The h Bar

0celo7

00:00

@ACuriousMind I think vector spaces do carry a canonical smooth structure if we take it to be compatible with the standard one on $\Bbb R^n$!

ACuriousMind

@0celo7 k. Take the maximum norm on $\mathbb{R}^n$. Is that thing smooth?

0celo7

?

ACuriousMind

@0celo7 I don't think it is - if it were, the unit ball should be a submanifold, but the square/cube has those awkward corners...

0celo7

I know

thinking...

dmckee

01:07

@ACuriousMind There's a short story by the name of "Schrödinger's Cat Woman" that involves mostly cats, but a few other animals as well rescued from the thoughtless abuse to which they are put in classrooms the world over.

DanielSank

01:33

^ ?

Sir Cumference

01:45

@ACuriousMind What does a duck say about protons? Quark, quark!

0celo7

why

if you were a master physicist I would understand

Sir Cumference

Like "quack, quack!"

That sound ducks make

TIL I learned that Newton's quote "If I have seen further, it is by standing on the shoulders of giants", was a diss towards his rival, Robert Hooke, who was kinda short.

My high school English class teacher clearly overanalyzed the quote.

Just like the people who think Schrödinger was in favor of QM when he came up with his cat.

0celo7

02:03

pretty sure he was

he was saying that the only physical thing in QM is measurement

everything else is irrelevant philosophy

there is no physical meaning to superposition

Sir Cumference

> Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics

Schrödinger's cat

Schrödinger's cat is a thought experiment, sometimes described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that may be simultaneously both alive and dead, a state known as a quantum superposition, as a result of being linked to a random subatomic event that may or may not occur. The thought experiment is also often featured in theoretical discussions of the interpretations of quantum mechanics. Schrödinger coined the...

Which cites a paper from Schrödinger

0celo7

thanks for repeating what I just said

(it's obvious you do not know any QM btw)

Sir Cumference

@0celo7 Meh, how much do you consider "any"?

0celo7

I guarantee you cannot state a full set of postulates.

Sir Cumference

@0celo7 I can grasp some of the main ideas of QM

That count?

0celo7

02:16

until you understand the mathematics, no

Sir Cumference

:(

Ah well, I'm looking into it

Regardless, I'd rather spend time learning GR. QM isn't too applicable in space (except things like degenerate gases)

0celo7

properly learning GR is too hard

Sir Cumference

ik. I'm trying to catch up on the maths

0celo7

the physicists are too lazy to write the math properly, and the math people reference the physicists for some stupid reason.

Sir Cumference

Well, if I'm going for a PhD in theoretical astronomy, it's on my list

Considering I'm an astro-nerd

0celo7

02:18

you will not learn GR the way I consider "proper," but I'm not a physicist.

Sir Cumference

So then what do you consider "proper"?

0celo7

Give me a few years

Sir Cumference

ಠ_ಠ

0celo7

My senior thesis might be a rapid, thorough introduction to mathematical GR

there are definitely some folklore theorems in GR I want to formally write proofs for

Sir Cumference

Why are you studying GR?

Aren't you majoring in nuclear engineering?

0celo7

02:20

I like geometry

Sir Cumference

Well then why not be a mathematician

You said you were sick of physics

0celo7

theoretical physics

Sir Cumference

Er...GR is pretty theoretical...

0celo7

I like the mathematical side

no hand waving physicist nonsense

Sir Cumference

But that's most of all theoretical physics

@0celo7 Huh?

0celo7

02:22

@SirCumference you don't know enough math to understand

Sir Cumference

This doesn't seem to be a mathematical conversation

0celo7

what?

Sir Cumference

Regardless, if you hate how physics doesn't provide explanations, why major in nuclear engineering?

0celo7

engineering does not attempt to explain in the way you think physics does

Sir Cumference

You'll end up studying QM or QFT

0celo7

02:24

I'm taking QM right now

QM is not theoretical

Sir Cumference

But you literally criticized it for not explaining where particles come from

0celo7

Where?

