stephen_{wolfram} Wolfram's automata BEFORE even hearing him
Just as Freeman Dyson publicly dismissed A New Kind of Science c. 2002; it turned out that he did not read the book. & pple who refused to read it referred to Dyson! twitter.com/jimalkhalili/statu…
New spaces in mathematics and physics https://ncatlab.org/nlab/show/New+Spaces+for+Mathematics+and+Physics
New Space in Physics will explain new concepts of space as applied to physics, including twistors, stringy geometry, derived and higher symplectic geometry, and noncommutative geometry, topos theory in quantum physics, and supergeometry. (My own paper just poses some problems.) https://t.co/EatvZx7rPm
pull tweet">https://twitter.com/johncarlosbaez/status/1117837769546428416
Tweet from John Carlos Baez (@johncarlosbaez), at Apr 15, 17:58
Yay! Mathieu Anel and Gabriel Catren's book New Spaces in Mathematics and Physics has officially been accepted by Cambridge U. Press. But they've chopped it in two: one on math, one on physics.
My chapter, "Struggles with the Continuum", is here:
pull tweet">https://twitter.com/johncarlosbaez/status/1117834503118942208
[20200507]
Physicists Criticize Stephen Wolfram’s ‘Theory of Everything’  Hacker News
[20191213]
Simone Sturniolo on Twitter: "@InertialObservr @__{ice9} @tequehead That we observe a single eigenvalue isn't what interpretations are about. Interpretations try to explain WHY we do. Which is the whole problem." / Twitter
pull tweet">https://twitter.com/SturnioloSimone/status/1205422218005622784
That we observe a single eigenvalue isn't what interpretations are about. Interpretations try to explain WHY we do. Which is the whole problem.
[20191207]
Mathematical formulation of the Standard Model  Wikipedia
https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_parameters
Renormalization scheme (point)
[20191207]
Mathematical formulation of the Standard Model  Wikipedia
https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_parameters
From the theoretical point of view, the Standard Model exhibits four additional global symmetries, not postulated at the outset of its construction, collectively denoted accidental symmetries, which are continuous U(1) global symmetries.
[20191208]
newtonian mechanics  Antigravity in an infinite lattice of point masses  Physics Stack Exchange
https://physics.stackexchange.com/questions/2196/antigravityinaninfinitelatticeofpointmasses
This is incorrect but Newton made the same mistake, so no downvote. The constant density over all space Newtonian gravitating system is not allowed, except in an expanding or contracting Newtonian cosmology, and there is no antigravity for the missing particle. The symmetry arguments are misleading, because the limit is subtle.
[20191208]
electrostatics  Paradox with Gauss' law when space is uniformly charged everywhere  Physics Stack Exchange
The quantities you want to associate with the infinite distribution (electric field, gravitational potential, whatever) depend on how you construct it, and there is no clear "natural" way to do it.
[20191209]
AVƎ on Twitter: "If you're interested in the animated anatomy studies; Here's a 1 minute tute on how to make your own (You'll only need Zbrush) : https://t.co/RMlLZKSLH0 They've definitely helped me improve my understanding, hope they help you :) https://t.co/pXZew0PP9k" / Twitter
pull tweet">https://twitter.com/NotArtofAve/status/1195466035924570113
[20191209]
AVƎ on Twitter: "2/6  Anatomy studies. Arm supination/pronation and flex.
pull tweet">https://twitter.com/NotArtofAve/status/1194694932574851072
[20191210]
1/(1  1/(1  1/(1  Dan Piponi))) on Twitter: "An explanation of dimensional regularisation, one of the more bizarre sounding ideas in physics, applied to classical electrodynamics. Should make it accessible to a wider audience https://t.co/3Dj0eG3Brv (Spot the 1/ε subtraction, related to my recent "moral truth" example.)" / Twitter
pull tweet">https://twitter.com/sigfpe/status/1204513555791278080
An explanation of dimensional regularisation, one of the more bizarre sounding ideas in physics, applied to *classical* electrodynamics.
[20200511]
pull tweet">\mathcal{L} on Twitter: "Are there any good QFT visualizations that facilitate genuine understanding and don’t mislead?" / Twitter
Are there any good QFT visualizations that facilitate genuine understanding and don’t mislead?
EPR is arguably the most controversial paper Einstein ever published,
todo
from ip Einstein Versus the Physical Review
Tweet from Path Integral Salesman (@litgenstein), at Dec 31, 01:53
It took place in the year that Heisenberg built the uncertainty principle, a year after Schrödinger demonstrated the equivalence of wave and matrix mechanics (2 QM formulations before thought to be in tension), and just after the death of the old quantum theory. Random excerpts: https://t.co/d1MREkwoBE
pull tweet">https://twitter.com/litgenstein/status/1211827581105754113
[20200413]
Your statement is 100% correct but misses the entire point  Lobsters [[security]]
There are books on threat modeling that actually go into a variety of models.
Tweet from @johncarlosbaez: In 1907 Einstein tried to combine special relativity with gravity  and very soon he realized gravity would make clocks tick slower, and would bend light
pull tweet">https://twitter.com/johncarlosbaez/status/1230905689809121280
It took him until 1915 to find the equations of general relativity. He needed the right kind of math.
[20200115]
Path Integral Salesman on Twitter: "I’ve been reading a lot of old conference proceedings. Here are some from the 1927 Solvay Conference attended by Einstein, Planck, Pauli, Born, Lorentz, Schrödinger, etc. https://t.co/1mD4Fdk4GS Responding to Einstein, Bohr says: “I do not know what quantum mechanics is.” https://t.co/ybyKjp6EHK" / Twitter
pull tweet">https://twitter.com/litgenstein/status/1211823189237456896
I’ve been reading a lot of old conference proceedings. Here are some from the 1927 Solvay Conference attended by Einstein, Planck, Pauli, Born, Lorentz, Schrödinger, etc. https://arxiv.org/pdf/quantph/0609184.pdf
Responding to Einstein, Bohr says: “I do not know what quantum mechanics is.”
[20191225]
(1) John Carlos Baez on Twitter: "For more, see Hubert Goenner's article "On the history of unified field theories". Part I: https://t.co/vapByPYAi4 Part II: https://t.co/YBIqX120Gg" / Twitter [[qft]]
pull tweet">https://twitter.com/johncarlosbaez/status/1209903923227549696
For more, see Hubert Goenner's article "On the history of unified field theories".
Part I: http://livingreviews.org/lrr20042
Part II: http://livingreviews.org/lrr20145
Physics stuff
Here's the page one up in the directory structure:
https://www.av8n.com/physics/
It's got a lot of very interesting math and physics information.
[20191202]
Paul Dirac: The Mozart of Science (2008)  Hacker News
https://news.ycombinator.com/item?id=20667889
The creativity of the Dirac equation really struck me when I first learned it. Basically, it uses a mathematical trick to write sqrt(a^2 + b^2) = a + b, which doesn't work for normal math, but does work if a and b anticommute: ab = ba. You can implement this with matrices, and in the resulting solution quantum spin just pops out. Astounding.
Tweet from George Corney (@Haxiomic), at Oct 1, 21:59 The author Wyatt Flanders makes incredible things! Here's his website https://t.co/RYAHVDDAM8 [[sim]] [[qft]]
The author Wyatt Flanders makes incredible things! Here's his website https://t.co/RYAHVDDAM8 and more details on the simulation https://t.co/b74Vm06VLV
pull tweet">https://twitter.com/Haxiomic/status/1179123732247384066
[20200101]
eh? I don't quite understand, what 'coupling' between gravity and other forces??
