B Entanglement: How Does it Work and Its Implications in Everyday Life?

[nnope]

I don't have much of a background in quantum physics so be patient with my questions please. Basically I want to know how does entanglement actually work? Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement?
Also just an extra question how does all of quantum mechanics translate to every day life? Does my bed disappear when I am not looking at it?

 

[Nugatory]

I don't have much of a background in quantum physics so be patient with my questions please. Basically I want to know how does entanglement actually work? Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement

That's an easy question: Neither. However, now that you know what it's not, you'll probably want to know what it is, and that's not such an easy question.

Also just an extra question how does all of quantum mechanics translate to every day life? Does my bed disappear when I am not looking at it?

Of course not, and nothing in quantum mechanics suggests that it might.

If you can get hold of the book "Sneaking a look at god's cards" by Giancarlo Ghiradi, it will give you much of the background that you need without demanding more mth thn you have.

 

[bhobba]

Here is the technical definition of entanglement. It's more at the I level than B but hopefully you will get the gist.

One of the foundational principles of QM is called the principle of superposition.

It says if a system can be in state |a> and |b>, without detailing just what they mean, then c*|a> + d*|b> is another state where c and d are any constants. I will for definiteness use 1/√2 for both in the following.

Ok now suppose we have two systems each can be in state |a> and |b> so you can have system one in state |a> and system 2 in state |b> - this is written as |a>|b> and conversely you can have system 1 in state |b> and system 2 in state |a> - this is written as |b>|a>. Now let's apply the principle of superposition to this combined system so you have 1/√2 |a>|b> + 1/√2 |b>|a> as a possible state. Such states are called entangled.

Now let's just observe system 1. We find, if we chug through the math, it acts as if it what is called a mixed state which I will not go into, but is the foundation of what's called decoherence which I will also not go into. You must study some textbooks for that one.

Of relevance here suppose when you observe system 1 and find its in state |a> then since its part of state |a>|b> system 2 is automatically in state |b>. And conversely if its in state |b> then system 2 is in state |a> - that's all pretty intuitive, but again if you chug through the math it shows your intuition is right.

Now that's all Bell is - simple really. So what's this whole thing about - paper after paper and talk of non locality etc etc. That's simple as well - but few will explain it to you - here will. It just a correlation - yes that's all. But you say, correctly, that's trivial - it can't be all it is. But believe it or not it is. The issue however, and this is the only thing, is it has statistical properties different to correlation's we find in the world around us - see Dr Chinese's explanation:
http://drchinese.com/David/Bell_Theorem_Easy_Math.htm

So it has statistical properties different to what we usually have. Well this is QM - do you expect it to be the same as classically? Of course not. But what some do is say - I want it the same as classical. OK - you look for some out and you soon find it - if you assume non-locality you can have it. That's where this whole FTL, non locality stuff comes from. But then you ask - why bother? And that is the whole secret to this business hardly anyone will tell you - just accept QM as it is and there is no issue - it's this butting your head against just accepting nature as it is, that's the issue. You want to fight against it, and you go down a rabbit hole of weirdness, non locally etc etc. Don't fall for it.

Of course this in no way diminishes the genius of Bell in figuring this all out - its what some people have taken from it - they have made it much harder than it is and confusion abounds with all sorts of silly statements even from people that should know better. Don't fall for it - don't go down the rabbit hole in trying to force QM to your intuition, as some say of people who get too caught up in trying to understand the foundations of QM (the saying came from Feynman). Its a legit area of study, but gee it confuses beginners. Just accept QM as it is and all is fine. Its a bit weird - just accept it. Later, when you have learned a lot more of QM that's the time to look at its foundations, you are prepared for it then and have a much greater chance of not going down that rabbit hole leading nowhere.

Thanks
Bill

 

[Khashishi]

First of all, you need to understand that the number of parameters needed to represent a state is larger in quantum mechanics than in classical logic. In classical logic, a system that has two eigenstates has only two possible states, e.g. up and down. But a quantum state can be in superposition, so there's infinite possible states. (In this case, the measure of the state space is equal to the number of points on a sphere.) If you have incomplete information about the state, then in classical logic, you represent this as a probability of each state A and B. It is essential to understand that a superposition between A and B is different than a classical probability distribution containing A and B. In the first case, the state is fully known (a so-called pure state); in the second, there is incomplete information. In quantum mechanics, you represent a state with incomplete information using a density matrix, which has an even larger state space.

The rules for combining two smaller systems into a larger system are different than in classical logic. In classical logic, if we combine two systems with two states each, we have a system with 2x2 or 4 states (e.g., up-up, up-down, down-up, down-down). In quantum mechanics, you have a system with 2x2 or 4 eigenstates, but infinite states, since states don't need to be eigenstates (they can be superpositions). You could have a pure state that is some superposition A*(up-up)+B*(up-down)+C*(down-up)+D*(down-down). A, B, C, and D are complex numbers, but with the restriction that A^2+B^2+C^2+D^2 = 1. Since there are two numbers in each complex number, if we ignore the overall phase, the size of the state space is 6D. Note that the 2 state system has a size of state space that is 2D (surface of sphere). If you have two 2-state systems, and you choose a state for each system, you are choosing a point in a 4D space. The point here is that the size of the state space of the combined system is bigger than the product of the sizes of state space of each subsystem. In other words, when systems are combined, it unlocks more possible states that can't be expressed by specifying the state of each subsystem. These additional states are called entangled states. In fact, almost all of the states in the combined system are entangled states.

 

[entropy1]

Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement?

You can look at it in the way of the principle of conservation, that the physical universe is filled with. In the case of entanglement this translates to: if one particle is up, the other must be down, and vice versa. There is no information transfered. There are several interpretations that each give a different explanation of how the quantity in question could be conserved without transfering info FTL. The bottom line, the math, shows conservation is possible. QM can be counter-intuitive. Another conservation is that of energy: in a closed system any energy lost by an element in it is gained by one or more other elements in it, so that the total energy remains the same.

 

[Ken G]

There have been a lot of good answers above, I've learned something from each. Here's my take: entanglement is where we learn that systems are fundamentally holistic, meaning all one thing rather than comprised of separate parts. It's just that being comprised of separate parts is kind of a special (perhaps even trivial) case of being all one thing, kind of like how a circular orbit is a special case of the allowed elliptical orbits. We don't say that orbits have to be either circular or elliptical, and we don't say that they should be circular but every now and then we encounter these bizarre elliptical ones, we just say circles are special cases of ellipses, and perhaps this is the view we should take about systems that act like they are made of separate parts as opposed to being all one thing.

What's more, when you have a vast internal complexity in a system, it tends to act more and more as though it was comprised of parts, sort of like how there are processes that exist in astronomy that tend to circularize elliptical orbits and that's why most orbits are indeed close to circular. So the conclusion is, our macroscopic experiences lead us to think that systems are fundamentally comprised of separate parts that work together, but quantum mechanics shows us this is a kind of emergent property of the specific way that complicated systems cover the tracks of their fundamentally holistic (quantum) character.

Note this insight is not forced on anyone, because to accept it is essentially to reject the Copenhagen approach to quantum mechanics. Bohr took the opposite view that systems are indeed comprised of parts and do in fact function classically, but the fact that these rules don't work for the quantum world is evidence that, in his words, "there is no quantum world." But one of Bohr's own principles is the principle of correspondence, which means that combining a sufficient number of quantum systems, or sufficiently exciting a single quantum system, must always give the same result as a classical experiment, so even he did allow that one must be able to interpret the classically real world as emergent from quantum mechanics. So although Bohr would likely have rejected the idea that reality is fundamentally holistic and only appears to be comprised of parts in the classical limit (since he took the classical limit as what reality is, essentially by definition), nevertheless I can invoke his own correspondence principle to support the idea that being comprised of parts is only the classical limit that stems from a reality that is fundamentally holistic, but which being made of parts emerges as a special case when all the entanglements are effectively broken.

