Can someone please explain quantum entanglement to me?

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Can someone please explain how the author, Domino Valdano, derives the percentages explaining quantum entanglement? The original post is by Thomas Ulrich. Any help would be greatly appreciated.
first click on my link posted here, then once in it just scroll to the bottom of the post and click on the link "Domino Valdano's answer..." The percentages he mentions are towards the middle of the page.

https://www.quora.com/Why-does-distance-not-matter-with-quantum-mechanically-entangled-particles
 

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  • #2
BvU
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and click on the link "Domino Valdano's answer..."
I don't get a page, just quora buggering me what my interests are and what my age is. Please post a direct link.
 
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Link works for me...

EDIT -- oh wait, just the first link to Quora, not the 2nd link...
 
  • #4
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Links are working for me now....
He doesn't derive the percentages (except for the 85% of 85% one that we'd logically expect given the others). Instead, he's describing the percentages observed in analogous experiments and predicted by quantum mechanics, and pointing out that they're inconsistent with what our classical intuition expects.

The analogous experiments are measuring the polarization of photons: which of the three boxes you choose to open is analogous to choosing to measure the polarization on one of three axes; the color of the ball is analogous to the two possible results (parallel and perpendicular) of that measurement.

You will find more and better explations here and here.
 
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DrChinese
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Can someone please explain how the author, Domino Valdano, derives the percentages explaining quantum entanglement? The original post is by Thomas Ulrich. Any help would be greatly appreciated.
first click on my link posted here, then once in it just scroll to the bottom of the post and click on the link "Domino Valdano's answer..." The percentages he mentions are towards the middle of the page.

https://www.quora.com/Why-does-distance-not-matter-with-quantum-mechanically-entangled-particles
:welcome:

Could you do us all a favor and simply copy Domino's comment to this thread? Quora wants me to create an account to see the "secret" information. That's a bit much.
 
  • #6
X53
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Links are working for me now....
He doesn't derive the percentages (except for the 85% of 85% one that we'd logically expect given the others). Instead, he's describing the percentages observed in analogous experiments and predicted by quantum mechanics, and pointing out that they're inconsistent with what our classical intuition expects.

The analogous experiments are measuring the polarization of photons: which of the three boxes you choose to open is analogous to choosing to measure the polarization on one of three axes; the color of the ball is analogous to the two possible results (parallel and perpendicular) of that measurement.

You will find more and better explations here and here.
He says: "Now here's the bombshell that should drop your jaw: you notice that when you open boxes A and C' (or C and A'), they only agree 50% of the time! Why is this shocking? Because 85% of 85% is 72%! If A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time, then by ordinary straightforward classical logic, A and A' would have to agree with C and C' a bare minimum of 70% of the time"

I don't understand why he says a bare minimum of 70%. This is all I don't understand. Please explain it.
 
  • #7
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:welcome:

Could you do us all a favor and simply copy Domino's comment to this thread? Quora wants me to create an account to see the "secret" information. That's a bit much.
Here you go:




Yes, you are missing something very important: 4 more boxes. There might be a way to explain it using fewer than 6 boxes, but the simplest and most straightforward way I'm aware of involves 6 boxes. You certainly can't do it with only 2 boxes. With 2 boxes, there is no indication of anything spooky going on, or anything different from classical physics. With 6 boxes, the spookiness becomes very apparent.

The reason entanglement is considered mysterious is that if you ask 5 different physicists at random about entanglement, they'll all say they understand it but there's a good chance they'll give you 5 completely different explanations for what's actually going on. :-)

(I believe the above is often true even if said physicists are experts on the foundations of quantum mechanics.)

Feynman famously said that the double slit experiment captured everything that was mysterious about quantum mechanics. But personally I think quantum entanglement is a much better example. It gets to the heart of what is weird about quantum mechanics in a very deep way, and how you describe what's happening is completely different depending on what interpretation of quantum mechanics you subscribe to.

So here is the simplest way I know of for presenting the EPR paradox of quantum entanglement (Bell's Inequality). Imagine you are the subject of a psychology experiment which involves 2 rooms. You are told by the hosts of the experiment that the 2 rooms are perfectly isolated from each other. You are assured that no wires go between the rooms, and they are both soundproofed and in Faraday cages so they protect against any radio waves or wireless signals being transmitted between them. There are two hosts of the experiment. The first host prepares 3 boxes (let's call them A, B, and C) and places them in one room on a table, sits down at the table and waits for you to come in the room. The second host prepares 3 other boxes (let's call them A', B', and C') and sets them on a table in the other room, and also sits down and waits for you. Each of the 6 boxes contains either a black or a white ball.

