The h Bar

Balarka Sen

16:00

depends on your definition of $|...|$ obviously

Slereah

Ah

I thought it would agree with the metric of $\Bbb R$ for numbers that are neither infinitesimal nor infinite

0celo7

why would it

Slereah

"In term of geometry, we will see that in a non-Archimedean field, each ball is both closed and open, the parallelogram law could turn into an inequality1, every triangle is isosceles, etc."

Whaaat

0celo7

Can someone explain the difference between $D,H,E,B$ in Maxwell's equations pls

@Slereah sounds like some crap to me

Slereah

$D \approx E \varepsilon$

Something like that

0celo7

16:05

tensors showing up in EM

why

Slereah

Vectors are tensors, doncha know

0celo7

what even is a tensor

Bernard Meurer

Gotta keep the flow :p

ACuriousMind

@BernardMeurer Careful with writing such things

I know you're joking, people seeing the flag don't

aaaand someone insisted on flagging that twice

0celo7

One person flagged twice?

Slereah

16:07

Burn the witch!

ACuriousMind

Or two people flagged once, I can't tell the difference.

Slereah

It's probably @0celo7

He's a mischievous little imp

Vogel612

@ACuriousMind you seem to have many enemies. some joking, some not

ACuriousMind

@Vogel612 Yeah, this one was joking. Alas, the auto-ban got him.

Obliv

molts menschen hasst du @acuriousmind

Vogel612

16:08

text is bad at conveying jokes..

/s or </sarcasm> could've helped here ...

0celo7

molts?

ACuriousMind

@Obliv ???

Obliv

wtf google translate

viele

molts is catalan

Slereah

"The metric d enables to consider the notion of convergence in K."

0celo7

lel

Slereah

16:09

See?

No worries about convergence, mate

0celo7

@ACuriousMind Ich hasse dich nicht :)

Slereah

It's all good

Vogel612

@Obliv isn't that the wrong way round?

ACuriousMind

@Obliv You wanted to say "many people hate you"? That'd be Viele Menschen hassen dich.

Obliv

grammar is for losers

Vogel612

16:10

right now it says "You hate many people"

ACuriousMind

Or Sie instead of dich. I don't know how formal you wanted to be to me :P

0celo7

I like to think I don't have to be formal to you, Bajoran-desu

Obliv

@0celo7 that's not even a title given to someone

weeb

i guess that makes you less of a weeb though..

0celo7

What is a "weeb"

ACuriousMind

No one has to be formal to me, Sie used at me makes me feel really old.

Obliv

16:13

@0celo7 tell me what a tensor is and i'll tell u

0celo7

A tensor is something that quacks like a tensor

Er, transforms.

Slereah

No that's a duck

Vogel612

@ACuriousMind I've been told that "back in the day" you'd be addressed with "Sie" as soon as you were 15 or older. Probs because it meant you often already had work

Obliv

I think the saying was transforms not quacks

@0celo7 a weeb is someone who acts like a weeb, then. suck on that

0celo7

@ACuriousMind What's "a manifold is diffeomorphic to the zero section of any vector bundle over it, and the zero section is in turn a deformation retract of the total space" in German?

Slereah

16:15

Why does the triangle inequality fails in non-archimedean fields, anyway

ACuriousMind

@Vogel612 Ah, that's still kind of the "official" rule, I think - but no one except burocrats seems to follow that one anymore

Obliv

@0celo7 ein Verteiler diffeomorph zum Null Abschnitt jedes Vektorbündel über sie , und der Null Abschnitt ist eine Deformationsretrakt des gesamten Raum wiederum I think google is nearly perfect in its translations so this will make sense to @acuriousmind

0celo7

I speak nontechnical German fluently (albeity rustily), and that sounds horribly butchered

ACuriousMind

@0celo7 Okay, I'll bite: Eine Mannigfaltigkeit ist diffeomorph zum Nullschnitt jedes Vektorbündels über ihr, und der Nullschnitt ist wiederum ein Deformationsretrakt des totalen Raums.

0celo7

Bite?

Obliv

16:17

aber du ist ein amerikaner?

0celo7

Nein, ich bin ein Berliner.

Vogel612

Calling plagiarism?

0celo7

@ACuriousMind Danke

Still don't know what you meant by "bite"

I want to learn how to math in German

Vogel612

@0celo7 taking the bait, probably

Slereah

I hope you like Fraktur then

0celo7

16:19

@Vogel612 what bait?

I wanted a translation; what's wrong with that?

Slereah

Hm, do the sums of Cauchy sequences always converge in non-archimedean fields?