 

[anothergol]

That's an easy question: Neither.

What do you mean, neither? Why/how can it not be an "invisible link"?

 

[anothergol]

But then you ask - why bother? And that is the whole secret to this business hardly anyone will tell you - just accept QM as it is and there is no issue - it's this butting your head against just accepting nature as it is, that's the issue. You want to fight against it, and you go down a rabbit hole of weirdness, non locally etc etc. Don't fall for it.

I've read this a lot, not to try to make sense of QM, to just acknowledge it and go on. I'm sure this makes sense for pro's in this domain, which seems to be very mathematically driven, but.. consider that not many here (unless I'm mistaken about the target of this forum) will go deeper in the maths, and are indeed there a little to make sense out of QM.
I mean, it doesn't mean we're idiots, if Einstein himself had problems accepting the nature of entanglement.

That is, facts like a particule is in superposition of states until observed, but the observed spin will be purely random (if I'm saying it right), that's not getting into the maths, that's understandable by everyone, but most importantly, there is something we can understand from that: that one can't use entanglement to communicate faster than light. We don't all need to view QM as black box of equations to make a little sense out of it.
If I took this example it's because we often see the unfortunate word "teleportation" used in the media. Understanding entanglement better makes us understand that it's in no way a teleportation. I consider this as "making sense out of QM", what entanglement means & doesn't mean from a.. more "real" aspect.

 

[Ken G]

What's more, it can be argued that quantum mechanics makes a lot more "sense" than does classical mechanics, for those who are mathematically inclined-- it's just that we (as a species, and often as individuals also) learned classical mechanics first, so it prejudiced our thinking. In support of this claim, I will point out some quotes by Parmenides and Zeno, who were both trying to use pure logic, almost 2500 years ago (!), to determine what the nature of reality "had to be", in order to make "sense" logically:

Parmenides:
How could what is perish? How could it have
come to be? For if it came into being, it is not;
nor is it if ever it is going to be. Thus coming
into being is extinguished, and destruction
unknown.

Sounds like gobbledygook, right? Actually, read closer, and then look up the no-clone and no-deleting theorems of quantum mechanics. Then consider this:

Zeno:
The hypothesis of the many, if examined sufficiently in detail, leads to even more ridiculous results than the hypothesis of the One.

More mystic mumbo jumbo? Read about the meaning of the "unitary" time translations in quantum mechanics. And while you're at it, google the "quantum Zeno effect," which no doubt sets the record for an observed phenomenon named after the longest elapsed time for someone who in some sense predicted or expected it.

The conclusion I am leading you toward is that when you take pure logic, and try to use it to infer how reality will behave, you end up with some of the crucial aspects of quantum mechanics, and nothing like classical mechanics. So I agree with you-- there may well be some fertile soil involved in "making sense" of quantum mechanics, if it is a much more logically accessible theory than Newton's laws, albeit seemingly strange.

 

[nnope]

How did we go from trying to understand entanglement to overly convoluted responses that are talking about God knows what and quoting God knows who?

 

[Ken G]

Well, I guess if you understand entanglement without any "convoluted" insights, we'd all love to hear it.

 

[bhobba]

IThat is, facts like a particule is in superposition of states until observed,

You have hit on the issue right there.

Even explaining superposition without math is impossible - and believe me I have tried.

A quantum object is in superposition all the time and in an infinite number of ways. What I suspect you are trying to say, and this is the other part of the issue, is superposition of what is being observed - which has a very specific meaning I can discuss - it leads to the so called preferred basis problem.

The above as you wrote it, because of that actually makes no sense. To formulate meaningful questions and get meaningful answers at the beginner level is very difficult. I did the best in my previous post based on the innumerable queries I have replied to on this forum. If what I said still makes no sense then really me, and I suspect many other science advisers, can't really help you. Some will simply tell you - study the real deal ie actual textbooks and leave it at that. I won't - I will do my best, but in the final analysis it really is the only way.

It is the very important issue that is at rock bottom of the confusion and misconception pop-sci accounts give such as teleportation etc. There is no teleportation. Even professionals like Brian Green resort to things like particles are in many places at once (I have heard him say it). He probably knows better (it's wrong BTW - QM is silent on such things - but even after studying advanced textbooks fell for that one myself - so Brian is well and truly excused - and why I said probably), but unless he wants to get in front of the camera and say - well I really can't tell you too much without some math and turn virtually everyone off that's what he is reduced to. It's to give a feel so to speak - but its wrong. We spend a lot of time here correcting such - like I said even I fell for some of that stuff and had to be corrected - with varying degrees of success. Its particularly bad in Quantum Field Theory without going into the details.

It will take time, but, with some effort, the following are at pretty close to the beginner level (you just need a smidgen of calculus) and will do just that:
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

I am sorry, truly I am, but its the only way.

Thanks
Bill

 

[nnope]

Zeno:
The hypothesis of the many, if examined sufficiently in detail, leads to even more ridiculous results than the hypothesis of the One.

More mystic mumbo jumbo? Read about the meaning of the "unitary" time translations in quantum mechanics. And while you're at it, google the "quantum Zeno effect," which no doubt sets the record for an observed phenomenon named after the longest elapsed time for someone who in some sense predicted or expected it.

So I read about this Zeno effect, I fail to see what the quote has anything todo with the concept.

How could what is perish? How could it have
come to be? For if it came into being, it is not;
nor is it if ever it is going to be. Thus coming
into being is extinguished, and destruction
unknown.

Sounds like gobbledygook, right? Actually, read closer, and then look up the no-clone and no-deleting theorems of quantum mechanics. Then consider this:

Im still failing to see the point. You've taken some quote by some guy born in 501 BC and assumed it sheds light on aspects of QM because it seems to allign with a concept on the subject. It seems to me that his philosophy is flawed anyway.

 

[nnope]

Well, I guess if you understand entanglement without any "convoluted" insights, we'd all love to hear it.

Thats not what I am trying to imply, I am just saying that some of the explanations given and the discussions had on these topics are so purposely convoluted that after I've spent 15 minutes trying to understand them I realize they can be explained in simpler terms.

 

[Ken G]

So I read about this Zeno effect, I fail to see what the quote has anything todo with the concept.

It has everything to do with the concept, because it is about superposition and how superpositions involve indefiniteness. Entanglement is a type of superposition that involves indefiniteness among several particles. The point of the Zeno effect is that in order for a system to evolve unitarily from having one definite value of a discrete variable to another, it must move through indefinite states in between, which requires that the system go unmeasured for a time. Since there exists measurements that collapse an entangled system into a Bell state, this means that in order for an entangled system to evolve unitarily into a different Bell state, it must go unexposed to Bell measurements for a time, otherwise the initial entanglement will be locked in. The name stems from Zeno's logical argument that change is impossible, which now must be modified to say that change between definite states is impossible.

Im still failing to see the point. You've taken some quote by some guy born in 501 BC and assumed it sheds light on aspects of QM because it seems to allign with a concept on the subject. It seems to me that his philosophy is flawed anyway.

