# [2020-01-19] 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

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!


# [2020-02-17] Nikita Lisitsa on Twitter: "Simulating Hamiltonian mechanics instead of Metropolis-Hastings algorithm: https://t.co/cVZiaTGP7u" / Twitter

Simulating Hamiltonian mechanics instead of Metropolis-Hastings algorithm:


# [2020-08-01]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 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

# [2020-06-23]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.


# [2019-01-26] general topology - What is a topological space good for? - Mathematics Stack Exchange [[topology]]

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.


# visualising QFT [[viz]][[qft]]

## [2019-02-11] Proton quarks empty mass calculation GIF : askscience [[qft]]

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

## [2019-02-11] (8) Empty Space is NOT Empty - YouTube [[qft]][[viz]]

visualisation of vacuum for a proton sized box

# [2019-02-24] Is it true that the Schrödinger equation only applies to spin-1/2 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 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"


## [2019-05-06] mm. can't say I really understand it..

The "vanilla" Schrodinger's equation (from non-relativistic QM) does not describe a spin-1/2 particle.
The plain, old Schrodinger's equation describes a non-relativistic spin-0 field.


# [2019-02-10] (6) Quantum Spin - Visualizing the physics and mathematics - YouTube [[spin]][[viz]]

Eugene Khutoryansky


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

# Tensors [[tensor]]

## [2019-02-23] Tensor Calculus [[tensor]]

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.


## [2019-02-23] Tensor derivative (continuum mechanics) - Wikipedia

https://en.wikipedia.org/wiki/Tensor_derivative_(continuum_mechanics)#Derivativeoftheinverseofasecond-ordertensor

## [2019-02-23] TensorsPoorMan.pdf

https://web2.ph.utexas.edu/~jcfeng/notes/Tensors_Poor_Man.pdf
some ok explanations for covariant derivatives ans some index notation

# [2019-02-11] Aharonov-Bohm Experiment [[quantum]][[study]]

• State "START" from [2019-04-20]
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


## [2019-02-22] Euler–Lagrange equation - Wikipedia [[lagrangian]]

Derivation of one-dimensional Euler–Lagrange equation


Derivation of one-dimensional Euler–Lagrange equation – this section is actually the one that makes sense of it

## [2019-02-22] basically

we have J = int F(x, f, f'). for any variaiton v, ge = f + e v. So, Fe = F(x, ge, g'e) and Je = int F(x, ge, g'e)
next, total derivative: dJe/de = int dFe/de dx
dFe/de = dx/de pFe/px + dge/de pFe/pge + dg'e/de pFe/pg'e

but dx/de = 0; dge/de = v and dg'e/de = v'
in general we can't just replace pFe/pge with pF/pf!!! but, we can use the fact that we are computing derivative at zero, and at zero ge is equal to f.

so, we get dJ/de|e=0 = int v(x) dF/df + v'(x) dF/df' = 0

use integration by parts to eliminate higher order derivatives of the variation

# SO3 vs SU2 https://labcit.ligo.caltech.edu/~ethrane/Resources/seminar/Ch2.Spinors.pdf[[reprtheory]]

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

# [2019-03-19] 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.


# [2019-03-20] 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.


# [2019-02-15] 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 field-theoretic counterpart of the classical four-potential.


# [2019-03-12] 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

# Tweet from Borja Sotomayor (@borjasotomayor), at Apr 2, 12:21 [[art]]

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.


# [2019-04-24] 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.

(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.


# chirality and helicity

## [2019-04-24] 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 finite-dimensional representations of the Lorentz group are labeled by two half-integers (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.


## [2019-04-24] 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

## [2019-04-24] 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

# [2019-06-20] Jacopo Bertolotti on Twitter: "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.… https://t.co/ji4cYUNRu8" [[spinor]][[viz]]

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.


# 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


# [2019-11-14] John Carlos Baez on Twitter: "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! (1/n) https://t.co/YHGDNpvfZX" / Twitter

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!


# 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.


# 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


## [2019-11-23] Experimental test of local observer independence | Science Advances [[quantum]]

eh, still didn't quite get what are the mscroscopic consequences of that?

