## Is entanglement that surprising?

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- Robert'); DROP TABLE *;
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### Is entanglement that surprising?

In Newtonian physics, objects have state, and the state has a "definite" value chosen out of some set of possibilities. In the case of an object's position, that set might be the entire space. In the case of something like an object's orientation around a particular external axis, that set is U(1). (IIRC, it doesn't matter for the point) Although there's no obvious reason to in purely Newtonian physics, the state of an extended system can similarly be modelled by choosing a definite value out of the tensor product of all the individual spaces. When two objects interact, their post-interaction states can both be modellded as functions of the pre-collision state, i.e. in the first simplest example, a logic gate which inverts the 1st signal it receives when the 2nd signal it receives is high, and outputs the inversion of the first signal, and a second signal that's high if either input was high. This fact of future states of objects being functions of past states that extend beyond the object itself is effectively the underpinning of causality.

In the logic gate example, the output of the gate is clearly dependent on its inputs, but also the space of possible outputs is restricted - it is impossible to produce a low signal on the 1st output while also producing a low signal on the 2nd output. This restriction means that the two output signals aren't independent of each other: knowing one tells you something about the other, but only if you know that the signals are a product of the logic gate and thus they are dependent on each other. (or rather, on a common process)

It seems to me that quantum entanglement is exactly analogous to this sort of casual dependence from classical physics, but the only difference is that we've expanded the possible space of states to include values "in between" all of the possible classical states. So, processes like the momentum entanglement of two products of a particle decaying is exactly like the momenta of two billard balls being "entangled" after collision, with the only difference being that the latter are forced to take classical (i.e. single-valued) values.

Is this a sensible way to think about entanglement, or am I missing something?

In the logic gate example, the output of the gate is clearly dependent on its inputs, but also the space of possible outputs is restricted - it is impossible to produce a low signal on the 1st output while also producing a low signal on the 2nd output. This restriction means that the two output signals aren't independent of each other: knowing one tells you something about the other, but only if you know that the signals are a product of the logic gate and thus they are dependent on each other. (or rather, on a common process)

It seems to me that quantum entanglement is exactly analogous to this sort of casual dependence from classical physics, but the only difference is that we've expanded the possible space of states to include values "in between" all of the possible classical states. So, processes like the momentum entanglement of two products of a particle decaying is exactly like the momenta of two billard balls being "entangled" after collision, with the only difference being that the latter are forced to take classical (i.e. single-valued) values.

Is this a sensible way to think about entanglement, or am I missing something?

...And that is how we know the Earth to be banana-shaped.

### Re: Is entanglement that surprising?

Yeah so you've hit on a key point about entanglement. Most descriptions of entanglement go something like: We put two electrons in a box and entangle their spins. Then separate the spins and spread them far apart. Now, say we're going to look at electron A. Since it is not in a well-defined spin state we don't know if we are going to get up or down when we measure it BUT, if we measures one spin to be UP we INSTANTLY know that the spin B at the other side is going to be DOWN and vice-versa. This is entanglement.

However, that description really misses out on the key point which is in my opinion much more subtle. Let me tell you another story. I have a left hand glove and right hand glove. I put each glove in its own box and then put those two boxes in another box. I then close that box and wave my wand over it and say "entangle" and shake it. Then I open it and separate the two boxes with one glove in each and separate the two far away. Again if we have the first box we don't know if we have the left or the right glove, BUT as soon as we open it if we find we have the LEFT glove then we know INSTANTLY that the other glove is the RIGHT glove and vice versa.

The point is these two descriptions are the same. What turns out to be important in the case of the electrons is that you can randomly pick whether you measure the x component of spin or the z component of the spin AFTER the spins have been separated but you will see correlations in the measurements. However, you would even expect this classically as well. What is important is that, for entangled particles, the strength of this correlation is STRONGER than would be classically allowed. This is a subtle point, and in the end I think a little frustrating because it seems like it just boils down to a quantitative difference in how the particles behave rather than a striking qualitative difference in the correlations.

