12:42 AM
One more question related to image attached above.

From where I(3) current is flowing?
My guess it that they will flow to lower potential and terminate at -ve terminal.

4 hours later…
5:11 AM
@YOU Hint: this question is testing your understanding of Kirchoff's [rules|laws|vague suggestions|whatever your book labeled them], and seen in the proper light the answer is unarguable. No guessing needed.

5:42 AM
@YOU Wheatstone bridge?

5:55 AM
how does one understand/think-about negative surface tension?
context from De Gennes talking about the vortex state: "In a London superconductor, the surface tension of a wall separating a normal and superconducting region becomes negative."
states this in motivation to considering the wall energy contribution to the thermodynamic potential

@dsm surface tension is the work needed to create a unit area of the surface. A negative surface tension would mean the surface does work as it is created. That implies the surface has a lower energy than the bulk.

6:12 AM
@JohnRennie interesting, so what exactly is the surface doing work on as it's formed in this context of a reversible process?

6:22 AM
@dsm I'm not familiar with the London superconductors. In emulsions a negative surface tension means the system spontaneously emulsifies to form a microemulsion i.e. the surface area spontaneously increases to the maximum possible.

woah, cool. that's spontaneous?

@dsm If the interface in a London superconductor is the boundary between superconducting and non-superconducting regions then I'd guess you'd get spontaneous rearrangement to get as much interface as possible i.e. a very fine scale network of the two phases.
@dsm I haven't done a lot of work with microemulsions so I don't have a lot of experience of them. As I recall when you mix the two liquids they spontaneously form an emulsion. To the eye this is less impressive than you might think as it just looks like they form a solution.

@JohnRennie I'm not at all familiar with emulsions, or a good amount of chemistry for that matter. are there microemulsion reactions like this that are reversible, or maybe quasi-reversible? say, an emulsion reaction like that which is temperature dependent and can go between the two states?

@dsm I don't know of any such systems offhand, but they must exist because surface tension is temperature dependent.

interesting, I feel like that's pretty analogous to these applied B-field (and temp) dependent superconducting vortex states

6:37 AM
@dsm it does seem an interesting analogy. I spent twelve years working as a colloid scientist and studying emulsions was a big part of that. But I've never worked in superconductivity. I might go off and find some stuff on London superconductors to see if I can see any relationship between the two fields.

that would be really cool to see any overlaps. I'm reading on this stuff for the first time, and De Gennes seems fairly concise and readable; this is ch.3 stuff
I'm off to try and correct my sleep schedule, the unending battle. will be interested to hear if you look into any similarities, cheers

7:34 AM
Krasnikov writes the tangent as tg

8:03 AM
Kranikov's book pretty nice for random details on weird spacetimes
pretty good intro to Misner space

4 hours later…
12:24 PM
I swear some people I work with have never heard of writing templates and instead just copy+paste+replace text repeatedly

12:48 PM
@PM2Ring Hii

1:12 PM
Challenge of the day:
> Find the orthgonal complement with integer components of any given vector $v$ in the hilbert space $\Bbb{P}_0(C)$

Hello @JohnRennie

@user8718165 hi

@JohnRennie are you working now?:-)

No, I'm chilling and eating lunch now :-)

@JohnRennie Ok please ping once you are done resting:-)

1:19 PM
@user8718165 that won't be until tomorrow.

8-)

@JohnRennie Okay:-)

glasses are convenient

1:53 PM
Hey

Yo, dumb question
iirc sweat functions by taking heat energy from the surface of the skin corresponding to the heat of vaporisation, right? Why does having air flow past the surface of the skin boost that though

What is iirc?
Blowing air increases the evaporation rate of sweat.

2:10 PM
"if i recall correctly"
and ye but why

@Phase because a breeze carries away air near the skin that is saturated with water vapour and replaces it with drier air.

hi

Alright so just to be even dumber, how is it that the saturation level of the air affects this? Also, does this mean that a droplet of sweat increases the saturation of the air significantly enough to need a breeze to replace it?

@Phase if the air is still the water vapour can only get away from the skin by diffusion through the air, and diffusion is surprisingly slow. So the air near the skin rapidly gets saturated with water and no further evaporation is possible.

oh right, i see now

2:17 PM
@Akash.B hi

thanks for the patience

@JohnRennie Just a little conceptual question...if you could help...a little bit only

@user8718165 yes?