# [2020-05-11]">Mel Andrews 𓃻 on Twitter: "Explain mean field theory to philosophers in one sentence GO!" / Twitter

Nathaniel Virgo
@NathanielVirgo
Level 2:
@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
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.


# [2020-05-11]">(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!


# [2020-05-25]">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
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.


# [2020-06-23]">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.


# [2020-07-09]Simulating physical reality with a quantum computer[[totweet]]

useful for my tweet thread for physical impl of quantum computations

# [2020-07-16]">(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)


# [2020-10-20]Dirac — Greg Egan

nice illustration of spinor states

# 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, Anti-photon - quite an interesting read


# 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 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



# [2019-10-09] Три книги - Dee Mon. Былое и думы — LiveJournal

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.


# 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 pa |0> |A> + pd |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

# [2020-08-11]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.


# [2020-09-15] 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


# [2020-07-04]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 long-range gluon interactions do not exist, this illustrates that gluons in the singlet state do not exist either.[7]


# Tweet from @wickrotate

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


# Excellent article, need to reread and process [[study]]

## [2020-07-13]On the Higgs Mechanism

However, there is one remaining case to consider. Suppose there exists a field ψi with non-zero Ki and with a non-zero self-interaction coefficient kii. Such a field, in isolation, satisfies the equation


## [2020-07-13]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.


## [2020-07-13]Self-energy - Wikipedia

The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass.


## [2020-07-13]Self-energy - 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 W-boson and the Z-boson get their masses through the Higgs mechanism; they do undergo mass renormalization through the renormalization of the electroweak theory.


## [2020-07-13]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.


## [2020-07-13]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.


## [2020-07-13]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.


# [2020-07-13]Klein–Gordon equation - Wikipedia

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


# [2020-07-13]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.


# [2020-07-13]On the Higgs Mechanism

Likewise the mass of an electron (for example) can be associated with the coupling between the two 2-spinor components of Dirac’s model.


# [2020-07-18]Klein–Gordon equation - Wikipedia

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.


# [2020-07-20] dirac gif

[[https://www.gregegan.net/images/DiracAnimation.gif][DiracAnimation.gif (GIF Image, 500 × 330 pixels)]]


# [2020-07-24]Shtetl-Optimized » Blog Archive » Rosser’s Theorem via Turing machines

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.


# [2020-08-01]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 Minkowski-metric.


# Tweet from michaelnielsen (@michaelnielsen), 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


# 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?


# 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 real-valued function E on it, and a number T called "temperature".


# [2020-05-01] [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 spin-statistics theorem. But the anyons of condensed matter are nonrelativistic.

# [2020-07-03]">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


@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


# [2020-06-18]">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 sodium-ammonia 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 sodium-ammonia solution, electrons pair up with opposite spins.


# [2020-06-15]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) 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


# Tweet from @lisyarus Quantum Chemistry Done Wrong

@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…

# 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]


# [2020-10-18] 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.


# Unruh effect

## [2019-09-02] The Unruh Effect | Space Time - YouTube

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.

## [2019-09-02] Эффект Унру — Википедия

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]


## [2019-09-02] Unruh effect - Wikipedia

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


## [2019-09-02] What causes the Unruh effect? : askscience

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.


## [2019-09-02] 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 detector--some 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 radiation-reaction force in response. Ultimately, then, the energy needed to excite the Rindler detector does not come from the background energy-momentum 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 back-emf countering whatever is accelerating her. The accelerating observer interprets this as her passing through a thermal spectrum of particles instead.


# [2020-07-19]Talk:Photon/Photons and Mass Debate3 - Wikipedia

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


# from Lisitsa: алгебры клиффорда и спинорные группы [[towatch]]

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


# [2019-04-14] CFDPython/14Step11.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…

# [2019-01-25] 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 12-5)


# [2019-01-23] 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


# ¬¬(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]]

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.


hmm….

