Entanglement and Bell inequality illustrated (see video)

Anonymous

Feb 3, 2018 09:08

BTW I found a really wonderful video yesterday:

Anonymous

Quantum Entanglement & Spooky Action at a Distance

Anonymous

Strange that I didn't find any good stack exchange answer which explains it well (as to why faster than light communication isn't possible using entanglement)

Anonymous

And the books are too convoluted to make sense. @BalarkaSen was asking about this a few months back

Cows

playing with posgres

Mithrandir24601

Feb 3, 2018 09:41

@DawoodibnKareem It's just a hat... Generally, it's considered a good thing when a country's culture spreads to another

Dawood ibn Kareem

I agree with you entirely. I am wondering why anyone would call a sombrero-wearer racist.

Unless they happened to be racist in addition to wearing a sombrero, of course.

Round and round the rugged rocks, the sombrero-wearing racist ran.

Mithrandir24601

Feb 3, 2018 10:26

@DawoodibnKareem So am I :P

Mithrandir24601

Feb 3, 2018 10:43

@Blue There's a few different answer to this: Some will say that it's what the maths says; others that you need to send classical information in order to get the right measurement basis as the density matrix is in a mixed state until that classical info is received. This is the closest 'commonly used' argument to what I'd say that the best answer(s) is/are. It's good most of the time but runs into issues when you start considering the same problem in the context of boosted frames

Anonymous

@Mithrandir24601 Sounds interesting. I don't know how the details of the issues which arise as a result of Lorentz boost of coordinate frames. Do you have any references/articles which discusses this? (I'm a bit rusty in SR....gotta revise....)

Mithrandir24601

Feb 3, 2018 11:03

@Blue It's along the lines of section IV of this - it's not saying QM is inconsistent (quite the opposite), but it does lead to some questions about when wavefunction collapse actually occurs and could the same density matrix look different to different observers, at which point the best thing to do is to delve into reference frames, where things get very interesting

Cows

Feb 3, 2018 11:24

Off to bed. Will continue coding in the morning. I have to master 15 tools. 7 automation strategies and some cs theory before monday. Also need to be fluent in architecture security and load balancing. Good times !!

2physics

Feb 3, 2018 13:08

Hi, any body can introduce some sources(books, papers, links or whatever) to know more about what discussed in this question? Thanks!

Anonymous

Feb 3, 2018 13:39

@0celo7 You had a course on fluid mechanics, right? I need some help regarding the math related to coalescing of liquid drops

0celo7

Feb 3, 2018 13:54

@Blue that’s not standard material, but ok

What’s the issue?

Yashas

Why is that the energies of atomic orbitals of lower atomic number are higher (in the same period)?

For example, the 2p orbitals of carbon is higher than that of oxygen.

(every textbook shows 2p orbitals to have higher energy than oxygen in the CO molecular orbital diagram)

bolbteppa

Feb 3, 2018 14:14

@Kolmin what is going on in proposition 1, looks absolutely crazy e.g. using Hahn-Banach to prove it yet it's probably just saying the properties of a norm, or probably a semi-norm, can be re-expressed in terms of convexity?

Tanuj

@JohnRennie thanks for replying back. Are you available right now?

0celo7

@bolbteppa who is kolmin and why are you talking about Functional Analysis without me

John Rennie

@Tanuj hi, yes I'm around. What did you want to know?

Tanuj

@JohnRennie I have posted my doubt in on uthe other room. The problem solving stratergies.

bolbteppa

6

Q: On Bourbaki's "Integration" - Why/What/How to read it

I have a question concerning the Bourbaki's book on integration. Whenever I find them referenced (in answers on this site as well), it looks like they aged more than volumes of the same series on other topics. Also, it looks like they were criticised from the outset (e.g. see Halmos' comment fro...

Who knew HB could be used to prove Holder and Minkowski

0celo7

Feb 3, 2018 14:34

@bolbteppa what?

Why would you need HB for that

Are they doing integration with values in a TVS or something?

bolbteppa

No it's on $\mathbb{R}^n$,
"Ch. I: Very general Holder and Minkowski inequalities, applicable to positive functions defined on a set, on which there is no topology or `integral' in sight (Ch.I, Props. 2,3).

Prop.1 uses the Hahn-Banach theorem (`geometric form') in $\mathbb{R}^n$; there is no free lunch.

The payoff : it expedites the (simultaneous) construction of the function spaces $L^p$, ($1 \leq p <+ \infty$) and the integral on $L^1$, even for vector-valued functions."
p. 6 https://www.ma.utexas.edu/mp_arc/c/08/08-234.pdf

Secret

@Mithrandir24601 I think that agrees with the various experiments such as entanglement swapping in time and the numerous spacelike entanglement experiments that tests bell inequality.

bolbteppa

Ahh, they use HB to prove something about (what will become) an outer measure as their very first result and use this to prove Holder and Minkowski, crazy

Secret

I am now inclined to believe that what actually happens is that in the frame of one of the subsystems after a measurement is being made, what happens in the other subsystem is a statistical mixture until the classical information carrying the outcome of the measurement of the other subsystems arrived to establish which of the correlated observables that the system have obtained

12

A: "FTL" Communication with Quantum Entanglement?