Then you need to know more about what he was saying. Parmenides was saying that if something (read "quantum state") exists now, then it must have always existed, and it could not cease to exist without having not existed before. This is precisely true of quantum states under unitary evolution, that's the no-cloning, no-deleting theorems in a nutshell. Of course Parmenides did not know quantum mechanics, the point is that he arrived at his conclusions using a form of logic that is apparently quite similar to the logical structure of quantum mechanics. And yes, he did that in 500 BC or something, that's the whole point-- this speaks to the issue of just how difficult to understand is the basic underlying structure of quantum mechanics, if it bears resemblance to one of the very first logical efforts that people tried to apply to the nature of reality. But yes, these kinds of insights might not be interesting to all people, I already knew that, the issue was more if the person asking the question and trying to struggle with the meaning of quantum mechanics would like to see it in that historical perspective or not.

 

[Ken G]

Thats not what I am trying to imply, I am just saying that some of the explanations given and the discussions had on these topics are so purposely convoluted that after I've spent 15 minutes trying to understand them I realize they can be explained in simpler terms.

Maybe 15 minutes isn't enough to distill the lessons of quantum mechanics. The danger is not to trivialize it, yet to get some feeling of how it fits into a larger perspective of all the ways nature could have worked.

 

[nnope]

It has everything to do with the concept, because it is about superposition and how superpositions involve indefiniteness. Entanglement is a type of superposition that involves indefiniteness among several particles. The point of the Zeno effect is that in order for a system to evolve unitarily from having one definite value of a discrete variable to another, it must move through indefinite states in between, which requires that the system go unmeasured for a time. Since there exists measurements that collapse an entangled system into a Bell state, this means that in order for an entangled system to evolve unitarily into a different Bell state, it must go unexposed to Bell measurements for a time, otherwise the initial entanglement will be locked in. The name stems from Zeno's logical argument that change is impossible, which now must be modified to say that change between definite states is impossible.

Then you need to know more about what he was saying. Parmenides was saying that if something (read "quantum state") exists now, then it must have always existed, and it could not cease to exist without having not existed before. This is precisely true of quantum states under unitary evolution, that's the no-cloning, no-deleting theorems in a nutshell. Of course Parmenides did not know quantum mechanics, the point is that he arrived at his conclusions using a form of logic that is apparently quite similar to the logical structure of quantum mechanics. And yes, he did that in 500 BC or something, that's the whole point-- this speaks to the issue of just how difficult to understand is the basic underlying structure of quantum mechanics, if it bears resemblance to one of the very first logical efforts that people tried to apply to the nature of reality. But yes, these kinds of insights might not be interesting to all people, I already knew that, the issue was more if the person asking the question and trying to struggle with the meaning of quantum mechanics would like to see it in that historical perspective or not.

Basically, you are saying that you can't use the ordinary line of logical thinking to explain QM it requires a different form of insight. That makes sense.

On a side note, 'Parmenides was saying that if something exists now, then it must have always existed, and it could not cease to exist without having not existed before.', the claim that if something exists now, means it must have always existed is flawed (pretty sure I didn't exist 100 yrs ago), only the latter part of that statement makes sense (unless I am dumb enough to completely misunderstand what is being said).

'this speaks to the issue of just how difficult to understand is the basic underlying structure of quantum mechanics', I guess you develop that understanding when you actually study QM. I am going to buy these books the guys have suggested above and try to develop my perception on the subject.

Thanks!

 

[Ken G]

On a side note, 'Parmenides was saying that if something exists now, then it must have always existed, and it could not cease to exist without having not existed before.', the claim that if something exists now, means it must have always existed is flawed (pretty sure I didn't exist 100 yrs ago), only the latter part of that statement makes sense (unless I am dumb enough to completely misunderstand what is being said).

That's what's so interesting about Parmenides' logic, it flies in the face of daily experience. But so does quantum mechanics! Parmenides was saying that the appearance of something that didn't exist before is a kind of illusion (so yes, either you are a kind of illusion, or the idea that you didn't exist 100 years ago is a kind of illusion). That really seems like nonsense, I agree with you. But then you learn quantum mechanics, and you discover that according to that theory, all closed systems evolve "unitarily", which yields a "no-cloning" theorem, and a "no-deleting" theorem. That means all quantum states are eternal, they neither appear nor disappear-- if you find a system in a quantum state, that state already existed somewhere else, and has been "teleported" to your system. So if you take this lesson literally, and you regard your identity as a kind of "quantum state" (never mind if that's a reasonable thing to do, people who regard quantum mechanics as a fundamental truth underlying all of classical reality have no choice but to regard that as true), then it is indeed an illusion that you came into being when you were born-- you merely acquired some pre-existing state of a system that you have no observational access to (that's the "illusion" part, like collapse of the wavefunction is a kind of illusion).

So it's eerie that there are these connections with a purely logical perspective on reality, and quantum mechanics, when we tend to regard the surprises of quantum mechanics as strange or even "illogical." We find it's the opposite of illogical-- it's just not like our experiences. So what does that mean? That's the tricky question that no one has really been able to wrestle with, and some prefer not to even ask the question.

 

[bhobba]

Basically, you are saying that you can't use the ordinary line of logical thinking to explain QM it requires a different form of insight. That makes sense.

Hmmmmm. Not so sure of that:
https://arxiv.org/pdf/quant-ph/0101012.pdf

But guys we seem to be getting off topic here - which is what entanglement is.

Can we stick to that. I did my best in my post - any queries?

Thanks
Bill

 

[nnope]

That's what's so interesting about Parmenides' logic, it flies in the face of daily experience. But so does quantum mechanics! Parmenides was saying that the appearance of something that didn't exist before is a kind of illusion (so yes, either you are a kind of illusion, or the idea that you didn't exist 100 years ago is a kind of illusion). That really seems like nonsense, I agree with you. But then you learn quantum mechanics, and you discover that according to that theory, all closed systems evolve "unitarily", which yields a "no-cloning" theorem, and a "no-deleting" theorem. That means all quantum states are eternal, they neither appear nor disappear-- if you find a system in a quantum state, that state already existed somewhere else, and has been "teleported" to your system. So if you take this lesson literally, and you regard your identity as a kind of "quantum state" (never mind if that's a reasonable thing to do, people who regard quantum mechanics as a fundamental truth underlying all of classical reality have no choice but to regard that as true), then it is indeed an illusion that you came into being when you were born-- you merely acquired some pre-existing state of a system that you have no observational access to (that's the "illusion" part, like collapse of the wavefunction is a kind of illusion).

So it's eerie that there are these connections with a purely logical perspective on reality, and quantum mechanics, when we tend to regard the surprises of quantum mechanics as strange or even "illogical." We find it's the opposite of illogical-- it's just not like our experiences. So what does that mean? That's the tricky question that no one has really been able to wrestle with, and some prefer not to even ask the question.

Oh, I get the point, it is basically like the recycling of matter. When I die I will return to the Earth and my matter will, over time, of course, reform into new life and objects. The matter that makes me has always been there, sure, but I didn't exist until I existed. In terms of QM, how does that all fit into the larger scheme of things? Surely, a system in a quantum state didn't exist in this universe before this universe came into existence, right? Or this where things clash with philosophy and we must draw the line for the sake of this forum?

 

[nnope]

Hmmmmm. Not so sure of that:
https://arxiv.org/pdf/quant-ph/0101012.pdf

But guys we seem to be getting off topic here - which is what entanglement is.

Can we stick to that. I did my best in my post - any queries?

Thanks
Bill

Sorry, you are right, ignore my last post.

 

[Ken G]

It's not really off topic, believe it or not, because one of the most practical applications of quantum entanglement is called "quantum teleportation," which is basically about how to send a signal that is a quantum state, using entanglement. Since the signal is a quantum state, it invokes the no-cloning theorem, which means there is no point in trying to eavesdrop on the quantum state-- if you intercept it, it will be detected, because you can't copy it and look it over. The eternal uniqueness of the quantum state is why it makes for secure communication.

