Is Quantum Entanglement Real?(nytimes.com)
nytimes.com
Is Quantum Entanglement Real?
http://www.nytimes.com/2014/11/16/opinion/sunday/is-quantum-entanglement-real.html
9 comments
Option 2 is similar to the Novikov self-consistency hypothesis of time travel, which states that if an action would cause a time travel paradox, its probability is zero.
Under this hypothesis, even if entanglement does allow changes to move faster than light--essentially travelling backward in time--any action that would expose this time travel would be forbidden. The scientist is physically prevented from making the "wrong" choice when setting the detector.
The problem with this hypothesis is that it seems essentially untestable.
Another way to think of option 2 is that the universe is 100% deterministic. Under this hypothesis, the speed of entanglement is only apparent, not real--like planning with a friend to both turn on your flashlights on opposite hilltops 2 hours from now. Without knowing that it was planned in advance, an observer would wonder how you reacted to one another so fast.
This is also impossible to fully test; at best you could prove that the consistency extends as far back as we can see into the past. And that is exactly what these scientists will be testing.
Under this hypothesis, even if entanglement does allow changes to move faster than light--essentially travelling backward in time--any action that would expose this time travel would be forbidden. The scientist is physically prevented from making the "wrong" choice when setting the detector.
The problem with this hypothesis is that it seems essentially untestable.
Another way to think of option 2 is that the universe is 100% deterministic. Under this hypothesis, the speed of entanglement is only apparent, not real--like planning with a friend to both turn on your flashlights on opposite hilltops 2 hours from now. Without knowing that it was planned in advance, an observer would wonder how you reacted to one another so fast.
This is also impossible to fully test; at best you could prove that the consistency extends as far back as we can see into the past. And that is exactly what these scientists will be testing.
The Novikov self-consistency hypothesis is pretty neat. I like the thought of the researcher travelling back in time to create the apparatus such that the result always confirms quantum entanglement. It's classical and not quantum so it's not clear to me how it relates. I'm not sure anyone (besides philosophers) takes the loopholes seriously.
Hmm. You can split atoms in 5 reasonably-simple steps but I haven't seen anyone describe how to do it recently. See C. L. Stong's Amateur Scientist column where a Van de Graaff generator is used to fire beta particles at a target. The only complicated part was the vacuum pump, which involved extensive hacking on a refrigerator compressor. Nowadays good-quality pumps are almost free for the shipping on eBay. Hmm...
Great. So your argument hinges on vitalism. Please, lets keep mysticism and religion out of a SCIENTIFIC debate.
I think you misunderstand. A complex system is a system with a complicated set of behaviors that emerges naturally from a large number of actors and a simple set of rules. See P.W. Anderson's article "More is different." No mysticism or religion involved.
Even with experiments still ongoing, quantum entanglement is most likely real. I think David Kaiser wouldn't suggest otherwise.
There's a real nice section in wikipedia re: the testing of quantum entanglement (see http://en.wikipedia.org/wiki/Quantum_entanglement)
"Systems which contain no entanglement are said to be separable. For 2-Qubit and Qubit-Qutrit systems (2 x 2 and 2 x 3 respectively) the simple Peres-Horodecki criterion provides both a necessary and a sufficient criterion for separability, and thus for detecting entanglement. However, for the general case, the criterion is merely a sufficient one for separability, as the problem becomes NP-hard.[59][60] A numerical approach to the problem is suggested by Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum in their paper "Geometrical aspects of entanglement".[61] Leinaas et al. offer a numerical approach, iteratively refining an estimated separable state towards the target state to be tested, and checking if the target state can indeed be reached. An implementation of the algorithm (including a built in Peres-Horodecki criterion testing) is brought in the "StateSeparator" web-app."
There's a real nice section in wikipedia re: the testing of quantum entanglement (see http://en.wikipedia.org/wiki/Quantum_entanglement)
"Systems which contain no entanglement are said to be separable. For 2-Qubit and Qubit-Qutrit systems (2 x 2 and 2 x 3 respectively) the simple Peres-Horodecki criterion provides both a necessary and a sufficient criterion for separability, and thus for detecting entanglement. However, for the general case, the criterion is merely a sufficient one for separability, as the problem becomes NP-hard.[59][60] A numerical approach to the problem is suggested by Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum in their paper "Geometrical aspects of entanglement".[61] Leinaas et al. offer a numerical approach, iteratively refining an estimated separable state towards the target state to be tested, and checking if the target state can indeed be reached. An implementation of the algorithm (including a built in Peres-Horodecki criterion testing) is brought in the "StateSeparator" web-app."
I have never been comfortable with the metaphors that tech reporters use for describing quantum entanglement.
They always talk as if it's a spooky interaction but the metaphor falls down. Here's an example: I take too halves of an Oreo cookie and send them in opposite directions. Then I use a detector to measure how much filling is on one half and instantly know how much was on the other half. Was that spooky?
I understand that at the physics level it's not like this, but the metaphors are never satisfyingly 'spooky' to me as I can easily think up a classical explanation.
They always talk as if it's a spooky interaction but the metaphor falls down. Here's an example: I take too halves of an Oreo cookie and send them in opposite directions. Then I use a detector to measure how much filling is on one half and instantly know how much was on the other half. Was that spooky?
I understand that at the physics level it's not like this, but the metaphors are never satisfyingly 'spooky' to me as I can easily think up a classical explanation.
I have a good analogy for entanglement, which will hopefully help you see the difference between classical (anti)correlations and quantum (anti)correlations.
Suppose you want to construct a pair of yes-no-question-answering boxes. The goal is that, however one box answers, the other box will answer the opposite way. The answers produced must be anti-correlated, but I'll just write correlated because it's 4 chars less!
Classical correlations are like a pair of boxes that consistently succeed for some specific question. (e.g. repeatedly asking the same question of any one box, will produce 50% yes and 50% no answers, with the other box answering exactly oppositely)
Quantum correlations are like a pair of boxes that consistently answer anticorrelatedly for any question. For example, if you ask the boxes the question left-or-right? one will answer left, the other right. If you ask up-or-down? one will say up the other down, front-or-back? --- anticorrelated. And so on for any question. Whether that's spooky, I don't know...
To throws some math into this, let's denote |x>, the state of a quantum system, and denote |xy> the joint state of a pair of quantum systems, one in state x, the other in y.
Consider the difference between a statistical mixture:
But who has seen this quantum stuff? Isn't |Psi-> just some math scribble on a piece of paper? In fact, |Psi-> is quite real---it is the spin state of the electrons in the unexcited Helium atom. We know there are 2 electrons, and we know they have opposite spins, but we don't know anything else about them. Hence if a He atom were to explode and the electons fly to distant sides of the universe, we still won't know what direction the individual spins are in, the only thing we know is their total spin is 0 -- hence they have opposite spin directions. This is how we get the for any question" aspect of q-entanglement.
It really makes sense if you think about these things as information, and q-measurements as answering well posed questions. From the point of view of information, a system is entangled whenever you know more about the system as a whole than about its parts: http://en.wikipedia.org/wiki/Joint_quantum_entropy#Propertie...
Suppose you want to construct a pair of yes-no-question-answering boxes. The goal is that, however one box answers, the other box will answer the opposite way. The answers produced must be anti-correlated, but I'll just write correlated because it's 4 chars less!
Classical correlations are like a pair of boxes that consistently succeed for some specific question. (e.g. repeatedly asking the same question of any one box, will produce 50% yes and 50% no answers, with the other box answering exactly oppositely)
Quantum correlations are like a pair of boxes that consistently answer anticorrelatedly for any question. For example, if you ask the boxes the question left-or-right? one will answer left, the other right. If you ask up-or-down? one will say up the other down, front-or-back? --- anticorrelated. And so on for any question. Whether that's spooky, I don't know...
To throws some math into this, let's denote |x>, the state of a quantum system, and denote |xy> the joint state of a pair of quantum systems, one in state x, the other in y.
Consider the difference between a statistical mixture:
50% of time produce |01> and 50% of time produce [10>
1/√2*|01> - 1/√2*|10> a.k.a |Psi->
But who has seen this quantum stuff? Isn't |Psi-> just some math scribble on a piece of paper? In fact, |Psi-> is quite real---it is the spin state of the electrons in the unexcited Helium atom. We know there are 2 electrons, and we know they have opposite spins, but we don't know anything else about them. Hence if a He atom were to explode and the electons fly to distant sides of the universe, we still won't know what direction the individual spins are in, the only thing we know is their total spin is 0 -- hence they have opposite spin directions. This is how we get the for any question" aspect of q-entanglement.
