Can someone explain, simply, hidden nonlocality/locality? EPR Paradox?

[SeventhSigma]

So I understand local realism (the moon is there when we aren't seeing it) and the notion that Bell's Theorem says that if local realism is true, then we could perform experiments that show observation is independent of reality and that we should expect certain probabilities to arise.

But we find that instead the probabilities are more in line with the notion of observation having some impact on the reality of the state and that the correlation between observation and reality is nonzero.

My questions:

1. So what does it mean to say that this rules out *local* hidden variable theories versus, say, a nonlocal one?

2. I assumed EPR Paradox was meant to show that if we had two entangled particles we could theoretically measure one property of one particle and one property of the other particle where these properties are canonically conjugate and somehow violate HUP -- but my understanding on this is shaky. Elaboration?

3. If local hidden variables are effectively ruled out, does this mean that nonlocal hidden variables are the only way to do? Does this mean we have to violate special relativity by assuming superluminal communication?

I feel like there are glaring contradictions here. I have to toss something out the window and I'm not sure what.

 

[DrChinese]

So I understand local realism (the moon is there when we aren't seeing it) and the notion that Bell's Theorem says that if local realism is true, then we could perform experiments that show observation is independent of reality and that we should expect certain probabilities to arise.

But we find that instead the probabilities are more in line with the notion of observation having some impact on the reality of the state and that the correlation between observation and reality is nonzero.

My questions:

1. So what does it mean to say that this rules out *local* hidden variable theories versus, say, a nonlocal one?

2. I assumed EPR Paradox was meant to show that if we had two entangled particles we could theoretically measure one property of one particle and one property of the other particle where these properties are canonically conjugate and somehow violate HUP -- but my understanding on this is shaky. Elaboration?

3. If local hidden variables are effectively ruled out, does this mean that nonlocal hidden variables are the only way to do? Does this mean we have to violate special relativity by assuming superluminal communication?

I feel like there are glaring contradictions here. I have to toss something out the window and I'm not sure what.

Good questions all!

1/3. It means you can reject hidden variables or reject locality. So you could logically advocate nonlocal hidden variable interpretations (such as Bohmian types) OR local non-realistic interpretations (such as Many Worlds Interpretation=MWI). Or you can skip the interpretation entirely and stick with the quantum formalism ("shut up and calculate").

2. You are correct, EPR thought they had beat the HUP. But now we know that doesn't actually happen as they envisioned, as experiments clearly show.

 

[SeventhSigma]

Thanks for the quick reply, but I admit I am still confused.

What would it take to falsify something like MWI or Bohmian mechanics? I feel like both of these invoke explanations for things that we can't test. "Well, this COULD explain how it works, but we don't really know why this is so but we'll say it's feasible ad-hoc."

I still struggle with the concept of entanglement. I've always heard it described as, for instance, putting a red ball in one box, a blue ball in the other, and then separating them by large distances and then making an observation. Similarly, it's like if I held up a quarter between us and then I looked at it. By knowing one part of the system, I know the other even before I measure it.

However, I'm confused by this. When you say reject HV or locality, it seems like entanglement demands me to accept realism because the states are determined before observation, whereas Bell's Theorem shows us why we have to reject local realism. I have no idea where I am going wrong, here.

If I go with Bohmian mechanics, am I basically saying "Sure, realism is actually true, but the probability differences we see that violate Bell's Theorem are due to nonlocal effects i.e. something that transmits the quantum effect at a speed greater than c."

But if I am going with MWI, and realism is "false," how does MWI explain the probability difference?

Is it accurate to say that entanglement and realism imply superluminal communication? If this is so, does it imply that it's sending messages back in time? Time dilation shows us that t=T/Gamma such that if v>c then we have the square root of a negative number. What on Earth does this mean?

 

[SeventhSigma]

Let me rephrase:

The experiments basically show that independence tests fail. If states were pre-determined, we'd expect certain distributions to occur which in practice do not.

So we explain the results either by holding reality constant or by holding hidden influences constant.

If reality/locality is false, then the states are able to communicate to each other what states they took on instantly, right? In other words, it's like putting a potentially-red-potentially-blue ball in one box and an identical ball in the other, separate them, observe one, and note that this potential ball "becomes" either red or blue and somehow communicates to the other ball that it needs to change its potential to the opposite color.

If reality/locality is true, then the states are predetermined like the sides of a die and there is just some other variable influence we are failing to take into account. For instance, in the example of a human rolling a die, maybe I am failing to account for the randomness because I am neglecting the initial state of the die, the force I throw it, the distance it drops, the rotations it undergoes, etc.