 

[zonde]

It's not really off topic, believe it or not, because one of the most practical applications of quantum entanglement is called "quantum teleportation," which is basically about how to send a signal that is a quantum state, using entanglement. Since the signal is a quantum state, it invokes the no-cloning theorem, which means there is no point in trying to eavesdrop on the quantum state-- if you intercept it, it will be detected, because you can't copy it and look it over. The eternal uniqueness of the quantum state is why it makes for secure communication.

Your argument is interpretation dependent. Idea that everything can be explained only with unitary evolution and nothing else is interpretation of QM. And it is rather questionable if that is a valid interpretation as it involves a lot of handwaving.
It is clear that unitary evolution can not replicate arbitrary quantum state (I would say a state represented by state vector so not to fall in some semantics trap), but it is clear that known quantum state modulo quantum phase can be replicated as that is exactly what amplification process is doing. So I would say it's quantum phase that can't be replicated, but quantum phase is not an explanation of all the observations we make.

 

[zonde]

I don't have much of a background in quantum physics so be patient with my questions please. Basically I want to know how does entanglement actually work? Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement?

There is no answer to your question and strictly speaking there can't be answer to your question within science. Science just test different models and the one that lasts is assumed to give pretty good answer to the question how things work.
There might be answer to the question: What are the possible ways how entanglement might work?
My answer would be that quantum phase is conserved non-locally and when the first measurement is made on one entangled particle then the other particle, because of some resonance type link, supplies the phase change required by measurement induced change of the first particle. I have to warn that this is my own interpretation of entanglement phenomena but the the good thing is that it is rather direct interpretation of QM formalism.

 

[anothergol]

You have hit on the issue right there.

Even explaining superposition without math is impossible - and believe me I have tried.

A quantum object is in superposition all the time and in an infinite number of ways. What I suspect you are trying to say, and this is the other part of the issue, is superposition of what is being observed - which has a very specific meaning I can discuss - it leads to the so called preferred basis problem.

I was talking about superposition the way I understood it. That is a particle has a probability wave (which I'd call "area") of being in a position/state, in which it is all at once, until the observation (which I'd call interaction, and btw, that simple "observation" bad choice of a word has to be at the origin of most hippie or religious deviations in the sea of youtube videos about all this) collapses this and one position/state is "picked" at random.
Well that's how I understood it. Is it not that?
I wasn't talking about superposition of what's being observed, because I don't even know what it means.

I've seen videos about superposition, are they vulgarizing it so much that the explanation is then wrong, if it can't be explained without maths?
Btw I'm pretty sure most people get attracted to QM through -visual- explanations, whether it's the double slit experiment, or stuff about entanglement. Obviously because it's weird, but I don't see how it's wrong to try to make sense out of it. Afterall, there are dozens of interpretations of all this, perhaps they're all compatible with what's observed, but they don't all have the same meaning at all. Maybe it doesn't matter which interpretation is right (if any) because it's not going to change the reality and not going to affect experimental results, but I don't think QM should be restricted to those who want to make something practical out of it. I mean, it's the nature of reality that's discussed, that's something. Before getting interested in QM, I would have sworn that randomness didn't exist (from what I understood, Einstein did as well, so it can't be that stupid). Then I'm told that randomness does exist and is at the base of reality. It doesn't matter a single bit if that doesn't affect my "big scale reality" (in which randomness has always meant something else anyway). QM will never directly change my life, perhaps indirectly through devices that I use but that's something else. But questionning what reality is (and that's in no way religious, I'm an atheist), I don't think that's unimportant.
Cosmologists work on many things that don't really have any utility, other than trying to figure out the universe, or what is reality again (dark matter).
Another example, gravity not being a "real" force. I'm sure that doesn't matter a single bit in the maths, where it's treated as a real force, but hell, gravity is another really weird thing, nothing wrong trying to know what it is. Just knowing that it's a deformation of space/time won't change the maths but it changes your vision of reality.

I'm sure the OP's question was not "explain entanglement with maths" but rather "how is entanglement generally interpreted" btw.
Yeah perhaps there are dozens of explanations for it, but that's what's interesting.

 

[Ken G]

Your argument is interpretation dependent.

But quantum teleportation, and secure communication of quantum states, is certainly not interpretation dependent, nor is the application of the no-cloning theorem to that important application. As to whether or not change is possible, etc., yes, that is a way to look at quantum mechanics, but not necessarily a consequence of quantum mechanics. It's basically saying, let's try to understand quantum mechanics by taking it to its logical extreme, and when you do that, you return to a kind of thinking that was first introduced long before there was anything remotely resembling Newton's laws.

 

[bhobba]

I'm sure the OP's question was not "explain entanglement with maths" but rather "how is entanglement generally interpreted" btw. Yeah perhaps there are dozens of explanations for it, but that's what's interesting.

I don't even know where to start with what you said.

I put a lot into my explanation - its the best I can do.

But I guess I have to start somewhere. You said:
That is a particle has a probability wave (which I'd call "area") of being in a position/state, in which it is all at once, until the observation (which I'd call interaction, and btw, that simple "observation" bad choice of a word has to be at the origin of most hippie or religious deviations in the sea of youtube videos about all this) collapses this and one position/state is "picked" at random.

Then you said:
I wasn't talking about superposition of what's being observed, because I don't even know what it means.

The first is about observing position - you virtually stated it outright. Then say you weren't talking about observation in what being observed - not even understanding what that means.

See the contradiction?

If I could explain it without a smattering of math I would have, but I can't, in fact I don't think anyone can. All I used was just a little bit of math - nothing hard - what's so difficult about it?

You sometimes see posts is physics the territory or a map of the territory. In fact its a mathematical model. You can't explain a mathematical model without math - can't you see that? You can try and succeed some of the time - but with superposition the jig is up.

Thanks
Bill

 

[zonde]

But quantum teleportation, and secure communication of quantum states, is certainly not interpretation dependent, nor is the application of the no-cloning theorem to that important application.

Quantum cryptography is important application of QM. Never heard that quantum teleportation is an important application.
About your point being interpretation dependent, yes, probably I should have rather replied to your post #18.

As to whether or not change is possible, etc., yes, that is a way to look at quantum mechanics, but not necessarily a consequence of quantum mechanics. It's basically saying, let's try to understand quantum mechanics by taking it to its logical extreme, and when you do that, you return to a kind of thinking that was first introduced long before there was anything remotely resembling Newton's laws.

Simply take your approach and explain possible model for quantum entanglement. That's the topic of this thread.

 

[_PJ_]

Entanglement is the property that two or more entities share a particular (set of) relationship.

 

[star apple]

Entanglement is the property that two or more entities share a particular (set of) relationship.

Assume Alice detector could detect vertical up or down, or horizontal left or right… an entangled pair was sent to both Alice and Bob, if Alice detected it as vertical down.. would Bob detect it as horizontal left or right? Or is it always vertical?

If vertical is dot and horizontal is dash.. can’t they send morse code.. Alice can use vertical and horizontal to form messages and Bob can receive it horizontal or vertical and decode the sentences.

All right. Where has I got it wrong?

 

[zonde]

Assume Alice detector could detect vertical up or down, or horizontal left or right… an entangled pair was sent to both Alice and Bob, if Alice detected it as vertical down.. would Bob detect it as horizontal left or right? Or is it always vertical?

Polarization entangled photons are analyzed using polarizers. You place a polarizer at certain angle and photon either passes through it or it doesn't.