It really makes sense if you think about these things as information, and q-measurements as answering well posed questions. From the point of view of information, a system is entangled whenever you know more about the system as a whole than about its parts: http://en.wikipedia.org/wiki/Joint_quantum_entropy#Propertie...
I take his oreo in space question and raise you the rotating oreo in space question.
You take a rapidly rotating oreo, break it in half and send the halves alway at ~c. Each experimenter asks: "Is the oreo, projected on an axis, is oriented core up or face up?"
For any axis chosen, answers will be anti-correlated, and of course the probability that they observe each is 50% (if I understood correctly, your |0>+|1>/|0>-|1> is equivalent to a 45 degree oreo decison axis).
You take a rapidly rotating oreo, break it in half and send the halves alway at ~c. Each experimenter asks: "Is the oreo, projected on an axis, is oriented core up or face up?"
For any axis chosen, answers will be anti-correlated, and of course the probability that they observe each is 50% (if I understood correctly, your |0>+|1>/|0>-|1> is equivalent to a 45 degree oreo decison axis).
Sure. And for what you described, that works fine.
But now, what if instead of measuring both oreos on the same axis, we measure then on slightly different axes?
In particular, let C(a) be the correlation coefficient between the orientation of the oreo measured along the z axis and its orientation measured at an angle a to the z axis.
You can derive a limit on the correlation that can be seen between any two angles (a and b, assume for simplicity coplanar with the z axis) - assuming the state of each oreo is a function of local variables like its speed and axis of rotation:
|C(a) - C(b)| - C(b - a) <= 1
For example, if you pick a and b both = 0 (measure everything along the positibe z axis, like you do in your comment), then the left hand side is just |(-1) - (-1)| - (-1) = 1, i.e. the QM prediction for that is perfectly replicable by tasty, tasty oreos.
But here's the thing: quantum mechanics breaks that limit for some angles. E.g. try it with a = pi/3, b = 2pi/3. Left hand side comes out as 1.5.
Informally, the absolute best correlation between a and b you can get with oreos is perfect linear correlation - what the inequality above is = 1. But with QM, you get a sine wave!
So rotating oreos seem like a good analogy to entanglement at first, but it's misleading. Turns out, neither rotating oreos nor any other classical system of local hidden variables can actually replicate the results of entanglement in QM. That's (a simplified form of) what Bell proved.
But now, what if instead of measuring both oreos on the same axis, we measure then on slightly different axes?
In particular, let C(a) be the correlation coefficient between the orientation of the oreo measured along the z axis and its orientation measured at an angle a to the z axis.
You can derive a limit on the correlation that can be seen between any two angles (a and b, assume for simplicity coplanar with the z axis) - assuming the state of each oreo is a function of local variables like its speed and axis of rotation:
|C(a) - C(b)| - C(b - a) <= 1
For example, if you pick a and b both = 0 (measure everything along the positibe z axis, like you do in your comment), then the left hand side is just |(-1) - (-1)| - (-1) = 1, i.e. the QM prediction for that is perfectly replicable by tasty, tasty oreos.
But here's the thing: quantum mechanics breaks that limit for some angles. E.g. try it with a = pi/3, b = 2pi/3. Left hand side comes out as 1.5.
Informally, the absolute best correlation between a and b you can get with oreos is perfect linear correlation - what the inequality above is = 1. But with QM, you get a sine wave!
So rotating oreos seem like a good analogy to entanglement at first, but it's misleading. Turns out, neither rotating oreos nor any other classical system of local hidden variables can actually replicate the results of entanglement in QM. That's (a simplified form of) what Bell proved.
Nice answer, thank you. Rose my interest to study some quantum mechanics to figure out how exactly this can happen.
You didn't read the article.
David Kaiser isn't even really a "tech reporter", he's one of the physicists behind the experiment described in the article, which addresses exactly what you're complaining about.
David Kaiser isn't even really a "tech reporter", he's one of the physicists behind the experiment described in the article, which addresses exactly what you're complaining about.
I think I wasn't clear. I'm not trying to call this one person out for failing here… The tech reporter part wasn't my point. Even physicists don't have very good metaphors to use. My point is that any analogy I've heard fails to convey the strangeness inherit in the underlying math.
That was Einstein's proposal, and it turns out not to be the case, I'm afraid. Claussen's experiment suggested that there's more to entanglement than delaying observation of mutually-dependent properties. Quantum teleportation seems to sew it up, but for that niggling little "were we forced to do what we did" doubt.
Interesting that Einstein's proposal with modified Malus's law for single photons produces a "local realism" explanation for the observed apparent Bell's violation in photon polarization experiments. At the Einstein's time they didn't have single-photon counters to confirm/deny, and today it seems that single-photon Malus looks like the classic one (though i didn't find articles directly confirming it, only other articles mentioning it as confirmed). Nevertheless, possibility that such reasonably looking variation of the pretty empirical law produces "local realism" explanation makes me believe that "local realism" battle is far from lost yet :)
The article was actually written by the MIT professor that's going to be doing the experiment.
I feel I'll never get to understand entanglement (I hope it's like monads :P). If it's not "spooky" but just half an Oreo... then what is so special about it and why would physicist study it then?
Let's play an imaginary game. It will be you and a friend as a team against the house, represented by me and my two assistants. Here's how the game works.
1. You and your friend can consult with each other before the game starts and agree on a strategy. You can build or obtain any equipment you think will help you play the game.
2. You and your friend, and any equipment you bring, meet me at the place where the game starts. I have two spaceships waiting. You and one of my assistants will get into spaceship A and go off into space. Your friend and my other assistant will go into spaceship B and go off into space. You and your friend can bring along whatever equipment you want.
3. My assistants will take you to separate locations in space. The locations will be at rest with respect to each other, and several light minutes apart. My assistants will establish synchronized clocks between the two locations, and then play starts. I'll only describe what goes on at your location. The same thing is going on at your friend's location.
4. There will be 1000 rounds, and each round lasts one minute. In each round my assistant will use a random number generator to generate a single bit, 0 or 1, and will tell you the bit. You can assume that this random number is truly random. There is no known way to predict it, and there is no correlation between it and the random number generator at the other location. The rounds start on a strict schedule so that you and your friend start round N on your respective ships at the same time.
5. After you are told the random number, you must generate a single bit, 0 or 1, by any means you wish. You can come up with it in your head. You can use any equipment you brought. You can read it from a list of predetermined bits you and your friend generated before the game started. You can try to communicate with your friend (or with anyone else) if you brought communications equipment, and use the results of that communication--but keep in mind you are several light minutes from your friend.
6. After the 1000th round, my assistant will fly you back to Earth where I will be waiting. My assistants will each give me the list of random numbers and responses. I will then compute your team score by adding up your scores for each round. Scoring for each round is as follows:
• If you both received a 1 in the round from the random number generators, then your team scores 1 point if you and your friend gave DIFFERENT bit values for that round. I.e., if the random bits were both 1, then you score if you gave 0 and your friend gave 1, or if you gave 1 and your friend gave 0.
• Otherwise, your team scores 1 point if you and your friend gave the SAME bit value for that round.
Your win prizes if your score is above 800.
Question: what is your plan?
You can win 75% of the rounds with a very simple strategy: always pick 0. You'll win the rounds where the random bits were 00, 01, or 10, and lose when they were 11. That turns out to be the best you can with non-quantum methods.
If you use entanglement you can do better. You prepare 1000 pairs of qubits, numbered 1 to 1000. The two qubits in each pair are entangled in what is called a Bell state. It's an equal superposition of the two states "both qubits are 0" and "both qubits are 1". What this means is that if you take these two qubits and you measure one and your friend measures the other, AND YOU MEASURE IN THE SAME BASIS (I'll explain that in a moment), you will either both get 0 or both get 1.
What I mean by measure in the same basis is this. Suppose your qubits are implemented by, say, polarized photons. A photon can be polarized at any angle from 0 to 360 (I'm going to use degrees instead of radians because I think that will be more comfortable for most). To make qubits out of this, you might decide that 0 is represented by polarization at 0 degrees, and 1 by polarization at 90 degrees. To see if a qubit is a 0 or a 1, you could try to pass it through a polarizing filter set to 90 degrees. If it comes through, it was a 1, and if it is blocked it was a 0. If we are using 0/90 degrees for our qubits, we say we are using the 0 degree basis.
What happens if you pass that qubit through a polarizing filter at 45 degrees? Half the time it will pass, and half the time it will be blocked. So a qubit that has a definite value in the 0 basis can be any value with equal probability in the 45 degree basis. How about if we measure using a 22.5 degree basis? It can still be any value, but now there is about an 85% chance it will have the same value as in the 0 degree basis. In other words, if someone generates a qubit with a particular binary value in the 0 degree basis, and you measure it in the 22.5 degree basis, 85% of the time you'll get the same value that the person who made it set it to in their basis.