Sir Cumference

Long ago

0celo7

I said it's not a fundamental theory

which is true

Sir Cumference

You mean QFT is different?

0celo7

02:26

I don't really care about QFT

it's not fundamental

it's not useful

Sir Cumference

Okay, what's fundamental?

0celo7

no clue

Sir Cumference

What

Do you want something fundamental, mathy or just useful?

0celo7

vtc as too broad

unclear as well

Sir Cumference

"vtc"?

0celo7

02:28

vote to close

common lingo around the "stack exchange"

Sir Cumference

Well, you're criticizing QFT for not being fundamental nor useful

But then you're interested in GR

You're also studying QM even though you are sick of physics

Why not be a mathematician?

0celo7

pure mathematics isn't useful

Sir Cumference

But...nor is GR

In your case

0celo7

which is why I study it in my spare time

Sir Cumference

ok

Well anyway, I'll be learning GR soon enough

That day will happen, 0celo

0celo7

02:31

from what book

Sir Cumference

When you ask me a math question, and I'll answer it

That's the goal

@0celo7 I dunno, whatever book my school gives me

0celo7

what school

Sir Cumference

I'm going to be an astrophysicist

College, maybe graduate school

0celo7

name?

Sir Cumference

We've been over this

0celo7

02:33

I don't remember every conversation.

Sir Cumference

I think I brought it up a while ago, along with my ACT scores. Not something I enjoy doing.

dmckee

04:08

@DanielSank You can get a audio version of the story for free from Escape Pod. Not sure if there is a gratis text version.

It's short and fun.

@SirCumference I trust then, that you will be marrying someone in the for profit sector, right?

That's one of the few fields with worse long-term prospect than particle physics. Especially (in both cases) if you do theory.

Sir Cumference

@dmckee I know. Though I'm not sure if I have any other options

0celo7

I thought @SirCumference was going to be a doctor

Sir Cumference

It's really the only passion I've got

@0celo7 I dunno...

I've also heard that people who get a PhD to be astronomers are really employable in tons of other fields, since they have math and science backgrounds

So that's a plus

dmckee

Then work hard. You really want to be one of the lucky ones.

Sir Cumference

Lucky, as in one of the employable ones, or the profitable astronomers?

0celo7

04:12

the homeless people in front of Union Station in DC are astronomers by training

dmckee

@SirCumference This is more or less true, but not is a way that is good for your blood pressure.

If you can find someone to actually take your training seriously, and if you particular skills are in some sense a match for their needs, then they might interview you.

Once you get it, you've got a path forward, but getting that toe through the door is not easy.

Takes some lucky and a lot of persistence.

Sir Cumference

I know...I've thought long and hard about this. I've never had this much of an interest in any other subject, though.

I'm reading about astronomy on my spare time. I don't have much else I'd be passionate in

I was born with a bad passion.

It could be worse, though. I could've been born with a passion for something like art or acting.

Welp, I'll see where life takes me.

Some of the astronomy professors in my school are literally telling me "Don't be an astronomer if you want to make money. Only be one if you really, reaaallly want to be one."

I'll think it through over time.

Secret

04:42

sciencedaily.com/releases/2016/08/160825100949.htm Perhaps people might need to start thinking about the Lie algebra of deceit

(For those who are confused on what I am talking about, I am once again hijacking mathematics: Suppose loosely speaking we have an interrogation operator given by the commutator [individual,group], then based on how this research suggests that deceit in group differ from that of individuals, it might be possible that the order of interview matters, which using the hijacked maths will mean [individual,group]=\=0

We also expect the interrogation operator given above may not be actually a Lie algebra, but some more generalised notion of noncommutativity. For example the result of the commutator might be the function of its arguments and violate one or more Lie algebra axioms

0celo7

@Secret why do a lot of Asians seem to do analysis

Secret

They tend to be good at maths. Another reason might had something to do with finance being one of the most lucrative carriers in Asian countries

Otherwise I am not very sure

0celo7

The analysis I'm talking about is not financial math

Although there seem to be quite a few Asians doing geometry, too

Ricci flow is full of Chinese names

CLN cites 4 different Chengs

CLN are three Chinese dudes

just looking through the biblio

Chen, Cheng, Chau, Chang, Cao, Chu, Ding, Hong, etc.

