TODO list for learning

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!

https://twitter.com/lisyarus/status/1229487593684901889

Simulating Hamiltonian mechanics instead of Metropolis-Hastings algorithm:

So what are spinors for anyway? Quantities that transform like a spinor appear in quantum mechanics: the coefficients in the Dirac-equation form a spinor, for instance, because when you rewrite the equation under a change of coordinates, in order for it to remain invariant, the Dirac-coefficients must transform as spinors do.

ok, this is a very clear spinor explanation

https://arxiv.org/abs/1001.1778

https://math.stackexchange.com/questions/1795583/what-is-a-topological-space-good-for/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.

https://dec41.user.srcf.net/h/III_L/advanced_quantum_field_theory/2_4

https://physics.stackexchange.com/questions/129667/is-it-true-that-the-schr%C3%B6dinger-equation-only-applies-to-spin-1-2-particles/129744

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 spin-0 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 non-relativistic fields and attempt quantizing, e.g. the Newton Cartan theory of gravity, we also get spin-0 boson! For this result (specific to quantizing Newtonian gravity), see:
Joy Christian's "Exactly Soluble Sector of Quantum Gravity"

by Eugene Khutoryansky

really good spin visualisations. ok, so spin is a unit quaternion, ok

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

SU2 – three-sphere; purely algebraically x² + y² + u² + v²
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

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.

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.

https://physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed

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 field-theoretic counterpart of the classical four-potential.

read all these course notes over again

https://www.bu.edu/tech/support/research/visualization/gallery/lattice-qcd09/

https://physics.stackexchange.com/questions/130649/an-electron-has-no-known-internal-structure-does-that-imply-it-has-an-unknown-o/130655#130655

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.

(Non-relativistic) 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 Stern-Gerlach 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.

A liberal arts curriculum (like the one at @UChicagoCollege) makes you a more well-rounded individual, and builds a lot of cross-cutting skills like good writing, critical thinking, building a good argument, etc.
I didn't really appreciate that when I was younger.

http://www.scholarpedia.org/article/Gauge_invariance

https://twitter.com/j_bertolotti/status/1141724827599941633

I am not satisfied yet, but this is my spin rotating around the x-axis, 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.

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

https://twitter.com/Haxiomic/status/1179112422503833601

https://twitter.com/johncarlosbaez/status/1195047685922807808

Murray Gell-Mann 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!

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.

https://twitter.com/lisyarus/status/1197887639980068864

Fascinating quantum mechanics experiment: measurements are subjective to observers, suggesting that there is no objective reality at a quantum level

https://twitter.com/martinkl/status/1195302299465326592

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.

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!

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.

useful for my tweet thread for physical impl of quantum computations

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.

(from hn)

Ballentine's book is a modern textbook that relies on that (as opposed to Shankar which you mentioned)

nice illustration of spinor states

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 high-energy world? Let's confine ourselves to the time-independent case, and write it in components. (a long thread<<EOF) https://t.co/foe5zQmzpi

Клейн-Гордон и Дирак логически вылезают из метрики п-ва 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 как-то получается у физиков на это наплевать и получать практически подтверждаемые результаты. :)
Но это не относится к вопросу интерпретации, это к вопросу вычислений.

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

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. 

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

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 long-range gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.

https://twitter.com/wickrotate/status/1280624828026740737

@wickrotate: @AsplingEric Try this https://t.co/A8Yk5kYMN6

Since the Higgs boson is a spin-zero particle, it is the first observed ostensibly elementary particle to be described by the Klein–Gordon equation

The analogous limit of a quantum Klein-Gordon field is complicated by the non-commutativity of the field operator. In the limit v << c, the creation and annihilation operators decouple and behave as independent quantum Schrödinger fields.

https://www.gregegan.net/images/DiracAnimation.gif

Why didn’t Gödel simply talk about soundness?  Because unlike consistency or ω-consistency, 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.

One way to make this work is to have αi that satisfy the equation, αiαj+αjαi=ηij+ηji, where ηij is the Minkowski-metric.

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?

https://twitter.com/johncarlosbaez/status/1200473111029698560

• [2021-06-19]
  

  I like to say: free energy is the energy minus the energy due to being hot. The "energy due to being hot" is temperature times entropy.
  

The best laymen explanation can be found in The symmetry and simplicity of the laws of physics and the Higgs boson by Juan Maldacena

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 spin-statistics theorem. But the anyons of condensed matter are nonrelativistic.