 

[Ken G]

Quantum cryptography is important application of QM. Never heard that quantum teleportation is an important application.

Quantum cryptography is an application of quantum teleportation, you simply teleport the quantum key so it can't be intercepted. The teleportation is the important step.

Simply take your approach and explain possible model for quantum entanglement. That's the topic of this thread.

The topic is not a "model" for quantum entanglement, quantum entanglement is already a model. The effort is in understanding the larger implications of the model. To that end, quantum teleportation is significant. The idea is, you entangle two particles, transport one a great distance, and use the entanglement as a kind of channel through which to teleport a quantum state. The reason this is relevant to secure communication is the no-cloning theorem, which says a quantum teleported signal cannot be intercepted without detection, because the signal can only go to one destination, to intercept it without detection would require cloning of the signal (which is trivial for classical signals).

So the relevance to understanding quantum entanglement is that we are getting a window into a very different world, one where states are never created nor destroyed, they are merely teleported from place to place. One can even regard the simple translation of a system from point A to point B as a teleportation involving entangled virtual particles, giving insight as to why systems tend to retain their integrity as they move across space. From this perspective, it is the classical world, where we seem to create and destroy states willy nilly, that is "weird," and it emerges from the complexity of combining ghastly numbers of logically simple quantum systems. The logical simplicity of the quantum systems is reflected in the no-cloning, no-deleting theorems, is manifested by entanglement, and seems very close indeed to what Parmenides intuited some 2500 years ago.

 

[star apple]

Polarization entangled photons are analyzed using polarizers. You place a polarizer at certain angle and photon either passes through it or it doesn't.

If you use a Stern-Gerlach devices on the ends instead of Polarizers.. there would be no correlations? And it's due to... ?

 

[zonde]

Quantum cryptography is an application of quantum teleportation, you simply teleport the quantum key so it can't be intercepted. The teleportation is the important step.

In quantum cryptography the information sent is classical. The aim is for both parties to share the same secret (classical) code. There is no such thing as "quantum key". The "quantum" in quantum key distribution does not describe the key but the method by which the key is sent.

The topic is not a "model" for quantum entanglement, quantum entanglement is already a model. The effort is in understanding the larger implications of the model.

Where did you get this? Let me quote OP:

Basically I want to know how does entanglement actually work? Is information being transferred faster than we can detect it or is there some invisible link between particles that causes the phenomenon we call entanglement?

OP asks about mechanism (model) behind particular phenomena (that goes by the name "entanglement").

 

[Ken G]

You can't explain a mathematical model without math - can't you see that? You can try and succeed some of the time - but with superposition the jig is up.

That may be pessimistic-- I agree that any plain English description is only going to recast what can be said much more succinctly mathematically, but any computer program can be said more succinctly in machine language-- we still use programming languages! So I think it's worth a try to capture the flavor of the mathematics of superposition in plain English.

Superposition essentially takes a situation we are all well acquainted with, which is having limited information about some situation such that we have to "entertain," if you will, multiple possibilities in our minds. I like the analogy of playing a card game, and assessing the probabilities that the opponents have various hands. But we are very clear this mixture is only in our minds-- the actual reality is one way or another. Superposition elevates that state of affairs into something much closer to the actual reality. Interestingly, there is no demonstrable difference in the classical realm, it's just that elevating our uncertainty into a kind of personal reality never seemed to have much point. But it has a point in quantum mechanics, because the multiple possibilities can interfere with each other and affect what you regard as the probable outcomes. We are used to having a separate probability for each of the potential states of the system, but in superposition, the potential different states combine into a whole new state that alters those probabilities.

When we include superposition of states of two particles, it ushers in entanglement. Entanglement allows the knowledge you have about the system (and the lack thereof, called the "indeterminacy") to be expressed in ways that refer to both particles. For example, if you have two coins that can be either heads (H) or tails (T), we could express what we know and don't know classically like "we don't know what either coin says but they are the same". If we elevate that state of affairs to the actual state of the system, and not just what we know and don't know, then not knowing what either coin is becomes indeterminacy in the H or T, but knowing they are the same means we have a superposition of HH and TT, a state that embodies the aspects of both HH and TT (i.e., that they are the same), without specifying H or T. That's a form of entanglement, because not only can we only state what we know by referring to both coins, but the two possibilities alter the probabilities beyond just what HH or TT alone would do (and that's called "interference").

Quantum teleportation means that if you have a superposition of HH and TT, you can still widely separate the two "quantum coins," and use the superposition as a kind of conduit for passing a quantum state from the vicinity of one coin to the other. That's a particular version of the interference between the HH and TT, and it allows secure communication of a bit via the teleportation of the state of a third "quantum coin."

 

[Ken G]

In quantum cryptography the information sent is classical.

Of course, all information is classical or we couldn't use it. The method of transport of the classical information is where the teleportation comes in. There's always teleportation there.

OP asks about mechanism (model) behind particular phenomena (that goes by the name "entanglement").

I didn't see the word "mechanism," did you? I saw "how does it work." That's not asking for a model, it's asking for an explanation of a model.

 

[zonde]

If you use a Stern-Gerlach devices on the ends instead of Polarizers.. there would be no correlations?

I would suggest you to try to look at some layman level descriptions of quantum entanglement if you are interested in this topic.You can try these links:
http://www.drchinese.com/Bells_Theorem.htm
http://quantumtantra.com/bell2.html
http://www.theory.caltech.edu/classes/ph125a/istmt.pdf
So if you will refer in your questions to things found in these links you will get better responses.
If you are particularly concerned about faster than light communication using entanglement you can try forum search with keyword FTL and entanglement.

 

[_PJ_]

Assume Alice detector could detect vertical up or down, or horizontal left or right… an entangled pair was sent to both Alice and Bob, if Alice detected it as vertical down.. would Bob detect it as horizontal left or right? Or is it always vertical?

If vertical is dot and horizontal is dash.. can’t they send morse code.. Alice can use vertical and horizontal to form messages and Bob can receive it horizontal or vertical and decode the sentences.

All right. Where has I got it wrong?

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

 

[nnope]

I would suggest you to try to look at some layman level descriptions of quantum entanglement if you are interested in this topic.You can try these links:
http://www.drchinese.com/Bells_Theorem.htm
http://quantumtantra.com/bell2.html
http://www.theory.caltech.edu/classes/ph125a/istmt.pdf
So if you will refer in your questions to things found in these links you will get better responses.
If you are particularly concerned about faster than light communication using entanglement you can try forum search with keyword FTL and entanglement.

Whats up with that quantum tantra link, by far the wierdest stuff I've read on the net since alien invasion conspiracies.
http://quantumtantra.com/interview.html
Is this a reliable link? The name itself (referncing hindu magical texts) is as much a joke as the contents on telepathy.

 

[Ken G]

You should probably delete it, it's inappropriate and not particularly useful.

 

[zonde]

Whats up with that quantum tantra link, by far the wierdest stuff I've read on the net since alien invasion conspiracies.
http://quantumtantra.com/interview.html
Is this a reliable link? The name itself (referncing hindu magical texts) is as much a joke as the contents on telepathy.

The page is http://quantumtantra.com/bell2.html. I probably should have added some disclaimer that only this page is about physics but the site itself is not recomended.

 

[anothergol]

Then you said:
I wasn't talking about superposition of what's being observed, because I don't even know what it means.

The first is about observing position - you virtually stated it outright. Then say you weren't talking about observation in what being observed - not even understanding what that means.

See the contradiction?