In general, if we have two qubits in the same state, and you measure one of them in one basis, and I measure the other in a basis that is T degrees different from yours, we will get the same measurement with probability cos(T)^2. E.g., if we use the same basis (T=0), then we get the same measurement all the time. If my basis is 90 degrees from yours, we'll get opposite measurements. If my basis was 45 degrees from yours, half the time my measurement would agree with yours and half the time it would not.
Here is how you use your prepared qubits to improve your game outcome. As I said, you take pairs of qubits and put that system of two qubits into an equal mix of the states "both qubits are 0" an "both qubits are 1". When you head off to space, you take one of the qubits from each pair, and your friend takes the other.
For round N, after you get the random bit from my assistant, you take your qubit for round N, and you measure it to see if it is a 0 or a 1. If my assistant gave you a 0 bit, you measure in the 0 degree basis. If my assistant gave you a 1 bit, you measure in the 45 degree basis. You report the result of your measurement as your bit.
Your friend measures in the 22.5 degree basis if he gets a 0 random bit, and he measures in the -22.5 degree basis if he gets a 1 random bit. He reports the result of his measurement as his bit. Here's a diagram showing the angles you each use depending on the random bit you receive:
So, in all cases except both random numbers being 1, which means that you want to pick the same bit as your friend, your measurements will agree with probability cos(22.5)^2 = 0.854.
In the case where both random numbers are 1, which means you and your friend want to NOT agree, you will agree with probability cos(67.5)^2 = 0.146, which means you will disagree with probability 0.854.
Net result: your probability of winning a given round is 0.854, which is quite a bit better than the 0.75 that is the best you can get with a non-quantum approach.
Try to duplicate this with a "half an Oreo" model of entanglement, and it won't work.
1. You and your friend can consult with each other before the game starts and agree on a strategy. You can build or obtain any equipment you think will help you play the game.
2. You and your friend, and any equipment you bring, meet me at the place where the game starts. I have two spaceships waiting. You and one of my assistants will get into spaceship A and go off into space. Your friend and my other assistant will go into spaceship B and go off into space. You and your friend can bring along whatever equipment you want.
3. My assistants will take you to separate locations in space. The locations will be at rest with respect to each other, and several light minutes apart. My assistants will establish synchronized clocks between the two locations, and then play starts. I'll only describe what goes on at your location. The same thing is going on at your friend's location.
4. There will be 1000 rounds, and each round lasts one minute. In each round my assistant will use a random number generator to generate a single bit, 0 or 1, and will tell you the bit. You can assume that this random number is truly random. There is no known way to predict it, and there is no correlation between it and the random number generator at the other location. The rounds start on a strict schedule so that you and your friend start round N on your respective ships at the same time.
5. After you are told the random number, you must generate a single bit, 0 or 1, by any means you wish. You can come up with it in your head. You can use any equipment you brought. You can read it from a list of predetermined bits you and your friend generated before the game started. You can try to communicate with your friend (or with anyone else) if you brought communications equipment, and use the results of that communication--but keep in mind you are several light minutes from your friend.
6. After the 1000th round, my assistant will fly you back to Earth where I will be waiting. My assistants will each give me the list of random numbers and responses. I will then compute your team score by adding up your scores for each round. Scoring for each round is as follows:
• If you both received a 1 in the round from the random number generators, then your team scores 1 point if you and your friend gave DIFFERENT bit values for that round. I.e., if the random bits were both 1, then you score if you gave 0 and your friend gave 1, or if you gave 1 and your friend gave 0.
• Otherwise, your team scores 1 point if you and your friend gave the SAME bit value for that round.
Your win prizes if your score is above 800.
Question: what is your plan?
You can win 75% of the rounds with a very simple strategy: always pick 0. You'll win the rounds where the random bits were 00, 01, or 10, and lose when they were 11. That turns out to be the best you can with non-quantum methods.
If you use entanglement you can do better. You prepare 1000 pairs of qubits, numbered 1 to 1000. The two qubits in each pair are entangled in what is called a Bell state. It's an equal superposition of the two states "both qubits are 0" and "both qubits are 1". What this means is that if you take these two qubits and you measure one and your friend measures the other, AND YOU MEASURE IN THE SAME BASIS (I'll explain that in a moment), you will either both get 0 or both get 1.
What I mean by measure in the same basis is this. Suppose your qubits are implemented by, say, polarized photons. A photon can be polarized at any angle from 0 to 360 (I'm going to use degrees instead of radians because I think that will be more comfortable for most). To make qubits out of this, you might decide that 0 is represented by polarization at 0 degrees, and 1 by polarization at 90 degrees. To see if a qubit is a 0 or a 1, you could try to pass it through a polarizing filter set to 90 degrees. If it comes through, it was a 1, and if it is blocked it was a 0. If we are using 0/90 degrees for our qubits, we say we are using the 0 degree basis.
What happens if you pass that qubit through a polarizing filter at 45 degrees? Half the time it will pass, and half the time it will be blocked. So a qubit that has a definite value in the 0 basis can be any value with equal probability in the 45 degree basis. How about if we measure using a 22.5 degree basis? It can still be any value, but now there is about an 85% chance it will have the same value as in the 0 degree basis. In other words, if someone generates a qubit with a particular binary value in the 0 degree basis, and you measure it in the 22.5 degree basis, 85% of the time you'll get the same value that the person who made it set it to in their basis.
In general, if we have two qubits in the same state, and you measure one of them in one basis, and I measure the other in a basis that is T degrees different from yours, we will get the same measurement with probability cos(T)^2. E.g., if we use the same basis (T=0), then we get the same measurement all the time. If my basis is 90 degrees from yours, we'll get opposite measurements. If my basis was 45 degrees from yours, half the time my measurement would agree with yours and half the time it would not.
Here is how you use your prepared qubits to improve your game outcome. As I said, you take pairs of qubits and put that system of two qubits into an equal mix of the states "both qubits are 0" an "both qubits are 1". When you head off to space, you take one of the qubits from each pair, and your friend takes the other.
For round N, after you get the random bit from my assistant, you take your qubit for round N, and you measure it to see if it is a 0 or a 1. If my assistant gave you a 0 bit, you measure in the 0 degree basis. If my assistant gave you a 1 bit, you measure in the 45 degree basis. You report the result of your measurement as your bit.
Your friend measures in the 22.5 degree basis if he gets a 0 random bit, and he measures in the -22.5 degree basis if he gets a 1 random bit. He reports the result of his measurement as his bit. Here's a diagram showing the angles you each use depending on the random bit you receive:
1---- friend -----0
| |
-22.5 0 22.5 45
| |
0----- you --------1
So, in all cases except both random numbers being 1, which means that you want to pick the same bit as your friend, your measurements will agree with probability cos(22.5)^2 = 0.854.
In the case where both random numbers are 1, which means you and your friend want to NOT agree, you will agree with probability cos(67.5)^2 = 0.146, which means you will disagree with probability 0.854.
Net result: your probability of winning a given round is 0.854, which is quite a bit better than the 0.75 that is the best you can get with a non-quantum approach.
Try to duplicate this with a "half an Oreo" model of entanglement, and it won't work.
Thanks! This is a pretty good description of a scenario where quantum effects can do something that a classical model can't.
The difference is that when you separate a quantum Oreo, until you actually observe which side has the creme on it, the universe hasn't decided yet. Once you observe one half, the universe instantaneously picks one of the two halves at random to contain creme, and one to be empty.
We know it must be this way due to statistics. However, that's the point where the Oreo analogy breaks down.
We know it must be this way due to statistics. However, that's the point where the Oreo analogy breaks down.
How do we know the universe hasn't decided?
You and I decide to test whether or not the universe has decided. We have Nabisco mail us quantum oreos, three at a time and we each choose randomly to measure one of them (this is analogous to measuring the spin of an electron in a randomly-chosen axis).