I've been trying hard lately to come up with an explanation for entanglement that doesn't rely on this quantitative aspect but can't seem to come up with it. Here is a nice video that explains the strength of the correlations pretty simply.

https://www.youtube.com/watch?v=ZuvK-od647c

And here's a game that you can't win classically but you can win quantum mechanically.

http://www.forbes.com/forbes/welcome/?/ ... oogle.com/\

edit: Just a bit more. You're essentially arguing for a "hidden variables" theory. In other words, there is some information that the particles share when they are created and they take this with them when they're apart, so when we find that they are correlated when they are far separated we shouldn't be surprised. However, it turns out that, if you go through the math and prove Bell's theorem, you find that such a theory is possible, but it requires a rejection of local causality.

I wish I could give a more intuitive less quantitative explanation for this but I can't at the moment!

However, that description really misses out on the key point which is in my opinion much more subtle. Let me tell you another story. I have a left hand glove and right hand glove. I put each glove in its own box and then put those two boxes in another box. I then close that box and wave my wand over it and say "entangle" and shake it. Then I open it and separate the two boxes with one glove in each and separate the two far away. Again if we have the first box we don't know if we have the left or the right glove, BUT as soon as we open it if we find we have the LEFT glove then we know INSTANTLY that the other glove is the RIGHT glove and vice versa.

The point is these two descriptions are the same. What turns out to be important in the case of the electrons is that you can randomly pick whether you measure the x component of spin or the z component of the spin AFTER the spins have been separated but you will see correlations in the measurements. However, you would even expect this classically as well. What is important is that, for entangled particles, the strength of this correlation is STRONGER than would be classically allowed. This is a subtle point, and in the end I think a little frustrating because it seems like it just boils down to a quantitative difference in how the particles behave rather than a striking qualitative difference in the correlations.

I've been trying hard lately to come up with an explanation for entanglement that doesn't rely on this quantitative aspect but can't seem to come up with it. Here is a nice video that explains the strength of the correlations pretty simply.

https://www.youtube.com/watch?v=ZuvK-od647c

And here's a game that you can't win classically but you can win quantum mechanically.

http://www.forbes.com/forbes/welcome/?/ ... oogle.com/\

edit: Just a bit more. You're essentially arguing for a "hidden variables" theory. In other words, there is some information that the particles share when they are created and they take this with them when they're apart, so when we find that they are correlated when they are far separated we shouldn't be surprised. However, it turns out that, if you go through the math and prove Bell's theorem, you find that such a theory is possible, but it requires a rejection of local causality.

I wish I could give a more intuitive less quantitative explanation for this but I can't at the moment!

- doogly
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### Re: Is entanglement that surprising?

But if your takeaway is that "This isn't so surprising, it's like the classical case but more correlated," and likewise for quantum probabilities, "This isn't so surprising, you just do the combinations with the square root of probability," then this is fine. It is fine not to be so surprised. Quantum mechanics is surprising when you're used to classical physics because it is different, but it is not so wildly different as to be mysticism or impossible to gain an intuition for if you practice and marinate in the quantitative juices of it all.

It does not need to be so mysterious as some people make it out to be. It is most certainly different, but it isn't silly or unpredictable.

It does not need to be so mysterious as some people make it out to be. It is most certainly different, but it isn't silly or unpredictable.

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- Eebster the Great
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### Re: Is entanglement that surprising?

Sure, but it is quite "mysterious" in the sense that these differences which at the surface might seem minor are still fundamental differences in the way reality works, and you can use these to create thought experiments which give extremely counterintuitive results. Similarly, special relativity might not seem so weird when you think of it as "just a small difference in the velocity addition formula," but it still implies some pretty weird stuff when you consider the lives of people on relativistic spacecraft, and general relativity might not seem so weird when you think of it as "just a geometric description of gravity as an inertial reference frame," but it gets pretty damn weird when you consider what that implies for black holes.

Sure, there is nothing "mystical" about quantum physics, but it certainly defies our intuitions in very substantial ways.