0celo7

Why do you care

Slereah

Why do you care about manifolds

0celo7

Manifolds are the most physical objects

I have not seen a non-archimedean field in the night sky

Slereah

Have you seen a manifold in the sky

0celo7

16:21

Yes.

Slereah

pix

Balarka Sen

@0celo7 Cantor set.

0celo7

The night sky is a manifold.

@BalarkaSen I haven't seen one of those either

Balarka Sen

You should look at a tree before looking at a night sky then.

Emilio Pisanty

0

Q: Why do we start learning physics so late?

When I was in school the only time physics like general relativity and special relativity were looked into were in AP classes. Why don't we teach the basic physics stuff in 7th-8th grade instead of in 9th grade, and then in 9th grade physics we teach people about particles, fusion/fission, GR, QF...

0celo7

16:22

@BalarkaSen What

Emilio Pisanty

*puts popcorn in the oven*

Obliv

@0celo7 are you so sure that the universe is locally euclidean??!?!

proof?

0celo7

Look around you

Balarka Sen

Boundary points of branches of a tree form a sufficiently high iteration of a cantor set :)

0celo7

@BalarkaSen Not the full thing, clearly.

Obliv

16:24

that's a physicists proof. for shame @0celo7

Balarka Sen

But there exists much more exciting fractal like patterns in the world.

John Rennie

@ACuriousMind: was it your downvote on the learning physics question posted a few minutes ago? I upvoted it to give the OP the rep to join the chat if they wanted, but your downvote took them back below 20 again.

0celo7

@Obliv I'm an engineer

What do you expect?

@BalarkaSen I don't actually like Bieber

Balarka Sen

Disappointed. But good.

0celo7

I have a whopping two songs on my iTunes with him

And I haven't listened to either

DanielSank

16:26

@Danu actually, if you cook them hot enough they might lose their heat and become one of the most unique, savory spices you've ever tried!

John Rennie

Not mainstream physics Shirley?

3

Q: What could happen if each of the four fundamental forces became stronger or weaker?

Theoretically, what could happen if: Strong interaction Weak interaction Gravitation Electromagnetism Became stronger or weaker? What would be the observable effects for each, separately?

electromagnetism forces gravity weak-interaction strong-force

DanielSank

@JohnRennie Perhaps, but 'tis a silly close reason.

Secret

http://physics.stackexchange.com/questions/23785/what-errors-would-one-learn-from-eliezer-yudkowskys-introduction-to-quantum-phy?rq=1

The gist of quantum mechanics: There is 'stuff' that contains a lot of information, that can superimpose and transform linearly and order matters, and that result in amazig things such as being in many places at the same time, probablistic outcomes, correlated results and much more

DanielSank

@JohnRennie Use "too broad".

John Rennie

@DanielSank A rose by any other name ...

DanielSank

16:29

@JohnRennie No no, the close reason matters: it tells OP how to improve.

0celo7

ROSEBUD IS THE SLED

DanielSank

"Not mainstream" tells them "go away, we don't talk about that here".

"Too broad" tells them to narrow the question and try again.

ACuriousMind

@JohnRennie Yes. It's not a useful question, and if it remains positively scored it will not be deleted by the roomba. 20 rep aren't that hard to get that users need pity upvotes, imo.

David Z

@JohnRennie It's standard model stuff, I wouldn't call it non-mainstream. I agree with Daniel.

Obliv

@secret have you found that post interesting or something?

DanielSank

16:30

I'm sure you'd be ok with a question like "if the electromagnetic force were to double in strength, what would be the effect on <some specific thing>".

No?

0celo7

@ACuriousMind 20 rep for you, maybe

John Rennie

@DanielSank No. When I want to read science fiction I open a book.

David Z

It might be a good question for Worldbuilding

John Rennie

Actually a tablet ...

Secret

@Obliv That's how I will explain everything about quantum (including the basic concept of the mathematical formalism) all in one sentence to a layman

DanielSank

16:31

@JohnRennie Ummm, that's an odd objection.

Understanding how the values of various constants affect Nature seems rather physicsy to me.

David Z

@DanielSank that seems totally fine to me. People write papers about that stuff.

Balarka Sen

So, what is spin of a particle?

I don't get it.

DanielSank

@DavidZ Normally I'd say "Who gives a $(&^ what gets accepted to journals?" but in this case I'll take what I can get :D

0celo7

Round and round the electron goes @BalarkaSen

Google on "Einstein-de Haas effect"

DanielSank

lol

Balarka Sen

16:33

OK. How does spin of a photon make sense?

0celo7

Spinors, dirac belts

John Rennie

@EmilioPisanty: did you decide my close vote was OK after all? I ask because I'm suddenly experiencing my usual angst about wielding the dupehammer.

