The h Bar

There are 20 socks, which makes 10 pairs of entangled socks in the closet

and when picked up and taken out of the dark closet (which we can assume that will be a measurement since the color will be determined) it can be either red or blue

Calculate the probability to get two socks of matching color

There is nothing quantum about just having ten pairs of differently colored socks.

12:44 PM

indeed, because we don't know whether the two socks we picked up are part of an entangled pair, the probabilities should be classical, I think

They are also not "entangled". They are just pairs of differently colored socks.

yup. The quantumness meter is at zero so far.

If you're talking about entangled states, there is no need to confuse the issue by calling these states socks. If you're talking about actual socks, there is no need to confuse the issue by calling them quantum or entangled.

Ditto for the entanglometer.

uh, the 10 pairs of socks are prepared in a way such that they basically act like 10 pairs of entangled qubits, such that when measured, their observables (in this case, red vs blue) always anticorrelate. Their color is not determined before being taken out of the closet

Here's a more rigorous version by taking out the obvious joke of finding socks in a dark closet in case it is confusing:

12:48 PM

Entanglement turns interesting when you involve non-commuting observables.

There's a nice book by Bell where he compares entanglement to finding you only have one glove in your pocket.

If it's your left glove, you know right away that the glove on your countertop at home is a right glove. But that's not interesting.

For the socks, you could define three color axes, red, green, and blue

Measure the color along one axis by looking at it in a red light, or a blue light, or a green light --- the sock is either bright or dark

[Rigorous version]
Suppose there's a box containing 20 electrons, which they are entangled to form 10 entangled pairs. All of these are singlet states (thus there are 10 singlet states) thus whenever a pair is measured, their spins always anticorrelate. Now, calculate the probability to measure any two electrons from the box, such that you get them both spin up

"Entangled socks" would also still be different colors under magenta lights, cyan lights, or yellow lights.

@Secret so? it is irrelevant whether they are entangled or not. For the observables you've specified so far, it's perfectly possible to provide a non-entangled model that will reproduce all the observations, and your observables will be unable to distinguish between the entangled and the non-entangled versions.

@Secret ^ ditto for that version, too

@Secret You should give some serious thought to a disciplined and thorough reading of Nielsen and Chuang.

amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/…

So what's interesting is if you look at a sock under red light, and I look at its partner under magenta light.

Entangled socks and classical socks have different correlations under those mixed tests.

Emilio: Exactly, this joke inspired question is in some sense really a demonstration of no communication theorem, if you don't know which are the correlated pair, then it is just an ordinary probability question (I think...)

Meanwhile, I think rob might be actually talking about the scenario where things gets interesting

12:55 PM

@Secret I'm usually trying to make things more interesting.

djsmiley2k

@Secret what is the point of this.

@djsmiley2k Me attempt to put a quantum twist to the famous "find matching socks in a dark closet"

djsmiley2k

I know neither if this joke is funny, or not funny, and i've even observed it!

Boom, there's a joke.

Jul 21 at 15:42, by AccidentalFourierTransform

@rob is that an allusion to measuring bell states along an axis somewhere between xyz axes, and show that the outcomes of their spins differ between classical and entangled states?

1:01 PM

@Secret Just so

@Secret In Bell-type measurements, entanglement doesn't add anything if the two measurements are on parallel axes or on orthogonal axes.

ah, you are referring to that cos shaped correlation diagram, where in classical, it will just look like a sawtooth

@Secret I think that you could construct such a correlation diagram in the experiments I have in mind, yes.

Quantum sock ver 2: (This time, I am pretty sure we can do quantum on it) Suppose you are in a dark closet, and there are 20 socks, which once again can be either red or blue if taken out of the closet. The socks are entangled in such a way such that the sock that is picked up always has a different color from the other 9 socks. Calculate the probability that two random socks taken out of the closet will have the same color

(Actually, I am not sure if such generalisation of GHZ state can be written down... need to check)

Let $\{red,blue\} = \{0,1\}$ Then
$$\lvert socks\rangle = \frac{1}{\sqrt{20}}(\lvert 1000...0\rangle + \lvert 0100...0\rangle + \cdots + \lvert 0000...1 \rangle)$$

uh, that does not look really entangled to me... hmm...

if it is 2 qubit, then we have the bell states:

$$\lvert socks\rangle = \frac{1}{\sqrt{2}}(\lvert 01\rangle \pm \lvert 10\rangle),\lvert socks\rangle = \frac{1}{\sqrt{2}}(\lvert 11\rangle \pm \lvert 00\rangle)$$

and then, the singlet state will ensure anticorrelation

o nvm then, it is all good, mistaken $\lvert abcdef...z\rangle$ as state vectors with many components and not tensor product of state vectors...

now to check entanglement...

1:22 PM

I hit a birb with my car :(

@Secret $\mathrm{div}\, B=0$ distributionally

skullpatrol

Is it dead?

@skullpatrol idk I didn't stop to examine the carnage

my car seems fine

ok, by definition of entanglement in terms of tensor product, the state is entangled, as required

however, I think I might need some minus signs somewhere...

Loong

@0celoñe7 Here we have suicidal seagulls on the road. But of course I am mostly afraid of the moose.

Q: What is a real world analog to spin?

abstrusegoose.com/342

Interestingly, I stopped asking that question

0

Spin is an elusive concept in physics which seems to have no "physical world" parallel -- that is, something that we can see to compare it to. We know spin can be defined as the quantifiable (it is quantized at 1/2 units) form of angular momentum. But, spin has direction too (because all particl...

spin is already something real, I think OP is asking what the classical analogue is, in which case there is none

(i think)

1:49 PM

Hello

Q. A thermometer is kept in air at direct sunlight. Whose temperature does the thermometer read, of air, of sun or something else?

@GerWyn the surface of the sun, no?

@Ocelone7, what does that mean?

Thanks for your advice , Does Griffith has textbook on EM? — user46899 2 mins ago

@GerWyn air

::facepalm::

somebody stop me from doing something rash

1:54 PM

@0celoñe7 What?

@user685252, how?

@GerWyn what is the thermometer in contact with?

does the amount of heat transfer by radiation enough to heat the thermometer to the surface of the sun, but I think convection should be quicker and dominating the process, right

Air, direct sunlight

so it should not be able to get to the surface of the sun temperature

1:57 PM

Can't it get tempretaure from sun rays?

What is "temperature?"

@EmilioPisanty stop!

@0celoñe7 Have you seen thermometers in sunlight go up to thousands of Kelvin? :P

::Throws cold water at Emilio to cool him down::

@user685252, temperature is degree of hotness or coldness of a body

Anonymous

1:59 PM

I guess some people don't know that electrodynamics and electromagnetics refer to the same thing. Maybe you could just point that out... (As Griffiths' book is named "Introduction to Electrodynamics")

@GerWyn and how is that hotness or coldness of a body transmitted to the thermometer?

Through contact

yes

the collisions of the air molecules

IIs "the collisions of the air molecules" another method?