Secret

The Chinese do contribute a lot in all science fields in general, you can find Chinese names in other research areas in numbers too. In some sense it is not surprising, back in the ancient Greeks, China already has a lot of scientific achievement from paper to gunpowder and some aspect of astronomy

0celo7

haha, this paper title

"On topological Tits buildings and their classification"

A cup, B cup, etc.?

Secret

05:02

On unrelated note, the above math hijacking thought have give rise another thought because it mixed with the motivation of defining a covariant derivative. I might experiment myself or ask the QM diff geom guys later on whether you can alway build a commutative operator from a bunch of commutators, and whether such notion is useful

Secret

sciencedaily.com/releases/2016/08/160825084633.htm Wow, biofuels are much worse in terms of carbon footprint than gasoline?

sciencedaily.com/releases/2016/08/160824172706.htm Attention addiction bias

John Rennie

05:28

@Dragonsheep the chat is a bit quiet at the weekends. You might want to try again later today (Monday). I have to say I find maths for mathematicians books deadly boring as for me maths is just a tool and I care only that it works.

John Rennie

05:48

@SirCumference Assuming you mean the world outside academia smart people are always readily employable and it doesn't matter what your PhD is in.

WhatAQuestion

08:26

what could be the ways of getting into research after school? (if someone knows i want to about research institutes in india)

Physics Meta

08:53

0

Q: Addition to the flags

There should be a flag to raise complaints like: 1) Lacks research efforts 2) Transfer to Chemistry SE Like this question: How supersonic plan could create shock wave?

feature-request

yuggib

09:56

@JohnRennie How can you be sure that it works if you don't check it? ;-P

John Rennie

@yuggib it works if the predictions it makes agree with the experimental observations. How can you be sure your maths works unless you do the experiments? :-)

yuggib

@JohnRennie That's (theoretical) physics, not mathematics. To be sure that a mathematics statement is correct (works), you have to write the proof (i.e. what builds up a book "maths for mathematicians"). And my question was "how can you use a tool if you don't know it is correct?" ;-)

John Rennie

@yuggib And there was me thinking that this is a physics site.

yuggib

@JohnRennie well, that does not prevent physicists to be mathematically ~~pedantic~~ correct :-D

David Z

11:08

@JohnRennie relatively employable, but the bar is pretty high these days for everybody

Sir Cumference

12:16

@JohnRennie Well, if I do decide to become an astronomer, my only solace will be that I'll earn enough rep on Astronomy SE to match my salary

John Rennie

@DavidZ In the UK right now there is a desparate shortage of clever, well motivated workers. If you can't get a job come to the UK. You have until two years after we sign article 50 :-)

Secret

http://physics.stackexchange.com/questions/277003/weird-light-dispersion
Classical diffraction problem in daily life

John Duffield

@0celo7 : who?

0celo7

12:33

@JohnDuffield what?

John Duffield

@0celo7 : who's the one person who can distract you away from math?

0celo7

@JohnDuffield Heidi Klum?

John Duffield

I don't suppose I could distract you with some physics? You know, some electron articles are absolutely dire. I'm on chapter 7: The electron. And if that doesn't cut it, I'm a tad unhappy because I've broken a cusp off one of my molar teeth. On a bank holiday weekend.

Secret

12:49

The time travel I have on the previous night has some plotholes because 1) It is from a dream and my dream recall is not photographic memory quality and 2) Dreams have weird logic on how things and causality works, which in the woken world, does not necessary makes sense

caption available shortly

0celo7

Did you just make that

Secret

nope I made that yesterday, spent 5 hours

ACuriousMind

what on earth am I looking at?

Secret

A timeline inforgraphic of the time travel story from my dream in the previous night

and I am going to elaborate shortly, (I need to figure out how to type it out in communication channel)

side note: The actual timeline inforgraphic that is constructed within my dream actually look a lot simpler and not very useful

John Duffield

@Secret : you cannot travel through time. Sorry.