@JohnRennie please have a look at this image imgur.com/l9JMTIQ

OK ... ?

2:22 PM
@JohnRennie will the magnetic field from the red point on the wire affect point P?
I think no

@user8718165 the magnetic field from a long wire is $B=\mu_0I/2\pi r$, where $r$ is the distance from the wire. So if you know the distance from the wire to the point $P$ you can calculate the field there.

@JohnRennie Ok but the magnetic field from the red point will only be perpendicular to the wire at that point...Can magnetic field lines from the red point on the wire bend and reach the point P? I can't get this thing...

I think I see what you're getting at, but the field isn't associated with a single point on the wire. The field at any point outside the wire is created by the whole wire not just the point on the wire in the plane of the point.
So the field at the point P is made up by the whole wire.

I was deriving the biot-savart law and got that $F \propto sin(\theta)$ due to the small current element $dl$

To calculate the field at P you include contributions from the whole wire.

2:39 PM
@JohnRennie ok got it... One last thing... but how does the mag field from a point on the wire not perpendicular to the point P reach the point P?The mag field lines always go perpendicular to the wire in circles?

@user8718165 if you consider some tiny length $d\ell$ of the wire then its magnetic field radiates out in all directions.
For an infinite straight wire the fields from all the elements add up with each other to give the pattern shown in your diagram.
So the pattern you see exists precisely because the fields from all the parts of wire reach the points outside the wire and add up there.

@JohnRennie Oh so as we are considering very small lengths the mag field radiates out in all directions?

The field lines shown in the figure are not due just to the red bit of the wire. They are the sum of the fields from all parts of the wire.

@JohnRennie Ok...got it a single electron moving also produces circular field lines...is the electron moving and the current carrying wire case different?

@user8718165 you need to be careful when dealing with a single electron.
If you are in the lab watching the electron speed past you then the field is initially very small, then it increases as the electron approaches, peaks as the electron passes you then falls again as the electron speeds off. So the field is time dependent. I have to confess I don't know what the equation for a field of this type is.
If you are in the rest frame of the electron, i.e. speed along beside the electron, then there is no magnetic field at all.

2:50 PM
@JohnRennie I didn't know these stuff. All I thought was the mag field around an electron or a wire is just a disk (group of disks for wire)around it...thanks for enlightening me

3:10 PM
@JohnRennie I have drawn some of the mag field lines (top view)...shorter field lines are weaker...can I think like this diagram for an electron and a very small current element or is it wrong? imgur.com/Ls6nh8l
They get stronger, reach max strength and again get weaker?

1 hour later…
4:14 PM
So, where's the betting pot on who'll nominate in the coming election?

gambling is a sin

So?

dunno
I just say stuff

Hmm...
Orthodox quantum mechanics basically said that we can assign an entity called a wave function when reasoning about how after experiments, we obtain different values for a given observable and each data point obtained is assigned to a state
Whereas in Bohmian mechanics, we have a stochastic distribution of bohmian particles initially, and then each of them are guided by a nonlocal wave function to its corresponding destinations
Thus in the former, each outcome is associated with a state (may be a mathematical tool or a real entity, depending on interpretation) and nothing else can be said about what happens "in between"
Whereas in the latter, the initial conditions are intrinsically uncertain, and there is a real wave function that permeates the whole system, guiding the bohmian particles to their destinations to give the required outcomes

5:02 PM
@knzhou What happened to that rope question?

For a given density operator

$\varrho = \sum | \phi _ { k } \rangle \left\langle \phi _ { k } |\right.$

Assuming it normalized (convex) implies

$\varrho = \sum p _ { k } \frac { | \phi _ { k } \rangle \left\langle \phi _ { k } | \right. } { \left\langle \phi _ { k } | \phi _ { k } \right\rangle }$

In addition, if we assume this decomposition is optimal, then we can define a function that is related to this state $\varrho$ by