[20191225]
(1) John Carlos Baez on Twitter: "Einstein worked obsessively on unified field theories until his death in 1955. He lost touch with his colleagues' discoveries in particle physics. He had an assistant try to teach him quantum field theory, but lost interest in a month. But there's more to this story… (6/n) https://t.co/f4C9e7iAHx" / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1209900884131401728
Schrödinger & Einstein helped invent quantum mechanics, but they didn't really believe in it, so they were sidelined for the rest of their careers. While others studied elementary particles, they criticized quantum theory and tried to invent "unified field theories".
Perhaps most spectacularly of all, in 2020, Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP*=RE. Here MIP* means the class of problems solvable using multiprover interactive proof systems with quantumly entangled provers (and classical polynomialtime verifiers), while RE means Recursively Enumerable: a class that includes not only all the computable problems, but even the infamous halting problem (!). To say it more simply, entangled provers can convince a polynomialtime verifier that an arbitrary Turing machine halts.
key ceremonies [[study]] [[security]]
Insane. Just think of the risk that this 'master key' exposed to the bank's employees.
Having access to something as insanely valuable as a bank 'master key' puts the employees at risk of blackmail, extortion, etc.
That's why you have HSMs, key ceremonies, Shamir's secret sharing etc. It's not just for trust, it's also for protection of those involved.
Unauthorized wire transfers can be undone, or covered by insurance. Loss of life cannot.
[20200709]
(1) 14 Subatomic Stories: Where Einstein failed quantum gravity  YouTube
weinberg spin 2 boson GR
[20200714]
pull tweet">Maissam Barkeshli on Twitter: "1/ The study of topological quantum matter has been one of the most popular and exciting developments in physics in the last 15 years, although there has been a steady stream of amazing developments for the last 50 years." / Twitter
The study of topological quantum matter has been one of the most popular and exciting developments in physics in the last 15 years, although there has been a steady stream of amazing developments for the last 50 years
[20200227]
bollu.github.io  code + contents of my website, and programming life
https://bollu.github.io/#leapfrogintegration
We have a system we wish to simulate using hamilton’s equations:
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1283210127781199873
@johncarlosbaez: ... I think the pictures and animations in the blog article here help bring topological matter down to earth.
Not all of it is easy to visualize, but the stuff that won Kosterlitz and Thouless the 2016 Nobel Prize is pretty simple  and gorgeous!
[20200709]
Спиральность частицы — Википедия
Спиральность — квантовое число[1], характеристика состояния элементарной частицы. Представляет собой проекцию спина частицы на направление движения. Используется при описании элементарных частиц, движущихся со скоростью света или близкой к ней. Является сохраняющейся лоренцинвариантной величиной для безмассовых частиц.[2][3]
helicity
[20200715]
Understanding quaternions and the Dirac belt trick (2010)  Hacker News
I am pretty sure I have studied every interpretation and explanation of spinors and the nonsimplyconnectedness of SO(3) rotations, and I eventually finally understood it  but, by ignoring explanations like the 'belt trick', rather than embracing them. I don't think this article makes it any better. As long as you're stuck on quaternions you're not going to be able to see what's going on, and the belt metaphor just adds complexity as well.
Tweet from Statebox  ステートボックス (@statebox), at Dec 18, 18:38
oh, my! you'd better watch out! snakes, time traveling and string diagrams! @RickandMorty what else will #categorytheory unleash?
thanks to @erikagain for pointing it out! https://t.co/Vv6m8i8JeN
pull tweet">https://twitter.com/statebox/status/1207369444852424704
[20200809]
Amazon.com: Lectures On Phase Transitions And The Renormalization Group (Frontiers in Physics) (9780201554090): Goldenfeld, Nigel: Books
[20200819]
pull tweet">Michael Nielsen on Twitter: "Somehow, the combination: quasiparticles + statistics + universality / RG + equilibrium is just mindbogglingly rich." / Twitter
Somehow, the combination: quasiparticles + statistics + universality / RG + equilibrium is just mindbogglingly rich.
[20200811]
Neutrino oscillation  Wikipedia
In the Standard Model of particle physics, fermions only have mass because of interactions with the Higgs field
Hm, and what about bosons?
[20200811]
quantum field theory  How does the Higgs mechanism work?  Physics Stack Exchange
The Higgs mechanism is no different from superconductivity, except the condensate responsible for superconductivity is a relativistically invariant scalar field.
If you have a bosonic field, its particles can be in a BoseEinstein condensate. When this condensate is charged, you call it a superconductor. A photon in a superconductor gets a mass, and this is the Higgs mechanism.
[20200811]
HiggsLectureNote.pdf  HiggsLectureNote.pdf
[20200812]
How can SU(2) group has 3 dimensional representation?  Mathematics Stack Exchange [[reprtheory]]
o construct the ndimensional irreducible representation of SU(2), use the spin j=(n−1)/2 angular momentum matrices as Jx,Jy,Jz.
Tweet from @akivaw
pull tweet">https://twitter.com/akivaw/status/1313727123325161472
@akivaw: Proof of Gödel’s Incompleteness Theorem in a Twitter thread
Peano Arithmetic (PA) is a formal proof system. Statements and proofs must follow a very strict syntax. 1/4
[20200819]
Fundamental Forces
One of the four fundamental forces, the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z. Since the mass of these particles is on the order of 80 GeV, the uncertainty principle dictates a range of about 1018 meters which is about 0.1% of the diameter of a proton.
[20200819]
pull tweet">Brian Skinner on Twitter: "@michael_{nielsen} @sigfpe I like this example. Generally bosonic systems store heat/entropy much more easily than fermionic systems. In a boson system, all the particles can store heat, while in a fermionic system only the ones near the Fermi surface can." / Twitter
I like this example. Generally bosonic systems store heat/entropy much more easily than fermionic systems. In a boson system, all the particles can store heat, while in a fermionic system only the ones near the Fermi surface can.
[20200819]
hmm. what if we 'store heat' carefully in a bosonic quasiparticle condensate, and then disturb it to make it fermionic again? What would happen?
[20200819]
pull tweet">Maissam Barkeshli on Twitter: "@michael_{nielsen} But we do live in a superconductor in a sense! The Higgs boson has condensed, which is the origin of mass, similar to how photons acquire mass in electronic superconductors. The idea of technicolor in particle physics is that the Higgs may be a pair of more fundamental fermions" / Twitter
But we do live in a superconductor in a sense! The Higgs boson has condensed, which is the origin of mass, similar to how photons acquire mass in electronic superconductors. The idea of technicolor in particle physics is that the Higgs may be a pair of more fundamental fermions
[20200820]
pull tweet">Vijay Mocherla on Twitter: "@michael_{nielsen} Check out the notes by David Tong from Cambridge. Ch3 of statistical physics notes is the shortest comprehensive summary of BEC I can think off. https://t.co/ED0PrMXvBK" / Twitter
Check out the notes by David Tong from Cambridge. Ch3 of statistical physics notes is the shortest comprehensive summary of BEC I can think off.
https://damtp.cam.ac.uk/user/tong/statphys/three.pdf
[20200821]
arXiv:0910.4855v1 [hepph] 26 Oct 2009  0910.4855.pdf
[20200823]
special relativity  Why don't we construct a spin 1/4 spinor?  Physics Stack Exchange
Dirac spinors actually belong to the 4dimensional reducible representation
(1/2,0)⊕(0,1/2).
Another 4dimensional representation is the irreducible (1/2,1/2)
to which the 4vectors belong.
As you can see, this is all just representation theory and there is no spin1/4
representation in 4 spacetime dimensions.
However, in 2
spacetime dimensions this is no longer valid and representations with fractional spins exist.
X Thus, in a given direction, the momentum has a maximum possible magnitude. The space of allowable momenta is called the Brillouin zone, and its shape depends on the arrangement of atoms in the crystal.
todo drill
from How can electrons be “topological”?