I obviously can't tell if I'm talking about something I don't understand, but the way I understood things, superposition is when a particle isn't being observed. Thus superposition of what is being observed (as you first wrote it), I don't understand what it means, but it cannot be what I was talking of.

I mean come on, I've seen a lot of movies about the double slit experiment, Schrodinger's cat, and entanglement. I thought I at least got these basic things right. But none of them used equations to explain these.
A particle's position & its spin are different things, but aren't both in superpositions until observed?

The only thing here that really seems to require maths btw, is Bell's theorem. Which is key, because when you don't understand it (& I don't), you have to take it for granted (which I don't like), while it's that important thing that proves that entanglement is real.
As it's often explained, that it's not like a pair of gloves in 2 boxes, whether it's a left or right hand in each box isn't decided at the beginning, it's both left & right until observed, & when observed & collapsed to a left or right hand at pure random, then the entangled glove will be the other hand. But yes, that one thing that proves it wasn't left or right from the beginning, I can imagine it can't be explained in simple ways.
..or is it another thing I misunderstood?
And back to teleportation (of information, faster than light), what makes it impossible is the fact that the collapse of the LR hand into a L or R, is purely random, right? Thus the correlation can only be done afterwards, by normal communication.

 

[star apple]

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

Such masterpiece explanation! Thanks!

 

[Ken G]

I obviously can't tell if I'm talking about something I don't understand, but the way I understood things, superposition is when a particle isn't being observed

That's not necessarily true, because if you have a superposition in regard to some observable, you can do an observation of a complementary variable without breaking the superposition in the original observable. So that might not be the best way to think about superposition. I think the best way to think about it is via the concept of "indeteminate" values of some observable-- whenever an observable has an "indeterminate" value in some state, then that state is a superposition with respect to that observable. But it does not need to be a superposition in regard to some other observable, it can have a definite value of something else. So there is no distinction between a "superposition state" and an "observed state"-- any time you observe anything and thereby give that observable a definite value, there will be other complementary observables that will be indeterminate and hence you have put the system into a superposition state with respect to those other observables.

In this light, we should say that entanglement is an example of a superposition with regard to the kinds of variables or attributes of systems that we normally regard as definite. It doesn't mean the entangled state doesn't have definite values for other observables! For example, the ground state of hydrogen is one in which the spin direction of the proton and electron are completely unknown, but it is known that they are opposite each other, whatever they are. So that's a prime example of the kind of information that is determined in entangled states-- mutual properties are determined, individual properties are indeterminate. So we have an observed state in regard to mutual properties (that kind of state can be observed by a "Bell measurement"), but a superposition state in regard to individual properties.

A particle's position & its spin are different things, but aren't both in superpositions until observed?

I'm pointing out they can be in superpositions after being observed as well. For example, after you observe a position, the momentum is in a superposition, and after you observe the spin in the up/down direction, the spin in the left/right direction is in a superposition.

The only thing here that really seems to require maths btw, is Bell's theorem.

And frankly, I think quantum teleportation is a better way to understand what is weird about entanglement than Bell's theorem. Bell's theorem is important for proving the untenability of local realism, but it generally doesn't come with a large "aha" feeling!

As it's often explained, that it's not like a pair of gloves in 2 boxes, whether it's a left or right hand in each box isn't decided at the beginning, it's both left & right until observed, & when observed & collapsed to a left or right hand at pure random, then the entangled glove will be the other hand. But yes, that one thing that proves it wasn't left or right from the beginning, I can imagine it can't be explained in simple ways.

We can try. The reason the gloves don't work is there is no "second aspect" to test (like the momentum in my position example, or the spin in a different direction than up/down), gloves have only individual properties not mutual ones. What is weird about entanglement is you can prepare two particles such that their spin components in all directions is indeterminate, but it is determined that they have the mutual property of being opposite each other. So there the only determined properties are mutual ones! Try that with gloves.

And back to teleportation (of information, faster than light), what makes it impossible is the fact that the collapse of the LR hand into a L or R, is purely random, right? Thus the correlation can only be done afterwards, by normal communication.

Right.

 

[anothergol]

mmmh.. maybe I'm misunderstanding what you wrote, but when you say "undeterminate", it sounds like the state/spin/whatever is only one value, but it's not known (yet).
Isn't it BOTH?

I mean, in the double slit experiment, surely the single particle that's interacting with itself, passed through both slits, isn't that what superposition is, all the possibilities being real, not that there is one and it's unknown?

You said: "The reason the gloves don't work is there is no "second aspect" to test (like the momentum in my position example)"
Which reminds me that I still don't fully understand what the uncertainity principle is really about.
I mean, from these 2 videos, for ex


I come from the audio world, and the analogy I'd make, is that the lower the frequency of a sinewave, the less precisely its "position" can be determined, because a low frequency needs enough time to even "exist". Like, a fourrier transform in a short window wouldn't detect a frequency for which the phase is larger than half of that window. (which isn't weird in any way)
But.. if that analogy is true, where is "randomness" involved here?
& that probability wave function for the position of the particle, does it mean
a) the particle is everywhere it is probable to be, until an interaction that forces it to pick?
b) the particle is somewhere it is probable to be, and interaction will only tell one position at a given time? (then I don't understand how the particle interacts with itself in the double slit experiment)
c) something else?You wrote "For example, the ground state of hydrogen is one in which the spin direction of the proton and electron are completely unknown, but it is known that they are opposite each other, whatever they are."
..so the spin direction is unknown, but it is definite? It's not both at once?
The way I understood it, the spin was both, and the observation forced it to be one, from that you can conclude that the spin of its entangled particle is the opposite. But "both" and "unknown" seems pretty different.
Or if you're saying that from the moment one thing (position) becomes known, its linked property (speed) then becomes blurry, ok, byt even this doesn't claim that whichever is blurry is "all possibilities at once", only that it's rough (but not random, and not "every possibility at once"). Well I'm more confused now than when I asked my questions.

Edit: there's this video that confused me the same way, and that was over 6 months ago, that says for how long I've been trying to understand this:
The audio-analogy I made is pretty much 1., and it says it's wrong... ok.
But 3. seems to be a combination of 1, with the probability wave adding the random factor to that position/speed link, resulting in "clear or blurry, but always random".
But I thought that the superposition was "the particle has lots of positions" ALONE.
And if it's not that, I'm even more confused about what makes the behavior of the particle -change- after interaction, in the double slit experiment.

 

[star apple]

Alice is measuring VERTICAL Axis
Bob is measuring HORIZONTAL.

For the sake of argument/completeness let's assume that there are only two dimensions and that whatever entangled "things" are being measured in a way that what Alice considers VERTICAL and HORIZONTAL are exactly identical to that which Bob does too. Bob and Alice or their detectors are exactly aligned relative to each other - obviously "Horizontal" and "Vertical" are orthogonal.

Alice would have an equal probability, measuring ONLY the vertical - of detecting UP or DOWN. However her result would ALWAYS show either UP/DOWN
Bob, measuring ONLY the horizontal would have equal probability of detecting LEFT or RIGHT. However his result would ALWAYS show either LEFT/RIGHT
This would be true regardless of entanglement.

Assume for a moment that there is no Bob. He nor any entanglement exists. There is only Alice and her detector and the thing she is measuring.
Alice has a CHOICE in measuring HORIZONTAL or VERTICAL The choice represents a fork in a probability tree. We assume there is equal probability in her making either choice and that she will with absolute certainty choose to measure H or to measure V there is no other option. She cannot fall asleep, forget or go do something else. She MUST make a choice, must choose either H or V.
Depending on what she cxhooses, she will then measure:

If H
U or D

If V
L or R

There are no other possibilities. No other results nor outcomes exist.