Secret

13:00

Well it's dreams, anything can happen in dreams. I am not talking physics here

Closest reconstruction of the timeline infographic saw within the dream

Next, onto the story...

1. (forgot how the dream starts)

John Duffield

Nothing happens in dreams. They're just dreams.

Secret

2. It is now evening and my family and our friend Syria are helping out to prepare a banquet in a pierside restaurant

3. suddenly, there's a burning plate of steak heading fomr the stage onto the rear head of Syria, knocking her out

4. She is later pronounced dead

5. My cousin and I knew exactly what to do, we quickly went outside, where the moon shines bright on the ocean

6. We then hold hands, and raised the other with our palms facing forward and then we started to focus

7. The scene fades into morning. We are now back form a few days ago where Syria have lodged an appication for a police officer role or something

8. We approach one of the policeman which look like this:

and we gave him a paper package. We then waited a few hours.

9. Moments later, Syria happily told us that her application is approved (thus history has changed, because previosuly she failed the application)

10. MY cousin and I then zipped back to the present (actually a few hours later than the time we left). As we peeked through the restaurant window, the mayor is now on the stage and preparing to present an award of execellance for Syria's service to the community (and yes, Syria is alive and well here)

11. 3 days later in the evening, my family went to the tea house to have some supper. There are a lot of high school and primary school students eating there too

John Duffield

Anybody want to talk physics?

Secret

12. To our suprise, the president and his wife are visiting us. Given his reputation, however, this send me and sister into alert

13. The president recognised our achievement (details not revealed in the dream) which is why they want to meet with us to discuss about something

14. The worry of me and sis is confirmed when the students started acting weirdly and camera flashes started to appear

15. No longer can keep my cool, I storm towards one of the students and demand her to delete the photos

ACuriousMind

@Secret Why are you telling us your dream in so much detail?

Secret

13:14

1) I want to share about it, including the emotions and reactions of the various characters (I have cut away some of the detail already) 2) It's a time travel themed dream, thus some of that might be important in piecing the plot together

It is the emotions of the characters that makes this a bit long winded, if that's what you are thinking

If nobody's interested, I can just stop here

John Duffield

Frank Wilczek : "To understand the electron is to understand the world". OK chaps, I've got work to do. Bye.

Secret

13:33

3) When I typed that dream, all names are actually filtered. I knew that none of them are real which is why I knew when typing them out, there won't be even the slightest chance of the so called awkward situation. For starters, I knew of nobody called Syria, and the internet can freely guess on how many and what type of brothers and sisters and cousins I have because it does not matter what the truth is when it came to my highly personal info

(because the golden rule of the internet is to never ever share highly personla information)

Secret

13:48

4) One more possibility is I have no idea how to summarise it wthout losing too much important plot points

Sir Cumference

Joke time

Why did the photon go on a diet?

He wanted to stay light!

Wait, photons have no mass, so...

Secret

Next time if I am going to share a long dream, I think I will just post a link to my blog instead

2

since those tend to be better summarised than the chat version

Pichi Wuana

14:33

I have two cars of same mass (2kg) and a spring between (not attached, however). If I release them they will have same speed but opposite direction. And then I do the experiment again and add 1 kg to one of the cars. A book states that in both cases the sum of their kinetic energies will not change. How can this be possible?

John Rennie

@PichiWuana The total final kinetic energy has to equal the potential energy stored in the spring.

Pichi Wuana

@JohnRennie I don't know anything about the spring. Not the k or the l...

John Rennie

@PichiWuana Right, but the energy stored in the spring is the same in the two experiments. All you changed in the second expt was to add 1kg to one of the cars, and that didn't change the energy stored in the spring.

Pichi Wuana

@JohnRennie How can we know that that the kinetic energy has to equal the potential energy stored in the spring? And how do we know that the energy stored in the spring didn't change?

I tried to understand it with the fact that $E = U_g + E_k + U_{sp}$ but I don't understand.