[20200811]
PPlect17.pdf lecture 17 – the Higgs Boson
[20200813]
lomb2ndEd.pdf Lomb: Polyglot  How I Learn Languages
[20200801]
Viktor T. Toth  KaluzaKlein theory
Tweet from John Carlos Baez (@johncarlosbaez), at Sep 9, 08:09
@gregeganSF If you search Wiki and Scholarpedia under "nbody choreography" you'll see people have techniques for proving existence of periodic solutions with various properties. Basic idea: principle of least action with periodic boundary conditions!
pull tweet">https://twitter.com/johncarlosbaez/status/1170957378432290817
[20190921]
ShtetlOptimized » 2013 » March The zone
https://www.scottaaronson.com/blog/?m=201303
Lenny gave a typicallymasterful summary, which for the first time enabled me to understand the role played in the AMPS argument by “the Zone” (a region near the black hole but outside its event horizon, in which the Hawking radiation behaves a little differently than it does when it’s further away).
Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Oct 16, 08:49
What's an Effective field theory (EFT), and why we care about it?
𝐈𝐧𝐝𝐞𝐱 (yes, there's an index for this twitter thread):
1. Decoupling
2. Effective
3. Renormalization
4. References
pull tweet">https://twitter.com/litgenstein/status/1163446510152900608
Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Aug 19, 14:45
3. Renormalization
It is equivalent to the demand that, when we vary the cutoff, physics remains the same; our fiddling can't mysteriously change physics. We shift the coupling constants λ → λ′ at every scale so that the cutoff Λ dependence is absorbed or cancelled.
pull tweet">https://twitter.com/litgenstein/status/1163446917847588864
Tweet from 〈 Zach  Kim 〉 (@litgenstein), at Aug 19, 14:51
3. Renormalization
The RG is our best method for taking advantage of the autonomy of scales in nature, or the fact that some scales decouple from other scales. While heavily simplified, this is the physical interpretation of renormalization attributed to Kenneth Wilson.
pull tweet">https://twitter.com/litgenstein/status/1163448384876736514
Tweet from John Carlos Baez (@johncarlosbaez), at Oct 16, 16:46
In physics, the complex numbers describe points in 2d space. The split complex numbers describe points in 2d Minkowski spacetime. The dual numbers describe points in 2d Galilean spacetime  the version of spacetime in classical mechanics before special relativity.
pull tweet">https://twitter.com/johncarlosbaez/status/1184495830843064322
[20190824]
Greg Egan on Twitter: "[1/4]
Welcome to HopfWorld! Every point on the surface of our own world has been replaced by a circle, creating a threedimensional sphere in four dimensions. If you take a rotating slice through that 3sphere (as shown in the second image), this is what the slice looks like: https://t.co/Rn12So6iKf" / Twitter
pull tweet">https://twitter.com/gregeganSF/status/1165249104672219136
[1/4] Welcome to HopfWorld! Every point on the surface of our own world has been replaced by a circle, creating a threedimensional sphere in four dimensions.
If you take a rotating slice through that 3sphere (as shown in the second image), this is what the slice looks like:
[20191009]
Три книги  Dee Mon. Былое и думы — LiveJournal
https://thedeemon.livejournal.com/140306.html
У КМ ровно две проблемы вследствие которых она не может быть объединена с релятивистской теорией.
1) основные уравнения (Шрёдингера, КлейнаГордонаФока и Дирака) постулированы, а не выведены из первых принципов.
2) вся теория КМ и КТП построена на разложеннии по малому параметру, смысл которого раскладывающим не известен. Я имею ввиду постоянную тонкой структуры, которая обратнопропорциональна постоянной Планка.
GR tensor – it's the only way to construct it? (from Physics from Symmetry book) [[study]]
[20160925]
gravitational waves
The last term, O(ε2 ω2 x2 ) , may be hard to understand for beginners. It says that, actually, the plane wave isn’t plane, it gets corrections that grow quadratically with distance. These corrections, which I do not spell out in detail, come from the nonlinear terms in Einstein’s equations. For trained physicists, however, it is easy to understand their physical origin: the gravitational wave carries energy, therefore has a tiny mass density, and therefore generates a gravitational field by itself. For LIGO, this is totally negligible: only if x becomes hundreds of millions of light years, this term becomes bothersome, but the actual gravitational source is not that far away, and/or does not shine for so many millions of years, so we never have a wave that stretches that far. To be precise: in practice you only need the linear parts of Einstein’s equations, and you have to build wave packets by superimposing these plane waves. Then, these wave packets don’t stretch that far, and the bothersome correction term never becomes large.
[20130215]
fusion
Nuclear fusion: lighter elements merge into heavier elements, using kinetic energy.
Energy has to bypass electrostatic repulsion, however, two factors are decreasing the temperature needed for the reaction:
1. Quantum effects: particles can tunnel through the electrostatic potential barrier
[20200219]
wigner's friend experiment is different from shrodinger's cat in that the entangled observer (the friend) is conscious [[quantum]]
[20200826]
Van der Waals force  Wikipedia
The van der Waals force has the same origin as the Casimir effect, arising from quantum interactions with the zeropoint field.[2]
[20200705]
Feynman diagram  Wikipedia
[20200713]
MathPages: Physics
[20200711]
Cracking a Black Hole Paradox  Sixty Symbols  YouTube [[study]]
read the papers
[20200714]
Reflections on Relativity [[read]] [[study]]
[20200718]
fine_{structure.pdf}
[20200718]
The Lamb Shift
[20200718]
The Hydrogen 21cm Line
The 1420 MHz radiation comes from the transition between the two levels of the hydrogen 1s ground state, slightly split by the interaction between the electron spin and the nuclear spin. The splitting is known as hyperfine structure.
[20201220]
need to split roughtly in 'facts' and 'actual todos/stuff I need to learn'
[20200720]
Visualizing quaternions  3blue1brown + Ben Eater
[20200720]
Wavefunction Visualizer
[20200720]
Ask Ethan #36: The Amazing Spinning Electron  by Ethan Siegel  Starts With A Bang!  Medium
So if we ask how do two hydrogen atoms can be configured together, there are two possible configurations: either in a spatiallysymmetric but spinantialigned state, or in a spatiallyantisymmetric but spinaligned state!
[20200730]
pull tweet">algebraic geometer BLM on Twitter: "@KSHartnett @stevenstrogatz @QuantaMagazine Sad that there was no room for one of the main storylines, the love/hate relationship/competition between symplectic and complex geometry." / Twitter
Sad that there was no room for one of the main storylines, the love/hate relationship/competition between symplectic and complex geometry.
[20200731]
Алгебры Клиффорда, часть 1  VK
Мы поступим так: не будем пытаться задать произведение любой пары элементов, а потребуем лишь, чтобы квадрат x² вектора x в смысле умножения в алгебре совпадал с его скалярным квадратом <x,x>. Собственно, так и определяется алгебра Клиффорда — как самая общая алгебра, удовлетворяющая этому соотношению (самая общая — в смысле некого универсального свойства в соответствующих категориях). Технически
Tweet from michael_{nielsen} (@michael_{nielsen}), at Aug 5, 22:37
pull tweet">https://twitter.com/michael_nielsen/status/1158492254639656966
I think I've shared this on Twitter before, but this is a fun introduction to all the incredibly interesting recent work on new phases of matter: https://t.co/SOuMBP3rgy (by @nattyover ).
Classically, a scalar field is a collection of an infinity of oscillator normal modes. It suffices to consider a 1+1dimensional spacetime ℝ×S1, in which the spatial direction is compactified to a circle of circumference 2π, rendering the momenta discrete.
https://hyp.is/adaalFGBEemsHa807OIUkQ/en.wikipedia.org/wiki/Canonical_quantization
[20191019]
statistical mechanics  Is there any proof for the 2nd law of thermodynamics?  Physics Stack Exchange
It's simple to "roughly prove" the second law in the context of statistical physics. The evolution A→B
of macrostate A, containing exp(SA) microstates, to macrostate B, containing exp(SB) microstates, is easily shown by the formula for the probability "summing over final outcomes, averaging over initial states", to be exp(SB−SA) higher than the probability of the inverse process (with velocities reversed). Because SB−SA is supposed to be macroscopic, such as 1026 for a kilogram of matter, the probability in the wrong direction is the exponential of minus this large difference and is zero for all practical purposes.
