Pauli matrices Puns

In my lecture notes they use S_x in the first line but then later they use sigma_x: https://imgur.com/a/1NcqVA4

What is the difference between these two?

I had an assignment where I was to calculate the expected value of sigma_x, sigma_y and sigma_z.This was done in the presence of a uniform magnetic field in the x direction (Rabi oscillation)

What I got is that the expected value of sigma_x = 0, sigma_y= sin(theta) and sigma_z=cos(theta).

I then got a finished code to plot two Bloch spheres with my given psi which had phi = pi/2 and theta = a trigonometric function.

When I then plotted the expected value of sigma_x, y and z to visualize how it changed depending on time and also in a second sphere plotted how |psi> changed depending on time, these were identical throughout the animation:(<sigma_x,y,z> to the right and |psi> to the left.

What is the reason behind this relation between these two? Why are they identical through time?

I know that the pauli matrices is a way of describing the electron's spin, but doesn't psi do that as well?

Should I always expect sigma_x,y,z to be the same as |psi>?

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In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory

L=12∂μϕ∂μϕ+αβ2cosβϕL=12∂μϕ∂μϕ+αβ2cos⁡βϕ

can also be described in terms of fermions as the massive Thirring model

L=ψ¯(iγμ−m)ψ−12g(ψ¯γμψ)(ψ¯γμψ)L=ψ¯(iγμ−m)ψ−12g(ψ¯γμψ)(ψ¯γμψ)

where the particle created by ψψ can be understood as a kink of sine-Gordon, and the particle created by ϕϕ can be understood as a bound state of two fermions from the Thirring model.

Unlike sine-Gordon, ϕ4ϕ4

L=12∂μϕ∂μϕ+12m2ϕ2−14λϕ4L=12∂μϕ∂μϕ+12m2ϕ2−14λϕ4

has only two vacua in the broken symmetry phase. I'm wondering whether here too we can write fermionic creation operators for the kinks, and rewrite the theory as a local field theory of the kink fields?

The reason I think we can is that we can do this for the quantum Ising model which has much in common with ϕ4ϕ4. The Ising model is defined on a 1d spin chain, and the ground states in the broken symmetry phase are where the 3rd component of the spins are either all pointing up or all down.

The operators ψ1(i),ψ2(i)ψ1(i),ψ2(i) are defined at each lattice point ii in terms of Pauli matrices as

ψ1(i)=iσ2(i)∏ρ=−∞i−1σ1(ρ)ψ1(i)=iσ2(i)∏ρ=−∞i−1σ1(ρ)ψ2(i)=σ3(i)∏ρ=−∞i−1σ1(ρ)ψ2(i)=σ3(i)∏ρ=−∞i−1σ1(ρ)

The infinite product part acts to flip the 3rd component of spin to create a kink, and the Pauli matrix part gives it the usual fermionic anticommutation relations.

It turns out in the continuum limit ψ1,2ψ1,2 act like two components of a free Majorana fermion. Can ϕ4ϕ4 also be expressed in terms of a Majorana fermion? What are the relations for the fermion field of ϕ4ϕ4 that are analogous to the relations for ψ1,2ψ1,2 in terms of Pauli matrices?

Hi all, I'm doing a couple of quantum questions at the moment and just have a quick question:

I must find the eigenvalues, λ, and eigenvectors, V, of the Pauli matrix σ_x

I've had no trouble finding these per se, getting

λ= 1, -1

V= [1 1], [1 -1]

(these should be column vectors but I don't know how to format that).

My issue is that I've looked at some answers online that give a root(1/2) in front of the eigenvectors. Where does this come from? How come this isn't true for all the Pauli matrices?

The Dirac and Pauli matrices have interesting properties that are sometimes very similar to those of quaternions but with slight differences, that makes me think, are they related?, do all of these objects belong to some more fundamental category?, and if they do, then why are they all over physics?.

Say I have a sum, 1a + ib + jc + kd, where 1,i,j,k are quaternions and a,b,c,d are vectors. I can choose to represent the quaternions as pauli matrices, but what happens to my vectors? Do I need to transform the vectors such that the pauli matrices can act on them?