John Rennie

The KE must equal the PE in the spring otherwise energy isn't conserved i.e. the total energy afterwards would be different to the total energy before.

Pichi Wuana

14:52

I understand that the sum of KE of one car plus the PE in the spring will always have the same value (so the mechanical energy of the car will be conserved), but not about the sum of both KE...

0celo7

@JohnRennie taking HF training

this is scary as hell

you can die from 2.5% skin exposure

@JohnRennie HF dissolves glass, how the hell do you store it

John Rennie

@0celo7 Gutta-percha

0celo7

@JohnRennie gonna throw Ce in HF and heat to 1700C >:3

in pure oxygen

John Rennie

It was nice knowing you :-)

0celo7

> Store in a cool, dry place away from
incompatible materials. HF reacts with many
materials therefore avoid contact with glass,
concrete, metals, water, other acids,
oxidizers, reducers, alkalis, combustibles,
organics and ceramics.

that's like...everything

> Store in containers made of polyethylene or
fluorocarbon plastic, lead, or platinum. Place
storage bottles in polyethylene secondary
containment trays.

who the hell has Pt beakers??

Secret

15:07

think platinum barrels

0celo7

I want a chunk of platinum :(

What's a fluorocarbon

Loong

@0celo7 I have a Pt crucible here.

Secret

It's basically a hydrocarbon with all H replaced by F
Telfon is one good exmaple
Fluorocarbons are extremely unreactive towards even the most aggressive chemcials, because of the strong CF bonds

0celo7

15:23

@Loong we do too

But it's pretty small

Loong

@0celo7 I still have a small scar from HF. It went through two gloves.

0celo7

@Loong I have to get training because the lab I need to use has HF in it. I pray I never have to use it myself.

Loong

two good ideas

Secret

What kind of expt you are doing that need HF besides glass etching?

0celo7

I don't need HF, I just said that.

I hope I never will need it.

Loong

15:29

@Secret I used it for breaking up of silicate in soil samples. That's actually quite similar to the reaction of glass etching.

John Rennie

@Secret It's used for etching certain metals.

e.g. titanium

And zirconium now I think about it. Many years ago I used HF for growing lamellar zirconium phosphate crystals.

DanielSank

@Secret HF is used for many things.

prokaryoticeukaryote

Hi

Anyone know anything about this reddit.com/r/science/comments/504wwz/… ?

sorry

I mean siliconrepublic.com/innovation/…

How can electrons be massless in that material?

Ahh, it mentions something called Dirac Electrons...never heard of them.

John Rennie

15:47

@prokaryoticeukaryote Dirac fermions. See for example:

9

Q: How do Dirac fermions arise in graphene, and, what significance (if any) does this have for high-energy physics?

Graphene has a honeycomb lattice (in the absence of defects and impurities). By considering the low-energy limit of the half-filled Hubbard model used to model the strongly interacting electron gas we find that the low-energy quasiparticles obey the dispersion relation for massless fermions. Thes...

condensed-matter graphene fermions

ACuriousMind

@prokaryoticeukaryote It's a rather strange material called a Dirac semimetal. I'm not sure how accurate it is to call the fermions participating in the conduction "electrons", though.

Loong

@prokaryoticeukaryote nature.com/articles/ncomms12516.pdf

dmckee

Is there a mathematically tractable, close to ordinary experience example of a system that a exihibits effective particle behaviors. Something we could, in principle, demo in the classroom or on a video?

Effective particle states are not something the non-specialists expects or knows how to interpret, and they are usually grossly misrepresented in the popular press.

prokaryoticeukaryote

@ACuriousMind @ACuriousMind too. So, this is clearly above my level of training. It sounds like a dirac fermion is one that is not its own anti-particle. I don't really get the significance of that. Obviously, I get that it not being its own antiparticle should imply several things, which might become more evident if I had more than 2 semesters worth of QM under my belt, but what does this have to do with being "massless"?

dmckee

It's be nice to be able to point at something relatively concrete and say, "No, it's kinda like that."

prokaryoticeukaryote

15:58

@Loong Thanks for posting that. I meant to post it, too

ACuriousMind

@prokaryoticeukaryote Nothing, actually. A "Dirac fermion" is just a name for a certain type of fermion, which can a priori be both massive and massless. It just turns out that in these "Dirac materials", conduction happens through states that "look like" the states of massless Dirac fermions.