Sure, there is nothing "mystical" about quantum physics, but it certainly defies our intuitions in very substantial ways.

- doogly
- Dr. The Juggernaut of Touching Himself
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### Re: Is entanglement that surprising?

Right, there is just this current of "Nobody understands quantum mechanics," which is not that helpful. Especially if the person who says it certainly does and it just being a Coyote about it.

LE4dGOLEM: What's a Doug?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

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Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

- Eebster the Great
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### Re: Is entanglement that surprising?

I'm not sure you're using "coyote" right.

- doogly
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### Re: Is entanglement that surprising?

Coyoto, like in Gunnerkrigg Court. Do you not read this one? Go read this one, it is the best thing.

LE4dGOLEM: What's a Doug?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

### Re: Is entanglement that surprising?

And if you've ever thought that quantum mechanical entanglement is cool, but doesn't go too far enough, check out Popescu-Rohrlich boxes.

Zµ«VjÕ«ZµjÖZµ«VµjÕZµkVZÕ«VµjÖZµ«VjÕ«ZµjÖZÕ«VµjÕZµkVZÕ«VµjÖZµ«VjÕ«ZµjÖZÕ«VµjÕZµkVZÕ«ZµjÖZµ«VjÕ«ZµjÖZÕ«VµjÕZ

- Robert'); DROP TABLE *;
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### Re: Is entanglement that surprising?

Twistar wrote:The point is these two descriptions are the same. What turns out to be important in the case of the electrons is that you can randomly pick whether you measure the x component of spin or the z component of the spin AFTER the spins have been separated but you will see correlations in the measurements. However, you would even expect this classically as well. What is important is that, for entangled particles, the strength of this correlation is STRONGER than would be classically allowed. This is a subtle point, and in the end I think a little frustrating because it seems like it just boils down to a quantitative difference in how the particles behave rather than a striking qualitative difference in the correlations.

I'm not really sure what the classical analogue of doing that is, and subsequently what I would expect to see if the universe were classical.

edit: Just a bit more. You're essentially arguing for a "hidden variables" theory. In other words, there is some information that the particles share when they are created and they take this with them when they're apart, so when we find that they are correlated when they are far separated we shouldn't be surprised. However, it turns out that, if you go through the math and prove Bell's theorem, you find that such a theory is possible, but it requires a rejection of local causality.

Sort of. IMO, we should expect to see them be correlated, just as we expect to see classical objects be correlated because they've interacted with each other/a common process before they were seperated. However, I've kinda got stuck on the fact that this is required to show up in the mathematics (you can't describe two entangled qubits in terms of smaller units) whereas in the classical scenario, the states can be described seperately, and the correlation doesn't "persist" in the same way after the particles have been seperated.

(Also, to be clear, I'm specifically imagining that the "true state" of the particle is the superposition, so while entangling two qubits creates a classical bit's worth of information, that bit is not destroyed or transmitted when we measure either particle, because we haven't actually changed the state of anything, we've just inferred the state of one thing based on the state of something we know correlates with it.)

...And that is how we know the Earth to be banana-shaped.

### Re: Is entanglement that surprising?

One slogan for entanglement is "correlation without correlata". In classical mechanics there's an (anti-)correlation between the handedness of two gloves, but we're used to thinking that the process that makes the two gloves (i.e. the glove factory) achieves this correlation by "first" giving the gloves definite handedness, which also fixes the correlation between them.

In quantum mechanics, the process of producing entangled pairs also results in a fixed correlation, but does not do so by giving the individual electrons a definite spin. So the shift in intuition that one must make is to stop thinking of correlation as a "consequence" of some other properties of objects, but rather as something that can exist on its own.

In quantum mechanics, the process of producing entangled pairs also results in a fixed correlation, but does not do so by giving the individual electrons a definite spin. So the shift in intuition that one must make is to stop thinking of correlation as a "consequence" of some other properties of objects, but rather as something that can exist on its own.

Our universe is most certainly unique... it's the only one that string theory doesn't describe.