You have a wrong understanding of quantum entanglement. What is entanglement? Quantum entanglement emerges naturally from the "only obvious way to do things" at the wavefunction level (distribute a wavefunction over all possibilities of two subsystems), and describes the fact that the general s...

for example here, in the answer given, the interference pattern of the other subsystem will look like there is no interference until the information that carry the correlation arrived that allow us to resolve the statistical mixture and hence recover the two interference patterns

Secret

Feb 3, 2018 14:56

wow, after watching that video linked by blue, I now started to understand how restrictive local hidden variables are:

Anonymous

@0celo7

Anonymous

I don't understand which distance they are considering as radius of meniscus

Secret

Having particles that conspire to measure the same or opposite depending on how the detectors are arranged is simply way too many correlations that should not be there

Anonymous

Shouldn't the radius of meniscus be the radius of upward facing arc of which the meniscus is a part of?

Anonymous

Feb 3, 2018 14:58

Rather than the height which they have shown? (Got it from here-Page 26 and here - Page 3)

Mithrandir24601

@Secret I haven't read through all that + links, but from a glance, it looks like what I know as 'time-bin encoding', while I'm looking at the questions that arise from asking things like "who measured first?" and "if you perform a boost (or rotation, or similar) on a frame, what happens to the density matrix that arises from measuring a single particle of an entangled pair", which is based more around the effects of reference frames, as opposed to entanglement

Anonymous

I would expect $r_m$ to be something like this

Mithrandir24601

@Secret This sounds right, apart from fiddly details about reference frames, which is (more or less) related to what that classical information is

0celo7

@Blue rm is on the picture

It seems to be the height from the plate to the side of the meniscus

Anonymous

Feb 3, 2018 15:05

@0celo7 Yeah, but that doesn't even look like a "radius"!

0celo7

I agree

Anonymous

Phew phew

0celo7

What you drew is more reasonable, namely the inverse of the curvature

Aka radius of curvature

But that’s not what they’re doing...so...

Keep reading and see if what they do makes sense in the end

Anonymous

Yeah. They should have just called it height or something.

Secret

hmm...

Now compare the above with the following qualitative "watered down" analogy

We prepared two marbles A and B, both colorless. Each carry an instruction of probability which reads as:

When touched, turn into (R)ed rA amount of the time or (Y)ellow yA amount of the time

similarly for B. Should we decide to touch either of them, they will change color, and we found there is no correlation between the colors R and Y.

We brought the marbles close together, leave that for some known amount of time t. The two marbles are still colorless.

Your marble experiment does not violate Bell's Theorem (or any other theorem of classical probability) and is therefore quite entirely irrelevant to the issue here. The wave function does not count as a hidden variable because it cannot *determinstically predict the outcomes of all measurements. In your marble experiment, we can easily explain the result by invoking some determinstic (though mysterious) force. — WillO Apr 29 '17 at 15:47

Anonymous

Feb 3, 2018 15:07

I have started to sympathize with you @0celo7. We share the hate for physicists :P

Secret

I think I might have some idea on where my analogy went wrong:

> Repeat Steps 1-3 many times and we found that R and Y are correlated in a way that agrees with the resulting probability of what happens when objects with some given instruction of probability (inferred during the preparation of the marbles) is being place close together for time t.

0celo7

@Blue all reasonable people do

Secret

I specified some fixed probability distribution on the marbles, thus introduced some determinism without knowing

Mithrandir24601

@Blue NOOOOOOOOOOOOO!!! COME BACK!!!

Anonymous

@Mithrandir24601 Lol. I still like physics

Mithrandir24601

Feb 3, 2018 15:09

@0celo7 OY! :P

Anonymous

@Yashas Ask the Chem QM guys. They can show you all the calculations. Orbitals for atoms are gross generalizations anyway

Secret

With the help of the video, I now understand why I cannot simply treat the outcome of entanglement particles as a sample space of correlated outcomes which is then randomly draw from it when a measurement is performed, because then I will have implicitly specified a scheme on how the particles will behave when being measured while the real case is that the particle have no such plans hence no dependence on how the detectors are arranged

Anonymous

MOT is a better version. But even that is an approximation (a very reasonable one though)

Mithrandir24601

@Secret you might want to check out Popescu-Rohrlich boxes

Secret

2

Q: Difference between PR correlations and entanglement correlations?

(As pointed out by helpful users, one of the bolded claims is interpretation dependent. Therefore, unless otherwise specified, Copenhagen interpretation is used throughout) Recall that for classical correlations, the observables are already determined even before a measurement, and thus knowing ...

quantum-mechanics non-locality

I have an unanswered question on this, I still yet to figure out how they work since I am so poor at dealing with inequalities (my brain go BSOD if I see 3 or more inequalities appeared in one line)

Sid

Feb 3, 2018 15:17

Hey guys!

bolbteppa

Of course they begin from topological vector spaces which are left modules over a valued division ring because of course you want to make sure your theorems apply to convex spaces with quaternion coefficients

Secret

This is indeed a wonderful video: THAT is entanglement in a nutshell

I think quantum textbooks should stop using the bell states to illustrate entanglement, and should use an entangled state where the observables are not opposite pairs

because once you see e.g. the above and e.g. when you have the following entangled state:

$$\frac 12 (|00\rangle + |01\rangle + |10\rangle - |11\rangle)$$

and then realise from the density matrices and reduced density matrix calculations, that whenever you get a 1 or 0 half of the time in subsystem A, you still get a 50:50 mixture of the interference pattern $\frac 1\sqrt{2} (|0\rangle \pm |1\rangle)$ until you have the classical information to resolve it, then the conclusion that there are no local hidden variables should be apparent

$\frac {1}{\sqrt{2}} (|0\rangle \pm |1\rangle)$

Anonymous

@Secret Nods! It was very confusing for me initially to grasp the general concept using the commonly used Bell states (which have the rotational invariance property). Discussing it in a more general setting would be much better.

Entanglement and Bell inequality illustrated (see video)

The h Bar

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