Now, if we're measuring them three at at time, there are only two plausible possibilities: one of us has all three cremes (this happens 2 out of every 8 trials) or one of us has two cremes (this happens 6 out of every 8 trials). If one of us has all the cremes, it doesn't matter which one each of us independently chooses to measure; we will both have the same outcome. If one of us has only two of the cremes (e.g., [M]e has two and [Y]ou have one), we agree 5/9ths of the time
Now, if we're measuring them three at at time, there are only two plausible possibilities: one of us has all three cremes (this happens 2 out of every 8 trials) or one of us has two cremes (this happens 6 out of every 8 trials). If one of us has all the cremes, it doesn't matter which one each of us independently chooses to measure; we will both have the same outcome. If one of us has only two of the cremes (e.g., [M]e has two and [Y]ou have one), we agree 5/9ths of the time
M M Y
M 1 1 0
M 1 1 0
Y 0 0 1
I have never found a good, simple analogy. The best I've got is still a mathematical explanation, but I think it can make it "click" for some people:
You have two photon detectors that you can rotate; one is in New York and one is in Paris. Two photons are entangled and one is sent to New York for measurement, and one is sent to Paris for measurement. What you find is that while each photon's polarization measurement is random, if you take the "random" values you get for both and compute their correlation over many trials, this value is a function of the difference in angles between the photon detector in New York and the photon detector in Paris.
But here's the kicker: each photon detector can be rotated while the photons are in flight, before they get there. So how is it that the correlation is a function of both photon detector angles then? Especially considering it is light that you're measuring, and nothing can travel faster than light. That's why it's called spooky action at a distance.
(Edit: Let me know if this makes any sense. I'm in a continual search for the simplest explanation of this phenomenon.)
You have two photon detectors that you can rotate; one is in New York and one is in Paris. Two photons are entangled and one is sent to New York for measurement, and one is sent to Paris for measurement. What you find is that while each photon's polarization measurement is random, if you take the "random" values you get for both and compute their correlation over many trials, this value is a function of the difference in angles between the photon detector in New York and the photon detector in Paris.
But here's the kicker: each photon detector can be rotated while the photons are in flight, before they get there. So how is it that the correlation is a function of both photon detector angles then? Especially considering it is light that you're measuring, and nothing can travel faster than light. That's why it's called spooky action at a distance.
(Edit: Let me know if this makes any sense. I'm in a continual search for the simplest explanation of this phenomenon.)
It makes sense, but I've never understood how do we know that photons don't already have this polarization at start, how do we know it's value is defined only on detection?
David Mermin wrote a classic paper that illustrates the strange statistical properties of entanglement in a way that doesn't require any physics knowledge.
http://web.pdx.edu/~pmoeck/lectures/Mermin%20shorter.pdf
"A simple device is described, based on a version of Bell's inequality, whose operation directly demonstrates some of the most peculiar behavior to be found in the atomic world. [...] The extraordinary implications of its behavior should be evident to anyone."
A quick search also turned up this animation that demonstrates Mermin's device:
http://faraday.physics.utoronto.ca/PVB/Harrison/BellsTheorem...
http://web.pdx.edu/~pmoeck/lectures/Mermin%20shorter.pdf
"A simple device is described, based on a version of Bell's inequality, whose operation directly demonstrates some of the most peculiar behavior to be found in the atomic world. [...] The extraordinary implications of its behavior should be evident to anyone."
A quick search also turned up this animation that demonstrates Mermin's device:
http://faraday.physics.utoronto.ca/PVB/Harrison/BellsTheorem...
That Mermin PDF is pretty interesting thanks!
Are you saying quantum entanglement is like a burrito?
J.S. Bell addresses this in the paper https://cds.cern.ch/record/142461/files/198009299.pdf with the following example: "Dr. Bertlmann likes to wear two socks of different colours. What colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can already be sure that the second sock will not be pink... " But it turns out that the quantum situation is much spookier.
Some questions:
- Can we use this to send large amounts of data around the world quickly? Can it replace intercontinential data links?
- Can we use this for interstellar communication channels of limited amounts of data?
- Can we use this to pass messages between two locations in a way that is immune to easedropping?
- What are other real-world applications of this?
- Can we use this to send large amounts of data around the world quickly? Can it replace intercontinential data links?
- Can we use this for interstellar communication channels of limited amounts of data?
- Can we use this to pass messages between two locations in a way that is immune to easedropping?
- What are other real-world applications of this?
It's a very common misconception that entanglement allows faster than light communication. It doesn't.
Describing quantum phenomena with real world metaphors always breaks down if we carry things far enough. I'm going to use coin flipping as a metaphor to make a specific point, but don't assume this metaphor will still work if you try to extend it. To even begin to understand entanglement you really need to look at the math. That being said, let's proceed.
The Setup: (this explains how the metaphor is being made, but you can skip to the payoff if you just want the what without any of the why).
We can think of a pair of entangled particles as a pair of coins. If we flip each coin, we have a fifty/fifty odds of gettings heads or tails. This is what we normally think of, in the macroscopic world, as a random outcome (It's not really, but let's not go there). An entangled pair of coins behaves very unusually. The outcome of flipping one coin is related to the outcome of the other coin. For example, if one coin comes up as heads, the other will always come up as tails, or vice-versa. Let's say we separate the two coins by several light years and then flip them. The strange correlation will hold. For a non-Quantum particle there are several possible explanations for this behavior. We might think that, somehow, the measurement of one particle causes the outcome of the other article to change. However, time depends on reference frame. If the two coins are in relative motion to each other in the right manner, which particle was measured first is relative (There is no universally preferred reference frame). i.e. One observer might correctly say that the first coin was measured before the second, but another observer might see things reversed. So, which measurement is the cause and which is the effect? Another notion is that the outcome was preordained when the coins were made. I'd have to go into the math a bit to adequately explain this, but with entangled quantum particles you can create experiments that demonstrate this is impossible. Tests of Bell inequalities are especially notable for this. This is Einstein's "spooky action at a distance", a behavior exhibited by entangled particles.
The Payoff:
So, if a measurement performed on two entangled particles is like flipping a pair of coins, how can we use that to communicate. Well, we can't. Not directly. You see, we can't force a coin to come up heads or tails. If we look at the outcomes of just one coin they will always appear random and uncontrollable. It's when we talk to the guy with the other coin that we'll say, "Hey, I knew what you were going to get because of what I got!". So, classical communication, limited by the speed of light, is necessary to figure out what these correlations are. So forget about FTL communication. However, what about communicating secrets? Well, that's a whole other kettle of fish! It turns out quantum correlations are fantastic for communicating secret keys. Google quantum cryptography.
As for other applications, google quantum computing. Entanglement is absolutely intrinsic to this field. There are also applications in medical imaging and metrology (i.e. standards of measurements).
Describing quantum phenomena with real world metaphors always breaks down if we carry things far enough. I'm going to use coin flipping as a metaphor to make a specific point, but don't assume this metaphor will still work if you try to extend it. To even begin to understand entanglement you really need to look at the math. That being said, let's proceed.
The Setup: (this explains how the metaphor is being made, but you can skip to the payoff if you just want the what without any of the why).
We can think of a pair of entangled particles as a pair of coins. If we flip each coin, we have a fifty/fifty odds of gettings heads or tails. This is what we normally think of, in the macroscopic world, as a random outcome (It's not really, but let's not go there). An entangled pair of coins behaves very unusually. The outcome of flipping one coin is related to the outcome of the other coin. For example, if one coin comes up as heads, the other will always come up as tails, or vice-versa. Let's say we separate the two coins by several light years and then flip them. The strange correlation will hold. For a non-Quantum particle there are several possible explanations for this behavior. We might think that, somehow, the measurement of one particle causes the outcome of the other article to change. However, time depends on reference frame. If the two coins are in relative motion to each other in the right manner, which particle was measured first is relative (There is no universally preferred reference frame). i.e. One observer might correctly say that the first coin was measured before the second, but another observer might see things reversed. So, which measurement is the cause and which is the effect? Another notion is that the outcome was preordained when the coins were made. I'd have to go into the math a bit to adequately explain this, but with entangled quantum particles you can create experiments that demonstrate this is impossible. Tests of Bell inequalities are especially notable for this. This is Einstein's "spooky action at a distance", a behavior exhibited by entangled particles.
The Payoff:
So, if a measurement performed on two entangled particles is like flipping a pair of coins, how can we use that to communicate. Well, we can't. Not directly. You see, we can't force a coin to come up heads or tails. If we look at the outcomes of just one coin they will always appear random and uncontrollable. It's when we talk to the guy with the other coin that we'll say, "Hey, I knew what you were going to get because of what I got!". So, classical communication, limited by the speed of light, is necessary to figure out what these correlations are. So forget about FTL communication. However, what about communicating secrets? Well, that's a whole other kettle of fish! It turns out quantum correlations are fantastic for communicating secret keys. Google quantum cryptography.
As for other applications, google quantum computing. Entanglement is absolutely intrinsic to this field. There are also applications in medical imaging and metrology (i.e. standards of measurements).