- Robert'); DROP TABLE *;
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### Re: Is entanglement that surprising?

That approach rubs me the wrong way. While I'm sure its mathematically valid, it seems iffy to imagine it that way, given that the actual theory of QM (AFAIK) talks about the states of particles in fairly absolute (although non-classical) terms, not in terms of abstract correlations, i.e. the state of a quantum system is in terms of |up>s and |down>s, not in terms of relative "correlated" or "anticorrelated."

...And that is how we know the Earth to be banana-shaped.

- Eebster the Great
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### Re: Is entanglement that surprising?

Robert'); DROP TABLE *; wrote:That approach rubs me the wrong way. While I'm sure its mathematically valid, it seems iffy to imagine it that way, given that the actual theory of QM (AFAIK) talks about the states of particles in fairly absolute (although non-classical) terms, not in terms of abstract correlations, i.e. the state of a quantum system is in terms of |up>s and |down>s, not in terms of relative "correlated" or "anticorrelated."

The quantum system here is the entangled pair. You cannot describe either particle individually without "missing" some information. That information happens to be in the anticorrelation between the mixed states of the two particles.

### Re: Is entanglement that surprising?

That approach rubs me the wrong way. While I'm sure its mathematically valid, it seems iffy to imagine it that way, given that the actual theory of QM (AFAIK) talks about the states of particles in fairly absolute (although non-classical) terms, not in terms of abstract correlations, i.e. the state of a quantum system is in terms of |up>s and |down>s, not in terms of relative "correlated" or "anticorrelated."

As Eebster pointed out, the state describes the combined two-particle system. Just to elaborate on that, entangled states are, by defnition, states that can't be separated nicely into a "first particle" state and a "second particle" state. So while the two-particle state is indeed talked about in absolute terms, the individual particles don't have a definite quantum state associated to them.

The best you can do if you want to somehow isolate the information about the first particle is to do a sum over the possible "second particle states" to get a "density matrix" which encodes a probability distribution (in the usual classical sense, not in the sense of quantum superposition) of what the first particle state is. But having the density matrices for each of the particles is not enough to reconstruct the full two-particle quantum state. That's what Eebster meant when he said the extra information is contained in the correlations.

Our universe is most certainly unique... it's the only one that string theory doesn't describe.

- Robert'); DROP TABLE *;
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### Re: Is entanglement that surprising?

I understand that, although it still sounds conceptually strange. Is it possible to write the dynamics equations purely or mostly in terms of how correlations evolve, or something like that? Some other way of looking at the model to make the correlations rather than the absolute states the first-class entities? It intuitively feels as though given the correlation between two quantum states is somehow intrinsically different than the one between Newtonian states, then we should to be able to make that more obvious than them simply being implicit in a combined wavefunction. (Which is still in terms of ups and downs, rather than sames and opposites) Newtonian examples would still have (anti)correlations being produced by physical interactions, and I can't shake the feeling that the fact that correlated Newtonian states are seperable is merely an "accident" of the fact that they have only classical states, rather than some intrinsic distinction from QM. (where classical and superpositonal states are equally valid)

(You may have noticed I'm having trouble actually articulating the issue I have with this, sorry for being unclear.)

(You may have noticed I'm having trouble actually articulating the issue I have with this, sorry for being unclear.)

...And that is how we know the Earth to be banana-shaped.

- Eebster the Great
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### Re: Is entanglement that surprising?

Classical physics is certainly a special case of quantum physics, if that's what you mean. It's the special case as the scale gets sufficiently large, called the "classical limit." And separability is due to decoherence and noise; technically there is still a ton of entanglement, but essentially entirely of a random, thermal nature. Thermodynamics virtually guarantees this thermal noise will completely dominate other quantum-scale phenomena in all but the coldest macroscopic systems.

If we knew about quantum physics in advance, classical physics would not be very surprising. And if we knew about relativity in advance, classical physics wouldn't be very surprising. But from the perspective of a species that knew about classical physics first, these other theories are very surprising indeed.

