1591: "Bell's Theorem"

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1591: "Bell's Theorem"

Postby Kozmo » Fri Oct 16, 2015 11:57 am UTC

Image

title="The no-communication theorem states that no communication about the no-communication theorem can clear up the misunderstanding quickly enough to allow faster-than-light signaling."

Another annoying misunderstanding of the theorem is when people think that it disproves hidden variables. In fact, Bell himself was one of the biggest advocates of a hidden variable interpretation of QM called Bohmian mechanics (pilot-wave theory). The theorem disproves *local* hidden variables. For more, Bell's collection of papers "Speakable and Unspeakable in Quantum Mechanics" is an excellent read!

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Re: 1591: "Bell's Theorem"

Postby mathmannix » Fri Oct 16, 2015 1:12 pm UTC

No bell prize for you!
I hear velociraptor tastes like chicken.

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Re: 1591: "Bell's Theorem"

Postby rmsgrey » Fri Oct 16, 2015 1:34 pm UTC

Apparently this comic is ahead of the curve...

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Re: 1591: "Bell's Theorem"

Postby cellocgw » Fri Oct 16, 2015 2:03 pm UTC

So does this corollary violate the Recognition Law? You know, " Dunno who he was, but his face rings a Bell"
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Re: 1591: "Bell's Theorem"

Postby Keyman » Fri Oct 16, 2015 2:06 pm UTC

rmsgrey wrote:Apparently this comic is ahead of the curve...
I get it, enough to catch your joke, but I'm pretty sure this is going to be (another) thread that just flies way over my head. I started falling behind the learning curve at school when the mathematical symbols started having curves...
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Re: 1591: "Bell's Theorem"

Postby ctdonath » Fri Oct 16, 2015 2:56 pm UTC

cellocgw wrote:"Dunno who he was, but his face rings a Bell"


Later, Dr. Frankenstein identified the body.
Leaning over his deceased assistant, he whispered "Ig, no bell prize for you."

Spoiler:
http://www.improbable.com/ig/winners/

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Re: 1591: "Bell's Theorem"

Postby burtonlang » Fri Oct 16, 2015 3:15 pm UTC

That's a lot of words to say in a nanosecond!

I can hardly imagine saying that in less than a second, and both production times and reaction times to the smallest of linguistic phenomena are usually on the order of milliseconds.

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Re: 1591: "Bell's Theorem"

Postby cellocgw » Fri Oct 16, 2015 3:21 pm UTC

burtonlang wrote:That's a lot of words to say in a nanosecond!

I can hardly imagine saying that in less than a second, and both production times and reaction times to the smallest of linguistic phenomena are usually on the order of milliseconds.


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Re: 1591: "Bell's Theorem"

Postby ctdonath » Fri Oct 16, 2015 3:27 pm UTC

Consider that in the time that it takes for light to get from >this< screen (yours you are reading right now) to >your< eyes, the CPU involved has already carried out a dozen instructions.

Not quite faster-than-light, but faster than time it takes light to get where it's going. That's a start.

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Re: 1591: "Bell's Theorem"

Postby Cervisiae Amatorem » Fri Oct 16, 2015 4:16 pm UTC

This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

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Re: 1591: "Bell's Theorem"

Postby orthogon » Fri Oct 16, 2015 4:24 pm UTC

Cervisiae Amatorem wrote:This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

Don't worry: it's quantum mechanics, so if you had understood it, you wouldn't have understood it.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1591: "Bell's Theorem"

Postby cellocgw » Fri Oct 16, 2015 4:46 pm UTC

orthogon wrote:
Cervisiae Amatorem wrote:This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

Don't worry: it's quantum mechanics, so if you had understood it, you wouldn't have understood it.


No, no! If you understood it, then you both understood and didn't understand it, and won't know which until the cat dies.
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Re: 1591: "Bell's Theorem"

Postby ctdonath » Fri Oct 16, 2015 4:51 pm UTC

Cervisiae Amatorem wrote:now I need ExplainExplainXKCD.