# На пути к теории всего https://nplus1.ru/material/2018/02/02/just-looking-for-some-action

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,


# 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.”


# [2019-02-11] A Journey to The Manifold SU(2): Differentiation, Spheres and Fiber Bundles [[study]]

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

# [2019-01-10]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

# [2019-01-23] Charts on SO(3) - Wikipedia

• State "STRT" from [2019-04-24]

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

## [2019-04-24] 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


S3 is a 4 dim sphere! hmm. although perhaps it's same thing as 3-ball 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?

# [2019-01-23] 3D rotation group - Wikipedia

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.


# [2019-01-24] How is a Lie Algebra able to describe a Group? – Jakob Schwichtenberg [[lie]]

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

# [2018-11-10] User ACuriousMind - Physics Stack Exchange

• State "STRT" from [2019-04-24]

# [2019-01-23] quantum mechanics - Spin operators in QM - Physics Stack Exchange [[spin]]

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


# [2019-01-26] * To semidecide this, just start generating every possible proof.

Gödel's first incompleteness theorem:

This property is semidecidable, but not decidable.


# [2019-01-26] * Suppose the property N[D[x_]D](y_) = (x_ ≠ y) is semidecidable for each x

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


# [2019-02-23] 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 self-contained chapters that introduce a single topic, discuss it in the necessary level of detail, and move on to the next topic.


# [2019-02-10] general topology - Triangulation of torus - understanding why - Mathematics Stack Exchange [[topology]]

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

# [2019-02-14] 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 EL-equations 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 Hamilton-Jacobi 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 HJ-equation is by the method of characteristics. The characteristic equations are precisely the Hamiltonian equations also learned in a typical mechanics course.


# [2019-02-14] 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 Euler-Lagrange equations, which is a set of coupled, non-linear partial differential equations. (The EL-equations are found by using L.)


# [2019-02-14] 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 non-singular 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.


# [2019-02-22] 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 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://math.stackexchange.com/questions/36683/math-and-music-theory-books[[musictheory]]

• State "STRT" from "TODO" [2019-02-21]

# The Reference Frame: Why are there spinors? [[spinor]]

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

# [2019-02-22] BookChapterLagrangian.pdf

chrome-extension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdfviewer.html?r=http://www.physics-quest.org/Book_Chapter_Lagrangian.pdf
whoa. that's something interesitng

# [2019-02-23] lec33.dvi - lec33.pdf

chrome-extension://gfbliohnnapiefjpjlpjnehglfpaknnc/pages/pdfviewer.html?r=http://www.tapir.caltech.edu/~chirata/ph236/2011-12/lec33.pdf
ok, this is kind of on the right track

# [2019-02-23] radiation.dvi - radiation.pdf

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

# Yoneda [[yoneda]]

## [2018-07-31] 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"

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


# [2019-03-04]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


# Higgs

## [2019-02-11] Higgs Mechanism

“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”.


## [2019-02-11] Higgs Mechanism

(Breaking of gauge symmetry is a bad thing, because the renormalizability, i.e. the removing of the infinities that pop-up in most quantum field theory calculations, depends on the existence of gauge symmetry


# [2019-04-24] at.algebraic topology - How to demonstrate (SO(3)) is not simply connected? - MathOverflow

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?

# [2019-04-24] Real projective plane - Wikipedia

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.


# [2019-04-24] 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


# [2019-04-24] 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.


# [2019-04-26] Quarks, Gluon flux tubes, Strong Nuclear Force, & Quantum Chromodynamics - YouTube [[viz]]

at 9:11 interesting visual explanation why the force is not decreasing for strong nuclear force

# [2019-01-17] Quantum Diaries

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


# [2019-01-17] Quantum Diaries

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


# [2019-02-10] 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)

# [2019-02-08] Spare me the math: the Lamb Shift | Gravity and Levity [[quantum]]

https://gravityandlevity.wordpress.com/2013/04/24/the-lamb-shift/
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!


# 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

# [2019-01-17] Looking inside the standard model: Electromagnetism, photons, and symmetry

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.


# [2019-01-23] what happens when computer: structural regular expressions [[study]][[project]]

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.