If we knew about quantum physics in advance, classical physics would not be very surprising. And if we knew about relativity in advance, classical physics wouldn't be very surprising. But from the perspective of a species that knew about classical physics first, these other theories are very surprising indeed.

### Re: Is entanglement that surprising?

Newtonian physics is more intuitive to us both because of the simpler equations and because there is survival value in it even with very low technology. What benefit does a caveman get from understanding subatomic particles? On the other hand, being able to predict where a thrown spear will strike? Now THAT requires an intuitive (if not numerical) grasp of parabolic motion under gravity and atmospheric drag.

- doogly
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### Re: Is entanglement that surprising?

if you think people can intuit Newtonian mechanics I have some Aristotles and Freshmen to introduce you to

Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers.

Or; Is that your eye butthairs?

### Re: Is entanglement that surprising?

As I said, we don't understand them numerically, but we do have the ability to gauge where a projectile will go, which means that the necessary understanding of acceleration and drag is happening on a subconscious level. Aristotle was not able to explain curved projectile motion in terms of laws and numbers, but he could certainly watch a stone being thrown and be able to predict its landing point just as any man can.

### Re: Is entanglement that surprising?

Have you heard about the Feynman sprinkler? There's no shortage of problems that are unintuitive and still fall firmly under Newtonian physics.

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- Eebster the Great
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### Re: Is entanglement that surprising?

Nevertheless, in the "classical limit," the two models are equivalent, and that classical limit coincides precisely with the world we are most familiar with. So it would be hard to argue this was a coincidence.

You are right that this is true more generally. For instance, the fact that all bodies experience the same gravitational acceleration (regardless of density) is not intuitive, and for the same reason: we live in a planet with a thick enough atmosphere that we never have a chance to observe this phenomenon.

You are right that this is true more generally. For instance, the fact that all bodies experience the same gravitational acceleration (regardless of density) is not intuitive, and for the same reason: we live in a planet with a thick enough atmosphere that we never have a chance to observe this phenomenon.

### Re: Is entanglement that surprising?

Yeah, Newtonian physics really isn't that intuitive. Take a look at this video discussing some common misconceptions. In particular, Newton's first law is very counterintuitive if you haven't been successfully ~~brainwashed~~ educated and it took quite a lot of persuading for the scientific community to accept that bodies did not naturally want to come to rest.

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- Zamfir
- I built a novelty castle, the irony was lost on some.
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### Re: Is entanglement that surprising?

ijuin wrote:As I said, we don't understand them numerically, but we do have the ability to gauge where a projectile will go, which means that the necessary understanding of acceleration and drag is happening on a subconscious level. Aristotle was not able to explain curved projectile motion in terms of laws and numbers, but he could certainly watch a stone being thrown and be able to predict its landing point just as any man can.

There's range of "naive physics" that we seem to be born with, or acquire easily through observation of our surroundings. But this has only a faint resemblance to classical physics. It's more a bag of rules-of-thumb, with a kind of curve-fitting through common observations. It has large gaps, and it is often completely wrong.

Or let's look at the example of a thrown object. There are multiple similar models of how baseball outfielders catch a ball, but none of them has the outfielder predict where the ball will land in advance. Instead, an outfielder keeps an eye on the ball, runs a curved trajectory that is continuously updated according to some weird intuitive rule (this is where the models differ), and the trajectory of player and ball intersect where the ball hits the ground. The procedure doesn't require a particular newtonian motion (would be hard anyway, with unpredictable wind gusts), just a smooth trajectory that intersects with the ground. And the player doesn't know where they will catch the ball, until the end. There might not even be enough visual information for that at all - various different ball trajectories can't be distinguished from a single view point.

See what I mean? When we seem to grasp some aspect of mechanics, it doesn't necessarily reflect a valid physical model, not even subconsciously. And from there to even basic classical mechanics is a huge step - read accounts from the 16th or 17th century, and you see smart people struggling jut to pin down the basics. Try to read the Principia Mathematica! It's a mess, and it took another century from there to the "Newtonian" mechanics that we learn.