Balarka Sen

Why's it "+1"? How does one see that?

DanielSank

@BalarkaSen Shankar's quantum book has an excellent explanation of spin.

Emilio Pisanty

0celo7

16:33

Take your belt, loop it around. That's a spinor. An electron is just a photon in a dirac belt configuration

Slereah

Take your belt, loop it around

0celo7

A 511 keV photon

Emilio Pisanty

@JohnRennie Yeah. Your answer in the first dupe is sort of inconclusive but the second answer does put in the numbers to say 'yeah, there's just no way here'.

Balarka Sen

@DanielSank I'll check it out.

DanielSank

@BalarkaSen Here's the basic idea:

Suppose I have some object in space.

Secret

16:35

It is something that has some sense of direction (e.g. at some orientation in space the probability that it is pointing "up" is 100%) and depends on the orientation on how it is measured. (for reasons I need to revise) always align with magnetic moment.

Spinors summarise their experimental properties well, but what actually it is, and why it is so sensitive to orientation, I have no idea

DanielSank

Now suppose I rotate my view of space around some axis.

Emilio Pisanty

@0celo7 Is it actually? I seem to remember a question asking whether there was a consistent quantum field theory built on that idea, but I've never been able to find it.

DanielSank

As I do this, the position of that object appears to change; that part is obvious.

0celo7

@EmilioPisanty That was me who asked it.

DanielSank

In addition the orientation of that object changes.

0celo7

16:35

I got banned for a week or so for it, too.

Maybe just two days

Emilio Pisanty

@0celo7 Yeah, I remember. Have you found it since?

0celo7

No.

DanielSank

Like, if I look at a floor tile and walk circles around it, the tile appears to be rotating relative to me, yes?

0celo7

Timaeus seems to think it's correct, but he's insane.

Other than that, there's JD.

It's an interesting idea, but it makes no sense when you actually look at it

Emilio Pisanty

@0celo7 Shame. As bad as that thread got, I would've liked for it to stick around. It would make an enormously useful pointer on a number of occasions.

Balarka Sen

16:37

@DanielSank Yes, I am aware of the idea. What I am unclear on is what the numbers mean. An electron can spin clock or counterclockwise: I am prepared to believe that based on Stern-Gerlach. What does it mean to say, then that a photon has spin "+1", if we denote clock/counterclockwise by +1/2 and -1/2?

0celo7

The main issue is of course how you get the photon to "go round and round"

Bernard Meurer

To whoever flagged my joke: I hope you live a very long life

5

Balarka Sen

lol

0celo7

@BernardMeurer Thanks :D

Balarka Sen

That's a good one

ACuriousMind

16:38

@BernardMeurer Reminds me of the Chinese blessing/curse May you live in interesting times ;)

Bernard Meurer

@0celo7 I knew it was you you mischievous devil

DanielSank

@BalarkaSen Patience, Grasshopper!

We're coming to that.

Balarka Sen

Ah, OK.

Emilio Pisanty

@0celo7 No. The main issue is that you can't turn a photon into an electron without making a positron. By the time you're done twisting your theory to fit the facts, it will look like QED.

DanielSank

@BernardMeurer Explain?

John Rennie

16:38

@0celo7 You're using a grinder on it? Are you insane? (More insane than usual that is :-)

0celo7

@EmilioPisanty There are lots of main issues, obviously, because it's wrong :P

DanielSank

@BalarkaSen Ok, it's obvious that if I turn a full rotation the object should look like it did before I rotated, right?

0celo7

Coming from a GR background, trying to bend light in on itself in a loop is what I see as the "main issue"

Balarka Sen

Yes, the object itself looks the same.

Emilio Pisanty

@0celo7 Sure. I would just like to be able to say "this has been discussed here previously, and no consistent and complete explanation was forthcoming".

0celo7

16:39

You could have some weird local geometry that does that...maybe

DanielSank

@BalarkaSen Ok, so in quantum mechanics, "same" means "same vector but multiplied by whatever phase you want".

Bernard Meurer

@DanielSank The other day someone came to rant to John Rennie, and after frustrated attempts to revert some vote said "I hope you die". During the same time a few people came to hate on ACM for close votes and things like that. Today I made a joke with him about it saying "I hope you die" in a reference to what happened to J.R., which he understood. People flagged and I got banned

DanielSank

Because the global phase in quantum is meaningless.

Balarka Sen

Sure.