John Rennie

@dmckee What is an Effective particle state? I Googled it but to no avail.

ACuriousMind

Where "looking like" probably probably means the dispersion relation is the same.

@JohnRennie I guess he means what's also called a "quasiparticle"

John Rennie

Like a condensed matter Dirac fermion then ;-)

Secret

Would a crowd with a vacancy moving about be a good example for what dmckee is looking for?

ACuriousMind

16:05

@JohnRennie Yes, I would assume dmckee's remarks are related to the topic being discussed ;)

dmckee

Hm. Well, I had in mind those quasi-particles that become the better (easier, clearer) basis for describing a system. The ones that specialists just start using every time they talk about the system in which they arise. Cooper pairs, phonons, and so on.

Not that I'm at all strong on the subject, but I've seen treatments where these thing arise and are applied.

Only those were at the grad-school level.

ACuriousMind

Well, the chat is a bit short on condensed matter people

dmckee

And in one case the speaker started with "An instaton is a topological soliton." and then launched into paragraphs of discussion which seems to mean something to some of the people around me.

@Secret The trick is to be able to convince your audience that the vacancy behaves—mathematically—like a particle with a mass. That it contributes to the momentum and energy of the system as if it were a particle.

John Rennie

A "Slinky spring" level description? Or are you looking for something more advanced than that.

dmckee

I don't know. What are the options? The "An instaton is a topological soliton" guy used a connected-pendulums-with-a-twist model that seems approachable at first, but he quickly headed for high altitude and I lost the thread.

Secret

16:14

If you are looking for non relativistic, then perhaps the momentum can be represented by how fast the vacancy move about in the crowd, and this depends on how fast each member of the crowd move about. For cooper pairs, I recall back in our uni there was one lesson where two students are assigned in pairs trying to push through a lattice of people. If the crowd is pre arragned with a specific instruction on how to move then it might be able to mathematically ilustrate the interactions of

the quasiparticle with the actual particles

As for energy, I am not sure

dmckee

ANy way. I'm off. Office hours and then my first class of the day.

0celo7

@ACuriousMind We've reached the age when nerds are writing textbooks

ref 544 in Hamilton's Ricci flow:

> Wachowski, Andy; Wachowski, Larry. The Matrix. Warner Bros. Studios and Village Roadshow Pictures, 1999.

Secret

For solitons, however, we have nice demonstrations like
https://www.youtube.com/watch?v=MADng1fqECY

Vortex rings are also nice demonstrations of quasiparticles (They move about as if they are a particle youtube.com/watch?v=pnbJEg9r1o8

0celo7

16:48

@ACuriousMind are you here?

Secret

> Well, the chat is a bit short on condensed matter people

The opposite of what's happening in my uni. We have too many condensed matter people and not enough theorist!

0celo7

@ACuriousMind Suppose I have a rep $G\to V$ of a group. Suppose the rep is reducible, and each irrep is an irrep for groups $G_1$ and $G_2$. Is $G=G_1\times G_2$?

DanielSank

@ACuriousMind I think this should not be closed.

@ACuriousMind Reporting in.

Secret

17:12

Dmckee is looking for nice class demonstration of quasiparticles, you have any good ideas on that?

ACuriousMind

17:26

@0celo7 now I am

@Secret There are condensed matter theorists. The two categories don't exclude each other

2

Secret

O, for that, we only have like 1, thus argument sorta holds

O maybe I should be a bit more specific, we have too many condesned matter experimentalist

so much that the maths part of the physics curriculum suffers quite a bit

We used to have a nonequlibrium stat mech theorist, but he had retired

0celo7

17:50

@ACuriousMind of you could answer my rep theory question that would be great

Although I might have found an easier linear algebra proof that works just the same

ACuriousMind

@0celo7 I'm not sure I understand the question - what do you mean by "each irrep is an irrep for groups $G_1,G_2$"? Are those supposed to be subgroups of $G$?