Hello,

I know that [;\sigma^\mu=(\textbf{1},\sigma^i);] with i=1,2,3 in 3+1 spacetime dimensions. But how do I know the components of the "vector" [;\sigma^\mu;] for other dimensions?

We want to find three matrices with the properties:

a_i * a_j + a_i * a_j = 2 delta_ij

a_i * b + b * a_i = 0

b^2 = 1

Aren't the properties of the Pauli matrices exactly following these relations?

What properties constitute proof of a group? All I know is the set has to be closed. What other steps do I need to do before I can prove this? Note, I'm not looking for someone to do it, I just don't know what to look for.

Like last year I share my extended list of 2021 ambient and related genres of music. The list is quite extensive, with 185 albums, but it covers lots of ground, ranging from new age to electroacoustic, or from modern classical to drone and dark ambient/more experimental; and from the more established artists to the more underground acts. But all have something in common, the ability to create one or various atmospheres/moods/feelings.

P.S. - every year I get messages to narrow it down to the top 10 or something. This list is not ranked and is vast in scope, meant for all the diggers out there. Happy digging, and Merry Christmas!

The list:

36 & Awakened Souls - The Other Side of Darkness

36 & Duenn - Distance As Power

A Winged Victory for the Sullen - Invisible Cities

Abul Mogard - In Immobile Air

AES Dana - (a) period.

Ai Yamamoto - Love Me Tender

Alessandro Cortini - Scuro Chiaro

Alex Smalley - Vanaprastha (The Man Who Went Into The Woods To Find Himself)

Alice Damon - Windsong

Alphaxone & ProtoU - Back to Beyond

Amulets - Blooming

An Moku - Less

Andrew Tasselmyer - Impulses

Andy Stott - Never the Right Time

anthéne - the slow wave

Arash Akbari - Fragments of Yearning

Arkadiusz Salwowski - Distance

Arovane - Reihen

Arrowounds - The Rise and Fall of the Melting World

Arushi Jain - Under the Lilac Sky

Balmorhea - The Wind

Bendik Giske - Cracks

Black Brunswicker - Temple of Spring

Black Swan - Repetition Hymns

Bobby Lee - Origin Myths

Brett Naucke - Mirror Ensemble

Burning Pyre & Canadian Rifles - The Snipe & The Clam

Byron Westbrook - Distortion Hue

Camp Of Wolves - Granite Creek

Carlo Giustini - Tutto Quadra

Celer - In Light of Blues

Chihei Hatakeyama - Late Spring

Christine Ott - Time to Die

Chuck Johnson - The Cinder Grove

Claire Rousay - A Softer Focus

Dave Depper - Europa

David Cordero - Lambda {λ}

David Granström - Empty Room

David Shea - The Thousand Buddha Caves

Dead Melodies - Fabled Machines Of Old

Devin Shaffer - In My Dreams I'm There

Domiziano Maselli - Lazzaro

eleh - Snoweight

Eluvium - Virga II

Emra Grid - threatening omens in the clouds

Erik Levander - Jökel

Espen Lund - ÆTONAL

Fallen - Ljós

Federico Durand - Herbario

Federico Mosconi - Dreamers and Tides

Field Works - Cedars

Floating Points, Pharoah Sanders & The London Symphony Orchestra - Promises

Florian T M Zeisig - Music For Parents

Frédéric D. Oberland - Même Soleil

Future Museums - Pre

i find it interesting that there are actually a lot of not woo people who also embrace the woo :

• Chiara Marletto and David Deutsch ( creator of the "hello world" of quantum algorithms ) present constructor theory as a potentially general theory, embracing both classical and quantum theory through counterfactual statements.
• Brian Josephson ( nobel prize winning developer of the Josephson junction ) is kind of working with Ilexa Yardley (who is crazy or a genius or both idk) to develop circular theory, a theory which amongst other things, says God can be represented by a circle.
• Jung and Pauli ( who created the Pauli matrices ) were homies and Jung had a lot of quantum mystical ideas so i think Pauli possibly at least entertained them, but im not sure.
• David Bohm ( who was advised by oppenheimer and kind of mentored by einstein) had his own kind of quantum mystical worldview of "unfolding wholeness".
• Von Foerster ( one of the influential cyberneticist and an important enough quantum physicist to attend the macy conferences ) developed the idea of an eigenforms or eigenbehaviors which he offered as a kind of quantum inspired sociological tool .