0celo7

@JohnRennie No

DanielSank

16:40

@BernardMeurer oi vey

0celo7

I take it in my hand, then rub it against sand paper

Scientific grade silicon carbide polishing paper

DanielSank

@BalarkaSen Ok! So spin is essentially the value of the phase you get when you rotate some quantum object one time.

John Rennie

@0celo7 it sounds fun. Where can I buy some cerium?

0celo7

Glorified sand paper

It gets really hot and smells like fire

Bernard Meurer

@DanielSank Yeah, ffs ¬¬

0celo7

16:42

@BalarkaSen In your terms, states in quantum mechanics live in a projective Hilbert space

Balarka Sen

@DanielSank OK. Everything is still vague about what "phase" means, as in I don't know how to compute it.

DanielSank

@BalarkaSen Phase means the thingy in the complex exponent in a quantum state.

Or, if you want a more down-to-earth definition, it's the number you have to keep track of to understand the results of e.g. double slit experiments.

Balarka Sen

I do know that; I don't know how to compute this in this context.

0celo7

@JohnRennie Alfa Aesar? I dunno

John Rennie

@BernardMeurer well I flagged it as invalid.

DanielSank

16:43

@BalarkaSen Not sure what you mean. Each type of particle has a certain (max) spin.

0celo7

I'm getting samples from colleagues

Balarka Sen

But I guess you'll eventually tell me why photon has spin +1, so go on.

DanielSank

@BalarkaSen Ah, heh... no that I do not know.

0celo7

@BalarkaSen Photon spin is not easy to understand, that requires QFT.

Balarka Sen

Boo. Thanks though, that's actually what I wanted to understand :)

DanielSank

16:44

I don't know diddly squat about relativity, and I'm pretty sure you need it to understand photon spin.

Emilio Pisanty

For photon spin try e.g.

42

Q: Why is the $S_{z} =0$ state forbidden for photons?

If photons are spin-1 bosons, then doesn't quantum mechanics imply that the allowed values for the z-component of spin (in units of $\hbar$) are -1, 0, and 1? Why then in practice do we only use the $\pm 1$ states? I have been told that this is directly related to the two polarizations of the p...

photons mass quantum-spin polarization helicity

0celo7

And it's not "spin" for a photon

DanielSank

The photons I deal with have no spin ;)

Bernard Meurer

@JohnRennie Thank you John

0celo7

It's helicity

Bernard Meurer

16:44

Have you considered the adoption thing?

Emilio Pisanty

@DanielSank That's some funky non-photon photons

Bernard Meurer

Now that DanielSank is married he'll want a child of his own, so I need you @JohnRennie :p

DanielSank

@EmilioPisanty Well, we use "photon" in a way that would make a lot of the regulars here vomit.

Balarka Sen

@0celo7 Re projective hilbert space. so what does "rotation" do to the state in the projective space?

DanielSank

@BernardMeurer Do you come with any special features?

0celo7

16:45

@DanielSank got married?

ACuriousMind

::reaches for vomit bag::

Balarka Sen

I can't connect to the ideas here.

0celo7

@ACuriousMind what

Bernard Meurer

@DanielSank I can bike, install linux on things, immolate grapes and dance

DanielSank

@EmilioPisanty Suppose I have a vibrating string. It has modes. If it's a quantum string those modes have quantized occupation.

Bernard Meurer

16:46

I can also not move for hours

John Rennie

Just out of curiousity, when you use the :: whatever :: thing is it compulsory to italicise it?

Bernard Meurer

@JohnRennie yes. It's in the constitution of the h bar

DanielSank

@EmilioPisanty Now, if instead of a string I have the electromagnetic field in a metal box, we call those occupation units "photons". So far so good.

Emilio Pisanty

@DanielSank Sure. So a cQED photon then.

ACuriousMind

@BalarkaSen In mathematese: A "state" in quantum mechanics is a one-dimensional complex subspace (a "ray") of the Hilbert space, i.e. an element of the projective space. A "phase" is the ambiguity in choosing a unit length representant of such a state, and rotations act as elements of the projective unitary group.

John Rennie

16:46

@BernardMeurer where does the meme come from?

DanielSank

@EmilioPisanty The thing is, in our lab, we have vibrating electromagnetic strings. In other words, we have one-dimensional, electromagnetic-wave-supporting objects.

Bernard Meurer

@JohnRennie We have created it from the ashes of string theory

Secret

But why is that object in question so sensitive to the sequence of rotations wrt it (i.e. in formal jargon(?) spinors depends on the sequence of rotations that transform it)

e.g. if I rotate it this way followed by that way, I get something different than rotating it that way than this way

Also if spin is the value of the phase, then why placing two spins together don't give interference patterns of some sort? (we should expect them to interfere if their nature is some kind of phase)?