Tweet from David Holz (@DavidSHolz), at Nov 7, 21:36
@michael_nielsen @patrickc A famous Silicon designer once told me "all speed comes from parallelism" & power efficiency as well. Clock speed by itself can be a VERY deceptive measure. Power usage increases linearly with parallelism, but exponentially with clockrate. Speed increases linearly with both.
pull tweet">https://twitter.com/DavidSHolz/status/1192556452121993216
[20191107]
Bartosz Milewski on Twitter: "@johncarlosbaez @sigfpe I even adapted his notation to profunctors. https://t.co/f7p0BErEip" / Twitter
pull tweet">https://twitter.com/BartoszMilewski/status/1192494002144067584
Einstein was a very important physicist 'n' all, but let's face it, the way he touches most of our lives in a technical capacity is that he gave us license to leave out our sigma signs.
John Carlos Baez
@johncarlosbaez
It's been called his biggest contribution to mathematics.
@BartoszMilewski
@sigfpe
I even adapted his notation to profunctors
[20191110]
michael_{nielsen} on Twitter: "@predzemshara The IPCC report is surprisingly good  try assessment report 5. There are, of course, many many books. I enjoyed Daniel Schrag's EdX class, though it focuses more on the earthsystem aspect, and only gradually moves onto humancaused climate stuff." / Twitter [[climate]]
pull tweet">https://twitter.com/michael_nielsen/status/1193629850721865728
The IPCC report is surprisingly good  try assessment report 5. There are, of course, many many books. I enjoyed Daniel Schrag's EdX class, though it focuses more on the earthsystem aspect, and only gradually moves onto humancaused climate stuff.
Georgi–Glashow model  Wikipedia
, the Georgi–Glashow model is a particular grand unification theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. In this model the standard model gauge groups SU(3) × SU(2) × U(1) are combined into a single simple gauge group SU(5). The unified group SU(5) is then thought to be spontaneously broken into the standard model subgroup below some very high energy scale called the grand unification scale.
[20200602]
pull tweet">(1) Sean Carroll on Twitter: "The Biggest Ideas in the Universe: idea #11 is Renormalization. We deal with "infinities" in quantum field theory by admitting that we don't understand arbitrarily high energies, and constructing "effective" theories instead. https://t.co/kZ8pnYJ5nA" / Twitter
The Biggest Ideas in the Universe: idea #11 is Renormalization. We deal with "infinities" in quantum field theory by admitting that we don't understand arbitrarily high energies, and constructing "effective" theories instead.
[20200619]
Breakthrough in inverse Laplace transform procedures  Hacker News
Yes. The Fourier transform characterizes on a circle (usually the unit circle in the complex domain) at different frequencies. It is properly defined for periodic signals.
The Laplace transform takes any exponential spiral in the complex plane, and reduces to the Fourier transform if you only care about the unit circle.
[20200619]
Breakthrough in inverse Laplace transform procedures  Hacker News
With Fourier you can analyze oscillatory characteristics of function (frequency and phase). With Laplace you can also analyze amplification/attenuation.
[20200626]
MathStory  Hilberts Problems(1).pdf
[20200630]
(2) Introduction to Energy Band Theory  Material Science  YouTube [[study]]
[20200703]
pull tweet">D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i on Twitter: "@johncarlosbaez @sarah_{zrf} Yeah, symplectic integrators are the way to go. They often conserve notquiteenergy which is the wrong thing to conserve but it still stops things getting out of hand." / Twitter
Yeah, symplectic integrators are the way to go. They often conserve notquiteenergy which is the wrong thing to conserve but it still stops things getting out of hand.
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1279106414493831169
@johncarlosbaez: The symmetry group of the forces other than gravity is SU(3)×SU(2)×U(1). SU(3) for the strong force and SU(2)×U(1) for weak and electromagnetic forces combined.
Why this group? Can we derive it from beautiful math?
Yes! But I don't know if it helps.
[20200314]
Dave Burke on Twitter: "RNA looks like DNA except the T is replaced with a U. The RNA moves out into the cell and is used to build proteins it specifies. This DNA>RNA>protein sequence is called the central dogma of molecular biology." / Twitter
pull tweet">https://twitter.com/davey_burke/status/1238672101545893889
RNA looks like DNA except the T is replaced with a U. The RNA moves out into the cell and is used to build proteins it specifies. This DNA>RNA>protein sequence is called the central dogma of molecular biology.
[20200314]
Dave Burke on Twitter: "Every cell in your body contains your full DNA or genome (3 bn base pairs). But each cell doesn't use all of the instructions, e.g. a skin cell shouldn't make an iris. This is where gene expression comes in. DNA in the nucleus is first copied to short strands of RNA." / Twitter
pull tweet">https://twitter.com/davey_burke/status/1238672100832862215
Every cell in your body contains your full DNA or genome (3 bn base pairs). But each cell doesn't use all of the instructions, e.g. a skin cell shouldn't make an iris. This is where gene expression comes in. DNA in the nucleus is first copied to short strands of RNA.
Geom algebra Vs vector
Geometric algebra is something that hasn't found a "killer app," if you will. The largest users of vector calculus are physicists and engineers, and those communities have 1) enormous existing literature using GibbsHeaviside vectors, and 2) enormous institutional investment in teaching them across departments. We haven't found a justification for switching that would outweigh the amount of inertia involved.
It's hardly a new thing. David Hestenes has been writing books about its advantages in physics since the 1960's.
Structure and Interpretation of Classical Mechanics  Wikipedia
Structure and Interpretation of Classical Mechanics (SICM) is a classical mechanics textbook written by Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer. The first edition was published by MIT Press in 2001, and a second edition was released in 2015. T
Tweet from @litgenstein
pull tweet">https://twitter.com/litgenstein/status/1253904085742313472
@litgenstein: astonishing how wrong Dirac was here https://t.co/4zHvPfQHuQ
[20200428]
(1) The Holographic Universe Explained  YouTube [[physics]]
https://www.youtube.com/watch?v=klpDHn8viX8&list=WL&index=13&t=0s
good intro to the holographic principle and ads/cft correspondense
scale invariance
[20200429]
Tensors Explained Intuitively: Covariant, Contravariant, Rank  YouTube
"contra"variant – when you increase basis vectors, the components decrease
[20200429]
Tensors Explained Intuitively: Covariant, Contravariant, Rank  YouTube
but if you describe a vector with dot products (with the bases), the associated dot products will double with the scaling of the basis vectors
[20200430]
A theory of everything  Garrett Lisi  YouTube [[qft]]
electric charge is a combination of isoweak and hyperchange?
higgs breaks the symmetry so weak particles are too massive?
overall, interesting, but looks pretty mad
he's saying there must be other particles like higgs?
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1262058096643325952
@johncarlosbaez: In 2987 Feynman wrote an essay explaining how negative probabilities could be used. Read it! He explains things well:
https://t.co/vQE8G21UUm
The idea is that negative probabilities are only allowed in intermediate steps of a calculation, not the final results.
