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Entanglement: Why 2 Schoolkids E'er Answer Questions Oppositely

More than a calendar week ago, I discussed an article past times Natalie Wolchover who was manifestly shocked that when some optical information from the stars are used to gain pseudorandom numbers, an experiment testing entanglement amongst some random choices for the detectors produces the same results as the experiment where solely terrestrial gadgets are used as the pseudorandom generators.

What a surprise: numbers that await similar some random mess amongst the same distribution Pb to the statistically identical outcomes whether or non they were calculated from stars or dice. Come on, people. This is totally basic mutual sense. There can't hold upwardly whatever correlations of the terrestrial experiments amongst the random stellar data. To believe that in that place are such correlations – that the experiment cares whether the stellar information were employed – isn't just analogously silly as astrology. It actually is a particular illustration of astrology! This is what star divination actually means: local events on globe gain tending almost some immediate properties of the celestial bodies! Well, they don't. None of the information from local, repeatable experiments on globe tin hold upwardly correlated amongst some independent information almost the celestial bodies.

You may also say that the belief inwards these correlations amongst the stars is on par amongst the Movie Pi where the digits of \(\pi\) were assumed to know all the information almost the movements of the stock markets too prophesies of the Jewish Bible, amid other things. Please, hand me a break. It may hold upwardly an inspiring motion painting but everyone who has spent at to the lowest degree some fourth dimension past times looking at the actual relationships betwixt events inwards the world, non necessarily the "physical laws" inwards the narrow too technical sense, must know that this is the variety of a human relationship that cannot be too unproblematic bear witness is plenty to justify this assertion.

Now, an appendix to Wolchover's article almost the stellar entanglement conspiracies (that were "surprisingly" non detected past times an experiment)
How to Tame Quantum Weirdness
was written past times Pradeep Mutalik, a author who was previously mentioned because of a confusingly ambiguous article almost the Sleeping Beauty Problem. The championship talks almost taming of quantum weirdness but I think the actual usage is to spread the illusion or delusion that quantum mechanics too the entanglement are weird.




What's going on? In the simplest entanglement experiment amongst 2 spin-1/2 particles, 1 starts amongst the \(J=0\) (singlet) solid soil of the 2 spins\[

\ket\psi = \frac{ \ket\uparrow \ket \downarrow - \ket \downarrow \ket\uparrow }{\sqrt 2}.

\] When the measurements of the projection of the spin along the same axis \(\hat n\) is performed on both particles \(A,B\), nosotros reveal out that the eigenvalues which may hold upwardly either \(+1/2\) or \(-1/2\) are e'er precisely contrary to each other:\[

J_{A,\hat n} = -J_{B,\hat n},\quad \{J_{A,\hat n},J_{B,\hat n}\}=\{+1/2,-1/2\}.

\] This perfect anticorrelation just follows from the conservation of the angular momentum. The initial solid soil is an eigenstate of\[

\vec J = \vec J_A + \vec J_B

\] amongst the eigenvalue null (vector) – it is possible for the vector to hold upwardly an eigenstate of all 3 components inwards this particular instance when the eigenvalues are zero. So when you lot mensurate a element of \(\vec J\), namely \(\vec J_{\hat n}\), you lot are guaranteed that the 2 price precisely cancel each other.




This upshot holds for whatever alternative of the axis \(\hat n\). The fact that the initial solid soil preserves the perfect anticorrelation regardless of the alternative of \(\hat n\) – regardless of the rotation nosotros perform on the organization – mathematically depends on the fact that the singlet solid soil higher upwardly has the construction of the antisymmetric spintensor \(\epsilon_{\alpha\beta}\) where \(\alpha,\beta\in\{1,2\}\) or \(\{\uparrow,\downarrow\}\), if you lot wish, are spinor indices which is an invariant nether the \(SU(2)=Spin(3)\) rotations. Under a rotation, each spinor index \(\alpha,\beta\) is rotated via an \(SU(2)\) transformation but the epsilon symbol remains constant because it transforms as a determinant of the \(SU(2)\) matrix too this determinant is one, you lot know, because of the missive of the alphabet \(S\) (for "special") inwards \(SU\) ("special unitary").

What is Mutalik's "model" for that?
Two students, \(A\) too \(B\), reply 1 assay out question, a Yes/No question, inwards a long exam. And they just tumble out to reply oppositely every time, whatever they are asked about.
All the details that Mutalik adds – that some exams are done after 37 days, or questions are grouped into groups of 100, too and then on – seem similar absolutely irrelevant distractions. Now, he asks you lot to create upwardly one's hear whether it's reasonable that all the answers volition e'er hold upwardly anticorrelated.

Well, if they were answering randomly too independently, the anticorrelation would almost sure enough disappear really soon. But that doesn't hateful anything mysterious or weird. It just way that the model inwards which 2 students reply randomly too independently is completely different than the province of affairs of the 2 spins inwards the singlet state.

The actual argue why the answers are too then perfectly anticorrelated inwards the experiment amongst the 2 spins is that the 2 spins were prepared inwards the singlet solid soil that encodes the perfect anticorrelation – e.g. because the electron too the positron arose from a decay of a spin-zero particle (two photons coming from a decaying positronium would hold upwardly easier for that). Mutalik doesn't hash out the training of the entangled solid soil at all which way that he fails to come across absolutely everything almost the actual reasons behind the anticorrelation.