# [2019-06-12]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


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


# [2019-02-11] The Picture Book of Quantum Mechanics: Siegmund Brandt, Hans Dieter Dahmen: 9781461439509: Amazon.com: Books [[quantum]]

• State "START" from [2019-02-27]

# Tweet from Nikita Lisitsa (@lisyarus), at Jul 11, 22:23

Representation theory of the group with 2 elements at work


# 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


# [2019-01-15] 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

# [2019-06-20] 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"

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 MIT-licensed, incremental, commented implementation of MLS-MPM for softbodies and fluids: https://t.co/q26gakgHD1


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


# [2019-08-02] 〈 Berger | Dillon 〉 (@InertialObservr) / Twitter

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


# [2019-06-12] Quantum Diaries https://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/[[readagain]][[stm]]

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

# [2019-07-27] Michael Nielsen

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


# [2019-05-04] Cadabra manual: Sphere https://cadabra.science/notebooks/sphere.html

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


# [2019-07-23] 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. –


# [2019-08-03] (6) Abhishek Singharoy on Twitter: "The first study of an entire cell organelle in all-atom 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

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 :)


# 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


# 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


# 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


# 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


# [2019-08-18] (1) Daniel Litt on Twitter: "The fundamental group of SO(3) is Z/2Z! https://t.co/MnJS0YnNrJ" / Twitter

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


# [2019-08-19] (1) Daniel Piker on Twitter: "New 'Live Soap' component for interactive form-finding of minimal surfaces with topology changes https://t.co/YuARGfXlSO" / Twitter

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


# 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)


# 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 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


# 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


# [2019-09-06] 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

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!


## [2019-09-06] 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

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.


## [2019-09-06] 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


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


# [2019-09-29] 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

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.


# [2012-08-10]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.


# [2019-08-28]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 michaelnielsen (@michaelnielsen), 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


# [2019-01-05]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).


# [2019-01-05]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/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.


# [2019-01-05]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.


# [2019-01-23]Can Representation Theory be Explained Using Basic Abstract and Linear Algebra? /r/math

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.


# 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...


# 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).


# [2019-07-18]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 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.


# [2019-12-20] 1/(1 - 1/(1 - 1/(1 - Dan Piponi))) on Twitter: "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." / Twitter

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.


# [2019-12-24] 〈 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

〈 Berger |
🎄
| Dillon 〉
@InertialObservr
Putting it all together, we get the leading order Feynman diagram that led to the discovery of the Higgs Boson.


# 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


# 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.


# [2020-02-27]bollu.github.io | code + contents of my website, and programming life

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.


# [2020-03-24]Are quantum fields in any way similar to classical fields? /r/askscience

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.


# Tweet from @nntaleb

@nntaleb: Witness here how salaried physicists are dismissing @stephenwolfram 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


## 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:


# [2019-12-13] 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

That we observe a single eigenvalue isn't what interpretations are about. Interpretations try to explain WHY we do. Which is the whole problem.


# [2019-12-07] Mathematical formulation of the Standard Model - Wikipedia

Renormalization scheme (point)


# [2019-12-07] Mathematical formulation of the Standard Model - Wikipedia

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.


# [2019-12-08] newtonian mechanics - Anti-gravity in an infinite lattice of point masses - Physics Stack Exchange

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.


# [2019-12-08] 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.


# [2019-12-10] 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

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


# [2020-05-11]">\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?


# 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


# [2020-04-13]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

It took him until 1915 to find the equations of general relativity.   He needed the right kind of math.


# [2020-01-15] 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

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.”


# [2019-12-25] (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]]

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


# 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.


# [2019-12-02] Paul Dirac: The Mozart of Science (2008) | Hacker News

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


# [2019-12-25] (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

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".


# 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.


# [2020-07-09](1) 14 Subatomic Stories: Where Einstein failed- quantum gravity - YouTube

weinberg spin 2 boson GR

# [2020-07-14]">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


# [2020-02-27]bollu.github.io | code + contents of my website, and programming life

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


# Tweet from @johncarlosbaez

@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!


# [2020-07-09]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 лоренц-инвариантной величиной для безмассовых частиц.[2][3]


helicity

# [2020-07-15]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 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.