(3/n) https://t.co/Rz14sNzhfa
[20200520]
Subatomic Stories: Antimatter  YouTube [[study]]
Of all of the claims of modern physics, perhaps the most amazing is that for every kind of known matter, there is a cousin version called antimatter. Antimatter is the opposite of ordinary matter and will annihilate into pure energy when it encounters matter. In episode 7 of Subatomic Stories, Fermilab’s Dr. Don Lincoln gives you the lowdown on this amazing substance.
quantum diaries explanations of higgs/symmetry breaking
Tweet from @litgenstein [[study]]
pull tweet">https://twitter.com/litgenstein/status/1266178085574946816
@litgenstein: easy twitter.com/samuelgwalters/sta… pic.twitter.com/oEjbxX…
[20200612]
Joe Rogan Experience #1203  Eric Weinstein  YouTube [[study]]
55:10 hopf worlds weinstein
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1275677652586823682
@johncarlosbaez: There's a theory to deal with this... it's standard stuff from analysis. I could explain it. Briefly, when you have a selfadjoint operator with continuous spectrum, its "eigenvectors" are not actually elements of the Hilbert space, but suitable integrals involving them are.
conductivity stuff [[physics]]
 fermi level – makes sense at low temperatures only? at higher, it shifts up https://youtu.be/mwlWIfNvt1w?t=154
 graphene – dirac cones – "no intertia"??
topological insulator?? https://en.wikipedia.org/wiki/Topological_insulator  energy bands – X axis is momentum?? https://www.youtube.com/watch?v=w3rFHJkUuIM
[20200623]
Majorana fermion  Wikipedia
In condensed matter physics, bound Majorana fermions can appear as quasiparticle excitations—the collective movement of several individual particles, not a single one, and they are governed by nonabelian statistics.
Tweet from John Carlos Baez (@johncarlosbaez), at May 10, 16:05
I'm digging into the foundations of arithmetic with my old internet pal Michael Weiss  the guy who wrote the famous "Photons, Schmotons" series. Turns out he's an expert on logic! He's teaching me a lot of stuff.
pull tweet">https://twitter.com/johncarlosbaez/status/1126865911858618369
[20190214]
Why The Schrodinger Equation Fails at Relativity : Physics
https://www.reddit.com/r/Physics/comments/ad23sp/why_the_schrodinger_equation_fails_at_relativity/
Physics students always say that the Schrodinger equation doesn't hold for SR, but it does. It's not the Schrodinger equation that fails though, it's the nonrelativistic Hamiltonian that fails. The Dirac equation is the Schrodinger equation, but with the Dirac Hamiltonian. The Schrodinger equation is valid.
[20190126]
Locally constant function  Wikipedia
https://en.wikipedia.org/wiki/Locally_constant_function
Every locally constant function from the real numbers R to R is constant, by the connectedness of R. But the function f from the rationals Q to R, defined by f(x) = 0 for x < π, and f(x) = 1 for x > π, is locally constant (here we use the fact that π is irrational and that therefore the two sets {x∈Q : x < π} and {x∈Q : x > π} are both open in Q).
[20190126]
Math3ma [[cattheory]]
[20190222]
interesting, some illustreated category theory?
books [[study]] [[electronics]]
/r/AskElectronics wiki
Well, there's a book Code by Charles Petzold that does a really solid job of explaining a lot of stuff from the very basics. Then there's This site, which is very useful too. You can download it's content in the form of a PDF book too.
https://www.allaboutcircuits.com/
[20190211]
Life on the lattice [[qft]] [[qcd]]
https://latticeqcd.blogspot.com/
some blog abbout lattice qft/qcd
[20190211]
[heplat/0506036] Lattice QCD for Novices [[qcd]]
https://arxiv.org/abs/heplat/0506036
[20190123]
pushout in nLab [[cattheory]]
https://ncatlab.org/nlab/show/pushout
[20190424]
try to understand it sentence by sentence..
[20190126]
logic  How can a formal system ever be nonobviously unsound?  Mathematics Stack Exchange [[logic]]
[20190308]
(2) Slut_{jack} on Twitter: "Q: wat is Functor F A: you can add F to both ends a > b F a > F b Q: FullyFaithful F? A: rm F from both ends F a > F b a > b Q: L left adjoint to R? A: Pulling L right turns it to R A: Pulling R left turns it to L L a > b a > R b L a > b" / Twitter
pull tweet">https://twitter.com/Iceland_jack/status/1103800222008991744
Nontransitive dice  Wikipedia
https://en.m.wikipedia.org/wiki/Nontransitive_dice
Tweet from Jibran Haider (@jibranhaider), at Jan 2, 09:11 [[numeric]]
I am very pleased to announce the open source release of the explicit solid dynamics toolkit implemented using OpenFOAM via @github.
pull tweet">https://twitter.com/jibranhaider/status/1048213796643393536
[20180610]
Hacker's guide to Neural Networks [[nn]]
https://karpathy.github.io/neuralnets/
[20180610]
How a Kalman filter works, in pictures  Bzarg
http://www.bzarg.com/p/howakalmanfilterworksinpictures/
[20181129]
myPhysicsLab Single Spring [[viz]]
https://www.myphysicslab.com/springs/singlespringen.html
3.00
[20181213]
Derivatives and dissections of data types  Lambda the Ultimate
http://lambdatheultimate.org/node/1957
Really interesting and informative site about physical simulations and mechanics, and the maths behind it.👍👍👍 [[viz]] [[sim]]
https://t.co/7hOPwcPQtR
depicted left is a physical simulation of a book tossed in the air. https://t.co/hlhYf0JPon
pull tweet">https://twitter.com/erkaman2/status/1100754929965301760
Tweet from John Carlos Baez (@johncarlosbaez), at Mar 23, 17:08 sheaf
A "sheaf" on a space X assigns a set of "sections" F(U) to any open subset U of that space, with the ability to restrict sections to smaller subsets, and to glue sections that agree on overlaps to get sections on bigger subsets!
Sheaves let us study local vs. global issues. https://t.co/thCy9U0zvq
pull tweet">https://twitter.com/johncarlosbaez/status/1109502266174636032
Linear algebra done right
[20190304]
plot of sin(z)/(z  mouse position) in the complex plane /r/math [[viz]]
This is generated with https://kisonecat.github.io/phaseplot/
Tweet from John Carlos Baez (@johncarlosbaez), at Apr 10, 03:21 [[cattheory]] [[baez]]
@michael_nielsen @stevenstrogatz @emilyriehl Maybe try "A prehistory of ncategorical physics" or "Quantum quandaries", both on the arXiv.
pull tweet">https://twitter.com/johncarlosbaez/status/1115801886743863296
Tweet from ¬¬(Dan Piponi) (@sigfpe), at Apr 10, 22:05 [[cattheory]]
@michael_nielsen What got my interest originally was learning that lattice meets and products of sets, groups, topological spaces etc. could all be defined using a single definition. And then learning that you could dualise by reversing the arrows and double the # of definitions blew my mind.
pull tweet">https://twitter.com/sigfpe/status/1116084820784766982
Таким образом, любой, даже самый маленький электрический заряд черной дыры полностью меняет тип сингулярности в ее центре.
[20190424]
Fundamental polygon  Wikipedia
https://en.wikipedia.org/wiki/Fundamental_polygon
[20180916]
The 5/8 Theorem  Azimuth
https://johncarlosbaez.wordpress.com/2018/09/16/the58theorem/
[20190210]
klein bottle [[topology]]
bend a cylinder as you would do for torus. then you need to match the circles, but in the direction opposite to cicle. in order to do that you'd have to pierce through the cylinder
[20190210]
armstrong p.138 van jampen theorem for simplicial complexes [[topology]]
Tweet from John Carlos Baez (@johncarlosbaez), at May 12, 17:51 [[baez]]
It looks like an island made of mathematics. It's actually a map of some definitions Xena knows.
Xena is a computer proof assistant. She's just been taught the definition of "perfectoid space"  the green star in the southeast. Click on the image to see it.
pull tweet">https://twitter.com/johncarlosbaez/status/1127602183636054017
Fundamental Design Issues of Gradle Build System
Gradle losing its grounds now that Bazel is getting momentum after years of being a closed source system.