DanielSank

We call the occupation units of those things "photons" even though there's actually charge oscillating in there and there's no polarization.

John Rennie

@BernardMeurer even by your standards that makes little sense :-)

Bernard Meurer

16:48

@JohnRennie The olympics are here, I need to up my game for such competitions

0celo7

too many people in chat

Balarka Sen

@ACuriousMind Hmm, e.g., if I look at the Schroedinger equation, a particular eigenspace of $\hat{H}$ is my state inside the "space of all wavefunctions", whatever that means, yes?

Bernard Meurer

@0celo7 Your mom's in chat

l00ser

DanielSank

So put that in your theoretical rigor and smoke it, @ACuriousMind.

0celo7

hello mom @ACuriousMind

Bernard Meurer

16:48

lol

Emilio Pisanty

@DanielSank Yeah, I guess I never figured to ask. I imagine the waves in a superconducting circuit aren't what you'd call polarized, then?

Bernard Meurer

What is rigor?

Emilio Pisanty

Because otherwise it's much the same as a laser focus as in cavity QED

Secret

@BalarkaSen Experimentally, only phase difference can be observed. That is what responsible for the intereference patterns in quantum experiments when you are measuring some observable

DanielSank

@EmilioPisanty Nah, no polarization. They usually live in 1D, so there's no polarization.

ACuriousMind

16:49

@BalarkaSen The Schrödinger equation just tells you how states evolve in time. Since it's linear, it evolves all elements of a ray to the same ray, so although it it writte on vectors it descends to a well-defined transformation on the rays.

Balarka Sen

I am looking at the time-independent one though.

ACuriousMind

For all the fuzz that physicists make about the Schrödinger equation, all that it tells you is that $U(t) = \exp(-\mathrm{i}Ht)$ is the time evolution operator.

Emilio Pisanty

@DanielSank That's a bizarre statement, though. "No polarization that we need to care about" definitely works. But at the end of the day you presumably have electric fields with little arrowheads at the end, right? (Even if they are quantum mechanical variables and all that rigamarole.)

Balarka Sen

Right.

ACuriousMind

@BalarkaSen That one is just the eigenvalue equation for $H$ - its solutions are states that don't change in time.

0celo7

16:51

@ACuriousMind How is that exponential defined?

Why does it converge

ACuriousMind

@0celo7 By Borel functional calculus, cf. Reed & Simon.

0celo7

Do you know any of the proofs?

Emilio Pisanty

@BalarkaSen That's a disease you should try and get rid of

amazon.com/…

↑ That's a good way to do it

ACuriousMind

@0celo7 I know where I can look them up if need be.

0celo7

@ACuriousMind Aha!

Balarka Sen

16:52

I'll have a look at it, thanks. I don't really know anything about physics, though.

Emilio Pisanty

The TISE is an important tool and everything, but the real physics is the TDSE.

Secret

@EmilioPisanty TDSE is also important when you need to calculate things relevant to photovotalics and molecular dynamics (where the fun begins)

Danu

@DanielSank so like... All of them together and then save the end result to put in dishes?

And how about for a longer time as opposed to really hot---I don't have a good stove available here...

John Rennie

@EmilioPisanty I don't think we ever used the time dependent form in my theoretical chemistry courses.

Emilio Pisanty

@JohnRennie Sure. But presumably all the experiments you performed took finite time ;-)

John Rennie

16:56

As I recall just calculating the equilibrium wavefunctions was hard enough back in the early 80s.

Secret

@Acuriousmind I know (a bit?) on why spinors depends on the sequence of group elements that transform it (rotations, boost or in general the poncaire group action). But why spins (the physical object itself) is so sensitive to how its orientation in hilbertspace changes that if a different sequence of transformations are used, you get a different result.

Are there any papers put forward on explaining what spin actually is, and why it behaves like spinors?

ACuriousMind

@Secret What?

Emilio Pisanty

@JohnRennie Even if you are only performing a spectroscopic experiment to see whether your system absorbs light of a given frequency or not (a.k.a "measuring eigenenergies"), in the end your experiment is taking a system, subjecting it to a time-dependent perturbation, and seeing whether it will resonate or not.

ACuriousMind

spin is something that labels representations of the rotation/Lorentz/Poincaré group. It tells you how the object behaves under rotation.

Emilio Pisanty

@JohnRennie All QM experiments are TDSE experiments. Some can also be understood using the TISE for almost everything.

But have a look in Tannor :), they make a pretty strong argument that using the TISE as a tool will kind of fool you into thinking it's ontologically more important than it is. Even if it is your operational tool of choice.

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