### Re: Is entanglement that surprising?

That's fine for catching the ball, but how about the pitcher? The pitcher does have to do all of his determination of where the ball will go before it is airborne, so to throw any pitch which he hasn't already practiced under the exact same distance snd weather conditions does require advance prediction. And the fact that pitchers throw a lot of no-hitter games aays that they do a good job of predicting where the ball will go.

### Re: Is entanglement that surprising?

Twistar wrote: What is important is that, for entangled particles, the strength of this correlation is STRONGER than would be classically allowed. This is a subtle point, and in the end I think a little frustrating because it seems like it just boils down to a quantitative difference in how the particles behave rather than a striking qualitative difference in the correlations.

Is that really true though? To me, the one surprising thing is how "two measurements at different angles" work in the first place. If you think about electron spin classically: if you prepare the spin at one angle (so the pole could be anywhere randomly in a hemisphere) then measure it at another angle (so the area of overlap between two hemispheres), you expect the correlation to be linear with the angle, from spherical geometry. But of course it isn't - it's cos

^{2}. That's the surprising thing, right there. Same thing for light passing through two polarizing filters at an angle. Surprise! Where'd that cos

^{2}come from?

But then you get over the surprise, and that's just how the universe works with angles and quantum stuff. Once you dig deeper and discover it's all about energies, the fact that it's something

^{2}is obvious in hindsight - energy is always something

^{2}- but I at least found it surprising at first.

Measuring the spin of entangled electrons at an angle is just cos

^{2}all over again. Prepare an electron and measure it at an angle, or measure one of an entangled pair then measure the other at an angle, it works the same way. Nothing surprising there at all, really.

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### Re: Is entanglement that surprising?

I have a pretty straightforward take on this, and it isn't really too unorthodox. Newtonian Physics is a model, and isn't "real". Intuitions based on reality and evolution (also based, more indirectly, on reality) have no expectations of correspondence. No surprises here.

- Zamfir
- I built a novelty castle, the irony was lost on some.
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### Re: Is entanglement that surprising?

ijuin wrote:That's fine for catching the ball, but how about the pitcher? The pitcher does have to do all of his determination of where the ball will go before it is airborne, so to throw any pitch which he hasn't already practiced under the exact same distance snd weather conditions does require advance prediction. And the fact that pitchers throw a lot of no-hitter games aays that they do a good job of predicting where the ball will go.

Well, pitchers do practice throws, all day every day from early childhood on...

In theory, you could use a two-step model for throwing. You have a certain pitch in mind that you want to throw. Step one, use a Newtonian physical model to derive the required release condition for the ball.Velocity, spin, location. Then in step two, find the required train of muscle commands to achieve that release condition.

There are some serious problems with this approach. One, the path of a pitch is heavily determined by spin effects, and those are nearly impossible to derive from first principles.A CFD calculation might perhaps count as such, but I hope we can agree that pitchers don't do those in their heads prior to a throw. An effective 'model' of spin effects is little more than a lookup table, based on previous observations. Practice, in other words.

Now, physics also won't give you the relation between nerve impulses and release condition either -those have to be learned from practice as well. But there's a snag: we can't reliably observe the result, if the result is the release condition. The ball goes much too fast for a human being to observe angle, speed, let alone spin axis and strength. All we we could do, in theory, is observe the end result (the ball path, especially its end point), and calculate back from there to the release condition . Or skip that step, and practice directly to build up a relation between muscle commands and end result, skipping the physics in between.

As you can see, there is not much room here for Newtonian mechanics, even less than for the catching example. What you need is a model like 'this sequence of nerve impulses will put the ball right there. Amplify this part of the sequence, and the ball goes a tad to the left. Delay that part of the sequence while weakening this other part, and the ball makes more of a hook but ends at the same point. Shorten yet another part, and the ball goes faster but more to the right and a bit up. ’

Such a model doesn't have to be physical at all, might even be difficult to base on physical principles. What you need is a well-calibrated interpolation routine, which seems to be what our brains are good at.