Tweet from Nikita Lisitsa (@lisyarus), at May 28, 15:10
A nice MO thread with examples of unnatural isomorphisms between functors: https://t.co/iCMsmBnf7T
pull tweet">https://twitter.com/lisyarus/status/1133375027548762113
Tweet from Roman Elizarov (@relizarov), at May 20, 22:48
The was the key realization that lead us to introduce structured concurrency in Kotlin Coroutines before we made their APIs stable: https://t.co/I70IkaUqFH
pull tweet">https://twitter.com/relizarov/status/1130591159775105026
[20190318]
Product Spaces [[topology]]
https://notgnoshi.github.io/productspaces/
[20171106]
https://www.reddit.com/r/AskElectronics/wiki/education [[electronics]]
Физик оправдал принцип космической цензуры https://nplus1.ru/news/2019/06/19/censorship
Visual complex analysis
[20190628]
John Carlos Baez on Twitter: "Fong and Spivak's book on applied category theory is coming out! I'm getting my copy in the mail soon! (cont)… "
pull tweet">https://twitter.com/johncarlosbaez/status/1144662487356231680
Fong and Spivak's book on applied category theory is coming out! I'm getting my copy in the mail soon! (cont)
[20181129]
Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60): V. I. Arnold, A. Weinstein, K. Vogtmann: 9780387968902: Amazon.com: Books [[math]] [[physics]]
https://www.amazon.com/MathematicalClassicalMechanicsGraduateMathematics/dp/0387968903
короче очень советую, если ты хочешь немного инсайтов в статистикумлдатасаенс без хуйни https://medium.com/@kozyrkov Cassie Kozyrkov – Medium
Tweet from Jamie Portsmouth (@jamportz), at Jan 3, 09:14 [[physics]] [[viz]]
Uploaded a new version of Fibre dynamical systems renderer, with a bunch more presets and tools for rendering GIF animations and turntables https://t.co/WfXyDtQLLp https://t.co/H8WySstKdI https://t.co/JBm7VYdb52
pull tweet">https://twitter.com/jamportz/status/1080607132750360576
Sam Walters ☕️ on Twitter: "My Einstein paper is posted on arXiv. (It resulted from my MathPhysics Symposium talk.) https://t.co/b7qp6baxIJ… "
pull tweet">https://twitter.com/SamuelGWalters/status/767888754543505408
[20190415]
how einstein got his field equations https://arxiv.org/abs/1608.05752
Tweet from Derek Lowe (@Dereklowe), at Oct 11, 15:03 [[study]]
Some chemical weirdness for Friday: the element copernicium: https://t.co/73IZYzWutJ
pull tweet">https://twitter.com/Dereklowe/status/1182657925321580548
[20190407]
A Proposal for Proquints: Identifiers that are Readable, Spellable, and Pronounceable
https://arxiv.org/html/0901.4016
[20191109]
Formalizing expresiveness of line editors /r/dependent_{types}
Tweet from Nikita Lisitsa (@lisyarus), at Nov 27, 08:41
@karlicoss Thank you! :3
I believe this thing will contain most of stuff that I post, in one way or another.
pull tweet">https://twitter.com/lisyarus/status/1199609128110436358
щас посмотрел видос пиздос, типа Планк не верил в фотоны (да и чуть ли не в атомы) до 20х годов
[20200522]
Physicists of reddits, what's the most Intetesting stuff you've studied so far?? /r/Physics
Honestly, no matter the subject, very old foundational articles.
Someone explaining extremely clearly and formally a very basic concept, because it was breaking new at the point of writing, is deeply satisfying. There's a clarity in those papers that's impossible to find mostly anywhere else.
[20200707]
A Concurrency Cost Hierarchy  Performance Matters
https://arbital.com/p/bayes_rule_proportional/?pathId=36904
The proportional form of Bayes' rule is perhaps the fastest way of describing Bayesian reasoning that sounds like it ought to be true. If you were having a fictional character suddenly give a Bayesian argument in the middle of a story being read by many people who'd never heard of Bayes' rule, you might have them say:
Similarly, if you were a doctor trying to explain the meaning of a positive test result to a patient, you might say: "If we haven't seen any test results, patients like you are a thousand times as likely to be healthy as sick. This test is only a hundred times as likely to be positive for sick as for healthy patients. So now we think you're ten times as likely to be healthy as sick, which is still a pretty good chance!"
Tweet from Eric Lengyel (@EricLengyel), at Jul 29, 11:11
Foundations of Game Engine Development, Volume 2: Rendering (FGED2) is now available on most Amazon websites worldwide!
pull tweet">https://twitter.com/EricLengyel/status/1155309290229358592
[20190804]
Sameorigin policy  Wikipedia https://en.wikipedia.org/wiki/Sameorigin_policy
[20190805]
Об Байеса  2: plakhov — LiveJournal
https://plakhov.livejournal.com/227597.html
[20190806]
reddit: the front page of the internet
https://www.reddit.com/r/dataisbeautiful/wiki/advice
Information about Colorblindness
There are colorblindness issues associated with many common color palettes that are rarely discussed among practitioners. Allow me to provide some useful information:
Tweet from @preskill
@preskill: If you are curious about the exciting recent progress on the black hole information puzzle, but don't want to wade into a lot of technical details, this review is a very good place to start. https://t.co/IOQlZUjEjN
Tweet from John Carlos Baez (@johncarlosbaez), at Aug 14, 03:29
pull tweet">https://twitter.com/johncarlosbaez/status/1161464741191012352
The free commutative monoid on X is
exp(X) = 1 + X + X²/2! + X³/3! + ...
whenever X is an object in a category with products and colimits obeying the distributive law. Now + means "coproduct", Xⁿ is defined using products, and Xⁿ/n! is Xⁿ modulo permutations.
(11/n)
[20191124]
Breit–Wheeler process  Wikipedia
https://en.wikipedia.org/wiki/Breit%E2%80%93Wheeler_process
The Breit–Wheeler process or Breit–Wheeler pair production is a physical process in which a positron–electron pair is created from the collision of two photons. It is the simplest mechanism by which pure light can be potentially transformed into matter.
[20200414]
(1) We certainly do have formal derivations of Lorentz covariance and the Einste…  Hacker News
(1) We certainly do have formal derivations of Lorentz covariance and the Einstein field equations, given in detail here:
http://wolframcloud.com/obj/wolframphysics/Documents/somere...
(2) The article above already discusses the derivation of the matter contribution to the Lagrangian density, the derivation of energymomentum tensor, and Lorentz transformations for elementary particles.
(3) Both Hawking radiation and black hole entropy, and connections between our formalism and the AdSCFT correspondence, are detailed here:
http://wolframcloud.com/obj/wolframphysics/Documents/somequ...
(4) We do not yet know how to do this.
(5) The quantum mechanics paper above makes, for instance, quite specific predictions about the location of stretched horizons around nonsemiclassical black holes.
(6) (7) This we are still working on.