What about using those entangled states to coordinate actions? You could plan ahead and say if you use heads or tails as binary, flip enough to get digits to use as (hopefully hospitable) coordinates and a time to meet. When the two parties meet successfully that location was coordinated using communication faster than light, no?
Maybe you could that same mechanism for superfast decision making communication in automated equipment. Drone dispersal, late stage missile targeting. Think shooting a bunch of missiles into the sky with a map of possible locations and then entanglement used to have each missile pick its target, no missile would hit the same target and no one would know which missile was going where at launch. Stuff like that works?
You could use it for frequency hopping on radios making tracing communication pretty difficult.
Maybe you could that same mechanism for superfast decision making communication in automated equipment. Drone dispersal, late stage missile targeting. Think shooting a bunch of missiles into the sky with a map of possible locations and then entanglement used to have each missile pick its target, no missile would hit the same target and no one would know which missile was going where at launch. Stuff like that works?
You could use it for frequency hopping on radios making tracing communication pretty difficult.
You could just stick a random seed and tell them to meet at a place determined by that seed. What's the difference?
The closest use is probably quantum cryptography, somehow, I'd guess. But that's still not FTL communication.
The closest use is probably quantum cryptography, somehow, I'd guess. But that's still not FTL communication.
I'm not sure how you use a random number generator to randomly generate values that generate knowledge about previous uses. Those missiles aren't picking their targets randomly, they know where the other missiles are going and where they have to go. No missile is going to hit the same target, with a random number generator they would.
Entanglement links 2 things together 10,000+ times the speed. There will be quantum FTL internet soon whether you like it or not. There already exists early technology for this: http://www.technologyreview.com/view/524186/quantum-internet...
Absolutely nothing in either the article you linked or the actual published paper the article links to [0] indicates that the experts think this points the way to FTL signalling of any type.
The article might have glossed over that, but the researchers wouldn't have. Anyone who thought they had a way to send information FTL would be heralding it from the rooftops, because that, and not quantum teleportation or quantum solid-state whatever, would be the main story.
Why? Because FTL signalling inherently means causality is broken. Effects can precede causes. You can send information back in time. This is inherent in the geometry of the Universe, as predicted by Special Relativity, one of the best-tested and most-validated theories we have to date. Special Relativity is validated every time anyone uses GPS, for example, and the prediction that FTL implies travel back in time is inherent to what Special Relativity is.
So I'm not going to take you at your word. The supposed FTL neutrinos which turned out to be some loose cables show what happens when the scientific world even thinks that Special Relativity might need to be modified.
[0] http://arxiv.org/abs/1401.6958
The article might have glossed over that, but the researchers wouldn't have. Anyone who thought they had a way to send information FTL would be heralding it from the rooftops, because that, and not quantum teleportation or quantum solid-state whatever, would be the main story.
Why? Because FTL signalling inherently means causality is broken. Effects can precede causes. You can send information back in time. This is inherent in the geometry of the Universe, as predicted by Special Relativity, one of the best-tested and most-validated theories we have to date. Special Relativity is validated every time anyone uses GPS, for example, and the prediction that FTL implies travel back in time is inherent to what Special Relativity is.
So I'm not going to take you at your word. The supposed FTL neutrinos which turned out to be some loose cables show what happens when the scientific world even thinks that Special Relativity might need to be modified.
[0] http://arxiv.org/abs/1401.6958
From my understanding, it cannot be used to transmit information because the measured property of the entangled photon or particle is not chosen by the the experiment. It is truly random.
It could be used to ensure that 2 locations have the same random data. This is useful in cryptography.
It could be used to ensure that 2 locations have the same random data. This is useful in cryptography.
Unfortunately communication through QE isn't possible: http://en.wikipedia.org/wiki/No-communication_theorem
But you can use it to double your bandwidth (http://en.wikipedia.org/wiki/Superdense_coding) and "store" bandwidth (http://strilanc.com/quantum/2014/05/03/Storing-Bandwidth-wit...)
The real world application is China using QKD to encrypt their military communications.
All components of a quantum system are always entangled. It's not some mysterious property that arises under unusual circumstances. In fact, I would argue that quantum entanglement is the defining feature of quantum mechanics that distinguishes it from classical mechanics.
However, the way that most articles (and even physicists) use the term "entanglement" is in a loose way. Within a good approximation, a multi-component quantum state can be represented as a tensor product of single component quantum states. When this isn't a good approximation anymore, you can say that the entanglement of the system is much more apparent.
To give an example of what I mean, there's a technique in quantum chemistry known as density functional theory (DFT), which is used to compute ground state energies of various molecules. For some molecules, it works pretty well. The benefit of DFT is that it is a fast calculation technique (well, as far as quantum chemistry goes), but it's speed comes at a price. Rather than using the Coulombic interaction of every pair of electrons to compute the energy of a molecule (or more technically, using every Coulombic interaction as terms in the Hamiltonian), a probability cloud of electron positions is computed instead, and this cloud is used as the energetic term.
This works really well for a lot of systems, but in some cases (superconductors, metals, solid-state physics, van der Waals interactions), this approximation falls apart because the effect of electron-electron correlation significantly affects the energy of the system. In this case, the full, non-separable wavefunction is required. The fact that this full wavefunction cannot easily be broken into an approximation of simpler, single electron wavefunctions means that the entanglement of the system is very apparent.
However, the way that most articles (and even physicists) use the term "entanglement" is in a loose way. Within a good approximation, a multi-component quantum state can be represented as a tensor product of single component quantum states. When this isn't a good approximation anymore, you can say that the entanglement of the system is much more apparent.
To give an example of what I mean, there's a technique in quantum chemistry known as density functional theory (DFT), which is used to compute ground state energies of various molecules. For some molecules, it works pretty well. The benefit of DFT is that it is a fast calculation technique (well, as far as quantum chemistry goes), but it's speed comes at a price. Rather than using the Coulombic interaction of every pair of electrons to compute the energy of a molecule (or more technically, using every Coulombic interaction as terms in the Hamiltonian), a probability cloud of electron positions is computed instead, and this cloud is used as the energetic term.
This works really well for a lot of systems, but in some cases (superconductors, metals, solid-state physics, van der Waals interactions), this approximation falls apart because the effect of electron-electron correlation significantly affects the energy of the system. In this case, the full, non-separable wavefunction is required. The fact that this full wavefunction cannot easily be broken into an approximation of simpler, single electron wavefunctions means that the entanglement of the system is very apparent.
I agree completely. Entanglement is everywhere.
To calculate the correct energy of the electrons in a molecule it's necessary to use entanglement. But these molecular examples may be explained using some weird classical models with local hidden variables, and with electrons that interact with each other to conspire and provide the right result of the measurement. The quantum mechanical explanation is actually more simple, but not "intuitive".
Almost all the discussions about entanglement discuss the strange case of two entangled particles that are far away. The distance between the particles is only a trick to:
* be sure that one of them can't communicate to the other and tell the result of the measurement
* be sure that there is no a local hidden variable theory that explain the result
To calculate the correct energy of the electrons in a molecule it's necessary to use entanglement. But these molecular examples may be explained using some weird classical models with local hidden variables, and with electrons that interact with each other to conspire and provide the right result of the measurement. The quantum mechanical explanation is actually more simple, but not "intuitive".
Almost all the discussions about entanglement discuss the strange case of two entangled particles that are far away. The distance between the particles is only a trick to:
* be sure that one of them can't communicate to the other and tell the result of the measurement
* be sure that there is no a local hidden variable theory that explain the result
why one hidden variable, when you could have one for each atom between the entangled? :)
For someone who is more of a mathematician than physicist, the following article might be of interest in this context: http://math.ucr.edu/home/baez/quantum/node4.html
The gist is that the state space of a multicomponent quantum mechanical system (think electrons in a metal) is given by the tensor product of the single component state spaces. As might be familiar from linear algebra, not every element in the tensor product of two vector spaces is simply a tensor product of two vectors. That's really all there is to entanglement, but unfortunately you can't explain that to a lay person.
I would argue that using the term "entanglement" to refer to the situation where "the entanglement of the system is much more apparent" or "tensor products are not a good approximation anymore" is completely reasonable. In contrast, when you say that "all components of a quantum system [that appears in nature] are always entangled" then this is trivially true in a technical sense, but highly misleading. To produce and stabilize non-trivial amounts of entanglement in a way that it can be harnessed for quantum information processing is certainly an interesting and highly non-trivial task which people are spending lots of effort on.
I don't think it's trivially true in a technical sense at all. It certainly didn't have to be the case that all quantum systems exhibit entanglement. Physics could have been different, such that entanglement is a property only some systems can have. And that would lead to drastically different conclusions. In fact, treating entanglement as something special is, at least for me personally, the highly misleading concept.