All of these people ( who are distinguished , minus Yardley ) , want to use a kind of quantum-inspired mode of thinking to describe human scale experience. I think that is kind of a wrinkle and kind of cool.

So SU(2) has three generators (associated in some way with the weak interaction bosons). These generators are the said to be the Pauli matrices as they have determinant =1 and they form a basis for the 2x2 unitary matrices. Please correct me if I'm wrong.

However when I try to form a basis for U(2), I end up with 4 matrices, the identity and the 3 pauli matrices. Why is the identity not one of the generators of SU(2)?

Representation of Lorentz Group

Hello. I have been asked to figure out the Lorentz group representation for a Spin-2 Field using the fundamental spinor representation and show how this object transforms for a study group. But I am having extreme difficult understanding the basic premise of Spinor Representations of the Lorentz Group.

Why for the Dirac field is it the direct sum (1/2,0)+(0,1/2) and not a tensor product instead?

Why is the EM field strength tensor given by (1,0) + (0,1)? Where does this come from? I understand that the spin is 1 for photons and therefore the object must be of this angular momentum (j=1, j=0) , hence the (0,1), but couldn't one have done (1/2,1/2) then as well?

For the Rarita Schwinger spin 3/2 particle, how is the representation (1/2,1/2) X ( (1/2,0)+(0,1/2)) = (1,1/2)+(1/2,1)? The dimensions don't even line up, one has 4x(2+2) = 6+6 , or 16 = 12 ??

Finally, for a spin-2 particle, would the representation not simply be (2,0) X (0,2) since j=2 and the dimension of the representation would need to be 5 since m=2,1,0,-1,-2. Then, don't the transformation matrices of the Lorentz group (rotations and boosts) need to be 5x5 to transform such an object? But this point also doesn't make sense to me because aren't there only 3 rotations and 3 boosts???

Apologies for the ignorance, but none of this is making sense to me and any advice would be greatly appreciated!!

This review consists of two parts: an overview with marked spoilers and unmarked mild thematic spoilers to help potential readers decide if this work is right for them, and a more in-depth analysis, which contains unmarked moderate spoilers for Orthogonal.

#Overview

Tenet: Don't try to understand it, feel it.

Me: Oh come on, Nolan. That's just lazy, now. You call this sci-fi? You know you can't just slap some vague technobabble on it and call it a day, right? I hate how so much science fiction feels the need to dumb it down for the masses. What's the point of hiring renowned physicists to consult on your movies if you end up with scenes where your pilot has to have wormholes explained to him when he's literally in sight of the one he's about to fly through? I wish there was something out there that puts in some actual effort in the worldbuilding, something smart. Something that doesn't treat its audience like idiots. Such a shame, too. Inverted matter looks really cool.

Monkey's paw: *curls*

...

Well, the good news is, I found a story like that. The bad news is, having read it, I now feel like an idiot.

Welcome to the world(s) of Greg Egan, who puts the 'hard' in 'hard science fiction' in more ways than one.^1 He's the author of works such as Permutation City and Sqchild's Ladder, which are considered some of the hardest science fiction novels ever. But while those are set in more-or-less our world, Egan's most valuable contribution to the genre (at least, in my opinion), is his alternate universes, which run on different laws of physics from ours.

Orthogonal is a trilogy of novels (The Clockwork Rocket, The Eternal Flame, & The Arrows of Time; roughly 1100 pages total) set in one such universe. I chose it as my first Egan work to read largely because of its concept, which was just too intriguing for me to resist. From the blurb on the website:^2

>In Yalda’s universe, light has no universal speed and its creation generates energy.

>On Yalda’s world, plants make food by emitting their own light into the dark night sky.