...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 

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 non-compact U(1)”.
This is why they can’t have nice things.
https://t.co/PbmBsaVXAs

from ip A Math Puzzle Worthy of Freeman Dyson | Quanta Magazine

I love condensed matter physics!  I hadn't even known dielectrons were a thing: normally electrons repel.  But in a sodium-ammonia solution, electrons pair up with opposite spins. 

(i) Space-time is a pseudo-Riemannian 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

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 quantum-chemical systems. github.com/lisyarus/chembook/r…

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

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.

Weight/mass of single photon in a box bouncing up and down

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

https://github.com/barbagroup/CFDPython/blob/master/lessons/14_Step_11.ipynb
go throught and make sure I understand how I compute things…

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 12-5)

https://www.reddit.com/r/math/comments/8i7x6s/everything_about_representation_theory_of_finite/dyq2qxg/

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

https://www.youtube.com/watch?v=BI7dbp3uIdY

https://twitter.com/lisyarus/status/1101210066059964418

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.

https://anvaka.github.io/fieldplay/?cx=-0.02210000000000001&cy=-1.8154000000000001&w=8.541&h=8.541&dt=0.01&fo=0.998&dp=0.009&cm=1

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,

https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathematics

https://github.com/sympy/sympy/issues/5396

The Born rule itself, he said, is thus an example of Wheeler’s “law without law.”

http://blog.sigfpe.com/2007/11/whats-all-this-e8-stuff-about-then-part.html

https://www.physicsforums.com/insights/journey-manifold-su2mathbbc-part/
really read this through and try to understand all the definitions. e.g. coordinate charts etc

• State "STRT" from [2019-04-24]
  

https://en.wikipedia.org/wiki/Charts_on_SO(3)#The_hypersphere_of_rotations

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.

http://jakobschwichtenberg.com/lie-algebra-able-describe-group/
well, ok, so the point we can associal lie algebra elements with lie groups elements via exponentiation

https://books.google.co.uk/books/about/Group_Theory_and_Physics.html?id=k2Fp3JA93oYC&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false

http://mathonline.wikidot.com/list-of-fundamental-groups-of-common-spaces

http://math.ucr.edu/home/baez/qg-fall2008/

https://twitter.com/lisyarus/status/1101517866250186752

• State "STRT" from [2019-04-24]
  

https://physics.stackexchange.com/users/50583/acuriousmind

https://physics.stackexchange.com/questions/295412/spin-operators-in-qm

to be precise, in quantum mechanics we are interested in projective representations because physically, two vectors that differ by a phase are indistinguishable.

To semidecide this, just start generating every possible proof.
Gödel's first incompleteness theorem:
This property is semidecidable, but not decidable.

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

https://physics.stackexchange.com/questions/8441/what-is-a-complete-book-for-introductory-quantum-field-theory

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 self-contained chapters that introduce a single topic, discuss it in the necessary level of detail, and move on to the next topic.

https://physics.stackexchange.com/questions/199827/is-there-a-reason-why-a-relativistic-quantum-theory-of-a-single-fermion-exists

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

If your manifold is guaranteed to carry other non-degenerate 2-tensors, 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, non-degenerate 2-form ωω).

https://motls.blogspot.com/2012/04/why-are-there-spinors.html
jeez, this guy is a graphomaniac…

ok, at least here they are treating variations with asymptotic terms…

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

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?

The projective sphere
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.

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

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.

https://www.youtube.com/watch?v=FoR3hq5b5yE
at 9:11 interesting visual explanation why the force is not decreasing for strong nuclear force

In fact, electric charge is a combination of hyper and isospin charges.

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

compact closed surfaces are spheres with handles and klein bottles (remove a disk, attach the mobius strip, which has a circular surface)

todo
from ip How Feynman Diagrams Revolutionized Physics | Quanta Magazine

https://jakevdp.github.io/blog/2012/09/05/quantum-python/

some supposedly simple argument about Lamb shift… still need to follow more carefully. maybe, visualise?

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

https://twitter.com/hmemcpy/status/1054089875526504452

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

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.

https://what.happens.when.computer/2016-08-30/structural-res/

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.

A basic first aid course.