When I was learning quantum mechanics, there were many concepts that confused and bothered me because people explained things in a loose and inaccurate way. Other incorrect statements that confused me for a long time include:
"Fermions cannot occupy the same quantum state. Bosons can."
"It's not possible to measure the position and momentum of a particle simultaneously."
And while not QM: "Mass can be converted to energy."
Essentially, schools teach the approximations first, which leads you to believe that reality works a certain way, and then you think of all sorts of situations where these rules lead to paradoxes and contradictions, and then you have to relearn everything the more accurate way, while trying to expunge the old, wrong stuff from your brain that likes to stick there.
In my undergrad, I thought of plenty of ways that "entanglement", based upon the way it was explained in class could be used to transfer information faster than the speed of light. The professor didn't have a rebuke against my argument (granted this was a chemistry professor, not a physics professor), and essentially it was because everyone was repeating wrong, catchy phrases to each other. I don't think "Entanglement is the fact that a multiparticle wavefunction cannot be decomposed" is a particularly complex idea to understand. Everything else kind of falls out of that statement.
In my opinion, the most accurate theory should be taught first, and then the less accurate approximations can be derived as limiting cases of the more accurate formulation. And if the math is too complex for the more accurate version, then clearly specify what fallacies or assumptions are being taken. One of my statistical mechanics books does this really, really well (the one by McQuarrie). Disclaimers are all throughout his book about how the equations apply to limiting cases and approximations, what those approximations are, and how using those approximations causes the result to differ from a more accurate theory.
When I was learning quantum mechanics, there were many concepts that confused and bothered me because people explained things in a loose and inaccurate way. Other incorrect statements that confused me for a long time include:
"Fermions cannot occupy the same quantum state. Bosons can."
"It's not possible to measure the position and momentum of a particle simultaneously."
And while not QM: "Mass can be converted to energy."
Essentially, schools teach the approximations first, which leads you to believe that reality works a certain way, and then you think of all sorts of situations where these rules lead to paradoxes and contradictions, and then you have to relearn everything the more accurate way, while trying to expunge the old, wrong stuff from your brain that likes to stick there.
In my undergrad, I thought of plenty of ways that "entanglement", based upon the way it was explained in class could be used to transfer information faster than the speed of light. The professor didn't have a rebuke against my argument (granted this was a chemistry professor, not a physics professor), and essentially it was because everyone was repeating wrong, catchy phrases to each other. I don't think "Entanglement is the fact that a multiparticle wavefunction cannot be decomposed" is a particularly complex idea to understand. Everything else kind of falls out of that statement.
In my opinion, the most accurate theory should be taught first, and then the less accurate approximations can be derived as limiting cases of the more accurate formulation. And if the math is too complex for the more accurate version, then clearly specify what fallacies or assumptions are being taken. One of my statistical mechanics books does this really, really well (the one by McQuarrie). Disclaimers are all throughout his book about how the equations apply to limiting cases and approximations, what those approximations are, and how using those approximations causes the result to differ from a more accurate theory.
I guess I was being generous when interpreting your statement that "all components of a quantum system are always entangled". For pure states, such a statement is trivially true in the sense any kind of interaction in the Hamiltonian will generically create entanglement.
For mixed states, your statement is of course false. It is unfortunately often the case in the real world that two subsystems are in a non-entangled quantum state.
Regarding your general theme: I understand that confusion can arise if seemingly informal language is taken verbatim as a formal statement. I do not think that the solution is to abolish the former, which can be extremely efficient to reason in and communicate with (you gave some examples in your post), but rather to educate on the interpretation. It is unfortunate that this is not always done, as your experiences suggest.
Regarding your general theme: I understand that confusion can arise if seemingly informal language is taken verbatim as a formal statement. I do not think that the solution is to abolish the former, which can be extremely efficient to reason in and communicate with (you gave some examples in your post), but rather to educate on the interpretation. It is unfortunate that this is not always done, as your experiences suggest.
You have good points. However I'm going to be a little nitpicky here. Mixed states aren't exactly "real" in the sense that what is a pure state for Alice can be a mixed state for Bob (I can provide an example if you don't know what I mean). So in that case the "lack" of entanglement is simply due to ignorance of which pure state the system is actually in.
The point is that entanglement always refers to an a priori choice of subsystems (say, Alice and Bob). This is the part that makes the phenomenon non-trivial. If there are other systems around (say, Eve the environment) then the joint state of Alice and Bob will be usually be mixed as a consequence of for the "trivial" reason that we discussed in the previous posts (to adapt a famous saying, almost all components of a quantum system are always mixed ;-). There is nothing "unreal" about mixed states, and not all mixed states lack entanglement. However, for mixed states, being entangled is no longer the generic behavior. The unavoidable interactions with the environment are the reason why it is hard to maintain entanglement between subsystems.
To say that we should do better and bring the environment back into the picture is missing the point if we are interested in the correlations between Alice and Bob. These do exclusively depend on their joint state (mixed or not).
To say that we should do better and bring the environment back into the picture is missing the point if we are interested in the correlations between Alice and Bob. These do exclusively depend on their joint state (mixed or not).
(Sorry for continuing the rather long discussion, but I'd like to achieve some resolution here.)
By "real", I mean that the concept of a density matrix is derived completely on top of the postulates of quantum mechanics in combination with the Born rule. There's nothing fundamental about mixed states; you can also have classical mixed states (e.g. deriving thermodynamics from classical statistical mechanics). It's essentially just taking the postulates for pure states and applying a layer of statistics on top of it. I believe it was von Neumann that originally did this? In other words, the density matrix formulation does not add any additional predictive capability to physics that the original QM from the 1920s did not already provide. It's just a more convenient tool for connecting QM to experimentally realizable systems. Do you disagree with this?
When you lose entanglement due to decoherence (specifically, the off-diagonal terms of the density matrix approaching zero), these correlations are lost because you're essentially performing a measurement. But they still exist in the whole Alice + Bob + you and your measurement device system! But then, this starts treading into the discussion of the whole unsolved measurement problem which I kind of wanted to lurk around, since no one ever gets anywhere with those discussions.
Indeed your last point ("To say that we should do better and bring the environment back into the picture is missing the point") is essentially the whole picture I'm focusing on. Perhaps my background with quantum chemistry has slanted the way I explain things on here, because you're never collapsing these systems when you perform simulations of them to calculate their properties.
By "real", I mean that the concept of a density matrix is derived completely on top of the postulates of quantum mechanics in combination with the Born rule. There's nothing fundamental about mixed states; you can also have classical mixed states (e.g. deriving thermodynamics from classical statistical mechanics). It's essentially just taking the postulates for pure states and applying a layer of statistics on top of it. I believe it was von Neumann that originally did this? In other words, the density matrix formulation does not add any additional predictive capability to physics that the original QM from the 1920s did not already provide. It's just a more convenient tool for connecting QM to experimentally realizable systems. Do you disagree with this?
When you lose entanglement due to decoherence (specifically, the off-diagonal terms of the density matrix approaching zero), these correlations are lost because you're essentially performing a measurement. But they still exist in the whole Alice + Bob + you and your measurement device system! But then, this starts treading into the discussion of the whole unsolved measurement problem which I kind of wanted to lurk around, since no one ever gets anywhere with those discussions.
Indeed your last point ("To say that we should do better and bring the environment back into the picture is missing the point") is essentially the whole picture I'm focusing on. Perhaps my background with quantum chemistry has slanted the way I explain things on here, because you're never collapsing these systems when you perform simulations of them to calculate their properties.
The density matrix is as real as the wave function when it comes to describing the corresponding subsystem. In the situation I was sketching, there is no measurement, no collapse, and the "measurement problem" does not play a role. Here is a concrete example: Suppose that you have three spins that are in a superposition of |000> and |111>. Alice has one the spins, Bob the other spin, and the third one belongs to the environment. The reduced state of any two of the three spins is NOT entangled. Therefore, Alice and Bob which will not be able violate any Bell inequality, win a CHSH game, distill Bell pairs, etc. if they only control two of the three spins. It is irrelevant that Alice is entangled with the joint system of Bob and Eve.
Again, the basic point is that the notion of entanglement refers to a choice of subsystems. Your statement that "All components of a quantum system are always entangled" is either trivializing the discussion or demonstrably false.
Again, the basic point is that the notion of entanglement refers to a choice of subsystems. Your statement that "All components of a quantum system are always entangled" is either trivializing the discussion or demonstrably false.
See my message to Lisper.
Going to watch interstellar. Let's see what entanglement really is!