0celo7

If a group splits as a product, are the projects subgroups?

Products, not projects

@ACuriousMind dammit I mean factors

ACuriousMind

@0celo7 Yes

0celo7

Then they are subgroups but that's what I need to prove

ACuriousMind

Into $A\times B$, you get $A\times\{1\}$ and $\{1\}\times B$ as subgroups isomorphic to $A$ and $B$

@0celo7 Please more clearly state what the given situation is here, then

Where does the representation map on the $G_i$ come from if they are not subgroups?

0celo7

18:08

I'll give you an answer in a bit when I have computer access.

vzn

@prokaryoticeukaryote amazing! thx for sharing! there are some aspects of physis that QM is assumed to be able to explain but the precise explanations are unknown/ unmapped. and then there are some phenomena that may be "BSM", aka beyond standard model... have been looking into some theories that link mass with fluid mechanics, but they are very early/ preliminary/ undeveloped at this point...

@Secret wondering why you posted this. reminded me of another remarkable article/ book re drug addiction

@Secret you have a blog? where? when? something to put in your profile

Secret

In general: I tend to share sciencedaily article that might be somehow related to physics and/or interesting. For this in particular, I am trying to highlight how it might be possible that sometimes we got stuck at problems and overlok something else might have something to do we tend to unconsciously seek for the reward of certain ways of thinking

As for my blog, my wiki is my blog in a sense

for those who want to catch up of that long winded dream (if vanishing any), I have tidied it up here
http://secretuniverse.wikia.com/wiki/The_Time_Travel_Tunneling_Effect_(Story)

(and yes it is long ,it is typical of movie dreams)

0celo7

ok @ACuriousMind

in Mathematics, 1 hour ago, by 0celo7

@BalarkaSen I've had two books say that the property $\mathrm{Hol}_{(p,q)}(M_1\times M_2,g_1\oplus g_2)\cong \mathrm{Hol}_p(M_1,g_1)\times \mathrm{Hol}_q(M_2,g_2)$ is obvious, but when I sit down to do it I get lost

Holonomy groups are defined by representations, so I figured there might be some instant proof of this using representation theory.

What I know is that $T_pM_1$ and $T_qM_2$ are invariant under the action of $\mathrm{Hol}_{(p,q)}$.

So the representation of that group is reducible.

I'm thinking I should be able to block diagonalize the linear map

Then the question is how to show each block is an element of each factor

ACuriousMind

18:27

What do you mean "holonomy groups are defined by representations"?

0celo7

They are defined by the action on $T_pM$

ACuriousMind

I also don't know what your notation means, what are the $g_i$ in the argument of Hol?

Secret

0

Q: Symmetry transformations, compute infinitesimal change

I am doing classical field theory. According to Peskin, for the field transformation $\phi \mapsto \phi e^{i \alpha}$ i.e. $f(\phi) = \phi e^{i \alpha}$. That's alright. My problem is that he then goes onto saying for an infinitesimal transformation, the differential is $\alpha \Delta \phi = \phi...

field-theory classical-field-theory

0celo7

@ACuriousMind $(M_i,g_i)$ is a Riem. mfld

Secret

I wonder if the OP's original calculation is better since it took account of all higher order effects of $\alpha$, or is that not relevant (well I am not very good at taking approximations)...?

ACuriousMind

18:29

@0celo7 I'm not following you - the holonomy group is defined as the subgroup of $\mathrm{GL}(T_p M)$ that you can get by parallel transport along loops based at $p$.

What about this is "defined by representation"?