$C _ { \Theta } ( \varrho ) = \sum p _ { k } C _ { \Theta } \left( \frac { | \phi _ { k } \rangle \left\langle \phi _ { k } | \right. } { \left\langle \phi _ { k 5:49 PM @TheEastWind My students gave an unsatisfying mix of 1/2 and 1/4, the two common answers. As far as I'm concerned, the right answer is 1/4 because of the linked paper, experimental results, and the argument of the OP. 6:06 PM @knzhou Thanks. @ACuriousMind I'll collect the money for bets. Not guaranteeing a payout, however :D Two rods lie end to end on a frictionless table.They are hinged at their common point. A force F is applied perpendicular to the rod at one end. What is the acceleration of the hinge? mass of the rods is m @anyone @KyleKanos You seem trustworthy and work in the financial industry! Take my money. 3 I get the answer as F/m 6:24 PM @Semiclassical I have finished reading this paper, and I think I now understood surreal trajectories better now: Surreal trajectories occurs because the first order dynamics of quantiles trajectories in Bohmian mechanics cannot cross each other Thus if the bohmian wave function is not perturbed strongly due to entanglement being established between the pointer device and the bohmian particle, the bohmian particle cannot "switch" trajectories (the switching is possible because the nonlocal wave function itself get perturbed by the entanglement as one tries to do a position measurement, thus leading to the expected outcome of quantum mechanics one thing to note: the trajectories never cross in configuration space for a single spinless particle, that's the same as not crossing in real space ok maybe I should say, trajectories cannot "switch" in some lower dimensional subspace of the configuration space (that's how the author of that paper treats it, he said the trajectories seemed to cross apparently, but that is an artefact because the trajectories are perfectly non intersecting in the full configuration space) i know i've seen some discussion on that point. lemme see if i can find it oh, he talks about that explicitly It's near the end of the paper just before the conclusion, unless you mean more extended discussion yeah i think i've seen it elsewhere as well 6:33 PM Meanwhile, the Bohmian result occurs for "slow" pointers. A pointer is "slow" if its states cannot separate quick enough after interacting with the Bohmian particle, thus the wave function is not perturbed until another measurement occurs, and hence the Bohmian particle continue to follow its usual trajectory i thought i saw it discussed in the context of trajectories for spinful particles so far I'm only seeing stuff in the vein of Gisin tho I need to re-read that 2016 paper where surreal trajectories is first reported, as I am curious on how they managed to get a bohmian measurement going in that paper yeah, and it seems the way they implement the "slow pointer" scenario is by using weak measurements and in that paper, they reference this paper by Hiley as far as why the trajectories appear surreal: pdfs.semanticscholar.org/cb11/… which in turn explicitly discusses the configuration space subtlety 6:52 PM That paper illustrate the points even clearly: The presence of the cavity modifies the wave function and hence the quantum potential. Thus we have the two kinds of trajectories going from bouncing off each other to simply passing over each other, both cases no trajectories are intersecting That explanatory paper also clarified to me what a true surreal trajectory, if it exist, will look like: There will be a nonlocal transfer of information between two positions. It will be cool if some experiments in the future will show something like that, because that will be a nonlocal interaction that is signalling in principle but we cannot exploit because it will be probablistic (ok sorry, entered scifi mode again) .... Now the only mystery is this paper: Quantum theory cannot consistently describe the use of itself to me the simple lesson is the one Gisin gives: BM insists that positions are always meaningful, but this is not the same as saying that position measurements "merely" reveal this otherwise hidden variable That is true, but I am terrible with reasoning about negative abstractions, which is why I tend to find a positive interpretation of the same thing there are cases in which you can take position measurements as playing this role, but it very much depends on your measurement apparatus I am not sure if that makes me bad at physics, but it is always more fulfilling to be able to explain why things happen, instead of why things is not necessary to happen You can regard BM philosophically as solving the measurement problem, but its application to any specific system requires you to be precise whereas part of the fun of quantum mechanics is how often you can get away with being imprecise about the setup :P 7:08 PM true meanwhile, I think I agree with the authors on how there should be more interesting things in Bohmian mechanics than just surreal trajectories, but I guess I will check them out later yeah I think Bohmian mechanics is more ontologically satisfying (which is good for more philosophical and scifi minded people like me), but I am also ok with quantum mechanics, because you can pack everything into the wave function and not worry about whether you need a particle to be somewhere in between that's one thing I do like about Gisin's paper: its admission that BM, whatever one can say about it philosophically, has not been fruitful in practice I'm not sure I like the examples he gives for possible experimental ideas---putting upper limits on the speed of nonlocal communication? mehhh---but I like that attitude (cont.) Or put it in another way, I am equally fine with treating quantum states as probabilistic blobs in Hilbert space or as real nonlocal wavefunctions guiding a probabilistic blob of bohmian particles Point is, it is because they are probabilistic blobs that makes them interesting Here's a question I'd love to see someone answer: Is there anything in the Bohmian story which is useful/instructive for building a quantum computer? 