You are allowed to open one box from each room. For example you could choose to open box A and box B'. Or box C and box C'. You can open them in either order... first you go into one of the rooms and open one of the 3 boxes there, and then you go into the other room and open one of them there. The hosts are locked in the rooms while you're walking between them and not allowed to communicate with each other.

The only caveat is that whatever box you choose to open in each room, you will never be allowed to find out what was in the other 2 you didn't open. This is strictly forbidden. However, you are allowed to repeat the same experiment as many times as you want. You can do it a thousand times in a row, or a million times in a row if needed. But each time the boxes are prepared freshly again and set back on the table, so you will never know each time what was in the box you didn't look in that time.

After repeating this experiment many times, you notice that 100% of the time when you open A and A' the color of the balls inside match each other. The same is true for B and B'. And the same is true for C and C'. Furthermore, you notice that when you open boxes A and B' (or B and A') they agree 85% of the time. And when you open boxes B and C' (or C and B') they also agree 85% of the time. Now here's the bombshell that should drop your jaw: you notice that when you open boxes A and C' (or C and A'), they only agree 50% of the time! Why is this shocking? Because 85% of 85% is 72%! If A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time, then by ordinary straightforward classical logic, A and A' would have to agree with C and C' a bare minimum of 70% of the time. If there is really no communication between the rooms, it means that the very laws of classical logic and probability do not work!

So at the end of all this, you are asked: do you think the experimenters were cheating somehow? Were they secretly passing information between the rooms without you realizing it? If we live in a single classical universe, then the answer would absolutely have to be yes--there's no way around it. It doesn't even matter whether the universe is deterministic or non-deterministic, or even if the experimenters had a secret switch that allows them to change the color of the ball inside to whatever they want after you choose which box you're going to open. However, it IS possible in our quantum universe to perform exactly this psychology experiment, and the experimenters would not need to communicate with each other in order to conduct it. Whatever is happening here just happens automatically in quantum mechanics, even if it involves two very distant isolated locations.

Basically, quantum entanglement means you have to accept one of 3 things; either:

1.) there is some kind of non-local influence which happens, even though it is not possible to use that to transmit meaningful information. Your choice of which box to open in one room somehow affects the outcome you'll get in the other room.

(Bohm)

or,

2.) every time you open one of the boxes, the universe splits into two universes and you see a black ball in one of the universes and a white ball in the other universe; the information about which box you chose to open is carried with you locally as you walk into the other room, and then the different universes interfere with each other and cancel out in just the right way once you reach the second room and make the second choice.

(Everett)

or, arguably the most radical of the 3, and yet the most widely accepted among physicists:

3.) the laws of classical logic and probability, which were considered to be "a priori true" for centuries, are in fact false. There are properties (like whether the balls in the boxes you chose not to open were black or white) which do not exist simultaneously with other properties, and so when you reason about them with probability, basic things like the probability sum rule (that you can add the probability of A happening to the probability of B happening to get the probability that A or B happened) and the multiplication of probabilities (that you can multiply the probabilities of two independent events to find the joint probability that both events A and B occur) fail.

(Bohr / Copenhagen)

Option 1 is not very compatible with relativity, unless you believe in a giant cosmic conspiracy theory.

Option 2 is nice because it preserves locality and classical logic. But it requires you to believe in a lot of extra universes which are unmeasurable.

Option 3 is nice because in some ways it's the simplest, but I see it as the most radical. It throws away basic assumptions that have held for thousands of years, and which are generally considered to be more fundamental than the principle of locality, determinism, or the idea that we live in a single universe. It's never been fully clear to me that it's actually fully coherent, or if so how. Although many people wiser than myself assure me that it is, so perhaps they're right.
 
  • #8
X53
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I don't get a page, just quora buggering me what my interests are and what my age is. Please post a direct link.
Here is the second link (Domino Valdano's explanation):




Yes, you are missing something very important: 4 more boxes. There might be a way to explain it using fewer than 6 boxes, but the simplest and most straightforward way I'm aware of involves 6 boxes. You certainly can't do it with only 2 boxes. With 2 boxes, there is no indication of anything spooky going on, or anything different from classical physics. With 6 boxes, the spookiness becomes very apparent.

The reason entanglement is considered mysterious is that if you ask 5 different physicists at random about entanglement, they'll all say they understand it but there's a good chance they'll give you 5 completely different explanations for what's actually going on. :-)

(I believe the above is often true even if said physicists are experts on the foundations of quantum mechanics.)