Drill
S(N) is { det = 1 } U(N) is { M*M = 1 } [[drill]] [[reprtheory]]
[20190314]
lorenzian vs riemannian manifold {spacetime vs space} [[drill]]
[20190123]
exponentiating the observable results in representations [[reprtheory]] [[drill]]
[20190823]
Cook–Levin theorem  Wikipedia [[drill]]
https://en.wikipedia.org/wiki/Cook%E2%80%93Levin_theorem
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NPcomplete
{Zu veil geld} too much money [[drill]]
[20190622]
universe is { 13.7 billion } years old [[drill]]
Margoluslevitin theorem: limit on QC . Processing rate is or order {10 ** 33} op/s per joule. Or, system needs time about {h / E} to flip the state to orthogonal [[drill]]
https://en.wikipedia.org/wiki/Margolus%E2%80%93Levitin_theorem
[20200707]
Upgrading the Particle Physics Toolkit: The Future Circular Collider  Harry Cliff, John Womersley  YouTube [[study]] [[drill]]
5:04 nice table of standard model.. perhaps I should memorize
hmm, quantum fields seem to be very poorly visualised. I wonder if I can do better with something very simple [[viz]] [[qft]]
[20191101]
John Carlos Baez on Twitter: "Take the real numbers. Throw in some square roots of +1 and some square roots of 1, all anticommuting. You get a Clifford algebra. Clifford algebras are important in geometry and physics  we need them to understand spin! They also display some amazing patterns. (1/n) https://t.co/IlnbpTbBqN" / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1190314607979585536
Take the real numbers. Throw in some square roots of +1 and some square roots of 1, all anticommuting. You get a Clifford algebra.
Clifford algebras are important in geometry and physics  we need them to understand spin! They also display some amazing patterns.
[20191001]
John Carlos Baez on Twitter: "@gregeganSF @monsoon0 @wtgowers @LauraDeming Okay, you've managed to cancel out any potential "insult" with an overload of praise. It was this paper: https://t.co/vlxpqR8G1w The stabilization hypothesis, homotopy hypothesis, cobordism hypothesis and tangle hypothesis are in here. No theorems, amusingly." / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1178816967601340417
Okay, you've managed to cancel out any potential "insult" with an overload of praise. It was this paper:
https://arxiv.org/abs/qalg/9503002
The stabilization hypothesis, homotopy hypothesis, cobordism hypothesis and tangle hypothesis are in here. No theorems, amusingly.
[20191030]
Jesper Cockx  Rewriting type theory /r/agda
[20191112]
Sofia 🧹 on Twitter: "Follow up, matrix multiplication is essentially the unique solution to the following problem: given dot :: (j > a) > (j > b) > c derive mmul :: (i > j > a) > (j > k > b) > (i > k > c) the solution is: mmul as bs i k = dot (as i) (flip bs k)" / Twitter
pull tweet">https://twitter.com/typeswitch/status/1193878474940960770
Follow up, matrix multiplication is essentially the unique solution to the following problem:
given
dot :: (j > a) > (j > b) > c
derive
mmul :: (i > j > a) > (j > k > b) > (i > k > c)
the solution is:
mmul as bs i k = dot (as i) (flip bs k)
[20191112]
Nikita Lisitsa on Twitter: "Hence we are forced to include this bizarre state into consideration. Are we missing some more states? Surely we are. This all boils down to representations of the SO(3) group and how those behave under tensor product  this is known as ClebschGordan decomposition. (8/8)" / Twitter
pull tweet">https://twitter.com/lisyarus/status/1194374457676247045
Hence we are forced to include this bizarre state into consideration. Are we missing some more states? Surely we are. This all boils down to representations of the SO(3) group and how those behave under tensor product  this is known as ClebschGordan decomposition. (8/8)
Tweet from 1/(1  1/(1  1/(1  Dan Piponi))) (@sigfpe), at Nov 30, 19:14
Feynman's book QED describes simplified path integral approach to optics. Field at point Q is integral of exp(iL/ℏ) over paths from source P to Q. Sort of Huygens' principle. Not correct but tried it anyway
pull tweet">https://twitter.com/sigfpe/status/1200840567799762945
Tweet from michael_{nielsen} (@michael_{nielsen}), at Nov 30, 18:57
Fun: a recent paper from Lenny Susskind, in which he heuristically derives Newton's laws, using ideas from holography and computational complexity theory https://t.co/M6a6weyP36 https://t.co/5ZljvKoJVr
pull tweet">https://twitter.com/michael_nielsen/status/1200836282399649792
Tweet from Quanta Magazine (@QuantaMagazine), at Dec 5, 19:02
pull tweet">https://twitter.com/QuantaMagazine/status/1202664570940252160
Tweet from michael_{nielsen} (@michael_{nielsen}), at Dec 6, 03:04
@3blue1brown I don't mean "similar", I mean there really is an isomorphism. You can use map everything in one problem over to the other, and use the same mathematics to solve them. Here's a table showing the ways different things correspond: https://t.co/iqNvlkScfH
pull tweet">https://twitter.com/michael_nielsen/status/1202785958074019840
Tweet from Juan Carlos ∞ (@PonceCampuzano), at Jan 8, 17:04
Studying or teaching Complex Analysis? This online book might be useful.
⭐️Complex Analysis: A Visual and Interactive Introduction⭐️
Thanks everyone for your suggestions and reporting issues to improve this project. https://t.co/ElaWs4XjIV
pull tweet">https://twitter.com/PonceCampuzano/status/1214850688506716160
[20191230]
Path Integral Salesman on Twitter: "If you want to study physics but your life just does not permit you the time or energy to do maths rigorously (or, at least, however rigorously we physicists do maths), check out these 3 friendly texts: https://t.co/G62SmoXuPc https://t.co/uFCqVj4Exs https://t.co/1QhwJVOKBI https://t.co/ZWhDtvFyju" / Twitter
pull tweet">https://twitter.com/litgenstein/status/1210643695046811648
Path Integral Salesman
@litgenstein
If you want to study physics but your life just does not permit you the time or energy to do maths rigorously (or, at least, however rigorously we physicists do maths), check out these 3 friendly texts:
[20200103]
vacuum
http://math.ucr.edu/home/baez/vacuum.html
[20191227]
mathematical_{offering.pdf}
chromeextension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdf_{viewer.html}?r=https://musicaeadoracao.com.br/recursos/arquivos/tecnicos/matematica/mathematical_offering.pdf
[20191227]
notes10.pdf
http://www.math.columbia.edu/~woit/notes10.pdf
topics in repr theory woit
[20191227]
404 Not Found
https://www.physics.indiana.edu/~dermisek/QFT_08/qftI21p.pdf
[20191227]
404 Not Found
http://www.damtp.cam.ac.uk/user/ch558/pdf/Representations.pdf
[20191231]
Klein–Gordon equation  Wikipedia
https://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation
Any solution of the free Dirac equation is, componentwise, a solution of the free Klein–Gordon equation.
[20191231]
Schrödinger field  Wikipedia
https://en.wikipedia.org/wiki/Schr%C3%B6dinger_field
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1231259529666420737
@johncarlosbaez: When you remove an electron from a quantum wire, the resulting defect can split into a "spinon" that acts like a particle with spin but no electric charge, and a "holon" that acts like a particle with no spin but positive charge!
This is called "spincharge separation".
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1231263103502802944
@johncarlosbaez: In 3 dimensions, an electron in a suitable solid medium can effectively split into *three* parts:
a "spinon" carrying its spin,
a "chargon" carrying its charge, and
a "orbiton" carrying the information about which orbital
Tweet from @litgenstein
pull tweet">https://twitter.com/litgenstein/status/1232891521109676033
@litgenstein: The jets are themselves reconstructed using recombination schemes which tell you what the properties of the jets are given the observed constituents of the jets. Perhaps it will surprise you that Voronoi diagrams find a use here too: pic.twitter.com/4NSVTE…
[20200307]
reference request  Atlaslike websites on specific areas of mathematics  MathOverflow
https://mathoverflow.net/questions/354327/atlaslikewebsitesonspecificareasofmathematics
[20200307]
Phil Lynch on Twitter: "My copy of the Bible finally arrived https://t.co/8XomO2d887" / Twitter
pull tweet">https://twitter.com/PhilipLynchGW/status/1236343035220365312
My copy of the Bible finally arrived
wheeler gravitation
[20200308]
On the shoulders of the giants  Hacker News
https://news.ycombinator.com/item?id=22515743
I’ll second designing data intensive applications as one of the most interesting, readable, and relevant technical books I’ve ever read.