This can all be represented with the following (Although the symbols represent operators and are in reality conjugated)

Alice chooses Horizontal or Vertical. There are no other options

IF Alice chooses H, the result can only be L or R
<V|U>=0
<V|D>=0
<H|L> + <H|R> = 1

OR
Alice chooses V and result must be either U or D
<H|U>=0
<H|R>=0
<V|U> + <V|D> = 1

Since the choice between V or H represents operation on states still part of the system, these can be combined, however, now the initial choice is only 50% of the entire probability contributions, but represents exactly 50%

<V|U> + <V|D> = 0.5 = <H|L> + <H|R><V|U> + <V|D> + <H|L> + <H|R> = 1
This encapsulates that there are only those possibilities. There is no possibility for, say choosing Horizontal and measuring UP.

Since we have established (for example simplicity) that Alice's chioce in measuring H or V is utterly equal, and that whether U/D or L/R within each choice are also completely equal :

<V|U> = <V|D> = <H|L> = <H|R>

and
<V| = <H|

|U> = |D> = |L> |R>

Experimentally, the results would agree here, that were the scene repeated, each particular result would occur on average 25 times in every 100 repeats.

__

Now, let's imagine that Alice "prepares" the entity before measurement. For the sake of simplicity the "preparation" only applies to the VERTICAL axis and it is prepared so that the state for this vertical axis is UP
After such "preparation", Alice again chooses what axis to measure and makes the measurement.
If Alice chooses VERTICAL, the result will ALWAYS be U
If Alice chooses HORIZONTAL, the result is ALWAYS L or R

There is STILL perfectly equal probability of L/R if she chooses H and Alice's decision to choose H or V is unaffected.

<V|D> = 0

The statement made earlier
<V|U> + <V|D> + <H|L> + <H|R> = 1
still holds. Although <V|D> can safely be omitted as it is now zero probability. (Just as we are not including operators for the probabity amplitudes that Alice might spontaneously turn into a banana - it's not going to happen, so there's no need to include it)

<V|U> + <H|L> + <H|R> = 1
And
<H|L> = <H|R> still, so this holds as before. Given that Alice still chooses perfectly equally between H and V, though,
<V|U> + <V|D> = 0.5 = <H|L> + <H|R>
also still holds.
we can omit <V|D> as mentioned, and see that
<V|U> = 0.5 = <H|L> + <H|R>

So the effect of the preparation does not affect the HORIZONTAL measurement (should Alice choose to make it) in any way whatsoever. Instead, it is only the VERTICAL that is affected.

Now forget the preparation and instead bring in Bob. Also we will eradicate any choice for Alice. She will ONLY measure VERTICAL. Bob will only measure Horizontal.
There is no <A(l)| or <A(r)| nor is there a <B(u)| or |B(d)> they simply do not exist at all.

However Bob WILL make A MEASUREMENT (either B(l) or B(r) only- no other possibility) and Alice will make A MEASUREMENT(either A(u) or A(d) only- no other possibility)

<A(u)|A(d)> + <B(l)|B(r)> = 1
<A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(l)> + <A(d)|B(r)> = 1

The effect of entanglement will cause whatever Alice measures (A(u) or A(d) that Bob's paired entity would, if measured in that axis, result in the opposite to that which Alice measured. That is, if Bob were ALSO to measure in the vertical, and Alice measured U then Bob would measure D. If Alice measured D then Bob would measure U
If Alice broke with tradition and measured Horizontally, then if her result was L and Bob also measured horizontally, Bob would obtain a result of R. HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever.
50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.

About these statements: “HOwever if Alice measured her entangled particle Vertically and Bob measured his entangled particle Horizontally, there would be no measurable detectable change whatsoever. 50% of the time Alice would detect U and 50% she would detect down. 50% of the time Bob would detect L and 50% of the time he would detect R just as if the experimentors, the particles, the detectors etc. were utterly isolated.”

Can you cite experiments that prove this? What if after Alice measured her entangled particle vertical and Bob tried to measure his particles horizontal, Bob won’t get any results (null results meaning neither left or right). Only if he measured vertical would he get result? Or maybe you were saying when Bob tried to measure vertical. It broke the entanglement?

Thanks again.

In the entangled scenario, if either could choose to measure either

<A(u)|B(d)> + <A(u)|B(l)> + <A(u)|B(r)> + <A(d)|B(u)> + <A(d)|B(l)> + <A(d)|B(r)> + <A(l)|B(u)> + <A(l)|B(d)> + <A(l)|B(r)> + <A(r)|B(u)> + <A(r)|B(d)> + <A(r)|B(l)> = 1

The probabilities are affected thus:

<A(u)|B(d)> = <A(d)|B(u)> = <A(l)|B(r)> = <A(r)|B(l)>
And
<A(d)|B(l)> = <A(d)|B(r)> = <A(l)|B(u)> = <A(l)|B(d)> = <A(r)|B(u)> = <A(r)|B(d)>

But because of the omission of
<A(u)|B(u)> + <A(d)|B(d)> + <A(l)|B(r)>
which would be included and contribute to the overall unity were there no entanglement, the individual probabilities as experienced by the individual experimenters are not noticeable unless the experimenters specifically compare notes.
Note that Alice is not changing the particle or encoding it in any way. It is either UP or it is DOWN (or more accurately, superposited UPDOWN, and measuring it will reveal which - measuring is in fact the activity of resolving this superposition into a real distinct state) - she cannot know beforehand which it will be, unless she PREPARES it as described above. However, preparation would "destroy the entanglement", Alice's particle would definitely be in whatever state she prepares it, but Bob would measure a now disentangled particle where the state would be again, determined through his measurement.

This is why it's not possible (regardless of how you encode the information) to transmit information using entanglement.

 

[bhobba]

I mean come on, I've seen a lot of movies about the double slit experiment, Schrodinger's cat, and entanglement. I thought I at least got these basic things right. But none of them used equations to explain these.

That's the problem.

They do not tell the truth. I will repeat it - they do not tell the truth.

There are very few books at the beginner level that do - I gave links to Susskinds books that do - I will do it again:
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465062903/?tag=pfamazon01-20

If you read them and have your thinking cap on, plus take your time (it's not a race) you will understand exactly what's going on including a much expanded version of what I wrote about entanglement before - plus the very important concept of how QM all by itself explains 'collapse' for all practical purposes, and exactly what the issue is with the explanation. Some say it explains it, and others saying - no - and other views as well - its actually a bit subtle - but after reading those books it will be a lot clearer.

So the first thing is forget whatever you have read - forget it - I will now tell you the truth - but it involves math - sorry - its just the way it is. I will make the math as easy as I can but there is no way out here - its the only way.

Ok to start with let's suppose a quantum system is described by a real number I will call its state - it never is but this is just for the purposes of explanation. Suppose its described by the number 6. 6 = 3+3. In quantum parlance 6 is said to be a superposition of 3 and 3. But 6 = 4+2 so 6 is also a superposition of 4 and 2. In fact if 6 = a+b then 6 is a superposition of a and b. That's all it is - its simple really. But note given any state a it can be broken down in innumerable ways so if a state, a = b+c, then a is said to be in a superposition of b and c but it is also a superposition of many many other states. This is what I mean when I say saying a quantum system is in superposition is pretty meaningless because any state is a superposition of many other states in many many different ways.