@patrickc Principles of Electrodynamics by Melvin Schwartz has the clearest derivation

https://twitter.com/EricAleman_/status/1139102125039005696

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 mega-complex that can reach incredibly high RPMs. #biology #cellbiology #flagellum #education #biologyanimation https://t.co/nWqX9bF9J5

https://twitter.com/SmartBiology3D/status/1142837932388167685

https://www.fast.ai/

• State "STRT" from [2019-02-27]
  

https://www.amazon.com/Picture-Book-Quantum-Mechanics/dp/1461439507

https://www.amazon.co.uk/Geometry-Physics-Introduction-Theodore-Frankel/dp/1107602602

Representation theory of the group with 2 elements at work

https://t.co/up4BlRMOYM

https://twitter.com/lisyarus/status/1149413911722151937

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

https://twitter.com/turbojedi/status/1151797865532014592

http://www.kevinboone.net/separation_variables.html
basically the point is that separation of variables is disguised chain rule – make sense

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

🌊 i've written a big reference for implementing the Material Point Method: https://t.co/UopvaXxotV
included: an MIT-licensed, incremental, commented implementation of MLS-MPM for softbodies and fluids: https://t.co/q26gakgHD1

https://twitter.com/nialltl/status/1122885806241263616

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 lowest-energy vacuum solutions do not
• For the Higgs, SSB is triggered entirely by the Higgs potential (below) https://t.co/e3vNaLRHy7

https://twitter.com/InertialObservr/status/1156595791378571265

https://twitter.com/InertialObservr

SSB is when the equations of motion satisfy a certain symmetry, but its lowest-energy vacuum solutions do not

https://math.stackexchange.com/questions/301860/obtaining-the-frac12-pi-factor-in-the-fourier-transform/301862#301862

https://mathoverflow.net/questions/265299/the-2-pi-in-the-definition-of-the-fourier-transform

omg, that's a really super intuitive explanation of chirality, helicity, interactions with Higgs and I think explains the representations as well.

http://michaelnielsen.org/

Geometric complexity: Understanding quantum computing as free fall in a curved geometry. And some preliminary investigations into how that curved geometry works.

This notebook computes the curvature of a 2-sphere by computing connection coefficients and the Riemann tensor components.

https://johncarlosbaez.wordpress.com/2018/12/01/geometric-quantization-part-1/

https://physics.stackexchange.com/questions/345588/gentle-introduction-to-the-formalism-of-quantum-zeno-effect?noredirect=1&lq=1

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. –

https://twitter.com/michael_nielsen/status/1117855694936371201

https://twitter.com/j_bertolotti/status/1140611372214038528
thread where Baez answers some questions about spinors

https://twitter.com/abhisekhsingha1/status/1157302336219312128

Abhishek Singharoy
@abhisekhsingha1
The first study of an entire cell organelle in all-atom 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 :)

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

https://twitter.com/johncarlosbaez/status/1160413211843104768

@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

https://twitter.com/johncarlosbaez/status/1161585331600150529

https://twitter.com/michael_nielsen/status/1160319447900545024

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

http://neuronovosti.ru/tms/

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

https://twitter.com/sigfpe/status/1162969025867124736

https://twitter.com/littmath/status/1162723903204220930

The fundamental group of SO(3) is Z/2Z!

https://twitter.com/KangarooPhysics/status/1135989061976563715

New 'Live Soap' component for interactive form-finding of minimal surfaces with topology changes

https://www.lesswrong.com/posts/Kbp8riSbpKv8jie8o/anki-decks-by-lw-users

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)

https://twitter.com/lisyarus/status/1166025743106809858

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 real-life problem
2. Solve it with different approaches
3. Explain each approach
4. Compare them and present the pros and cons https://t.co/FBQyAbNFXz

https://twitter.com/ChShersh/status/1166317343561175042

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

https://twitter.com/InertialObservr/status/1139242278755553280

https://mathinsight.org/conservative_vector_field_find_potential

https://mathinsight.org/conservative_vector_field_find_potential

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!

https://en.wikipedia.org/wiki/Particle_filter

https://explained.ai

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 non-justification of “well your iphone can’t do that”

https://twitter.com/isislovecruft/status/1175557098375004160

https://www.math3ma.com/blog/the-yoneda-perspective

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.

https://meltingasphalt.com/interactive/going-critical/

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.

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.

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

https://twitter.com/michael_nielsen/status/1191167713789399041

https://twitter.com/lisyarus/status/1108299018969464832
https://projecteuclid.org/download/pdf_1/euclid.bams/1183555452

https://www.edx.org/course/hardware-of-quantum-computer

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).

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/cond-mat/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.

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.

I highly recommend [this book](http://www.amazon.com/Representations-Characters-Groups-Second-Gordon/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.

