The h Bar - 2016-01-14 (page 2 of 3)

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8:00 AM

@ChrisWhite Thanks for cleaning up my pictures :)

@ChrisWhite SUCKER ;)

(congrats)

Hi guys... physics.stackexchange.com/questions/229168/… <- cool question

"Can the uncertainty principle be explained intuitively to a non-scientist"

What do you think of this explanation (perhaps suitable to programmers): You can't write a program to measure the time it takes to measure something, without altering the actual time it takes to measure it.

ie. The measurement actually takes time. You can of course measure it from outside... infer it... from outside. But that's cheating... and in reality nothing is "outside".

@Dagelf Seems okay as an analogy, but it isn't an explanation really. It doesn't give any insight into why it is the way it is

user54412

It's also dangerously close to the measurement fallacy some of those questions allude to: the uncertainty principle is not a statement about measurement limitations, but rather a statement about how a system cannot even have small uncertainties in position/momentum or whatever simultaneously.

@0celo7 You said you were, my lord.

Yo, how do I show that the derivative generates translations?

Suppose I have $V(t)$.

Now I cook up a translation operator $T_{\delta} = \exp(\delta (d/dt))$ or some such thing.

Maybe there should be an $i$ in there.

8:11 AM

Taylor expaaaand

yah

So I Taylor it

Act on $V(t)$

note that it's the translation

Hi, I want little help in math any one can?

1+1 /= 3

Then I get $(T_\delta V)(t) = \left( \sum_{n=0}^\infty \frac{\delta^n}{n!} D^n V \right)(t)$.

8:12 AM

how to convert this to quadratic 3x^2 = l^2+x^2-2lx?

@MuhammadRaza Maybe you should go to Mathematics

^ Yes.

That's a straight-up math question.

I guess my thing about translations is too...

I'm trying to get to a physics thing though.

w/e

@DanielSank Yes, which is $V(t+\delta)$

@Danu I'm too stupid to see why.

@ChrisWhite Fair point... but can't we get very philosophical about the whole concept of "an uncertainty"? Yes, it's not an instrument problem - it's a fundamental observation about reality.... but we're still the observer and to observe we use perception and thinking tools, so it is not, then, perhaps a "feature" of our way of observation... our way of thinking... and by extension, a complex fundamental measurement problem?

8:13 AM

Not kidding, I don't get it.

It's the Taylor expansion of $V$ around $t$

^ If you do a taylor series of V also

You'll see they match

zomg you're right I'm so dumb.

user54412

In other news, I got a rejection from a prestigious fellowship I applied for (no surprise, really). They haven't even sent out acceptances, but they certainly knew they wanted to reject me. I think this makes me the only person who's worked with my adviser who hasn't gotten this or an equivalent fellowship.

The only tricky thing is the multiplication: It's by $(t+\delta)-t=\delta$

8:14 AM

@tpg2114 Don't you think that's what the question asks for - a metaphor to help people who have little grasp of physics or mathematics, feel that it makes sense? Ie. a metaphor or analogy?

$V(t + \delta) = \sum_{n=0}^\infty (\delta^n / n!) V^{(n)}(t)$

@DanielSank yeah

Which is what I wrote before.

My god I was being a total retard.

Thanks.

^lel

No problem

I needed a rubber ducky.

3

8:15 AM

Eh? :P

Rubber duck debugging

Rubber duck debugging is an informal term used in software engineering for a method of debugging code. The name is a reference to a story in the book The Pragmatic Programmer in which a programmer would carry around a rubber duck and debug their code by forcing themselves to explain it, line-by-line, to the duck. Many other terms exist for this technique, often involving different inanimate objects. Many programmers have had the experience of explaining a programming problem to someone else, possibly even to someone who knows nothing about programming, and then hitting upon the solution in the...

@ChrisWhite Idk, but I think it's pretty common to send out rejections before acceptances.

@Dagelf No, it was asking for an intuitive explanation of the physical reason behind it. I don't think it was asking for more analogies.

I recall a CERTAIN UNIVERSITY WHERE YOU WORK doing this to me @ChrisWhite

user54412

:( Sorry

8:16 AM

@ChrisWhite Pffft, I never got a fellowship in my life.

That's fine @ChrisWhite :P

Three stars in a row. I'm on fire!

We all like rubber duckies

Hmm... five stars in a row?

^no

8:17 AM

::crickets::

I guess there are a lot of good people applying for your fellowship @ChrisWhite

The competition is probably much stiffer than for PhD spots

Don't beat yourself up about it

user54412

I really want to gather data on things like PhD admission rates and fellowships in my field, but people are rather cagey about it.

user54412

Academics will always pretend that anyone who doesn't get a position "didn't really want one, and left to do better things," which is obviously not always the case.

So are you not getting any fellowship? Or is this just one rejection with more replies still to come?

@ChrisWhite LOL really?

That's so incredibly naive!

@ChrisWhite Academia is pretty in denial about how many jobs it can support.

user54412

8:22 AM

There's more to come. I just like sharing bad news.

I feel like everyone goes to grad school thinking they'll get a professorship, or at least they sort of let that hazy idea sit in their heads.

Then everyone sort of realizes that's impossible / they don't want it.

@ChrisWhite Good :)

It's odd, because getting a PhD is incredibly valuable in other lines of work.

user54412

@DanielSank Not going to lie: I wouldn't have gone to grad school if I actually internalized the odds of that happening. But I intentionally didn't think too hard on it.

@ChrisWhite yeah it's weird. I think a lot of folks are like that.

Yet, so far the people with whom I went to grad school are doing well in non-university jobs.

8:24 AM

@ChrisWhite Sigh...

One friend went to Wall Street to do crazy math, another is doing really well in a photonics company, I'm at Google, etc. etc.

I'm also in the process of thinking long and hard about WAT DO

user54412

I mean, at some level I'm afraid part of my motivation to do anything comes from irrational drive against poor odds.

2

user54412

I don't really want to give that up.

I really don't feel like I can be happy in any non-academics situation, but that's probably also just because I can't imagine anything else since I've wanted this for so long

What's bothering me most of all is that even if I somehow "make it" and get somewhere in academics, my personal life will probably be shitty because of it.

8:26 AM

@Danu I think that's a terrible indoctrination forced on you by academia's refusal to admit that anything worth while / interesting happens outside of university halls.

@Danu Yeah, and there's that.

@DanielSank What's the $\delta$ in that notation?

I mean, when I got a job at Google doing quantum mechanics people joked that I was now an "engineer".

Since I'm super focused on having a happy family life etc. (to the point where I think it's definitely more important than any job I'll have), this is a huge problem for me.

@DanielSank ...and you still show that you're pissed about it once every week or so ;D

@Danu I haven't mentioned that in months.

@Bass It's a variable representing a number.

Nothing special.

Poor choice of notation, perhaps.

user54412

@Danu Of course, every one of my profs is happily (I presume from what I've seen) married, most with children.

8:28 AM

@DanielSank So it's like an "infinitesimal $\epsilon$"?

@Bass No, it's literally any real number.

Oh I see.

user54412

Every time I hear an academic proselytizing about the importance of family and how they wouldn't be here without their spouse, I want to ask them point blank if that means single people should just quit now.

@Danu I'm not pissed about the label, I'm dismayed that academia pretends that the majority of the rest of the world doesn't exist and misleads students to think that:

2

1) Only academia does interesting science.

2) Everyone should be a professor / it's the "best" job.

This leads to a lot of undue depression because it's impossible for everyone to live up to the insane expectation that they'll make it as a prof.

It's not even what most students should do.

@ChrisWhite I can't say anything specific about my professors, but based on the vast majority of my married friends with children, I would say that appearing to be happily married is pretty often just an appearance

8:31 AM

Agreed :P

user54412

@tpg2114 Ok, true enough.

@DanielSank I was just saying that to piss you off :P

@Danu I know.

You're clear as a book, dude.

On purpose, dude.

Else you'd actually get pissed off again ;)

...that metaphor doesn't quite work...

Books aren't that clear...

Like, not in the electromagnetic sense.

8:33 AM

textbook? :P

@DanielSank D'oh

"Clear as a bell"?

I never understood that one.

I gotta get going... Go to my lectures :\

CFTTTTTTTTT

ciao

aka more advanced string theory than what we do in string theoryyyyyy

(string theory is frigging boooriiiiiiiing)

Cya

@ChrisWhite And most of my professors are very successful and most are single, so it is possible to be unattached and have things go well

I think giving credit to their spouse is more like "Thank you for not killing me for working 24/7" :)

8:36 AM

@DanielSank It also leads to many people doing PhDs just because they don't want to leave academics, people who don't really have academic ambitions.

@Bass Well, I don't have academic ambitions, but I went for a PhD on purpose.

I wanted the training.

Hey @DanielSank

I wanted to go from n00b to I-can-build-stuff-and-figure-things-out in a short amount of time.

In some industries, non-academic jobs require PhD's because of the training they get

That's what an experimental PhD is.

Hi, TanMath.

8:38 AM

What I do not like about you is that you never respond to a message unless you happen to be in the room...

user54412

I've debated my professors on this, because I'm reasonably sure an astro PhD is not a requirement for any outside-academia work (they largely oppose me on this).

Btw, how late do you stay up @DanielSank

2:00am?

@DanielSank Right, academic ambitions was too narrow. I meant, people who don't really want to do the PhD. They just want to stay at the university. In maths and physics this might be rare, but I have seen such people in literature and sociology and such topics.

user54412

Sure, it makes us hireable as data scientists or maybe traders, but a year interning would teach me more about data science, and my BS was enough for finance.

@ChrisWhite That could be true for an astro PhD -- there probably isn't much work outside of academia in that field. Government work like NASA exists (are you lumping that into academia?). In aerospace, the vast majority of jobs are in private industry and they all want PhD's

8:41 AM

@MuhammadRaza if you need math help, go to the math chat room, not this one or the PPCG one...

I mean all companies want people with PhD's, not that all jobs require a PhD

user54412

@tpg2114 Yeah, the few NASA astronomers I consider to be essentially academics.

@ChrisWhite And national labs? Do they hire astros?

user54412

Same thing -- there's a small handful of computational astro jobs there, and they behave like (and interact with) university-based academics.

Yeah, okay. National labs are the same in aerospace. It's really just an academic position without the teaching, which makes it pretty awesome

8:43 AM

Yay! Finally we have transitioned to the new SE version!

@TanMath Is English your first language?

Yes...why?

@TanMath I'm trying to figure out whether or not several of your recent comments indicate a massive lack of respect.

3

I guess they do.

I'm blocking you now.

I won't receive any more of your pings etc.

user54412

@tpg2114 The more I think about it the more I want to teach classes and advise PhD students.

@ChrisWhite Do it!

user54412

8:45 AM

Of course, perhaps actual experience with those will change my mind ;)

ok...well that is not how I wanted this to go...

I really like the idea of advising PhD students

Heh, I doubt it.

I give up...

@tpg2114 It's really really hard, fyi.

8:46 AM

Teaching, maybe... doing like intro to calculus, no way

@DanielSank I can imagine. It's hard to teach people in general, but particularly hard to teach them when you don't already know the answer

And to put it out for anybody who cares...I respect @DanielSank ...but it doesn't matter anymore looks like...

And to teach them to figure out the answers themselves

user54412

The problem with teaching is doing large required classes that have uninterested students. That's pretty demotivating, I'll admit.

@tpg2114 yeah, and your mortgage depends on them getting the answer so you can get funding...

Yeah, I wouldn't be all that into that. My brother actually really likes teaching those classes though

8:47 AM

@ChrisWhite I had to do that sort of.

It sucked.

Quantum mechanics course, and half the students didn't seem to care at all.

user54412

Some of my best courses, though, were large introductions where everyone was eager to learn -- I really like the idea of being the person who first explains to freshmen how E&M really works.

@DanielSank For all the reasons my boss is... uhhh... the spawn of Satan... he's made getting funding look so ridiculously easy

So I have to give him credit for that

We've never had to worry about funding in our lab, and we almost always have more projects/grant money than students or staff to use it all up

@tpg2114 Wow. Where are you again?

Georgia Tech

Cool

8:51 AM

Right now, we probably have... 20 active projects in our lab, but only 6 students and 4 post docs

In the past, we've had as many as 30 students

user54412

By the way, I assume the reason we're all here and not snorting platinum-infused cocaine off supermodels in our brand-new sports cars (or whatever suddenly-rich people do) is that we didn't win the lottery.

What if I decided to put physics chat in the dashboard of my sports car?

You don't know my life.

Yeah... no lottery winning going on here.

@ChrisWhite Well, the check hasn't cleared yet.

yo whats up??

9:16 AM

You know, I do agree I may have been rude, but that is since I am pretty impatient...

winter break is going to end within a couple of days, and my next chance to work on this project will be spring break!

I am sorry @DanielSank

This is what I am about to do -> :'(

9:38 AM

QM question: Let's take a wall with a slit that is so narrow that if two particles cross each other in the slit, then they *must* scatter (or the probability that they scatter is very high). If they scatter, they hit the wall and won't be detected at the other side of the wall, where we have detectors. Now imagine a second slit. With just one particle, in one direction, this is the standard double slit experiment (with very narrow slits, but I suppose that most double-slit experiments must have narrow slits).

10:34 AM

I think there would be an interference pattern, but I'd be very grateful if someone with more quantum experience could confirm that.

The outgoing particle pair is some kind of EPR pair, isn't it? The superposition $(|a\downarrow b\uparrow\rangle+|a\uparrow b\downarrow\rangle)/2$ forms an entanglement. Though, it would be useless for actual EPR experiments, since there's no way to collapse the superposition into one of these states after the wall.

Does this all make any sense?

3 hours later…

1:49 PM

@0537 I'm trying to learn multiple integrals...oh my god

2:38 PM

@ChrisWhite Why would I contaminate my precious cocaine with platinum?

@Bass Uh...what? What do you mean "timed to cross the wall simultaneously" or "the probability that they scatter is very high"? Quantum objects don't have a definite speed, and to say that the "probability they scatter is very high" you'll have to either give the actual interaction Hamiltonian or make plausible that that's actually what you get when you make the slit narrow.

(When browsing a scifi forum recently, in post 2222)
http://hi.gher.space/forum/viewtopic.php?f=4&t=1093&start=30

That users idea is very similar to that 2 time hamiltonian particle in a box attempt I have tried earlier (discussed with Acuriousmind about 2 weeks ago), which is later pointed out to not work because the hamiltonian can only afford a single parameter that describe the system's evolution
---

However what I am currently focused on is wondering about something else:

It is kinda amazing that all the lifeforms we knew of can reflect visible light (except microorganisms)

so if I understood correctly, because of the diffraction limit, microorganisms are only visible either under shorter wavelengths of light, or other ways of image such as neutrons, electron microscopy etc.?

@Secret Ever looked through a microscope? :P

You can see bacteria under a light microscope, it's just a bit difficult because they're transparent and small

But if you color them, it's pretty doable

Thanks for reminding
oops, I am thinking about nano sized things like viruses (should have made that clear) (but it is debatable on whether they are alive, really)

@ACuriousMind have you took any biology labs before? I always enjoy watching things like euglena swimming around, and stained streptococcus aureus forming chain like pretty patterns etc.?

@ACuriousMind Say we have an electron cannon on the left and a positron cannon on the right of the wall. The cannons are synchronized, so they emit a particle at every full second. If the wall has one very small hole, then we have the following possibilities: a) at least one of the particles hits the wall, b) the particles annihilate each other inside the hole, c) they both pass the hole. I'd like to do a Gedankenexperiment where the whole apparatus is designed to minimize the probability of c).

2:53 PM

@Secret Haven't done a single shred of biology since school

Does that make sense?

I see. Last time I did it is back in year 3 taking a microbiology class

By "pass the hole" I mean: get detected at the other side. By "hit the wall" I mean get detected inside the wall.

@Bass I don't think you can say "the particles annihilate each other inside the hole". If you're considering them as quantum objects, I don't think you'll be able to localize the annihilation interaction that precisely.

And I'm not convinced you can design the apparatus to "minimize c)"

@ACuriousMind And if I say "the particles annihilate each other"? In the absense of any particle detection, we just assume they have annihilated each other.

2:57 PM

@Bass well, you'd be able to detect the photons they emit upon annihilation, wouldn't you?

@ACuriousMind But certainly if the hole is like, 3 meters wide, the probability of c) is higher than if the hole's diameter is $100nm$, no?

@Bass I'm not convinced of that. Applying classical reasoning like "if it's narrower they must be more likely to meet" doesn't always go over well in quantum physics.

I'm not saying you're wrong, I'm just saying I have no actual reason to believe you're right

@ACuriousMind Yes. I wanted to express that the location of the annihilation doesn't matter.

You'd have to describe the entire setup carefully quantum-mechanically, and doing that in a setting where there can be annihilation is going to be a pain

Could you tell me what the purpose of this experiment would be? Maybe we can resolve your underlying question without this experiment?

@ACuriousMind Well but I'm sure LHC is designed such that the particles follow a path that's as narrow as possible, to increase the probability for scattering, no?

3:02 PM

@Bass Not sure. Scattering takes place in a "localized region", but it doesn't occur at a point. All the talk of "scattering" and "collision" is classical metaphor.

The moment you are imagining little balls flying around you're being classical, and I wouldn't trust any conclusion about the quantum theory you draw from that image

Balls, lol

They're Möbius bands

9 hours ago, by DanielSank

You are such a troll.

1

Q: Minor design updates to site

You may have noticed some minor updates to site design this week, they are part of a SE network-wide update to a new base css framework. The updates allow us to: Use SVG icons for retina display Fix layout bugs More easily add new features to all of our sites in the future But more import...

discussion design

@ACuriousMind gdi

I had a mathy question for you but I forgot it

@ACuriousMind also nice, quoting the puppetmaster

@ACuriousMind Yes, probably there are better setups/experiments for my purpose. If we have two particles (or generally, two quantum systems) $a$ and $b$ which are both two-state systems with base states $|a\uparrow\rangle$, $|a\downarrow\rangle$, $|b\uparrow\rangle$, $|b\downarrow\rangle$.

Then the separate systems are described by superpositions $c_1|a\uparrow\rangle+c_2|a\downarrow\rangle$ and $d_1|b\uparrow\rangle+d_2|b\downarrow\rangle$, right?

$c_i,d_i\in\mathbb C$

3:12 PM

@Bass Well, those are at least possible states for them

Whether they are "described" by that or not depends on whether they are in those states or not ;)

So the combined system is $c_1d_1|a\uparrow b\uparrow\rangle+c_1d_2|a\uparrow b\downarrow\rangle+c_2d_1|a\downarrow b\uparrow\rangle+c_2d_2|a\downarrow b\downarrow\rangle$.

@ACuriousMind Okay but if we can pick $c_i, d_i$, we can pick them as $c_1:=\langle a\uparrow|\psi\rangle$ etc, so we know that the states are described by these superpositions.

Right so far?

@Bass Ah...I understand what you mean, right.

@ChrisWhite When I do our gen-eds I simply teach to the subset of the class that cares. That about 1/3 of the "for poets" class and about 2/3 of the algebra/trig intro sequence (mostly would-be healthcare professionals of various sorts.)

@ACuriousMind Now, to allow for entanglement, the combined system allows for states that are not just tensor products of the separate systems, so we must write new coefficients: $e_{11}|a\uparrow b\uparrow\rangle+e_{12}|a\uparrow b\downarrow\rangle+e_{21}|a\downarrow b\uparrow\rangle+e_{22}|a\downarrow b\downarrow\rangle$

This is the most general state of the combined system, right?

Yes. (Side note: Using 2D systems to think about entanglements is possibly the worst choice one could make)

3:19 PM

@ACuriousMind Is it? Okay, more on that later.

Oh! @ACuriousMind What's a good reason to use abstract tensor notation? Coordinate freeeeee is not an acceptable answer.

"I hate indices" is similarly bad.

@0celo7 How am I supposed to know? The only place I've ever encountered abstract indices is in rare questions here on Physics.SE

@ACuriousMind Oh, not abstract indices. Standard math notation.

$g(X,Y)$, etc.

Ah.

Well, coordinate-free is the answer.

Mathematicians prefer to have symbols for the abstract mathematical objects, not for the numbers one calculates stuff with

Yeah, but what do you do when you encounter a crappy looking object?

Like $R_i{}^jR_{jk}$

3:23 PM

@Bass Yes, because $\mathbb{C}^n\times \mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$ have the same dimension if and only if $n=2$, and the difference between the two spaces is precisely what entanglement is about.

@0celo7 You'd have to encounter such things often enough in the mathematical context for the mathematician to maybe change their mind

@ACuriousMind Hmm.

Now, the experiment is set up so that the states $|a\uparrow b\uparrow\rangle$ and $|a\downarrow b\downarrow\rangle$ would be detected at $t=t_0$, but the other ones later at $t=t_1$. Like in the Renninger negative-result experiment, where one hemisphere of the detector has a smaller radius than the other, so if a particle (with spherical wavefunction) is not detected at the inner hemisphere,

we know that the wavefunction has been changed to one where all amplitudes that would hit the inner hemisphere have been removed.

@ACuriousMind Makes sense so far?

Great PSE deleted most of my draft.

Good thing I backed it up.

@ACuriousMind If I imagine a scattering event as in some region in space, where initially there is nothing, then some waves (e.g. assume they are all circular) got all superimposed together, and then these waves then depart with both their phases and amplitudes changed, is this still a classical mindset and thus not a good way to understand scattering?

I imagine it as a partial wavefunction collapse. Those eigenstates that would have lead to detection have been "removed" from the state.

3:27 PM

@Bass Yes, but I don't like that this seems to be going towards a discussion of collapse :P

@ACuriousMind I don't think my question has to do with quantum interpretation or measurement, if you mean that :) but I'm not 100% sure..

@Secret Of course. Waves are just as classical as particles.

@Secret If the waves are going around Dirac belts, yes, it's good. /s

@Bass We'll find out, continue

Is the best understanding of quantum is something that is neither wave like nor particle like, but can superimpose linearly?

3:30 PM

So, if we don't have detection at $t=t_0$, then we know that $e_{11}=e_{22}=0$. Thus, the only states left in the superposition are $|a\uparrow b\downarrow\rangle$ and $a\downarrow b\uparrow\rangle$, because the other states would have lead to detection.

So this particle pair is now entangled, isn't it? If particle $a$ is measured to be $\uparrow$, then we know without measurement that $b$ is in $\downarrow$.

@Bass Yes.

Whohoo! Then I think my "question" is already answered. I was just wondering whether one could build entangled particles without a measurement event to occur.

About the other thing: Now we have two two-state systems that are entangled.

Where's the problem?

@ACuriousMind (I mean the problem you mentioned here)

@ACuriousMind Is the best understanding of quantum state is something that is neither wave like nor particle like, but can superimpose linearly? and that we can either model these things as path integrals or C* algebra?

@ACuriousMind Let $\Phi^{\mu'}{}_{\mu}$ be the Jacobian of the coordinate transformation $x^\mu\mapsto x^{\mu'}$ and $\Phi_{\mu'}{}^{\mu}$ its inverse. A $(k,l)$ tensor field is an object with components $t^{\mu_1\cdots\mu_k}{}_{\nu_1\cdots\nu_l}$ with the property that its components $t^{\mu_1'\cdots\mu_k'}{}_{\nu_1'\cdots\nu_l'}$ in the transformed coordinate system $x'$ are

$$t^{\mu_1'\cdots\mu_k'}{}_{\nu_1'\cdots\nu_l'}(x')=\Phi^{\mu_1'}{}_{\mu_1}{\cdo‌ts} \Phi^{\mu_k'}{}_{\mu_k}\Phi_{\nu_1'}{}^{\nu_1}\cdots\Phi_{\nu_l'}{}^{\nu_l}t^{ \mu_1 \cdots\mu_k}{}_{\nu_1\cdots\nu_l}(x)$$

crap

@Bass Doesn't the "standard" way of producing them already do that? Let a photon do pair production. It produces an electron and a positron whose individual spin is unknown, but whose spin together must be that of the photon, and that gives an entangled electron-positron state

3:41 PM

@ACuriousMind Oh. I see. :D I see I keep asking long complicated questions which have easy answers...

Mornin folks

@Bass In this case, there is none. People just sometimes managed to confuse themselves in this case, but that wasn't the issue here

0

Q: Why sum of gravitational and inertial acceleration here?

In attempt to describe the consequences of the Equivalence Principle: When there are gravitational accelerations present, as for example in the gravitational field of the earth, the space cannot be the flat Minkowski space. Indeed, in the Minkowski space we can have $$Γ^λ_{μν}=0$$ everywhere. Th...

general-relativity special-relativity equivalence-principle

This person put unicode in TeX dollar signs

???

it works though.

the Greek letters are upright, it looks strange

3:45 PM

@ACuriousMind So both $\mathbb C^2\times\mathbb C^2$ and $\mathbb C^2\otimes\mathbb C^2$ have complex dimension 4. You said and the difference between the two spaces is precisely what entanglement is about. But, as we just saw, entanglement is still possible here.

@alarge My computational fluid dynamics course begins today and I have to decide a language to use, I'm going with python for now, do you agree with this decision?

I suppose the solution is some kind of vector space completion, but I'm not sure which and how.

Protip: Whenever h bar sensed I asked a wrong question, it will went dead air for at least 2 hours

This is supported by at least 1 month of evidence

@Bass The point is that although, abstractly, $\mathbb{C}^2\times\mathbb{C}^2\cong\mathbb{C}^2\otimes\mathbb{C}^2$, the map $\mathbb{C}^2\times\mathbb{C}^2\to\mathbb{C}^2\otimes\mathbb{C}^2, (\psi,\phi)\mapsto\psi\otimes\phi$ is not an isomorphism, and its image are precisely the non-entangled states.

@ACuriousMind And the vector space completion of the image is the whole tensor product, right?

3:55 PM

@Bass If you mean the span by "vector space completion", then yes. Completion has another technical meaning, which one has to do in the infinite-dimensional case.

@ACuriousMind Oh ok. I just mean something like "the smallest vector space that contains the image of your map as a subset". Thanks a lot for your help!!

Ah yes. Completion in the limit sense.

Based on what I have discussed with the users some time earlier in this chat, it seems whatever a quantum state is, it seemed to be neither wavelike nor particle like (because both are classical notions). The maths (whether it is state vector, density matrices, C* algebra or path integrals) however seemed to suggest they always obey superposition

@Bass Yep, that's what one calls the "span". And no problem :)

I thought the span was the set of linear combinations

...yes, it is

4:02 PM

That's not what @Bass said

It is.

@0celo7 It's equivalent, just try to think of a smaller vector space than the space of linear combinations.

There isn't one.

I know, but that's not what you said

Linear combination of what

That's my question

@0celo7 The elements of the image of ACM's map.

Ah.

4:05 PM

(while respecting the addition structure they inherited from the homomorphism)

well.. not homomorphism..

bi-homomorphism

whatever

:26538472 and yes, they got smarter, they always are. They are always good at ensuring $$\dot{Q}+\dot{A}\neq 0$$

4:27 PM

@Secret even the cranks never have to suffer from this treatment. This is intriguing and worrying at the same time

How the heck did you reply to your own message?

Ah, I think I know

@ACuriousMind Yes, I do.

well, I did not know it actually worked

looks like I can refer to my previous messages in my chat in the future without having to retype every single thing when someone ask me about them

@Secret You could always just post the link

8 secs ago, by ACuriousMind

@Secret You could always just post the link

Like this.

Ah, so that's how to write a quote. Noted

How to do it is just post the permalink, in this case http://chat.stackexchange.com/transcript/message/26835261#26835261

Chat turns it into that quote automatically

4:32 PM

great, nice to know

anyway, if my understanding so far is ok, I am going to just continue to stick close to the maths whenever I deal with quantum problems.

(another question will follow shortly)

40 mins ago, by Secret

Based on what I have discussed with the users some time earlier in this chat, it seems whatever a quantum state is, it seemed to be neither wavelike nor particle like (because both are classical notions). The maths (whether it is state vector, density matrices, C* algebra or path integrals) however seemed to suggest they always obey superposition

@ACuriousMind any good reference books or articles that taught people how to develop a correct mindset to interpret the physics in the equations?

@Secret What equations?

Equations in general, that are used in physics. Because I am still having the problem on when to start thinking about the physics when I am some step in the algebra of some equations of a model

all the questions I have asked so far in the past either suffered from interpreting the physics of the equations too early or too late, hence resulting in nonsensical premises, wrong assumptions etc.

I know the physical meaning of the final answer is important, but there are cases where one need to engage the physical intuition when midway through the problem. I often found I am very bad at these despite having done many problems during my undergrad

@Secret I don't know what you would be after. Physics is the art of describing the world with equations. Every physics book teaches you how to phrase a certain aspect of the world in equations. What more than "standard physics" are you looking for?

I am looking for general guidelines on when to start trying to interpret the algebra to seek for a physical meaning, because I either interpret my results too early in the calculations or too late, and in both cases result in nonsensical physical interpretations

4:48 PM

@Secret Honestly, that's not what I think your problem is. Most non-sensical questions you've asked about quantum mechanics in this chat, for instance, resulted from you doing wrong math or not understanding what you were supposed to do in the first place.

@DanielSank optical theorem is a result in QFT that roughly says, because of unitarity of the S-matrix, if I have a certain loop diagram and cut the diagram along one of the loops then I can write the imaginary part of the scattering amplitude in terms of products of lower order loops. In particular, the imaginary part of a 1-loop amplitude can be written as the square of tree level diagrams.

at least that's how it's formulated in momentum space

but for my project to be complete I need to find a formulation in position space which is more annoying because there I don't have $S^{\dagger}S = 1$ as an easy characterization of unitarity

I only have correlation functions

5:06 PM

@FenderLesPaul I feel like that theorem is probably a theorem in statistics all dressed up in QFT.

Kind of like Wick's theorem.

I'm a little vexed that I don't know it.