Feynman famously said that the double slit experiment captured everything that was mysterious about quantum mechanics. But personally I think quantum entanglement is a much better example. It gets to the heart of what is weird about quantum mechanics in a very deep way, and how you describe what's happening is completely different depending on what interpretation of quantum mechanics you subscribe to.

So here is the simplest way I know of for presenting the EPR paradox of quantum entanglement (Bell's Inequality). Imagine you are the subject of a psychology experiment which involves 2 rooms. You are told by the hosts of the experiment that the 2 rooms are perfectly isolated from each other. You are assured that no wires go between the rooms, and they are both soundproofed and in Faraday cages so they protect against any radio waves or wireless signals being transmitted between them. There are two hosts of the experiment. The first host prepares 3 boxes (let's call them A, B, and C) and places them in one room on a table, sits down at the table and waits for you to come in the room. The second host prepares 3 other boxes (let's call them A', B', and C') and sets them on a table in the other room, and also sits down and waits for you. Each of the 6 boxes contains either a black or a white ball.

You are allowed to open one box from each room. For example you could choose to open box A and box B'. Or box C and box C'. You can open them in either order... first you go into one of the rooms and open one of the 3 boxes there, and then you go into the other room and open one of them there. The hosts are locked in the rooms while you're walking between them and not allowed to communicate with each other.

The only caveat is that whatever box you choose to open in each room, you will never be allowed to find out what was in the other 2 you didn't open. This is strictly forbidden. However, you are allowed to repeat the same experiment as many times as you want. You can do it a thousand times in a row, or a million times in a row if needed. But each time the boxes are prepared freshly again and set back on the table, so you will never know each time what was in the box you didn't look in that time.

After repeating this experiment many times, you notice that 100% of the time when you open A and A' the color of the balls inside match each other. The same is true for B and B'. And the same is true for C and C'. Furthermore, you notice that when you open boxes A and B' (or B and A') they agree 85% of the time. And when you open boxes B and C' (or C and B') they also agree 85% of the time. Now here's the bombshell that should drop your jaw: you notice that when you open boxes A and C' (or C and A'), they only agree 50% of the time! Why is this shocking? Because 85% of 85% is 72%! If A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time, then by ordinary straightforward classical logic, A and A' would have to agree with C and C' a bare minimum of 70% of the time. If there is really no communication between the rooms, it means that the very laws of classical logic and probability do not work!

So at the end of all this, you are asked: do you think the experimenters were cheating somehow? Were they secretly passing information between the rooms without you realizing it? If we live in a single classical universe, then the answer would absolutely have to be yes--there's no way around it. It doesn't even matter whether the universe is deterministic or non-deterministic, or even if the experimenters had a secret switch that allows them to change the color of the ball inside to whatever they want after you choose which box you're going to open. However, it IS possible in our quantum universe to perform exactly this psychology experiment, and the experimenters would not need to communicate with each other in order to conduct it. Whatever is happening here just happens automatically in quantum mechanics, even if it involves two very distant isolated locations.

Basically, quantum entanglement means you have to accept one of 3 things; either:

1.) there is some kind of non-local influence which happens, even though it is not possible to use that to transmit meaningful information. Your choice of which box to open in one room somehow affects the outcome you'll get in the other room.

(Bohm)

or,

2.) every time you open one of the boxes, the universe splits into two universes and you see a black ball in one of the universes and a white ball in the other universe; the information about which box you chose to open is carried with you locally as you walk into the other room, and then the different universes interfere with each other and cancel out in just the right way once you reach the second room and make the second choice.

(Everett)

or, arguably the most radical of the 3, and yet the most widely accepted among physicists:

3.) the laws of classical logic and probability, which were considered to be "a priori true" for centuries, are in fact false. There are properties (like whether the balls in the boxes you chose not to open were black or white) which do not exist simultaneously with other properties, and so when you reason about them with probability, basic things like the probability sum rule (that you can add the probability of A happening to the probability of B happening to get the probability that A or B happened) and the multiplication of probabilities (that you can multiply the probabilities of two independent events to find the joint probability that both events A and B occur) fail.

(Bohr / Copenhagen)

Option 1 is not very compatible with relativity, unless you believe in a giant cosmic conspiracy theory.

Option 2 is nice because it preserves locality and classical logic. But it requires you to believe in a lot of extra universes which are unmeasurable.

Option 3 is nice because in some ways it's the simplest, but I see it as the most radical. It throws away basic assumptions that have held for thousands of years, and which are generally considered to be more fundamental than the principle of locality, determinism, or the idea that we live in a single universe. It's never been fully clear to me that it's actually fully coherent, or if so how. Although many people wiser than myself assure me that it is, so perhaps they're right.
 