I'm interested in why you think those statements are false?
I'm not the OP, but here is an example: The statement
"It's not possible to measure the position and momentum of a particle simultaneously."
can be interpreted as that it is not possible to acquire any joint information about position and momentum, which is incorrect.
"It's not possible to measure the position and momentum of a particle simultaneously."
can be interpreted as that it is not possible to acquire any joint information about position and momentum, which is incorrect.
The correct statement for the first one is that the wavefunction for a system of fermions must be antisymmetric under the exchange of any two particles (the wavefunction flips sign). For a system of bosons, it stays the same.
The correct statement for the third one is that energy is not a substance; it's a number that is conserved as a result of the invariance of physics under time translations (see Noether's theorem). Thus, mass has an energy associated with it (see stress-energy tensor), and a particle that has mass can be converted into other particles that do not have mass, but energy is just a property that remains constant (except under GR, but then that's a whole other can of worms).
bmnmasdas pointed out what I meant with HUP.
The correct statement for the third one is that energy is not a substance; it's a number that is conserved as a result of the invariance of physics under time translations (see Noether's theorem). Thus, mass has an energy associated with it (see stress-energy tensor), and a particle that has mass can be converted into other particles that do not have mass, but energy is just a property that remains constant (except under GR, but then that's a whole other can of worms).
bmnmasdas pointed out what I meant with HUP.
Hmmm...
DFT is a method. It has been used by physicists for the last 40 years to model the solid state. What you put forward in your third paragraph is not quite right - things are more subtle.
What you seem to be suggesting is that we should be free of the Kohn-Sham framework[1,2] or find the exact XC functional. Not surprisingly, the results of calculations depend on how the functionals were constructed. But that doesn't mean "DFT" is bad. DFT's just the method. There is no approximation in DFT. It is in itself exact for the description of the ground state.
[1]:https://www.princeton.edu/mae/people/faculty/carter/ecdocs/E... [2]: http://scitation.aip.org/content/aip/journal/jcp/127/2/10.10...
DFT is a method. It has been used by physicists for the last 40 years to model the solid state. What you put forward in your third paragraph is not quite right - things are more subtle.
What you seem to be suggesting is that we should be free of the Kohn-Sham framework[1,2] or find the exact XC functional. Not surprisingly, the results of calculations depend on how the functionals were constructed. But that doesn't mean "DFT" is bad. DFT's just the method. There is no approximation in DFT. It is in itself exact for the description of the ground state.
[1]:https://www.princeton.edu/mae/people/faculty/carter/ecdocs/E... [2]: http://scitation.aip.org/content/aip/journal/jcp/127/2/10.10...
Yeah, I know. My rant further down the page on inaccuracies in teaching is coming back to haunt me now. Ironic, isn't it? I was glossing over specifics and loosely conflating concepts to form a point.
> All components of a quantum system are always entangled.
No, that's not true. If it were then there could never be direct observation of quantum interference because entangled particles do not self-interfere.
It is true that entanglement is very common, and an unentangled state is the unusual case. But it's not true that unentangled states (or, to be precise, unentangled degrees of freedom) don't exist.
No, that's not true. If it were then there could never be direct observation of quantum interference because entangled particles do not self-interfere.
It is true that entanglement is very common, and an unentangled state is the unusual case. But it's not true that unentangled states (or, to be precise, unentangled degrees of freedom) don't exist.
I think either you're confused on an issue or I'm confused on what you're trying to say. Quantum interference is observable with even a single particle.
> because entangled particles do not self-interfere
Entangled particles certainly can, and do interfere (as mentioned, electrons in an atom are entangled and definitely interfere; there's a whole field devoted to calculating this effect), so I'm not sure exactly what you mean here. Can you give me, in ket notation, an example of an unentangled state? (And if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product).
> because entangled particles do not self-interfere
Entangled particles certainly can, and do interfere (as mentioned, electrons in an atom are entangled and definitely interfere; there's a whole field devoted to calculating this effect), so I'm not sure exactly what you mean here. Can you give me, in ket notation, an example of an unentangled state? (And if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product).
> (And if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product)
This reasoning does not make sense. The notion of entanglement is not invariant under "global" operations, nor should it be.
This reasoning does not make sense. The notion of entanglement is not invariant under "global" operations, nor should it be.
> Quantum interference is observable with even a single particle.
Yes, but only if that particle is in an unentangled state. If that particle is entangled then the only way to observer the interference is to make measurements on both the particle whose interference you wish to observe and the particle with which it is entangled.
This is simply the old canard about measurement "destroying" interference (because measurement and entanglement are the same thing).
> Entangled particles certainly can, and do interfere
That's true, but the way in which they interfere is different, and the procedure you need to perform to observe the interference is likewise different.
> Can you give me, in ket notation, an example of an unentangled state?
|U> + |D>
Or if you want two unentangled particles:
(|U1> + |D1>)(|U2> + |D2>)
as opposed to the entangled state:
|U1>|D2> + |D1>|U2>
(Where U and D are intended to designate something like spin Up or spin Down, but that doesn't really matter.)
> if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product
That's news to me. How does that happen?
Yes, but only if that particle is in an unentangled state. If that particle is entangled then the only way to observer the interference is to make measurements on both the particle whose interference you wish to observe and the particle with which it is entangled.
This is simply the old canard about measurement "destroying" interference (because measurement and entanglement are the same thing).
> Entangled particles certainly can, and do interfere
That's true, but the way in which they interfere is different, and the procedure you need to perform to observe the interference is likewise different.
> Can you give me, in ket notation, an example of an unentangled state?
|U> + |D>
Or if you want two unentangled particles:
(|U1> + |D1>)(|U2> + |D2>)
as opposed to the entangled state:
|U1>|D2> + |D1>|U2>
(Where U and D are intended to designate something like spin Up or spin Down, but that doesn't really matter.)
> if you're referring to a direct tensor product of two single particle states, I'm still considering that an entangled state since it can unitarily evolve out of that configuration into one that can't be written as a tensor product
That's news to me. How does that happen?
This debate has really been bothering me and making me anxious the last couple of days. I haven't been able to sleep. I need to know something, are you self-taught in quantum mechanics or do you have a PhD in theoretical physics?
I'm not doubting your argument, (for all I know you're a well-known physics professor), I would just really like an answer to this question, as I think it would put my mind at ease.
I'm not doubting your argument, (for all I know you're a well-known physics professor), I would just really like an answer to this question, as I think it would put my mind at ease.
Self-taught. Why does that matter? (I do have a Ph.D. but it's in CS.)
P.S. It turns out you were right about this:
"it can unitarily evolve out of that configuration into one that can't be written as a tensor product"
That turns out to be true (and it retrospect it's obviously true because otherwise it would not be possible to create entangled pairs.) But you are wrong in your claim that therefore the antecedent state is also entangled. A state that can be factored is not entangled by definition.
P.S. It turns out you were right about this:
"it can unitarily evolve out of that configuration into one that can't be written as a tensor product"
That turns out to be true (and it retrospect it's obviously true because otherwise it would not be possible to create entangled pairs.) But you are wrong in your claim that therefore the antecedent state is also entangled. A state that can be factored is not entangled by definition.
> Self-taught. Why does that matter?
It doesn't. All that matters is that the science is correct (see Ron Maimon for instance; self-taught but far more knowledgable than most physicists). However, I get in far too many discussions involving QM online (mostly Reddit) where I learn that I wasted my time arguing with a 14 year old that watched "Through the wormhole" or something.
> P.S. It turns out you were right about this
You sound surprised. My graduate research is in quantum chemistry (and related areas), so I should have at least a few concepts correct. As someone with more of a QC background, perhaps my definition of what theoretical physicists consider "entangled" is inaccurate, so I am reading up on the matter. But I'm finding their specification of "entangled" to be an unintuitive and unobvious choice of wording.
It doesn't. All that matters is that the science is correct (see Ron Maimon for instance; self-taught but far more knowledgable than most physicists). However, I get in far too many discussions involving QM online (mostly Reddit) where I learn that I wasted my time arguing with a 14 year old that watched "Through the wormhole" or something.
> P.S. It turns out you were right about this
You sound surprised. My graduate research is in quantum chemistry (and related areas), so I should have at least a few concepts correct. As someone with more of a QC background, perhaps my definition of what theoretical physicists consider "entangled" is inaccurate, so I am reading up on the matter. But I'm finding their specification of "entangled" to be an unintuitive and unobvious choice of wording.
> I wasted my time arguing with a 14 year old
Well, I'm about to turn 50 so you don't have to worry about that. :-)
FWIW, I wrote this:
http://www.flownet.com/ron/QM.pdf
> You sound surprised.