Tweet from @johncarlosbaez
pull tweet">https://twitter.com/johncarlosbaez/status/1236359942619070464
@johncarlosbaez: Also, everything is wiggling around, not fixed. So it's hard to visualize what a proton does in water. But it's important, because this governs how acids behave.
Water is amazingly tricky stuff!
For much more, read my blog article:
[20200319]
John Carlos Baez on Twitter: "@seanmcarroll The CRC Handbook of Chemistry and Physics. Imagine how much work it took to collect all that knowledge…" / Twitter
pull tweet">https://twitter.com/johncarlosbaez/status/1240670369775665153
The CRC Handbook of Chemistry and Physics.
Imagine how much work it took to collect all that knowledge...
[20190129]
John Baez on Research Tactics  Machine Intelligence Research Institute [[research]] [[learning]]
https://intelligence.org/2014/02/21/johnbaezonresearchtactics/
[20190209]
some instapaper notes
look for problems in between disciplines
talk to smart people
always simplify problems and try solve them until you simplified enough
[20190521]
How I learn and practice music with anki /r/Anki [[music]] [[spacedrep]]
[20190722]
ok, interesting, he basically learns systematically fingering, chords etc
[20190213]
The Frustrating Success of Our Best Theory of Physics – The Third Triumvirate [[relativity]] [[physics]]
https://thirdtriumvirate.wordpress.com/2019/02/13/thefrustratingsuccessofthestandardmodel/
fucking hell, really awesome explanation for standard model.. read it again!
[20190612]
very intuitive explanations how to get physical fields from symmetry justification; and rationale for Higgs field
https://vk.com/wall9471321_26902 Фундаментально ли время во Вселенной
 State "START" from "TODO"
[20190424]
[20190506]
В 2013 году команда исследователей из Италии экспериментально продемонстрировала этот феномен. Подводя итоги своей работы, ученые сообщали: «Мы показываем, как статическое запутанное состояние двух фотонов можно рассматривать в качестве развивающегося с точки зрения наблюдателя, использующего один из двух фотонов как часы — для оценки временного развития другого фотона. Однако сторонний наблюдатель может показать, что глобально запутанное состояние не развивается».
[20200716]
Topology Illustrated  Mathematics Is A Science
[20200716]
Topology Illustrated (2015)  Hacker News
[20201203]
The fundamental Group of the Torus is abelian  YouTube
The fundamental Group of the Torus is abelian
video 'proof'
[20201220]
Twostate quantum system  Wikipedia
The twostate system cannot be used as a description of absorption or decay, because such processes require coupling to a continuum. Such processes would involve exponential decay of the amplitudes, but the solutions of the twostate system are oscillatory.
[20201220]
Twostates_{03.tex}  Twostates_{03.pdf} [[quantum]] [[study]]
good summary of two state systems
 energy can be chosen arbitrarily such that eigenvalues are + eps
 pauli matrices are basis for the observables (!)
 I guess mixing of basis states only happens if they have complex amplitudes? otherwise both just rotate?
 right, so during the state evolution, hilbert state (all of it?) simply rotates https://www.youtube.com/watch?v=xMaGm9u8
[20201220]
The Feynman Lectures on Physics Vol. III Ch. 8: The Hamiltonian Matrix
Now the interesting thing is that if the molecule is known to be in some state at some instant, it will not be in the same state a little while later.
[20201220]
The Feynman Lectures on Physics Vol. III Ch. 9: The Ammonia Maser
Note that each of the Eqs. (9.8) and (9.9) look just like what we had in Section 8–6 for the equation of a onestate system. They have a simple exponential time dependence corresponding to a single energy. As time goes on, the amplitudes to be in each state act independently.
right, ok, even though it 'seems' that the basis state doesn't change because it 'merely' changes the phase, in some other basis you'd see basis states rotating
so it's not any less important effect
[20150111]
Тензор энергииимпульса
Подматрица 3 x 3 из чисто пространственных компонент
T^{ik} \ = \ \left( \begin{matrix}
T^{11} & T^{12} & T^{13} \\
T^{21} & T^{22} & T^{23} \\
T^{31} & T^{32} & T^{33}
\end{matrix} \right)
есть 3мерный тензор плотности потока импульса, или тензор напряжений со знаком минус. В механике жидкости диагональные её компоненты соответствуют давлению, а прочие составляющие — тангенциальным усилиям (напряжениям или в старой терминологии — натяжениям), вызванным вязкостью.
Для жидкости в покое тензор энергииимпульса сводится к диагональной матрице ~{\rm{diag}}({{\rho}c^2},~p,~p,~p), где ~{\rho} есть плотность массы, а ~p — гидростатическое давление.
NATO phonetic alphabet  Wikipedia https://en.m.wikipedia.org/wiki/NATO_phonetic_alphabet [[study]]
symplectic.ipynb [[symplectic]] [[tostudy]]
Tweet from @gravity_{levity}
pull tweet">https://twitter.com/gravity_levity/status/1339271605852246022
@gravity_levity: Here's something else weird about copper. Electrons in its interior are flying around at (literally) a million miles per hour. If you take a census of their momentum, you'll find that all the values sit neatly inside a geometric surface ("Fermi surface") that looks like this: pic.twitter.com/44CCA2...
Tweet from @nplusodin
pull tweet">https://twitter.com/nplusodin/status/1351837811834580992
@nplusodin: Немецкие физики впервые обнаружили кристаллы Паули, возникающие за счет неразличимости фермионов.
Мы уже писали об этом открытии, а теперь статья о нем была опубликована в Physical Review Letters
Tweet from @Dereklowe
pull tweet">https://twitter.com/Dereklowe/status/1348692521040359424
@Dereklowe: Here's a more detailed look at the mRNA vaccines  their mode of action and how they're delivered. The emphasis is on the years (decades) of research in a variety of fields that was fortunately ready to be deployed this year:

processing on [20210131]
Tweet from @mekarpeles [[chinese]]
pull tweet">https://twitter.com/mekarpeles/status/1338041556763254784
@mekarpeles: For any TOTAL CHINESE BEGINNERS who are finding it challenging to find Chinese learning materials, here's a thread of resources I wish I knew about sooner. twitter.com/mekarpeles/status/...
[20190805]
Metamorphisms  Bartosz Milewski's Programming Cafe https://bartoszmilewski.com/2019/01/03/metamorphisms/
Tweet from Nick Sharp (@nmwsharp), at Jul 24, 13:25
Check out the fastforward preview for our SIGGRAPH 2019 paper "The Vector Heat Method"! We found a way to parallel transport vector fields with heat flow, and it opens up awesome applications. Talk is Wed July 31 at 11:30 in Room 153. With @yousufmsoliman and @keenanisalive. https://t.co/jXiP4zxqjt
pull tweet">https://twitter.com/nmwsharp/status/1153993638134910977

[20210122]
ECAP10 Joscha Bach on AI singularity.pdf
[20210126]
Syllabus for Classics of Computer Science [[tostudy]] [[hci]]
[20190818]
kitspace/awesomeelectronics: A curated list of awesome resources for electronic engineers and hobbyists https://github.com/kitspace/awesomeelectronics
[20190117]
Maldacena: The symmetry and simplicity of thelaws of physics and the Higgs boson https://arxiv.org/pdf/1410.6753.pdf
[20190921]
A visual introduction to machine learning http://www.r2d3.us/visualintrotomachinelearningpart1/ [[ml]]
[20200724]
ShtetlOptimized » Blog Archive » The Busy Beaver Frontier [[toread]]
an 18page survey article about the Busy Beaver function: the staggeringly quicklygrowing function that probably encodes a huge portion of all interesting mathematical truth in its first hundred values, if only we could know those values or exploit them if we did.