0celo7

you're defining the group by its action on a vector space, by definition a representation of an abstract group

@ACuriousMind If you know how to prove that above equation, great, I'll gladly forget about this algebra

I'm straying too far from my isle of ignorance

ACuriousMind

@0celo7 That the r.h.s. is a subgroup of the l.h.s. is clear. I have a feeling that you should get equality by considering projecting a loop in $M_1\times M_2$ down to $M_1$ and $M_2$, but I can't see how to show that's a group homomorphism.

0celo7

I agree with your first sentence.

And yes, projecting a loop makes sense.

But how to actually do that is confusing me.

prokaryoticeukaryote

18:52

@vzn Which theories are those?

@ACuriousMind So based on your exchange with @dmckee, @JohnRennie, etc, is it correct to say that the "electrons" mentioned in the article are quasiparticles?

In the sense that skyrmions are quasiparticles?

0celo7

What about Skyrim?

prokaryoticeukaryote

@0celo7 haha

Skyrmion

In particle theory, the skyrmion (/ˈskɜːrmi.ɒn/) is a hypothetical particle related originally to baryons. It was described by Tony Skyrme in 1962 and consists of a quantum superposition of baryons and resonance states. It could be predicted from some nuclear matter properties. Skyrmions as topological objects are important in solid state physics, especially in the emerging technology of spintronics. A two-dimensional magnetic skyrmion, as a topological object, is formed, e.g., from a 3D effective-spin "hedgehog" (in the field of micromagnetics: out of a so-called "Bloch point" singularity ...

ACuriousMind

@prokaryoticeukaryote Yes, although how far they are from actual free electrons I don't know

prokaryoticeukaryote

Science reporting needs to do a better job

I mean, why can't they just call them charge carriers, and note that they are electron-like? Why call them electrons?

0celo7

19:28

@ACuriousMind Is it clear to you that $T_pM_1$ and $T_qM_2$ are invariant under the combined holonomy group?

now, we can split the combined tangent space as $T_{(p,q)}M_1\times M_2=T_pM_1\oplus T_qM_2$

so I think an isometry $f\in \mathrm{Hol}_{(p,q)}$ splits as $f=f_1\oplus f_2$

where each $f_i$ acts on one of the tangent spaces

so now you have to argue that each $f_i$ belongs to one of the factor holonomy groups

@ACuriousMind Ok, a loop in the combined space is a product of loops in the factors. So a loop in $M_1\times M_2$ is of the form $(\gamma(t),\lambda(t))$

What needs to happen now is that $f_1$ should depend ONLY on $\gamma(t)$

and $f_2$ depends ONLY on $\lambda(t)$

hmm...

DanielSank

19:51

PSA: I was just chatting with a coworker who is a light user of our site. He noted:

> I do notice that a surprising number of the comments basically amount to telling off the asker... not sure what that's about.

This is a very level-headed individual who comes here with the best intentions.

Whether or not this observation is a reflection of anything objective is irrelevant. That this is the first impression gleaned by a cool headed individual is not in the best interests of the site.

vzn

@prokaryoticeukaryote particles ≈ solitons/ space ≈ fluid... have some refs/ papers on that. maybe simple place to start is here, have collected many other angles wired.com/2014/06/the-new-quantum-reality

DanielSank

@dmckee @Danu @ACuriousMind @DavidZ see previous comment.

Worth keeping in mind. I'm trying to get this person to participate more.

vzn

@DanielSank totally sympathize with your efforts to make site more userfriendly, but did you ever read that SE ceo article "sand vs pearls"? think you are fighting uphill battle that is not limited to this SE

0celo7

@ACuriousMind Does parallel transport furnish a homomorphism from the loop group to the isometry group?

Certainly yes

that might be the answer...

David Z

20:29

@DanielSank That's not particularly useful feedback without knowing more about what constitutes "telling off". Like, if they're talking about comments saying that the question is off topic, does that represent something we should change? Plus, it is just one person's opinion. It's worth keeping in mind only to the extent that it's representative of all our potential new members.

Danu

@DanielSank I'm not sure exactly why I am being pinged for this :P

Other than that, it's a shame he/she/it sees it that way... I second @DavidZ's comment. What if the person thinks it's rude for us to tell people that their question is off-topic?

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