No, I'm not. (How does one "sound surprised" in an on-line conversation?)
> perhaps my definition of what theoretical physicists consider "entangled" is inaccurate
An entangled state is one that can't be factored. See e.g.
http://www.theory.caltech.edu/people/preskill/ph229/notes/bo...
section 2.4.1.
(I am a bit nonplussed by how someone who does graduate research in quantum chemistry can not know this. It's a pretty basic concept.)
Well, I'm about to turn 50 so you don't have to worry about that. :-)
FWIW, I wrote this:
http://www.flownet.com/ron/QM.pdf
> You sound surprised.
No, I'm not. (How does one "sound surprised" in an on-line conversation?)
> perhaps my definition of what theoretical physicists consider "entangled" is inaccurate
An entangled state is one that can't be factored. See e.g.
http://www.theory.caltech.edu/people/preskill/ph229/notes/bo...
section 2.4.1.
(I am a bit nonplussed by how someone who does graduate research in quantum chemistry can not know this. It's a pretty basic concept.)
You really shouldn't be nonplussed about it (which, I'm not sure if you intended it this way, but calling it a "basic" concept seems a little passive aggressive. I could equally say that someone self-taught in QM should know the "basic" fact that product states would unitarily evolve out of that configuration). It just depends on what area you focus on and what your background is. Scott Aaronson says on his blog that he has explained Bell's Theorem to QFT professors that had never heard of it. Just wasn't relevant to their work. Does that make them bad physicists for not knowing such a well-known part of QM?
Heck, it's better than a professor I had that did DFT work who thought the single-particle wavefunction was the most fundamental aspect of quantum mechanics. Nevermind the fact that DFT is trashed for its lack of ability to account for electron correlation.
(And I do mean trashed. I was at the Gordon Research Conference in quantum chemistry this past summer where Peter Gill gave a lecture titled "the obituary of DFT". And if anyone has a right to rag on it, it's certainly him.)
Heck, it's better than a professor I had that did DFT work who thought the single-particle wavefunction was the most fundamental aspect of quantum mechanics. Nevermind the fact that DFT is trashed for its lack of ability to account for electron correlation.
(And I do mean trashed. I was at the Gordon Research Conference in quantum chemistry this past summer where Peter Gill gave a lecture titled "the obituary of DFT". And if anyone has a right to rag on it, it's certainly him.)
> I could equally say that someone self-taught in QM should know the "basic" fact that product states would unitarily evolve out of that configuration.
Well, that would depend on how far my studies have gotten me, no? My general assumption is that anyone who actually does QM for a living knows at least as much as I do, and almost certainly a great deal more. (Case in point: I presume that QFT is quantum field theory, but what is DFT?) I prefer to view this as humility rather than passive aggression. In any case, I don't think either one of us should be losing any sleep over it :-)
But can we agree that there are states that can be factored, and states that can't, and that this is a useful distinction to make? And that this distinction is physical, i.e. that it produces observable effects? (And not just observable, but interesting and useful?)
Well, that would depend on how far my studies have gotten me, no? My general assumption is that anyone who actually does QM for a living knows at least as much as I do, and almost certainly a great deal more. (Case in point: I presume that QFT is quantum field theory, but what is DFT?) I prefer to view this as humility rather than passive aggression. In any case, I don't think either one of us should be losing any sleep over it :-)
But can we agree that there are states that can be factored, and states that can't, and that this is a useful distinction to make? And that this distinction is physical, i.e. that it produces observable effects? (And not just observable, but interesting and useful?)
> But can we agree that there are states that can be factored, and states that can't, and that this is a useful distinction to make? And that this distinction is physical, i.e. that it produces observable effects? (And not just observable, but interesting and useful?)
Oh certainly. I've never disagreed on this haha.
Oh certainly. I've never disagreed on this haha.
If you say so. "All components of a quantum system are always entangled" sounds like a contrary claim to me, but I don't want to quibble over it.
It does make an interesting puzzle, though, how it can be physically possible to prepare a state that is both unentangled and pure. I don't actually know the answer to that off the top of my head.
It does make an interesting puzzle, though, how it can be physically possible to prepare a state that is both unentangled and pure. I don't actually know the answer to that off the top of my head.
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I see nothing counter-intuitive about quantum entanglement. Photons travel at the speed of light--time does not exist for them. Alter one, the entangled one is instantaneously connected.
The issue is with instantaneous. What does that mean in a relativistic context? Depending on the speed of the observer, "instantaneous" changes. This is fine in reconciling some story in the future, but if there is an action happening instantaneously with something else, then we need a notion of same instant. This is easy to add to have something working, but it is extremely hard to add it in a principled way.
That does not work because light speed has a limit. It is true that the photon does not experience time. Imagine a photon traveling a distance of 1 light year towards us( we are stationary). In it's reference frame it will do so immediately but in our it takes 1 year. For the photon to travel to us in zero time in both frames, the speed of light would have to be infinite, which we know it isn't.
"If you think you understand quantum mechanics, you don't understand quantum mechanics."
- Richard Feynman
I wish you comment were downvoted instead of karmakaze's one.
He is expressing an opinion and even if he is wrong, it is still an interesting idea, and shows some effort. A decent short explanation could show the mistake, and make a good comment->answer combo.
Instead you quoted a comment which is out of context ( Feynman's comment is intended for physicists of his level ), contributing nothing.
( Please don't take this as a personal attack ( it isn't), but more a thought what's wrong with HN in light of recent debate )
He is expressing an opinion and even if he is wrong, it is still an interesting idea, and shows some effort. A decent short explanation could show the mistake, and make a good comment->answer combo.
Instead you quoted a comment which is out of context ( Feynman's comment is intended for physicists of his level ), contributing nothing.
( Please don't take this as a personal attack ( it isn't), but more a thought what's wrong with HN in light of recent debate )
No, you're right - it was snide and I should have reconsidered it.
Good opportunity to again promote »The Theoretical Minimum« [1] by Leonard Susskind (born June 1940, director of the Stanford Institute for Theoretical Physics with research interests in string theory, quantum field theory, quantum statistical mechanics and quantum cosmology). It is pretty accessible and a key takeaway is that there is a lot of misinformation in the wild and especially on the internet when it comes to (modern) physics as he tell his class not only once when someone asks about something he read somewhere.
[1] http://theoreticalminimum.com/
[1] http://theoreticalminimum.com/
The site looks interesting, but it's difficult to find the information that is related to the discussion. Does this site have a page that discusses specifically entanglement? EPR paradox? Bell inecuality? I'd like to see a link to the specific relevant page and not a link to the general site.
Here is the course on quantum entanglement [1] but depending on prior knowledge it may be wise to first go through the courses on classical [2] and quantum [3] mechanics. He tries to keep everything as self-contained as possible but does not go through the very basics things like Lagrangians and Hamiltonians every time.
[1] http://theoreticalminimum.com/courses/quantum-entanglement/2...
[2] http://theoreticalminimum.com/courses/classical-mechanics/20...
[3] http://theoreticalminimum.com/courses/quantum-mechanics/2012...
[1] http://theoreticalminimum.com/courses/quantum-entanglement/2...
[2] http://theoreticalminimum.com/courses/classical-mechanics/20...
[3] http://theoreticalminimum.com/courses/quantum-mechanics/2012...
This is really cool. I took a (very) basic class on modern physics with Susskind; awesome guy and great at explaining things. Will have to read through this!
Watch, not read, these are video recordings of courses. About 20 courses with about 10 lectures each, usually about 2 hours.
I assume that photons act as waves and not particles. Though they have quantized energy (frequency), there's no reason for me to think that they have locality. If so...
The most plausible explanation I can think of is a Monty Hall paradox at the source of the emitter. Thousands of photon pairs? How are they generated? Is their emission dependent on the destination via say, pilot wave resonance? Either resonance or waves that travel backwards in time. Experiments of entanglement speed should point towards one or the other.
The most plausible explanation I can think of is a Monty Hall paradox at the source of the emitter. Thousands of photon pairs? How are they generated? Is their emission dependent on the destination via say, pilot wave resonance? Either resonance or waves that travel backwards in time. Experiments of entanglement speed should point towards one or the other.
The human brain may or not be deterministic, but it is certainly a complex system. For the results to be so consistent for the multitude of experiments that have been performed, it seems highly unlikely that #2 is the case. I think in this case it's pretty fair to apply Occam's razor.
On a side note, I hate titles for popular physics articles. The next article titles: "5 super simple steps to splitting the atom" "20 crazy tips for growing high temperature superconductors" "Make free cash farming Higgs bosons"