To put it in social media terms:
Cueball responded to the headline before the post started loading, confusing lag with bandwidth.

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Re: 1591: "Bell's Theorem"

Postby Flumble » Fri Oct 16, 2015 5:16 pm UTC

orthogon wrote:
Cervisiae Amatorem wrote:This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

Don't worry: it's quantum mechanics, so if you had understood it, you wouldn't have understood it.

Yet another common misconception –it is generally agreed upon that no human can understand the whole of quantum mechanics intuitively.
It is perfectly* feasible** to understand the reasoning behind some theorem within QM. :D (although you will not understand any (fermionically) entangled theorem)

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Re: 1591: "Bell's Theorem"

Postby doogly » Fri Oct 16, 2015 5:22 pm UTC

No, you can do this, it just takes a few years of effort. But still, more like a phd than a lifetime. And undergrad physics majors should even be able to grok bell's theorem. It is not so bad.
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Re: 1591: "Bell's Theorem"

Postby rhomboidal » Fri Oct 16, 2015 6:34 pm UTC

It took me a nanosecond or two, but I think I misunderstand this one.

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Re: 1591: "Bell's Theorem"

Postby ijuin » Sat Oct 17, 2015 4:16 am UTC

Flumble wrote:
orthogon wrote:
Cervisiae Amatorem wrote:This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

Don't worry: it's quantum mechanics, so if you had understood it, you wouldn't have understood it.

Yet another common misconception –it is generally agreed upon that no human can understand the whole of quantum mechanics intuitively.
It is perfectly* feasible** to understand the reasoning behind some theorem within QM. :D (although you will not understand any (fermionically) entangled theorem)


We don't have an intuitive grasp of quantum mechanics because there was no evolutionary pressure for it. What use is knowledge of subatomic particles to a hunter-gatherer? Before we started messing with electricity in the 18th century, the only quantum-scale phenomena that mattered to us were chemical reactions.

On the other hand, we intuitively grasp Newtonian mechanics because the Newtonian paradigm simply and reasonably-accurately describes our everyday experiences. We are very good at calculating ballistic motion in a non-numerical manner (i.e. being able to predict where a thrown rock, spear, or other projectile will go), because that is relevant to our daily survival.

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Re: 1591: "Bell's Theorem"

Postby doogly » Sat Oct 17, 2015 2:42 pm UTC

It is actually startling just how piss poor people's intuition for classical mechanics is.
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Re: 1591: "Bell's Theorem"

Postby Mental Mouse » Sat Oct 17, 2015 3:05 pm UTC

doogly wrote:It is actually startling just how piss poor people's intuition for classical mechanics is.


Yeah, what we've actually got in wetware is an approximation from a more-or-less trained neural network. Often rather less than more.

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Re: 1591: "Bell's Theorem"

Postby rmsgrey » Sat Oct 17, 2015 4:36 pm UTC

doogly wrote:It is actually startling just how piss poor people's intuition for classical mechanics is.


The main point of divergence between people's intuition and classical mechanics is Newton's First Law - our actual experience is "everything stops" rather than "objects in motion stay in motion", so friction, drag, and other dissipative effects are built in to our intuition, while they're add-ons for classical mechanics.

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Re: 1591: "Bell's Theorem"

Postby doogly » Sat Oct 17, 2015 6:34 pm UTC

Any basics on inertia, the difference between acceleration and velocity. Anything with rotation, that's not obvious.
People do abysmally on conceptual or proportional type questions.
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Re: 1591: "Bell's Theorem"

Postby ViperFUD » Sat Oct 17, 2015 6:52 pm UTC

Thread starts with quantum, moves to evolutionary psychology / neural structures before the end of the first page..

I love you, XKCD forums.

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Re: 1591: "Bell's Theorem"

Postby GuesssWho » Sat Oct 17, 2015 11:21 pm UTC

ViperFUD wrote:Thread starts with quantum, moves to evolutionary psychology / neural structures before the end of the first page..

I love you, XKCD forums.

Totally, totally agreed.