# 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


# [2020-08-19]">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.


# [2020-08-11]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?

# [2020-08-11]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 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.


# [2020-08-12]How can SU(2) group has 3 dimensional representation? - Mathematics Stack Exchange[[reprtheory]]

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


# Tweet from @akivaw

@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


# [2020-08-19]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 10-18 meters which is about 0.1% of the diameter of a proton.


# [2020-08-19]">Brian Skinner on Twitter: "@michaelnielsen @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.


# [2020-08-19]">Maissam Barkeshli on Twitter: "@michaelnielsen 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


# [2020-08-20]">Vijay Mocherla on Twitter: "@michaelnielsen 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


# [2020-08-23]special relativity - Why don't we construct a spin 1/4 spinor? - Physics Stack Exchange

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.


# 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”?

# Tweet from John Carlos Baez (@johncarlosbaez), at Sep 9, 08:09

@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!


# [2019-09-21] Shtetl-Optimized » 2013 » March The zone

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).


# 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


# 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.


# 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.


# 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.


# [2019-08-24] 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 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://t.co/Rn12So6iKf" / Twitter

[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:


# [2019-10-09] Три книги - Dee Mon. Былое и думы — LiveJournal

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.


# [2016-09-25] gravitational waves

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.


# [2013-02-15] 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


# [2020-08-26]Van der Waals force - Wikipedia

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


# [2020-07-18]The Hydrogen 21-cm 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.


# [2020-07-20]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 spatially-symmetric but spin-anti-aligned state, or in a spatially-anti-symmetric but spin-aligned state!


# [2020-07-30]">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.


# [2020-07-31]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 michaelnielsen (@michaelnielsen), at Aug 5, 22:37

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 ).


# [2019-10-19] 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.


# [2019-11-07] Bartosz Milewski on Twitter: "@johncarlosbaez @sigfpe I even adapted his notation to profunctors. https://t.co/f7p0BErEip" / Twitter

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


# [2019-11-10] michaelnielsen 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 earth-system aspect, and only gradually moves onto human-caused climate stuff." / Twitter [[climate]]

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.


# 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.


# [2020-06-02]">(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.


# [2020-06-19]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.


# [2020-06-19]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.


# [2020-07-03]">D ␣ a ␣ n ␣ P ␣ i ␣ p ␣ o ␣ n ␣ i on Twitter: "@johncarlosbaez @sarahzrf 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." / Twitter

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.


# Tweet from @johncarlosbaez

@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.


# [2020-03-14] 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

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.


# [2020-03-14] 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

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 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 - 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

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


# [2020-04-28] (1) The Holographic Universe Explained - YouTube [[physics]]

good intro to the holographic principle and ads/cft correspondense
scale invariance

# [2020-04-29]Tensors Explained Intuitively: Covariant, Contravariant, Rank - YouTube

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

# [2020-04-29]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

# [2020-04-30]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

@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.


# [2020-05-20]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

# [2020-06-12]Joe Rogan Experience #1203 - Eric Weinstein - YouTube[[study]]

55:10 hopf worlds weinstein

# Tweet from @johncarlosbaez

@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.


# [2020-06-23]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 non-abelian 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.


# [2019-02-14] Why The Schrodinger Equation Fails at Relativity : Physics

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.


# [2019-01-26] Locally constant function - Wikipedia

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).


# books [[study]][[electronics]]

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.


# [2019-02-11] Life on the lattice [[qft]][[qcd]]

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

# 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.


# 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

# 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


# [2019-03-04]plot of sin(z)/(z - mouse position) in the complex plane /r/math [[viz]]

This is generated with https://kisonecat.github.io/phase-plot/

# Tweet from John Carlos Baez (@johncarlosbaez), at Apr 10, 03:21 [[cattheory]][[baez]]

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


# 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.


# [2019-02-10] 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

# 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.


# 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


# 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


# [2019-06-28] 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)… "

Fong and Spivak's book on applied category theory is coming out! I'm getting my copy in the mail soon! (cont)


# 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


# Tweet from Derek Lowe (@Dereklowe), at Oct 11, 15:03 [[study]]

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


# 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.


# [2020-05-22]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.


# 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!


# [2019-08-06] reddit: the front page of the internet

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

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)


# [2019-11-24] Breit–Wheeler process - Wikipedia

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.