>As a child Yalda witnesses one of a series of strange meteors, the Hurtlers, that are entering the planetary sys

I don't want to step on anybody's toes here, but the amount of non-dad jokes here in this subreddit really annoys me. First of all, dad jokes CAN be NSFW, it clearly says so in the sub rules. Secondly, it doesn't automatically make it a dad joke if it's from a conversation between you and your child. Most importantly, the jokes that your CHILDREN tell YOU are not dad jokes. The point of a dad joke is that it's so cheesy only a dad who's trying to be funny would make such a joke. That's it. They are stupid plays on words, lame puns and so on. There has to be a clever pun or wordplay for it to be considered a dad joke.

Again, to all the fellow dads, I apologise if I'm sounding too harsh. But I just needed to get it off my chest.

Ok so, hear me out before ripping me to shreds. I am a first-year physics major in research with quantum computing at my university, so I haven't taken quantum yet but I've gone through about half of Griffiths. I am basically going off of whatever self-studying I've been doing since the beginning of the year, bare minimum high school computer science, and some of the Qiskit global summer schools.

Problem:

The model for quantum machine learning that my research group uses is simulating a time-dependent Hamiltonian with small delta t. I have figured out how to simulate a time-independent Hamiltonian (as long as it can be decomposed into a sum of Pauli matrices), but have failed thinking of ways (or rather, understanding the papers with time-ordered matrix exponentials?) of simulating its time-dependent cousin.

"Solution":

Like the title said, I was thinking of just creating a function that outputs the Hamiltonian at some time t_i, then decomposing it into the sum of (the tensor product of) pauli matrices and simulating that for some small delta t. (which means I'd have two incrementing values, the t_i at which I'm evaluating the Hamiltonian and the delta t for which I'm simulating the state of the Hamiltonian at time t_i).

An important restriction that might make things simpler is declaring that the Hamiltonian could be restricted to the form of the sum of (the pauli matrices times some time dependent function) (i.e. the time-dependent tunneling amplitude of qubit A times the pauli X gate that acts on A).

I'm pretty aware that this idea is implausible and my computer is likely to blow up in the process. The Trotter decomposition for each t_i would get messy if I wanted to avoid as much error as possible, but I already know that the fact that I'm simulating the Hamilton at t_i for some delta t sounds pretty error-ridden, which is why I'm asking for suggestions for better ideas. Thanks!

Do your worst!

I'm surprised it hasn't decade.

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

It really does, I swear!

Because she wanted to see the task manager.

They’re on standbi

Pilot on me!!

Nothing, he was gladiator.

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

When I got home, they were still there.

I won't be doing that today!

The work being described is by Prof S. James Gates and it has a serious basis. He has noted that the supersymmetric equations of string theory contain some binary codes built in. These are the same as codes sometimes used in computing for error correcting. I think he means the self dual 8-bit Hamming code in particular.

Gates has hyped this quite a bit suggesting that it is a sign that we are living in a computer simulation as in the film "The Matrix".

In fact these codes are ubiquitous in several areas of mathematics. They are associated with sphere packings, lattices, reflection groups, octonions and exceptional Lie algebras (especially E8) It is not particularly remarkable to see these coming up in string theory. There are other string theorists looking at these structures in a less hyped way to understand the role of algebraic concepts such as octonions and E8. See e.g. papers by Mike Duff and collaborators.

People working on quantum computing are also looking at these codes which are examples of stabilizer codes that can be generated as eigenvectors of Pauli matrices. They hope that the codes can be used to prevent decoherence and that this would make multi-qubit quantum computation feasible.

It is not as if they have discovered sequences of coded instructions that the laws of physics are following.

It is an interesting intellectual exercise to think about the way the universe might run like a computer or quantum computer.

Source : https://www.reddit.com/r/MandelaEffect/comments/fnorc6/regarding_actual_computer_code_discovered_in/?utm_source=amp&utm_medium=&utm_content=post_body

Could it be possible to code at quantum level to store larger source of energy in less space?

It's a Random thought. Your suggestions are welcome.

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Where ever you left it 🤷‍♀️🤭

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

There hasn't been a post all year!

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "