The h Bar

user116211

8:03 AM

Hey @JohnRennie, you wrote in your answer:

user116211

> since this probability is just the charge density that means the charge density varies smoothly throughout the atom.

user116211

What do you mean by smooth charge density?

Manolis Lyviakis

how can you have an accelerating motion with constant magnitude of speed. :(

user116211

@ManolisLyviakis its unit vector must be changing.

Manolis Lyviakis

change of directio resulting in an accelerating motion doesnt come intuitively to me

say i have acceleration=C (constant) if i integrate that what do i get?

user116211

8:11 AM

@ManolisLyviakis $$\dot{ \mathbf v} = \dot v~\mathbf e_{\theta} + v~\dot{\mathbf e_{\theta}}$$; simple application of chain rule.

user116211

@JohnRennie, Feynman in his last lectures mentioned:

user116211

> The wave function $\psi(\mathbf r)$ for an electron in an atom does not, then, describe a smeared-out electron with a smooth charge density. The electron is either here, or there, or somewhere else, but wherever it is, it is a point charge.

Slereah

Well yes

That's non relavistic QM for you

The measurement is of a point particle

user116211

Although I'm dubious of what he wanted to mean by point

Slereah

doesn't work for QFT, tho

user116211

8:14 AM

@Slereah Of-course, he was giving lectures in non-relativistic realm QM.

Slereah

It means that when you consider a non-relativistic electron, you can consider an arbitrarily small volume in which the probability of presence of the electron is 1

Manolis Lyviakis

what is the derivative of a unit vector

user116211

@Slereah oh.

user116211

@ManolisLyviakis $$\dot{\mathbf e_{\theta}} = -\mathbf e_r$$

Slereah

The wavefunction just describes the probability of finding it somewhere

But one measured, it is exactly located somewhere

Manolis Lyviakis

8:16 AM

O_o how did you come up with that

user116211

@Slereah: Feynman was just telling where Schroedinger mistook in interpreting the probability density $P$ as charge density and probability current density $\bf J$ as electric current density.

user116211

@Slereah yep.

Manolis Lyviakis

velocity $v=υ_xi+υ_yj$ in 2d where i,j unit vectors

user116211

@ManolisLyviakis Polar coordinates; covered in every introductory mechanics book and calc 1 course.

Manolis Lyviakis

then the derivative of v is the derivatives of υ_χ u_y am i wrong?

Slereah

8:35 AM

@MAFIA36790 bit mean considering he invented quantum mecanis basically

Can't have everything right on the first go

Slereah

8:49 AM

There's quite a lack of pre-QM explanations of the atom structure, I feel

The only one I can remember is ring-shaped electrons

user116211

@Slereah You mean the Bohr dude's model?

Slereah

Well then Rutherford experiment was in like 1910

And QM was around the mid 20's

There was 15 years without an adequate model for the atomic structure

History of physis texts rarely mention models of that era

user116211

@Slereah ah! a good question for HSM

Slereah

Probably

Let's ask

user116211

@Slereah what happened in those years? Any discovery?

user116211

8:56 AM

Before de Broglie?

user116211

@Slereah okayish, let you give me the opportunity ;P

Slereah

There's always discoveries

0

Q: Atomic models in the 1910's and early 1920's

The Rutherford model that invalidated the plum pudding model occured in 1909, while the first model for quantum mechanics was around 1924, leaving a period of 15 years without an adequate model for the atom, as the Rutherford planetary model did not work out due to the emission of radiations. Tha...

There we go

user116211

@Slereah Hmm, there is actually no mention, no discussions on that in any book ;\

John Rennie

9:25 AM

@MAFIA36790 and you believe Feynman over me???

@MAFIA36790: you realise I now deliberately leave out the \mathrm just to annoy you :-)

user116211

@JohnRennie huh? hmm.

user116211

@JohnRennie Well, there were two d in your post; so I used \mathrm to distinguish the operator and yeh, I'm \mathrm monster ;)))

John Rennie

Re Feynman's comment: I think this is largely a matter of terminology. In principle there exists position eigenfunctions for a particle, and in principle you can construct the wavefunction of an electron in an atom froma superposition of these position eigenfunctions.

But so what? I could just as well start from momentum eigenfunctions in which the particle is completely delocalised and build up the wavefunction from those.

Slereah

Well yes, but if you measure the position you collapse it into a position eigenvector :p

John Rennie

@Slereah if you measure the position precisely you can collapse it into a position eigenstate, but that requires an infinite energy to do. In practice you collapse the particle into superposition of eigenstates with a lower uncertainty.

Slereah

9:38 AM

Yes but we're talking theory ere

Let's go nuts

Secret

10:27 AM

[After more than 3 weeks of corrections from self analysis]
Now the question is then, what do those antidiagonal (and their equivalents in other basis) of the density matrices physically mean, if they are not part of the partial traces of the subsystems?

Begin with the following partially entangled state
\begin{align}
\lvert@\rangle=\sqrt{\frac{1}{3}}\lvert ud\rangle-\sqrt{\frac{2}{3}}\lvert du\rangle
\end{align}
, and using the convention $\lvert u\rangle$ and $\lvert d\rangle$ for spin up and spin down states respectively. Spin right and spin left states are labelled $\lvert r\rangle$ and $\lvert l\rangle$ respectively and given by.
\begin{align}
\lvert r\rangle=\sqrt{\frac{1}{2}}\lvert u\rangle+\sqrt{\frac{1}{2}}\lvert d\rangle\\
\lvert l\rangle=\sqrt{\frac{1}{2}}\lvert u\rangle-\sqrt{\frac{1}{2}}\lvert d\rangle

DanielSank

Hi everybody.

Secret

(Background: 2 days ago, a calculation error result in deriving the wrong conclusion that $\dot{\rho}_A$ and $\dot{\rho}_B$ nonzero, which would have implied that Alice and Bob can encode information by assigning classical bits as follows:

1. Begin by making 100 replicates of the state $\lvert @\rangle$
2. Distribute one pair of the 100 replicates to Alice and Bob.
3. Alice and Bob go on their separate ways in at least 1 light year away
4. Alice and Bob then measure (in their ow pace) all 100 replicates. This should return a sequence of ups and downs on their paper with ratios of 1:2 for A…

@DanielSank How to prove using no communication theorem that any conceivable time derivative of the density matrix of a two level two particle composite system does not have nonzero elements in all entries marked by *
i.e. if we have (under the standard basis $\lvert 00\rangle$,$\lvert 10\rangle$,$\lvert 11\rangle$ and $\lvert 01 \rangle$)
\begin{align} \dot{\rho}= \begin{pmatrix} * & * & * & \\ * & * & & * \\ * & & * & *\\ & * & * & * \end{pmatrix} \end{align}
Then how to use no communication theorem to show that all * must be zero?

DanielSank

10:48 AM

What is the "no communication theorem"?

I've been in superconducting information for almost ten years and I've never heard of it :P

Secret

@DanielSank
https://en.wikipedia.org/wiki/No-communication_theorem

It's the no go theorem that an entangled state cannot be used to transmit information superluminally between two parties because if the parties measure their system in isolation, they cannot determien whether the measurement is obtained from them measuring it, or because the entangled state have already projected into an eigenstate caused by the other party measuring it

I think Susskind in p. 223-226 give something similar in that he showed how the density matrices of Alice are unchanged by a unitary evolution in Bob's sub…

DanielSank

@Secret I'm confused about your basis.

user116211

Hey @DanielSank o//

user116211

okay, I'm not a LaTeX guy; that's why I'm asking:

DanielSank

@Secret Well how do you know they should be zero?

@MAFIA36790 \o

user116211

11:03 AM

I've seen many using \begin{align*} \end{align*} and also some people using \begin{align} \end{align}; what's the difference between the two?

Slereah

Plz stop using @ as a symbol

DanielSank

@Secret the basis ordering you've chosen seems weird to me as it is not the kronecker product of two copies of the same single particle basis.

user116211

@Slereah oh, man ;(

user116211

Although I've used the later and frankly speaking both render the same output at least in PSE.

Secret

@Danielsank For a bloch sphere, it has two base states $\lvert 1\rangle$ and $\lvert 0 \rangle$ corresponds to spin up and down. Therefore, for a two qubit system, the basis vectors of the composite system are given by tensor products thus giving 00 01 10 11 (in this order)

If they (or at least the 8 entries that will be partially traced to give Alice's density matrix when the hamitonian has terms dependent on what bob did to his subsystem (or vise versa for Alice)) are nonzero, then the density matrix of the other party will have a time dependence and the encoding of classical bits via a …

DanielSank

11:12 AM

@Secret Yeah ok, that's not the order you wrote above.

Secret

@DanielSank Sorry typo. Clarification: The basis used for the big calculation above is (in this order) is (in susskind's noration) uu ud du dd which in conventional notation 11 10 01 00

DanielSank

Yeah ok.

@Secret did you try writing everything out explicitly?

Secret

11:30 AM

I think so, for example, the aforementioned partially entangled state, its coordinate vector in this basis is $(0 \sqrt{\frac{1}{3}} -\sqrt{\frac{2}{3}} 0)$

DanielSank

Uh, ok but your goal is to see what happens if you have dynamics on one particle... right?

Act a Hamiltonian on one particle and see which terms in the density matrix change.

My guess is you could do that reasonably easily using index notation.

Secret

Do I act the hamitonian on the density matrix like how we usually do for state vectors, or do we need to wrote it as something like $H\rho H$?

DanielSank

Well there are a few ways you can go about this.

The equation of motion for a density matrix is easy to compute.

You have $i \partial_t \Psi = H \Psi$.

(turning on mathjax, one moment)

So then

$\partial_t \rho = \partial_t (|\Psi\rangle \langle \Psi |)$

$=\partial_t | \Psi \rangle \langle \Psi | + |\Psi \rangle \partial_t \langle \Psi |$

=$-iH |\Psi\rangle \langle \Psi | + i |\Psi \rangle \langle \Psi | H $

$= -i [H, \rho]$

I'm on a bad internet connection. Sorry for delays.

Anyway, that's the equation of motion for the density matrix.

So now just use index notation to keep track of everything and see if you can prove your desired result.

FWIW if you have a propagator $U$ for the state taking $\Psi \rightarrow U \Psi$, the equivalent expression for the density matrix is $\rho \rightarrow U \rho U^\dagger$.

user116211

12:24 PM

3

A: About time and time dilation

We are only allowed to add quantities with the same units. Time and distance can't be added just like apples and oranges shouldn't be mixed. To add them, one must first convert them to quantities of the same unit, and a speed is needed. The speed of light in the vacuum $c$ is the right speed th...

user116211

Was it necessary to write this:

user116211

> Your question is equivalent to a question "how do mathematicians dare to say that 2+2=4 if 2+2=37 is equally good if not better", and so on. Well, the alternative is not better. It's demonstrably rubbish.

user116211

I like his metaphors ;)

0celo7

@yuggib what

Jim

@MAFIA36790 37 is bigger than 4, bigger is always better, therefore 2+2=37 is better than 2+2=4

Slereah

12:35 PM

Guys

What's a good GR approximation for an object

Like just a hunk of metal

Perfect fluid?

user116211

@Jim ;D

Jim

@Slereah nothing. That is a standard GR approximation for a random hunk of metal

Slereah

Not a v. good approximation

Jim

depends on context

Slereah

Perfect fluid is probably better I'd say

But I'm wondering if there is better

Jim

12:37 PM

what are you using this approximation for?

Slereah

Like some state equation that is approximately correct for solid objects

Computing the metric generated by metal plates

Jim

how big is the metal plate

Slereah

Either I use the Polyakov ation and pretend they are 2D or I try to do something a bit more realistic

Not sure yet

Jim

bigger than a breadbox?

Slereah

Either infinitely thin or with a small thickness, and either infinitely large or with boundaries

Depends on what is solvable

0celo7

12:39 PM

@ACuriousMind I'm still super confused by the Lie group thing...

Jim

@Slereah so it is potentially anything at all except nonexistent?

0celo7

why does $\mu$ analytic near $e$ mean $\mu$ is analytic everywhere

Slereah

Well they're not called LIE for nothing

0celo7

I know that $G$ is generated by any neighborhood of $e$

Slereah

@Jim Ideally with thickness and boundaries, but I'm not sure this will pan out

The size is like

Apparatus size

So bigger than a breadbox, probably

Jim

12:41 PM

smaller than a building?

Slereah

yes

Jim

then a good approximation in GR is nothing

Slereah

Perfect fluid it is

Jim

the effect that it will have on the metric is negligible

Slereah

I am currently not too worried about measurements

More about effects

0celo7

12:43 PM

> To sum it up, my question is: Mathematical techniques used to describe physical phenomena are not necessarily specifically invented for physics and do not necessarily have any meaningful physical interpretation. How come these techniques are able to produce correct (can be verified by experiment) results?

Oh god

Slereah

I guess a broader question is

What's the state equation for a metal object

What are the pressures in it

Can I assume 0 pressure

Or would that be a bit much

Jim

good question, but now you're outside the scope of GR

Slereah

I guess let's start with infinite plates

Jim

infinite plates are a different story

Slereah

I don't like abandonning all Killing vectors in one go :p

Hm, I forget the metric for 2 Killing vectors $x, y$, and I am far away from Stephani

Woe is me

Infinite plates I'm guessing is similarish to Domain wall metric

Apparently static with plane symmetry is $$ds^2 = -f^2(x) dt^2 + \frac{1}{f^2(x)} dx^2 + g²(x) (dy^2 + dz^2)$$

Jim

1:12 PM

yeah, plane symmetry is definitely a good idea

frankly, with such a large metal sheet, you may find that aphysical effects develop in your metric, which corresponds to the notion that one should not be able to have an infinite sheet of metal in our universe. Also, don't forget to make it an FRW metric because an infinite sheet affects the cosmological scale

Slereah

There's even an exact solution for plane symmetric static spacetimes

Although not closed form

Jim

someone is arguing with me that "point" has no definition in geometry

Slereah

Tho I can throw FRW in the trash, really

Jim

my answer to them? link to google search

Slereah

Since the point is to then find the solution wit boundary terms :p

Not to have an actual infinite plate

I'm doing a metal plate not domain walls

Maybe I will even do me a lazy thing and use a Gaussian for the plate energy distribution

I don't want to use mollified Heaviside funtions, those are a bother

Jim

1:21 PM

is this a hobby thing or are you doing it for actual research?

Slereah

More of a hobby

I ain't getting paid for this

Maybe I should start with a Polyakov thing, tho

Easier to start

Jim

I'm sure it has been done. But if you do end up creating a metric for spacetime with a metal sheet of arbitrary dimensions, you'll see that as the dimensions get closer to the scale of a breadbox, the difference between your metric and one without the object rapidly falls to zero

Slereah

Well obviously

But I'm more interested in the form than the scale of the measurement

Plus

There isn't just a metal plate!

There is dynamic Casimir effect involved

I'm guessing if I want to do plates, a round plate probably is better than a square one

Round one is gonna be all Bessel functions

Not a fucking clue what kind of function a square has

Danu

@Jim lolwut

Slereah

Like what is even the classical gravitational field of a cube

arxiv.org/pdf/1206.3857.pdf

Thank you internet

0celo7

1:33 PM

@Jim link?

@Slereah LINK TO ABSTRACT

Danu

That's not GR @Slereah

0celo7

> James M. Chappell,∗ Azhar Iqbal, and Derek Abbott
School of Electrical and Electronic Engineering,
University of Adelaide, South Australia 5005, Australia

Danu

> Principle of superposition

Ain't nobody got time for Newtonian physics

0celo7

Why are electrical engineering students writing that paper anyway

Slereah

$$V(x,y,z) = -G\rho \sum_j [\sum_i (\frac{xyz}{x_i} \ln (x_i + r) - \frac{x_i^2}{2}\arctan(\frac{xyz}{x_i^2 r})) )]^{L-x_j}_{x_j = -L-x_i}$$

Gross

Thinking about it, maybe I should also start my thing in linear GR

Might be prudent

Plus realistic at this scale

And I'm sure the solution of the wave equation for a cylinder exists in EM

(BESSEL)

0celo7

1:45 PM

@Slereah that's not even GR...

Slereah

Well let me tell you what GR will look like with 0 Killing vectors

A mess

0celo7

no conserved quantities!

Slereah

At least linear GR will be all linear, baby

user116211

Wow, a post is making reference of Vixra paper ;)

Slereah

Does it reference the papers written by Jesus

user116211

1:47 PM

;D

user116211

0

Q: Feynman path integral interpretation of the Aharonov Bohm effect

I have recently been reading about the interpretation of the Aharonov Bohm effect via Feynman's path integral (see vixra.org/pdf/1403.0950v1.pdf). I do not know whether I am missing something, but I do not understand why when evaluating the action they have to take into account the potential even...

quantum-interpretations path-integral

0celo7

@Slereah what

Jim

Definition: A "point" in geometry is a location. It has no width, length, or depth. It has no volume; only coordinates of the location. Now, please prove to me there is no time dilation. — Jim 1 hour ago

Slereah

what

Oh no

This paper on the dynamical Casimir effect is in French

BUT WAIT

Well, a thesis, technically

I don't think a lot of physics papers are still in French

It's pretty rare to find papers that aren't in english, french, german or russian

I've seen a handful of chinese and japanese papers, but that's about the extent of it

John Rennie

2:09 PM

That does not help to work out the answer! Stop trying to find duplicates but start to actually help! — Kristens Taurins 3 hours ago

Comments I could have left (© dmckee 2016):

Hi Kristens.

Being British I tend to be somewhat reserved, so I tend not to tell people when I think they are being a feckless, idle parasite more interested in getting other people to do their work than in showing any effort for themselves.

In these circumstances I might point to a question that I think is a duplicate partly because it is a duplicate, but also as a hint that if the OP was willing to get off their arse and do some work the linked question would be a good place to start.

user116211

May 30 at 13:49, by ACuriousMind

@0celo7 I have been told that reading French papers without speaking actual French is a skill a mathematician has to acquire

Slereah

Stiff upper lip and all that

user116211

It applies to physics too ;]

Slereah

Tell me @JohnRennie

Do you know Lily the Pink

user116211

The Scaffold - Lily The Pink

►

Slereah

2:20 PM

The very same, yes

Though that is not the correct version

@Jim good lord

Hi all

Hello

John Doe?

We have had bad experiences with other Johns in the past.

Slereah

Especially John D's

John Doe

2:27 PM

@Ocelo7 Not so much Mr Doe as unknown name...

user116211

@0celo7 John Doe is the dummy user of SE's tour.

user116211

@Slereah Hmm.

John Doe

@MAFIA36790 Really? Think I skipped the tour...

Slereah

It's quite unfortunate that GR history usually only teaches about the usual stuff from te early 20th century when curved cosmological models have existed since the 19th century

user116211

Qmechanic

2:32 PM

0

Q: Why does math work for describing and solving physics problems?

My question is a general one. But to explain what it is asking let's first a look at "solving" of an electrical circuit using Kirchhoff's laws as an example. (And this example takes a considerable amount of the question's real-estate but please keep in mind it is only an example to base the act...

soft-question history mathematics epistemology

Too broad? Off-topic?

user116211

@Qmechanic I would definitely say it's off topic.

Slereah

Off topic

I say flog 'em

0celo7

2:42 PM

Just got an email from a prof with an emoticon

user116211

@0celo7 Do profs do such that?

0celo7

@MAFIA36790 Hmm?

Qmechanic

@Emilio Pisanty : Thanks for the bounty on this meta.SE question.

Obliv

3:06 PM

hey @0celo7 can u answer a quick question for me. it's a question in the lab manual. Describe the situation in which the object submerged and the fluid have the same density

I know buoyancy is independent of densities, it is due to a pressure difference in the fluid

So the buoyant force still occurs in this example. Would it be the case that the buoyant force is equivalent to the weight of the object?

Emilio Pisanty

@Qmechanic No worries. I'm still at a complete loss as to why this isn't implemented.

Obliv

@0celo7 you have until 3pm tomorrow to answer me. thx

Qmechanic

@EmilioPisanty : Me too.

Balarka Sen

3:22 PM

@Jim It doesn't.

At least, not in Euclidean geometry.

That's why such a framework is an example of a "synthetic" framework - you write down a bunch of axioms about an undefined thing and do math with them.

@Jim Yes, and that definition is only an intuitionistic definition in Euclidean geometry as you don't define "width", "length", "depth", "volume" or even "location" before defining what a point is.

Kyle Oman

Anyone here with a solid grounding in stats?

user116211

@KyleOman Cross Validated Chat room? Nevertheless, welcome :)

user116211

Title of the Day:

user116211

0

Q: Mag.-flux build up...hate it

"An old bell ringer". After a few minutes of running, the steel pole of transformer, slowely becomes magnitized. Are there any unique metals that would prevent the mag.-flux build up, in the steel transformer?

magnetic-fields

Kyle Oman

yeah I popped in on crossvalidated too, looks quieter there though ;)

user116211

3:31 PM

@KyleOman You can leave message there; but they are generally quieter at this time ;/

Kyle Oman

and I'm mulling over something trivially simple, where I think I know the answer, but it's for a journal article so I need to be sure :/

yuggib

@BalarkaSen I doubt there is anything "intuitionistic" about that definition

Balarka Sen

@yuggib I meant intuitive, oops.

yuggib

@BalarkaSen ;-P

skill patrol

Did Italy qualify? @yuggib

yuggib

3:42 PM

freudian slip?

Balarka Sen

I guess so.

yuggib

@skillpatrol no... T__T

skill patrol

:(

yuggib

with awful refereeing

lost in overtime to croatia

skill patrol

The refs can ruin any game.

yuggib

3:44 PM

yeah, but it is not worth to complain to much

skill patrol

true

yuggib

still, we ended up with like 4 people with 4 fouls, and 3 or 4 fouled out

they did not have a single fouled out

(in fiba you're fouled out with 5)

Obliv

wow it was a close game regardless..

AND italy lost to germany in eufa QF 1-1 to germany D:

2 close games in 2 different sports

yuggib

it happens

but in basketball we were a good team, in football...not so much ;-P

user116211

Please don't talk about EURO ;((

Balarka Sen

3:47 PM

@yuggib You're a mathematician, right?

user116211

@BalarkaSen Mathematical Physicist

yuggib

@BalarkaSen I have a Ph.D. in mathematics

user116211

;)

yuggib

and a master in physics

Balarka Sen

@yuggib Ah. What do you work on?

user116211

3:48 PM

@BalarkaSen Would you come tomorrow and save these questions?

yuggib

I work on mathematical physics/analysis of PDEs mostly

Balarka Sen

@MAFIA36790 Huh?

Ah, I see.

user116211

Tomorrow is AMA.

Balarka Sen

I don't know what that means.

user116211

@yuggib would be our guest.

user116211

3:49 PM

15

Q: Ask Me Anything 12th July: guest's introduction and questions

I will be the next AMA guest. So here it is a brief introduction of myself, and you can suggest some topic/questions that can be discussed during the session. Academic Background. I obtained a master degree in theoretical physics almost ten years ago, working on the regularization of path integr...

discussion chat-events ask-me-anything

user116211

and links therein.

yuggib

@0celo7 so, are you convinced you should read Jech's book?

0celo7

@yuggib no, why on Earth would I do that

will it help me understand geometry and topology

Balarka Sen

@MAFIA36790 Curios event.

yuggib

@0celo7 topology, maybe yes ;-P

John Rennie

3:56 PM

@Slereah yes, though admitting you know the song is instant uncool points. That doesn't affect me since as a Hawkwind and Pink Floyd fan I am uncool beyond any hope of redemption - at least, that's what my 14 year old niece tells me.

0celo7

@JohnRennie I don't even know what Hawkwind is.

And your niece sounds mean.

yuggib

@0celo7 it will help you find models where things behave ~~much bizarrely~~ better

0celo7

@yuggib Not very interesting

yuggib

@0celo7 how could you say if you do not know?

0celo7

I'm mainly interested in topological Hausdorff spaces with a countable base, which are also locally homeomorphic to Rn

John Rennie