Even though I have no clue what we were misunderstanding in the first place LOL

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Re: 1591: "Bell's Theorem"

Postby addams » Sun Oct 18, 2015 1:53 am UTC

cellocgw wrote:
orthogon wrote:
Cervisiae Amatorem wrote:This comic was over my head, so I went to ExplainXKCD. That's over my head as well, so now I need ExplainExplainXKCD.

Don't worry: it's quantum mechanics, so if you had understood it, you wouldn't have understood it.


No, no! If you understood it, then you both understood and didn't understand it, and won't know which until the cat dies.

Lovely.
The ideal xkcd exchange.
So complete and so unfinished.

EDIT: I wouldn't want it to end there.
I'll disagree with someone to attempt to start it, again.

ijuin wrote:We don't have an intuitive grasp of quantum mechanics because there was no evolutionary pressure for it. What use is knowledge of subatomic particles to a hunter-gatherer? Before we started messing with electricity in the 18th century, the only quantum-scale phenomena that mattered to us were chemical reactions.

On the other hand, we intuitively grasp Newtonian mechanics because the Newtonian paradigm simply and reasonably-accurately describes our everyday experiences. We are very good at calculating ballistic motion in a non-numerical manner (i.e. being able to predict where a thrown rock, spear, or other projectile will go), because that is relevant to our daily survival.

...Well...
Sitting around the camp fire, after the spear had been thrown and the fire's use for cooking had been exhausted;
With no pressure from threat to life or limb, we, the human animal, started conversations about Philosophy.

Navel Gazers: Taoists listening to the quiet, then agreeing Harmony is nice.
Harmony is complementary vibrations and many humans intuitively grasped the concept.

The development of the human mind is not always pushed by despair.
We have made great intellectual leaps pulled by sweet desire.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
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Re: 1591: "Bell's Theorem"

Postby mikrit » Sun Oct 18, 2015 6:56 pm UTC

cellocgw wrote:So does this corollary violate the Recognition Law? You know, " Dunno who he was, but his face rings a Bell"
//ducks and runs

That's Pavlov.
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Re: 1591: "Bell's Theorem"

Postby ctdonath » Mon Oct 19, 2015 3:09 pm UTC

mikrit wrote:
cellocgw wrote:That's Pavlov.


No, that's an old joke, to wit:

A church's bell ringer passed away. So they posted the position and a man came in with no arms wanting the job. The clergy weren't sure he could do it, but he convinced them to let him try it.
They climbed the bell tower and the guy ran toward the bell and hit it with his head. They gave him the job.
The next day he went to ring the bell, tripped, bounced off the bell and fell to the sidewalk below. Two guys were walking past.
One asked, "Do you know this guy?"
The second guy responded, "No, but his face rings a bell."

The next day, the dead bell ringer's twin brother comes in for the again vacant bell ringer position. He also has no arms. They lead him up to the bell tower, he runs at the bell, trips and falls to the sidewalk below.
The same two guys walk by.
The first asks, "Do you know him?"
The second guy responds, "No, but he's a dead ringer for his brother."

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Re: 1591: "Bell's Theorem"

Postby mikrit » Mon Oct 19, 2015 6:25 pm UTC

But how could he know that the two dead men were brothers, if he didn't know them? He must have been lying about that - so he was the murderer!

(Sorry, I have been watching Columbo reruns.)
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Re: 1591: "Bell's Theorem"

Postby orthogon » Tue Oct 20, 2015 9:59 am UTC

rmsgrey wrote:
doogly wrote:It is actually startling just how piss poor people's intuition for classical mechanics is.


The main point of divergence between people's intuition and classical mechanics is Newton's First Law - our actual experience is "everything stops" rather than "objects in motion stay in motion", so friction, drag, and other dissipative effects are built in to our intuition, while they're add-ons for classical mechanics.

I was going to say this. And in addition to stopping moving, objects also spontaneously start moving of their own accord: for example, plates and pans piled precariously on a draining board. Ah, we explain, like friction, gravity is a force, albeit an invisible and mysterious one that requires no contact and works through a vacuum. The whole thing is circular: "an object remains in blah blah unless acted upon by a force" and "F=ma" sound great until you start asking what a force is, and have to admit that a force is something that causes a mass to accelerate.