# [2020-04-14](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/some-re...
(2) The article above already discusses the derivation of the matter contribution to the Lagrangian density, the derivation of energy-momentum tensor, and Lorentz transformations for elementary particles.
(3) Both Hawking radiation and black hole entropy, and connections between our formalism and the AdS-CFT correspondence, are detailed here:
http://wolframcloud.com/obj/wolframphysics/Documents/some-qu...
(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 non-semiclassical black holes.
(6) (7) This we are still working on.


# Drill

## [2019-08-23] Cook–Levin theorem - Wikipedia [[drill]]

In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-complete


## [2020-07-07]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

# [2019-11-01] 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

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.


# [2019-10-01] 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

Okay, you've managed to cancel out any potential "insult" with an overload of praise.   It was this paper:
https://arxiv.org/abs/q-alg/9503002
The stabilization hypothesis, homotopy hypothesis, cobordism hypothesis and tangle hypothesis are in here.  No theorems, amusingly.


# [2019-11-12] 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

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)


# [2019-11-12] 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 Clebsch-Gordan decomposition. (8/8)" / 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 Clebsch-Gordan 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


# Tweet from michaelnielsen (@michaelnielsen), 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


# Tweet from michaelnielsen (@michaelnielsen), 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


# 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


# [2019-12-30] 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/G62SmoXuPchttps://t.co/uFCqVj4Exshttps://t.co/1QhwJVOKBIhttps://t.co/ZWhDtvFyju" / Twitter

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:


# [2019-12-27] notes10.pdf

http://www.math.columbia.edu/~woit/notes10.pdf
topics in repr theory woit

# [2019-12-31] Klein–Gordon equation - Wikipedia

Any solution of the free Dirac equation is, component-wise, a solution of the free Klein–Gordon equation.


# Tweet from @johncarlosbaez

@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 "spin-charge separation".


# Tweet from @johncarlosbaez

@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

@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…

# [2020-03-07] Phil Lynch on Twitter: "My copy of the Bible finally arrived https://t.co/8XomO2d887" / Twitter

My copy of the Bible finally arrived


wheeler gravitation

# [2020-03-08] On the shoulders of the giants | Hacker News

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

@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:


# [2020-03-19] 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

The CRC Handbook of Chemistry and Physics.

Imagine how much work it took to collect all that knowledge...


# [2019-02-13] The Frustrating Success of Our Best Theory of Physics – The Third Triumvirate [[relativity]][[physics]]

https://thirdtriumvirate.wordpress.com/2019/02/13/the-frustrating-success-of-the-standard-model/
fucking hell, really awesome explanation for standard model.. read it again!

# https://vk.com/wall-9471321_26902 Фундаментально ли время во Вселенной

• State "START" from "TODO" [2019-04-24]

# [2020-12-03]The fundamental Group of the Torus is abelian - YouTube

The fundamental Group of the Torus is abelian


video 'proof'

# [2020-12-20]Two-state quantum system - Wikipedia

The two-state 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 two-state system are oscillatory.


# [2020-12-20]Twostates03.tex - Twostates03.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=x-M-a-Gm9u8

## [2020-12-20]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.


# [2020-12-20]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 one-state 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

# [2015-01-11]Тензор энергии-импульса

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 3-мерный 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 энергии-импульса сводится к диагональной матрице ~{\rm{diag}}({{\rho}c^2},~p,~p,~p), где ~{\rho} есть плотность массы, а ~p — гидростатическое давление.


# Tweet from @gravitylevity

@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

@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

@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:


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# Tweet from @mekarpeles [[chinese]]

@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/...


# Tweet from Nick Sharp (@nmwsharp), at Jul 24, 13:25

Check out the fast-forward 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


# [2020-07-24]Shtetl-Optimized » Blog Archive » The Busy Beaver Frontier[[toread]]

an 18-page survey article about the Busy Beaver function: the staggeringly quickly-growing 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.