2 so far I haven't seen any examples of such my own suspicion is that, when it comes to quantum software/algorithms, BM is not going to help much BM can deal with n-level systems, but it does so by insisting that that system is embedded in a configuration space of appropriate size 7:15 PM I think that the trajectories are so sensitive to the hardware that a trajectory plot will be useful to figure which parts go to where. This is easier to be used as a blueprint than to consider all possible ways a quantum state can be manipulated and wrote into a wave function which the information on where to place what is indirectly contained in the wavefunction the story works, but it seems unlikely to be a convenient framework for quantum algorithms So I don't see that route being very productive I mean, a quantum engineer will probably get more used to seeing a plot of level sets of the cumulative probability density than statistics on the outcomes (the former is more obvious on just what happens when you place some hardware at location X). But yeah, the challenge is that trajectories are more computationally expensive to compute than just computing the wave function evolution. Definitely useless for software design since they give similar algorithm and logic But a quantum computer is also -hardware-, i.e. an actual experimental apparatus that can make measurements on that state and that seems more plausible as an inroads for an interested Bohmian It is also more intuitive to reason about level sets. Most people probably have experience on reading contours already thus the training of future quantum hardware engineers should be easier with the Bohmian framework since it retains some classically intuitive notions in some form to put it a little differently: designing algorithms was part of making a computer, but so was designing transistors this is just speculation, though 7:21 PM Thus I will think this way: 1. The orthodox view will be more convenient for software designs, since it is the logic of the operators that is more important and quantum mechanics have a nice mathematical structure to deal with the logic, unlike in bohmian where you need to worry about an extra pde which will slow down the software development. 2. The Bohmian view is important in giving a picture on the assembly of the hardware I think that 2) is at least plausible whether it happens, of course, remains to be seen I should wrote a program to compute trajectory some day, after my chemistry PhD... there is a lot of things in the Bohmian view that is not explored, and its interplay with the orthodox view it depends on what part of the Bohmian interest group you're talkign about, of course The bohmian view also gain a boost recently due to that nature paper that pretty much nuke most of the interpretations if you're talking about philosophers, then yeah---not a lot of computation going on there i know there are some people who have worked on it as far as molecular dynamics go i don't know how popular that really is, but it is out there in the literature 7:25 PM yeah there are some examples of bohmian formulation of path integrals in molecular dynamics, they are still pretty rare though to me the question of whether BM is useful is as important a question as whether it's real it sure give a more intuitive way to think about quartile trajectories, which can help to visualise the probability and statistics better, but for more technical level, I guess we need more people to apply it to analyse quantum experiments to be sure "The second point listed above is interesting: one should distinguish quantum-position and Bohmian-position measurements. The latter are measurements that provide information about the position of Bohmian particles. It would be interesting to find out how to characterize such Bohmian-position measurements without the need to fully compute all the Bohmian trajectories." that's another interesting bit of the Gisin paper > It would be interesting to find out how to characterize such Bohmian-position measurements without the need to fully compute all the Bohmian trajectories." yeah 7:34 PM I think that will be very important since it will provide a framework to design better weak measurement devices it goes to your point about the approach seeming to impose a substantial computational hurdle 7:45 PM that also 8:35 PM Damn, @Chair beat me to setting a bounty on the book-bending question @EmilioPisanty the following question is probably just a sign of inexperience but I take some density operator$\rho$on a product space$\mathcal{H}_A\otimes \mathcal{H}_B$it seems that$\text{Tr}_B[(A_1 \otimes I_B)\rho (A_2\otimes I_B)] = A_1(\text{Tr}_B \rho)A_2$Mathematically, I can prove that. But I'm having a hard time convincing myself about the intuition. okay, no, that's fine. Take the trace of both sides and you see that it's just$\langle A_1 A_2\rangle$in two different ways There's also$\text{Tr}_B[(I_A\otimes B)\rho]=\text{Tr}_B[\rho(I_A\otimes B)]\$
But if I'm tracing over the second space, then operators acting only on that space had better respect that trace
etc

9:05 PM
quite randomly, I came across this short note: pubs.acs.org/doi/pdf/10.1021/ed071p434
now, it starts off well enough
but something seems off as it gets to the end

9:22 PM
@Secret this is an interesting paper in the vein of Gisin: arxiv.org/abs/1802.03783