  • #9
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He says: "Now here's the bombshell that should drop your jaw: you notice that when you open boxes A and C' (or C and A'), they only agree 50% of the time! Why is this shocking? Because 85% of 85% is 72%! If A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time, then by ordinary straightforward classical logic, A and A' would have to agree with C and C' a bare minimum of 70% of the time"

I don't understand why he says a bare minimum of 70%. This is all I don't understand. Please explain it.
I think that may just be careless wording. You calculate 72.5%, you get 72.49%, you figure that maybe your measurements aren't perfect... but if you're down in the 60s you have to think that something else is going on.
But that's just me guessing. The sources that I linked to above will take you to much better explanations, and I'd be comfortable writing off the quora answer as just wrong.
 
  • #10
zonde
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Can someone please explain how the author, Domino Valdano, derives the percentages explaining quantum entanglement?
As Nugatory said it's analogy of photon polarization entanglement experiment.
To get the numbers you have to use three different angles for polarization measurements of entangled photons: 22.5 deg., 0 deg., -22.5 deg. So that ##\cos^2(\pm22.5^\circ)=0.8536## while ##\cos^2(\pm45^\circ)=0.5##
 
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  • #13
DrChinese
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So is your question: what the formula is for calculating matches/coincidences? Or why is that the formula? Or?

It really doesn't make sense to talk about one person's response on another board, when there are many here prepared to answer a particular question you might have. What about quantum entanglement do you want to know?
 
  • #14
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He says: "Now here's the bombshell that should drop your jaw: you notice that when you open boxes A and C' (or C and A'), they only agree 50% of the time! Why is this shocking? Because 85% of 85% is 72%! If A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time, then by ordinary straightforward classical logic, A and A' would have to agree with C and C' a bare minimum of 70% of the time"

I don't understand why he says a bare minimum of 70%. This is all I don't understand. Please explain it.
Because
"A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time"
means
"B and B' disagree with A and A’ 15% of the time and B and B' disagree with C and C' 15% of the time"

To simplify things note that A always agrees with A', B with B' and C with C'. So we need only write A, B or C. If you prefer to spell it out, that's up to you.

A can only disagree with C if either A or C disagrees with B while the other agrees. (Both disagreeing would put A back in agreement with C). Thus the maximum disagreement between A and C would be if something were to exclude any double disagreements. In which case A disagreeing with B and B agreeing with C is 15% and A agreeing with B and B disagreeing with C is another 15%. So the maximum total disagreement (no doubles) is 15+15% =30%. So the minimum agreement is 70%. Not approximately but exactly.

Likewise if you prefer not to assume there is a hidden fairy who excludes double disagreements, you must remove them from the calculation. You can do it explicitly with 15% of 15% or, much simpler, just multiply the probabilities. Either way you get 85% squared which is 72.25%.
 
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Because
"A and A' agree with B and B’ 85% of the time and B and B' agree with C and C' 85% of the time"
means
"B and B' disagree with A and A’ 15% of the time and B and B' disagree with C and C' 15% of the time"

To simplify things note that A always agrees with A', B with B' and C with C'. So we need only write A, B or C. If you prefer to spell it out, that's up to you.

A can only disagree with C if either A or C disagrees with B while the other agrees. (Both disagreeing would put A back in agreement with C). Thus the maximum disagreement between A and C would be if something were to exclude any double disagreements. In which case A disagreeing with B and B agreeing with C is 15% and A agreeing with B and B disagreeing with C is another 15%. So the maximum total disagreement (no doubles) is 15+15% =30%. So the minimum agreement is 70%. Not approximately but exactly.

Likewise if you prefer not to assume there is a hidden fairy who excludes double disagreements, you must remove them from the calculation. You can do it explicitly with 15% of 15% or, much simpler, just multiply the probabilities. Either way you get 85% squared which is 72.25%.
I should add that the illustration puts A, B and C effectively in an order with B in the middle. If the same numbers apply to any number of cases then it applies to B, C and D or to C, D and E etc. So the "maximum disagreement" is additive. In practice a continuous variable like polarization angle is used. The arithmetic then implies that the correlation vs angle difference is linear: Λ - shaped. QM predicts a cosine dependency which is consistent with Malus's Law. These are shown on the Wikipedia diagram - just ignore the axes as it's drawn for electron spin, not photon polarisation. The maximum departure from the straight lines is at 45 degrees for electrons; it would be 22.5 degrees for photons. The arithmetic then falls out as per post #10.
 
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