...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...

https://twitter.com/sigfpe/status/1206000218027610112

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).

https://twitter.com/sigfpe/status/1206001431691419648

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 bad-quality 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.

https://twitter.com/hillelogram/status/1207382046890496002

https://twitter.com/sigfpe/status/1208051225255538688

1/(1 - 1/(1 - 1/(1 - Dan Piponi)))
@sigfpe
The p-adics 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.

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.

https://news.ycombinator.com/item?id=21832980

https://ahelwer.ca/post/2019-12-21-quantum-chemistry/

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

https://t.co/KuaIG2bIdj

https://twitter.com/InertialObservr/status/1213543568754634752

http://sbolstandard.org

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.

https://twitter.com/johncarlosbaez/status/1218225086202703873

https://bollu.github.io/#stuff-i-learnt-in-2019

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.

http://math.ucr.edu/home/baez/spin_stat.html

In the canonical picture, quantum fields are operator-valued 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.

https://twitter.com/ValFadeev/status/1216677220023963648

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 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

https://twitter.com/johncarlosbaez/status/1117837769546428416

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.

https://en.wikipedia.org/wiki/Mathematical_formulation_of_the_Standard_Model#Free_parameters

Renormalization scheme (point)

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.

https://physics.stackexchange.com/questions/2196/anti-gravity-in-an-infinite-lattice-of-point-masses

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.

https://physics.stackexchange.com/questions/39654/paradox-with-gauss-law-when-space-is-uniformly-charged-everywhere

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.

https://twitter.com/NotArtofAve/status/1195466035924570113

https://twitter.com/NotArtofAve/status/1194694932574851072

https://twitter.com/sigfpe/status/1204513555791278080

An explanation of dimensional regularisation, one of the more bizarre sounding ideas in physics, applied to *classical* electrodynamics.

Are there any good QFT visualizations that facilitate genuine understanding and don’t mislead?

todo
from ip Einstein Versus the Physical Review

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

https://twitter.com/litgenstein/status/1211827581105754113

There are books on threat modeling that actually go into a variety of models.

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.

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/quant-ph/0609184.pdf

Responding to Einstein, Bohr says: “I do not know what quantum mechanics is.”

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/lrr-2004-2

Part II: http://livingreviews.org/lrr-2014-5

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.

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.

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

https://twitter.com/Haxiomic/status/1179123732247384066

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".

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.

weinberg spin 2 boson GR

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

https://bollu.github.io/#leapfrog-integration

We have a system we wish to simulate using hamilton’s equations:

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!

https://t.co/SseLaMU2zI

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 лоренц-инвариантной величиной для безмассовых частиц.[2][3]

helicity

I am pretty sure I have studied every interpretation and explanation of spinors and the non-simply-connectedness 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.

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

https://twitter.com/statebox/status/1207369444852424704

Somehow, the combination: quasiparticles + statistics + universality / RG + equilibrium is just mindbogglingly rich.

In the Standard Model of particle physics, fermions only have mass because of interactions with the Higgs field

Hm, and what about bosons?

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 Bose-Einstein 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.

o construct the n-dimensional irreducible representation of SU(2), use the spin j=(n−1)/2 angular momentum matrices as Jx,Jy,Jz.

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

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 10-18 meters which is about 0.1% of the diameter of a proton.

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.

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

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

Dirac spinors actually belong to the 4-dimensional reducible representation
(1/2,0)⊕(0,1/2).

Another 4-dimensional representation is the irreducible (1/2,1/2)

to which the 4-vectors belong.

As you can see, this is all just representation theory and there is no spin-1/4

representation in 4 spacetime dimensions.

However, in 2
spacetime dimensions this is no longer valid and representations with fractional spins exist.

todo drill
from How can electrons be “topological”?

@gregeganSF If you search Wiki- and Scholarpedia under "n-body 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!

https://twitter.com/johncarlosbaez/status/1170957378432290817

https://www.scottaaronson.com/blog/?m=201303

Lenny gave a typically-masterful 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).

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

https://twitter.com/litgenstein/status/1163446510152900608

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.

https://twitter.com/litgenstein/status/1163446917847588864

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.

https://twitter.com/litgenstein/status/1163448384876736514

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.

https://twitter.com/johncarlosbaez/status/1184495830843064322

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 three-dimensional sphere in four dimensions.
If you take a rotating slice through that 3-sphere (as shown in the second image), this is what the slice looks like:

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, Клейна-Гордона-Фока 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.

The last term, O(ε2 ω2 |x|2 ) , 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 non-linear 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.