Now you have the general idea you ready for one of the fundamental concepts of QM, in fact its the foundational concept Dirac built his version of QM on, called the principle of superposition. Instead of real numbers we will now write states using a new notation |a>. |a> is called a ket and its simply fancy notation for the system is in state a. What a is don't worry about - its simply an abstract symbol for the state of the system - I haven't even told you what a state is - and neither did Dirac - its simply symbolic. Now for the statement of the principle of superposition - if a system can be in state |a> and state |b> then it can be in state |c> = d*|a> +e*|b> where d and e are any two complex numbers. If you don't know what a complex number is don't worry about it - I won't be using the concept - but if you want to understand QM at a reasonable level you should learn what they are. Now we have extended a bit what states are - we know you can multiply them by complex numbers and you can add them together. Its not a great deal to know - but basically it's what they are - strange hey - its just a simple mathematical concept - technically its called a vector space - but that's just a technical mathematical name for the principle of superposition.

OK - how does this fit in with wave-functions? Suppose I have states |xi> and these states have the property that if you observe the position of a system in |xi> then it always always will be in position xi. Ok let's apply the principle of superposition to these states of definite position so |a> = c1*|x1> + c2*|x2> ++++ cn*|xn> or using the summation notation |a> = ∑ ci*|xi>. Here is where we now apply another principle of QM called the Born Rule. This only applies if the ci are what's called normalized without going into what that is, but again its something you should eventually come to grips with. What the Born Rule says is if you observe state |a> for position then the probability of getting xi as the answer is |ci|^2. Now suppose the xi is so fine it can be considered as not discreet, but as a continuous real number x - the actual position - physicists say - suppose it goes to a continuum. Then the ci also are continuous and we have a function dependent on x, c(x). c(x) is called the wave-function. It has the following simple property - if Δx is small when you observe a system for position the probability for result to lye between x and x + Δx is Δx*|c(x)|^2.

Ok you now know what a superposition is and a wave-function is. Technically a wave-function is the coefficients of expanding a state in states of definite position. Now for some technobabble - states of definite position are called eigenfunctions of position. States of definite momentum are called eigenfunctions of momentum. States of definite spin are called eigenfunctions of spin. In fact states of a definite anything are called eigenfunctions of what that thing is.

So when speaking of superposition its rather vacuous unless you also say another thing - what is it a superposition of ie what the eigenfunctions it is a superposition of. For a wave-function it is superposition's of eigenfunctions of position - but there are many other things it can be a superposition of eg momentum or spin.

This is a lot to take in. Once you have understood it read the reply I previously gave on what entanglement is and see if things are now clearer.

If it isn't then I don't know any other way of explaining it. Remember physics is a mathematical model - its not a visual model, its not a philosophical dielectric - it's a mathematical model. Mathematics is unavoidable. Those that try to avoid it actually end up instead confusing people and to be blunt telling downright lies, like for example a particle is in many positions at once or takes all paths simultaneously. It doesn't - they are simply trying to get across in pictorial terms what's going on - but what they really end up doing is telling if not downright lies, at best half truths. Now I don't want to be too hard on those that write such populations - if they didn't do it then they would have to say something like what I said - in fact its what Susskind does. This turns most people off, so they resort to what they do and we have many misconceptions amongst beginners.

Also once you grasp it I can very elegantly explain the double slit:
https://arxiv.org/abs/quant-ph/0703126

You probably won't understand the above off the cuff, but give it a look and I will 'decode' it for you - but only if you get what I have said before.

Thanks
Bill

 

[anothergol]

I've already tried to make sense of complex numbers to be honest, because I needed them for my work (FFT's outputting complex numbers), but never really manage to. All I understood is that it was a purely mathematical trick to achieve things.

And I course don't understand (yet) what you just explained, but so you're saying that what's explained in all those videos, isn't a valid interpretation of what you just wrote?
Are you saying that in the double slit experiment, saying "the particle takes all paths simultaneously" is wrong, or rather "that's not precisely what the maths say, it's one possible interpretation, but not necessarily the truth"?

 

[_PJ_]

What if after Alice measured her entangled particle vertical and Bob tried to measure his particles horizontal, Bob won’t get any results (null results meaning neither left or right). Only if he measured vertical would he get result? Or maybe you were saying when Bob tried to measure vertical. It broke the entanglement? Thanks again.

Alice measuring spin on axis V will always get a result of either U or D
Bob measuring spin on axis H will always get a result of either L or R

_
Do not confuse A & B's measurements or effects of entanglement with with the idea that if you prepare an object at, say 45 degrees (partway between, say U and R) and then measure V, the result will be U with greater probability than D
If measured H, the result will have greater probability of R than L

I've already tried to make sense of complex numbers to be honest, because I needed them for my work (FFT's outputting complex numbers), but never really manage to. All I understood is that it was a purely mathematical trick to achieve things.

And I course don't understand (yet) what you just explained, but so you're saying that what's explained in all those videos, isn't a valid interpretation of what you just wrote?
Are you saying that in the double slit experiment, saying "the particle takes all paths simultaneously" is wrong, or rather "that's not precisely what the maths say, it's one possible interpretation, but not necessarily the truth"?

QM operations are complex. That's the nature of the beast.
The simplification that a 'aparticle takes all paths simultaneously' is possibly best understood (at least for me) in the underlying mathematics from the roots in Fourier Transformations as with signal processing.

If you hear a piano note, it can be represented as a soundwave of a specific frequency - this would be considered a pure wave.
However, Fourier analysis exemplifies (and actually, is how MP3 and other audio techologies allow for sounds to be encoded digitally) that even an apparent pure wave which has an amplitude at a given point and cycles according to the particular phase - could be represented by the combination of other frequencies of waves (which through interference can cancel and reinforce ) at particular amplitudes and phases - the contributions made to the outcome varies for each of these waves and is called a Fourier coefficient. Whilst some coefficients may be tiny and others less trivial, that non-zero contributions are made means that increasing the range of the frequencies and phases that contribute always increases the accuracy to which the ensemble wave matches the pure tone. This reaches a limit at infinity - that is, after the infinite range of waves are summed over (by amounts governed by their respective Fourier coefficients) the result exactly matches the pure tone.

It's a lot more simple in concept than trying to describe it in words - so here's a more abstract generalisation - Imagine a piano with an infinite number of keys and the infinite number of Beethoven's playing that piano press each key with varying strengths so some are louder, some are softer and with ever so slightly different timing - although you may expect the result to be a cacophonic noise, the interference of the soundwaves results in a perfect middle C

This is absolutely true of SP and the mathematics employed is well understood, and it is this same mathematics that underpins much of quantum process - which is why so many consider that it is a strange and counter-intuitive worlds - the mathematics of infinite and periodic phenomena describe the actions of real, assumed "non-periodic" physics. The uncertainty principle is also encapsulated within the same mathematics when considering the description of a particle at a given position, there is an equal and non-zero probability for every possible momentum state.
So the notion of a "particle" choosing every single trajectory" is not strictly accurate, but the mathematics that describe and predict a resulting trajectory from the given inputs are the same as the mathematics that describe phenomena where wave interference cancels out to reveal a single result - The PROBLEM, really, is with our intuition and assumptions as to what is meant by "a particle" or that such an entity moves from A to B.

 

[star apple]

Alice measuring spin on axis V will always get a result of either U or D
Bob measuring spin on axis H will always get a result of either L or R

_
Do not confuse A & B's measurements or effects of entanglement with with the idea that if you prepare an object at, say 45 degrees (partway between, say U and R) and then measure V, the result will be U with greater probability than D
If measured H, the result will have greater probability of R than L

So what’s where they got the words Alice and Bob.. from the letter A and B. Didn’t know that before.

Even if Alice measured in the vertical, the reason Bob could still measure the horizontal was due to Bob collapsing the wave function or breaking the entanglement?