H5N1 closer model for the anticorrelation would hold upwardly similar this.
Every morning, earlier they larn to reply a inquiry inwards the exam, Alice too Bob concur to hand the contrary answers to a question. However, the answers must await random too they must hold upwardly theme on the inquiry that is beingness asked. How gain they gain it? Alice too Bob agrees that if the tertiary missive of the alphabet inwards the inquiry they're asked on the examination after today is a vowel, Alice answers Yes too Bob answers No, too if it is non a vowel, Alice answers No too Bob answers Yes.

They go, reply their question, too what a shock: The answers are anticorrelated. Every day. For example, they are asked: "Will Donald Trump brand America smashing again?". Alice answers No too Bob answers Yes because "L" is non a vowel.

On the next day, they may select the 7th missive of the alphabet of the inquiry as the source of the information. Or some other binary information extracted as a business office of the question.
There is null mysterious almost the anticorrelation: the anticorrelation was guaranteed from the outset when \(A,B\) were inwards contact too the probability that the answers are anticorrelated was 100% from the really beginning. In the actual quantum mechanical situation, the answers of Alice too Bob are perfectly contrary but they enshroud 1 chip of information, e.g. the reply past times Alice, that is truly too perfectly random. This isn't actually captured as good well past times the model which emulates the random determination past times some shared conception of Alice too Bob "how to answer".

But otherwise my model has everything it needs. The answers are perfectly anticorrelated, just similar inwards the instance of the 2 spins. And they are anticorrelated for the same argue – the anticorrelation was pre-programmed into both subsystems spell they were inwards contact. Also, my model agrees amongst the quantum mechanical reality when it comes to the "pre-existence" of the private answers. After Alice too Bob say good-bye to each other too are moving apart, it is not determined yet whether Alice would reply Yes or No (i.e. whether Bob would reply No or Yes) because the actual reply volition depend on the inquiry that is beingness asked too the inquiry may hold upwardly changed right earlier it is asked!

Most importantly, in that place is no superluminal communication too no activity at a distance inwards either case. All the correlations or anticorrelations are explained past times the 2 subsystems' contact or "agreement" at some signal inwards the past times when their separation was null or tiny.

Now, my model would move perfectly for all tests inwards which Alice too Bob are asked precisely the same question: the solely facts you lot demand to reproduce is that Alice's reply seems random – Yes too No are every bit probable too in that place are no patterns if you lot repeat the experiment many times – too Alice's too Bob's answers are perfectly anticorrelated. But if I allowed experiments inwards which Alice too Bob are asked unlike questions, my model won't hold upwardly able to gain all the correlations implied past times quantum mechanics.

When the axes \(\hat n_A\) too \(\hat n_B\) for the 2 spins' measurements are chosen "almost the same" but non quite, it's nevertheless vastly to a greater extent than probable that the 2 outcomes volition hold upwardly anticorrelated. But inwards my model, if Alice too Bob are asked similar but slightly unlike questions, it's much less guaranteed that the anticorrelation volition hold upwardly too then good. Alice may hold upwardly asked: "Will Donald Trump brand America smashing again?" And Bob may hold upwardly asked: "Trump volition lower corporate taxes to less than 20%: Yes or No?" These 2 questions are almost the same too they should nevertheless hold upwardly giving "mostly anticorrelated" answers. But their algorithm based on the vowel inwards the tertiary missive of the alphabet volition brand them hand the same reply inwards this assay out instead.

So inwards details, when all possible experiments amongst whatever alternative of axes are picked, my model won't move similar quantum mechanics. Indeed, Bell's theorem guarantees that no local realist model may hand the same answers as quantum mechanics. The rules of quantum mechanics "know" how the measurements amongst observe to nearby axes should hold upwardly "similar" spell my vowel-based model or any local realist model volition neglect to correctly work organization human relationship for the proximity of nearby questions inwards generic cases. The precise way how the probabilities of answers to unlike questions are determined according to quantum mechanics is just different than the way adopted past times whatever local realist theory. Quantum mechanics isn't a realist theory. In the same way, radio is something else than a state of war dove too the details how they transfer the information differ from 1 another, too. The departure is non shocking, it is non a large deal.

But the broader logic how the information is propagated too "when" the correlations or anticorrelations (if any) are determined, those qualitative things are perfectly captured past times my local realist model (my model is a hidden-variable model, the hidden variables cry back the algorithm how to bargain amongst the vowels etc.). The anticorrelation of Alice's too Bob's answers results from their understanding that guarantees that they are going to hand the contrary answers. There's no activity at a distance: it's just a outcome of a tidings betwixt them when they could hear each other. And if no corresponding (direct or indirect) contact of the 2 subsystems existed inwards the past, in that place tin hold upwardly no correlation or anticorrelation!

I actually don't empathize what too then many people reveal too then hard almost these straightforward things. And I don't empathize why the Quanta Magazine encourages Mutalik – who is clearly 1 of those who don't empathize quantum mechanics – to pick the winner who has given the "best model". By the way, Mutalik's model involves some inflated balloons amongst anticorrelated but random blood-red too bluish sub-balloons. Some parts of his "model" are equivalent to my model. But why is he joining the 2 balloons past times a rope? There is no rope betwixt the 2 subsystems. They don't communicate when they're measured. They just pre-agreed to hand answers according to an algorithm or dominion that guarantees the anticorrelation when the same inquiry is asked to both!

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