I wonder if his majesty @0celo7 has fluttered in yet today.

http://chat.stackexchange.com/search?q=secret&Room=71&User=121322&page=1&pagesize=50&sort=newest

It does seems that, I have big confusion on the concepts of "measurement", "tensor product" and "representations"

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

Back in my uni, this is taught in a lose manner as an outer product of matrices, and covered nothing on the more abstract meaning. It has been 3 months and I am still trying to digest the first few paragraphs

All the quantum problems I have done so far in the undergrad does not involve tensor products

http://www.amazon.com/Modern-Quantum-Chemistry-Introduction-Electronic/dp/0486691861

I have already read this book, but it seems that quantum knowledge gap is still there. I should try another book and maybe the feymann lectures

"My understanding of the concept of "measurement" and how operators are related to it is very bad "
^ That's true of most physicists.

It's a difficult thing to think about. In a sense, do not have a truly satisfying understanding of this yet.

5:22 PM

@DanielSank In the path integral formulation of Euclidean QFT, Wick ordering is the convolution of a Gaussian measure with the expression in the fields to be Wick ordered, so probably yes.

If they ask me how to compute the energy, momentum of some eigenstates of a system (e.g. potential well, steps, coloumb potential) , I know how to set it up (and do the algebra if need to, barring some memory issues on solving some more complicated nonlinear ODE and PDEs)

But whenever I want to investigate some toy model (to try to help me understand something and answer my loads of conceptual questions I have in mind for quantum alone). I always get the maths *concept* misremembered and result in dodgy maths and nonsensical physical interpretations that often only others can point it out …

Further, one can show that the generating function for the connected amputated correlation functions is precisely such a convolution of the potential.

in particular, as that link have showed, any of these toy models that involve a tensor product or some measurement I always got it wrong and lost track on the physics and all I see is algebra that I know the rules in computing them, but don't know where all the physics are

I love it. I just love it.

0

Q: How should Christoffel symbols be written (in LaTeX)?

I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols. It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat right-aligned, at least in print. I found this way of writing them in several works of literature ...

general-relativity differential-geometry notation conventions tensor-calculus

Not one close vote.

This is such an amazing example of the fact that when we vote to close stuff as "off topic" it's really because the questions are just unclear.

This question is very well written, and because of that we can all see the relevance to physics and understand that physicists are the right people to give relevant answers, even if the topic really isn't physics at all.

Dammit @ACuriousMind...

@DanielSank The question is only 20 mins old, and it is off-topic, specifically by @Qmechanic's own post on the subject.

5:34 PM

@ACuriousMind Yet he edited it and didn't VTC.

I'm telling you, clarity is the key. Crappy questions are magnets for "off topic" votes even when the real problem is something else.

Grrr
http://www.feynmanlectures.caltech.edu/III_01.html

Let's start on page 1

@DanielSank What puzzles me is the answer. As a mod, one is hesitant to cast the binding close vote as the first vote, and editing a question doesn't mean one thinks it is on topic. (I've added the HW tag or teXified many posts I though were off-topic)

"I've added the HW tag or teXified many posts I though were off-topic"
Good point, me too.

@DanielSank Certainly true. When the question already looks bad, people are doubtlessly more prone to finding a reason to close it

@ACuriousMind Yeah, but I think a lot of the time "off topic" is the wrong reason.

I think what's really going on is that "off topic" is a way to avoid having to tell OP what is wrong.

"Off topic" let's you tell yourself "this doesn't belong here, not my problem."

I think it's interesting that this Christoffel symbol post didn't get a VTC from @Qmechanic, and instead got an answer. I bet that happened because it's so clearly written that it's easy for a physicist to look at it and say "yeah, I get why that's being asked, and why I as a physicist should provide an answer".

5:38 PM

For me, I have at least 4 off topic questions simply because my premise is wrong, thus it corrupted the whole question to the point of unfixable

in addition, my bad communication skills make them very long and people simply don't have the patience to read them

In the end I just think we should use "unclear what you're asking" more and "off topic" less.

@Secret Brevity is important.

It is quite possible that in light of Acuriousmind's recent comment on the issue, my physics intuition is so bad that I probably have confusion on what I am confused at

and quantum mechanics is the most disasterous of mine

@DanielSank I think "off-topic" might be more popular because it is a more objective ring to it. For "unclear what's being asked", there are always the people who are mind-readers and know exactly what OP is asking

(Oddly enough, they rarely actually edit the question to make to more clear to others)

A lot of question that are labelled as "unclear what you are asking", I actually can understand what the OP wants

On the other hand, my questions are most freuquently closed with this reason because of the aforementioned reasons

0

Q: Tagging Mistakes Erased with Question

Can tags I made on Physics that have been rejected be forgiven when the question is marked as duplicate or closed?

discussion support feature-request tags closed-questions

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