### Re: Is entanglement that surprising?

Yeah. That seems like a similar misconception as to what's going on inside a chess grandmaster's head.

It's tempting to think that the difference between a chess grandmaster and an ordinary player is that the grandmaster is thinking, like, 8 moves ahead or something.

A grandmaster can, of course, on occasion drill down quite deeply, especially in simple situations like the endgame. However, aside from the endgame and the start (where they may have rote memorised a whole load of opening moves) mostly it's about pattern recognition: They've played so many games that they just know that when all the pieces are in certain places, making a certain move advances their position.

After all, if all they did was consciously analyse x moves ahead, there's no way they could play and win a hundred games simultaneously like they sometimes do to show off.

No, it's more typically an instinctive thing - drilled into their subconscious via thousands of games - finding out what works and what doesn't and storing the result as a 'gut feeling'.

Likewise, as Zamfir says, there's no way a pitcher or catcher solves mathematical equations even subconsciously; It's all just practice and repetition: "If I throw it like this, under these conditions then the ball goes here"

That's why you can master a video game where the physics works totally different to the real world. It's not about equation-solving, it's simply practice.

They say it takes 10,000 hours to master any skill, and that's why.

It's tempting to think that the difference between a chess grandmaster and an ordinary player is that the grandmaster is thinking, like, 8 moves ahead or something.

A grandmaster can, of course, on occasion drill down quite deeply, especially in simple situations like the endgame. However, aside from the endgame and the start (where they may have rote memorised a whole load of opening moves) mostly it's about pattern recognition: They've played so many games that they just know that when all the pieces are in certain places, making a certain move advances their position.

After all, if all they did was consciously analyse x moves ahead, there's no way they could play and win a hundred games simultaneously like they sometimes do to show off.

No, it's more typically an instinctive thing - drilled into their subconscious via thousands of games - finding out what works and what doesn't and storing the result as a 'gut feeling'.

Likewise, as Zamfir says, there's no way a pitcher or catcher solves mathematical equations even subconsciously; It's all just practice and repetition: "If I throw it like this, under these conditions then the ball goes here"

That's why you can master a video game where the physics works totally different to the real world. It's not about equation-solving, it's simply practice.

They say it takes 10,000 hours to master any skill, and that's why.

### Re: Is entanglement that surprising?

lgw wrote:Twistar wrote: What is important is that, for entangled particles, the strength of this correlation is STRONGER than would be classically allowed. This is a subtle point, and in the end I think a little frustrating because it seems like it just boils down to a quantitative difference in how the particles behave rather than a striking qualitative difference in the correlations.

Is that really true though? To me, the one surprising thing is how "two measurements at different angles" work in the first place. If you think about electron spin classically: if you prepare the spin at one angle (so the pole could be anywhere randomly in a hemisphere) then measure it at another angle (so the area of overlap between two hemispheres), you expect the correlation to be linear with the angle, from spherical geometry. But of course it isn't - it's cos^{2}. That's the surprising thing, right there. Same thing for light passing through two polarizing filters at an angle. Surprise! Where'd that cos^{2}come from?

But then you get over the surprise, and that's just how the universe works with angles and quantum stuff. Once you dig deeper and discover it's all about energies, the fact that it's something^{2}is obvious in hindsight - energy is always something^{2}- but I at least found it surprising at first.

Measuring the spin of entangled electrons at an angle is just cos^{2}all over again. Prepare an electron and measure it at an angle, or measure one of an entangled pair then measure the other at an angle, it works the same way. Nothing surprising there at all, really.

Yes that's my point. The correlation goes like a cosine rather than linearly as would be expected for two classical systems. My point is that for example, the percent difference in the possible amount of correlation between quantum vs. classical isn't really that much. From that perspective it's just a quantitative difference in the amount of correlation. I guess you're arguing that the fact the correlation goes as the cosine of the angle as opposed to linear in the angle actually constitutes a qualitative difference.

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