That's not to deny that Newton's laws are profound, far reaching, accurately predictive and a work of consummate genius. Once you have that definition, you can start quantifying various forces and establish laws that relate forces to other things (distance, extension of a spring, etc). But I think this is worth remembering when looking at more recent developments in Physics. I was seriously unimpressed when presented with Schrodinger's equation at university. Why that equation, I asked. Schrodinger appeared to have come up with it by tirare ex rectum. But now I see that it is, in itself, just as valid or not as F=ma, which really serves only to define force. The validity is in the predictions that can eventually be made once you have measured some of the quantities in real life and put those numbers into it.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1591: "Bell's Theorem"

Postby Flumble » Tue Oct 20, 2015 10:50 am UTC

orthogon wrote:Schrodinger appeared to have come up with it by tirare ex rectum. But now I see that it is, in itself, just as valid or not as F=ma, which really serves only to define force. The validity is in the predictions that can eventually be made once you have measured some of the quantities in real life and put those numbers into it.

Did he come up with it through tirare ex rectum (which I'm definitely going to use –thanks!– for any random proof) or was it a nice equation fitting the data and extending the relations/equations known to him?

I still can't conceptualize light (or any particle) as a particle-wave though. Nor the world as a continuous field with, for some reason, potentials that stay together (potentially –heh– with a discrete value from the integral over it) instead of just spreading out or fading away... which is especially true if the field representations of QM don't mean that it's like a 3D array with (probability) values that progress over time.

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Re: 1591: "Bell's Theorem"

Postby Kit. » Tue Oct 20, 2015 11:37 am UTC

orthogon wrote:I was seriously unimpressed when presented with Schrodinger's equation at university. Why that equation, I asked. Schrodinger appeared to have come up with it by tirare ex rectum.

If I remember correctly, Schrödinger derived it from the principle of least action applied to a wave-particle.

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Re: 1591: "Bell's Theorem"

Postby doogly » Tue Oct 20, 2015 12:21 pm UTC

Yes. Hamilton + de Broglie = Schrodinger. It might be a little harder to make peace with when you first see it in a course, because it's taught prior to the least action style classical mechanics?
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Re: 1591: "Bell's Theorem"

Postby rmsgrey » Tue Oct 20, 2015 1:31 pm UTC

The key moment of genius for Newtonian mechanics is the idea that things tend to keep doing what they're doing unless something stops them - that you need to invoke a force to explain why things stop rather than it being the natural state of things.

Another way of looking at it is that friction, gravity, etc are things we invent to explain the difference between our simple mathematical model, and what we actually observe.

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Re: 1591: "Bell's Theorem"

Postby ps.02 » Tue Oct 20, 2015 5:19 pm UTC

orthogon wrote:Schrodinger appeared to have come up with it by tirare ex rectum.

I don't know Latin, but even I can tell the phrase is bogus as rectum is clearly not in the ablative mood. Anyway, it looks like the word you want is anus, as in ex ano.

You have the watch the endings of words about alimentary endings.

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Re: 1591: "Bell's Theorem"

Postby orthogon » Tue Oct 20, 2015 9:47 pm UTC

Thanks, everyone. I did engineering rather than physics and Schrödinger's equation was the only quantum physics we got, so I missed a whole load of context.

Regarding the Latin, yeah, I realised that I probably needed a declension, and actually tried Google translate, but the results were less satisfactory to my ear than my original, which I thought had the cadence of reductio ad absurdum about it. There's also something meta or self-referential about the way I created the phrase itself by a process of tirare ex rectum.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1591: "Bell's Theorem"

Postby tomandlu » Wed Oct 21, 2015 9:56 am UTC

Kit. wrote:
orthogon wrote:I was seriously unimpressed when presented with Schrodinger's equation at university. Why that equation, I asked. Schrodinger appeared to have come up with it by tirare ex rectum.

If I remember correctly, Schrödinger derived it from the principle of least action applied to a wave-particle.


Didn't Feynman basically say that you could solve most physics problems by using the assumption that the answer will be the one requiring the least energy - and that it was a really lousy way to solve a problem.
How can I think my way out of the problem when the problem is the way I think?

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Re: 1591: "Bell's Theorem"

Postby orthogon » Wed Oct 21, 2015 10:03 am UTC

tomandlu wrote:
Kit. wrote:
orthogon wrote:I was seriously unimpressed when presented with Schrodinger's equation at university. Why that equation, I asked. Schrodinger appeared to have come up with it by tirare ex rectum.

If I remember correctly, Schrödinger derived it from the principle of least action applied to a wave-particle.


Didn't Feynman basically say that you could solve most physics problems by using the assumption that the answer will be the one requiring the least energy - and that it was a really lousy way to solve a problem.

Why, because it was usually too much effort? ;-)
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1591: "Bell's Theorem"

Postby tomandlu » Wed Oct 21, 2015 10:50 am UTC

orthogon wrote:
tomandlu wrote:
Kit. wrote:
orthogon wrote:I was seriously unimpressed when presented with Schrodinger's equation at university. Why that equation, I asked. Schrodinger appeared to have come up with it by tirare ex rectum.

If I remember correctly, Schrödinger derived it from the principle of least action applied to a wave-particle.


Didn't Feynman basically say that you could solve most physics problems by using the assumption that the answer will be the one requiring the least energy/action - and that it was a really lousy way to solve a problem.

Why, because it was usually too much effort? ;-)


Well, if he was being consistent, it probably involved too little... ;)
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Re: 1591: "Bell's Theorem"

Postby TomPace101 » Wed Oct 21, 2015 1:24 pm UTC

Kozmo wrote:...
Another annoying misunderstanding of the theorem is when people think that it disproves hidden variables. In fact, Bell himself was one of the biggest advocates of a hidden variable interpretation of QM called Bohmian mechanics (pilot-wave theory). The theorem disproves *local* hidden variables. For more, Bell's collection of papers "Speakable and Unspeakable in Quantum Mechanics" is an excellent read!


It is annoying, especially since even Griffiths (the typical undergraduate text) explains it perfectly, although admittedly in a footnote.

Furthermore, even without hidden variables you're still stuck with the non-locality. That is, the wave function of both particles is affected by the measurement even though only one of them is local to where the measurement takes place.

So, nature is inherently non-local, and Bell's inequality tells us nothing about hidden variables that it doesn't also say about life without them. It's certainly a revolutionary discovery, but not any kind of nail in the coffin for determinism, as often portrayed.

~~~
Edit to add: I'm not saying non-locality means FTL communication is possible, which is the annoying misunderstanding that the comic itself was pointing out. Guess there are lots of misunderstandings.

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Re: 1591: "Bell's Theorem"

Postby doogly » Wed Oct 21, 2015 1:36 pm UTC

Wave functions are not local to anywhere. That is a categorical error. A state vector is an element of a Hilbert space.

Let's say you have an electron in a box. You would like to say something like, "The electron is localized to this box." Great! What are you referring to? It is not the quantum state which lives in the box. It is that if you take a detector operator, let's call it A (maybe you are detecting by measuring the energy, so it should be H? the point is, I don't care.), which is one of those Hermitian operators we hear so much about. The measurement operation is localized, and since it returns zero everywhere outside the box, you can say the electron is inside the box.

In the EPR case, the results of any operator A which Alice might perform are not at all effected by what Bob does, and that is why we say this preserves locality.

Nature is, as far as we can tell, entirely local. It is possible that quantum gravity will futz with this, but that'd be it.
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Re: 1591: "Bell's Theorem"

Postby Kit. » Wed Oct 21, 2015 2:41 pm UTC

orthogon wrote:I did engineering rather than physics and Schrödinger's equation was the only quantum physics we got, so I missed a whole load of context.

Then you missed it all.

Try Dirac's "Principles...". It's a fascinating read.


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