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

The van der Waals force has the same origin as the Casimir effect, arising from quantum interactions with the zero-point field.[2]

read the papers

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.

So if we ask how do two hydrogen atoms can be configured together, there are two possible configurations: either in a spatially-symmetric but spin-anti-aligned state, or in a spatially-anti-symmetric but spin-aligned state!

Sad that there was no room for one of the main storylines, the love/hate relationship/competition between symplectic and complex geometry.

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

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 ).

https://hyp.is/adaalFGBEemsHa807OIUkQ/en.wikipedia.org/wiki/Canonical_quantization

https://physics.stackexchange.com/questions/10690/is-there-any-proof-for-the-2nd-law-of-thermodynamics

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.

@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.

https://twitter.com/DavidSHolz/status/1192556452121993216

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

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 earth-system aspect, and only gradually moves onto human-caused climate stuff.

, 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.

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.

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.

With Fourier you can analyze oscillatory characteristics of function (frequency and phase). With Laplace you can also analyze amplification/attenuation.

Yeah, symplectic integrators are the way to go. They often conserve not-quite-energy which is the wrong thing to conserve but it still stops things getting out of hand.

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.

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.

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.

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 Gibbs-Heaviside 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 (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

https://twitter.com/litgenstein/status/1253904085742313472

@litgenstein: astonishing how wrong Dirac was here https://t.co/4zHvPfQHuQ

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

"contra"variant – when you increase basis vectors, the components decrease

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

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?

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

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

https://twitter.com/litgenstein/status/1266178085574946816

@litgenstein: easy twitter.com/samuelgwalters/sta… pic.twitter.com/oEjbxX…

55:10 hopf worlds weinstein

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 self-adjoint operator with continuous spectrum, its "eigenvectors" are not actually elements of the Hilbert space, but suitable integrals involving them are.

• 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
  

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 non-abelian statistics. 

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.

https://twitter.com/johncarlosbaez/status/1126865911858618369

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 non-relativistic Hamiltonian that fails. The Dirac equation is the Schrodinger equation, but with the Dirac Hamiltonian. The Schrodinger equation is valid.

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).

https://www.math3ma.com/

/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/

https://latticeqcd.blogspot.com/
some blog abbout lattice qft/qcd

https://arxiv.org/abs/hep-lat/0506036

https://ncatlab.org/nlab/show/pushout

https://math.stackexchange.com/questions/3007684/how-can-a-formal-system-ever-be-non-obviously-unsound

https://twitter.com/Iceland_jack/status/1103800222008991744

https://en.m.wikipedia.org/wiki/Nontransitive_dice

I am very pleased to announce the open source release of the explicit solid dynamics toolkit implemented using OpenFOAM via @github.

https://twitter.com/jibranhaider/status/1048213796643393536

https://karpathy.github.io/neuralnets/

https://www.myphysicslab.com/springs/single-spring-en.html
3.00

http://lambda-the-ultimate.org/node/1957

https://t.co/7hOPwcPQtR
depicted left is a physical simulation of a book tossed in the air. https://t.co/hlhYf0JPon

https://twitter.com/erkaman2/status/1100754929965301760

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

https://twitter.com/johncarlosbaez/status/1109502266174636032

This is generated with [https://kisonecat.github.io/phase-plot/](https://kisonecat.github.io/phase-plot/)

@michael_nielsen @stevenstrogatz @emilyriehl Maybe try "A prehistory of n-categorical physics" or "Quantum quandaries", both on the arXiv.

https://twitter.com/johncarlosbaez/status/1115801886743863296

@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.

https://twitter.com/sigfpe/status/1116084820784766982

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

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.

https://twitter.com/johncarlosbaez/status/1127602183636054017

Gradle losing its grounds now that Bazel is getting momentum after years of being a closed source system.

A nice MO thread with examples of unnatural isomorphisms between functors: https://t.co/iCMsmBnf7T

https://twitter.com/lisyarus/status/1133375027548762113

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

https://twitter.com/relizarov/status/1130591159775105026

https://notgnoshi.github.io/product-spaces/

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)

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

https://twitter.com/jamportz/status/1080607132750360576

https://twitter.com/SamuelGWalters/status/767888754543505408

Some chemical weirdness for Friday: the element copernicium: https://t.co/73IZYzWutJ

https://twitter.com/Dereklowe/status/1182657925321580548

@karlicoss Thank you! :3
I believe this thing will contain most of stuff that I post, in one way or another.

https://twitter.com/lisyarus/status/1199609128110436358