I don't understand how to reconcile these differences because I feel like there are contradictions either way. I can either say potential states communicate instantly to materialize into a real, observable state and violate the notion that information is traveling faster than c (which would be fine if c wasn't so well-established already as an upper limit. Does entanglement in this case cast doubt on c?), or I can say that there's some sort of underlying influence I am failing to take into account.

Why do most people in QM opt for the notion that local realism is false? What exactly rules out the notion of variable influence? I understand that Bell's Theorem shows that the independence tests fail, but why does this rule out *local* variables as opposed to nonlocal? What would the difference between local and nonlocal be in this context? In other words, what is the link between "The independence tests fail" and "Therefore, all local hidden variables are ruled impossible"?

Sorry for all the questions but I've struggled with this for a long time and I'm frustrated that I feel no closer to really understanding QM.

 

[DrChinese]

1. What would it take to falsify something like MWI or Bohmian mechanics? I feel like both of these invoke explanations for things that we can't test. "Well, this COULD explain how it works, but we don't really know why this is so but we'll say it's feasible ad-hoc."

2. I still struggle with the concept of entanglement. I've always heard it described as, for instance, putting a red ball in one box, a blue ball in the other, and then separating them by large distances and then making an observation. Similarly, it's like if I held up a quarter between us and then I looked at it. By knowing one part of the system, I know the other even before I measure it.

3. However, I'm confused by this. When you say reject HV or locality, it seems like entanglement demands me to accept realism because the states are determined before observation, whereas Bell's Theorem shows us why we have to reject local realism. I have no idea where I am going wrong, here.

...

4. Is it accurate to say that entanglement and realism imply superluminal communication? If this is so, does it imply that it's sending messages back in time? Time dilation shows us that t=T/Gamma such that if v>c then we have the square root of a negative number. What on Earth does this mean?

1. I am not sure these can be falsified.

2. Something like this. Except it is the relationship which is defined, NOT the properties themselves. So there is the idea that a+b=-1 or a+b=0 INSTEAD OF the idea that a=+1, b=-1, and a+b=0. So there really is no blue or red because that glosses over the idea that you can vary what you are observing with polarization around 360 degrees.

3. So from my 2, you can see that realism is not required. a and b are not defined, their relationship is.

4. You could say there is the implication of superluminal influence. I call that quantum non-locality since no useful information is transferred. It is redundant.

 

[SeventhSigma]

Right, but if the relationship is defined, and I materialize the properties of A by observing it, is this not somehow transmitting "information" to B, as if A is saying "Hey, B, I am equal to 1 so based on our relationship you need to become -1"? even if A and B are far apart?

 

[dm4b]

1/3. It means you can reject hidden variables or reject locality. So you could logically advocate nonlocal hidden variable interpretations (such as Bohmian types) OR local non-realistic interpretations (such as Many Worlds Interpretation=MWI). Or you can skip the interpretation entirely and stick with the quantum formalism ("shut up and calculate").

Doesn't Aharanov's formulation of Time Symmetric Quantum Mechanics add another little spin on this. I believe his idea was that if there appeared to be missing information, via hidden variables, or what have you, perhaps this is because we are looking for it in the wrong place - the present! Anyhow, that's what led to his two vector formulation of QM, with one of the wave vectors "propagating" from the future to the present.


Anyhow, seems like on the surface this might allow for locality without the use of hidden variables? I've never heard that explicity stated though, in the little bit of reading I have done on TSQM.

 

[DrChinese]

Let me rephrase:

The experiments basically show that independence tests fail. If states were pre-determined, we'd expect certain distributions to occur which in practice do not.

So we explain the results either by holding reality constant or by holding hidden influences constant.

If reality/locality is false, then the states are able to communicate to each other what states they took on instantly, right? In other words, it's like putting a potentially-red-potentially-blue ball in one box and an identical ball in the other, separate them, observe one, and note that this potential ball "becomes" either red or blue and somehow communicates to the other ball that it needs to change its potential to the opposite color.

If reality/locality is true, then the states are predetermined like the sides of a die and there is just some other variable influence we are failing to take into account. For instance, in the example of a human rolling a die, maybe I am failing to account for the randomness because I am neglecting the initial state of the die, the force I throw it, the distance it drops, the rotations it undergoes, etc.

I don't understand how to reconcile these differences because I feel like there are contradictions either way. I can either say potential states communicate instantly to materialize into a real, observable state and violate the notion that information is traveling faster than c (which would be fine if c wasn't so well-established already as an upper limit. Does entanglement in this case cast doubt on c?), or I can say that there's some sort of underlying influence I am failing to take into account.

Why do most people in QM opt for the notion that local realism is false? What exactly rules out the notion of variable influence? I understand that Bell's Theorem shows that the independence tests fail, but why does this rule out *local* variables as opposed to nonlocal? What would the difference between local and nonlocal be in this context? In other words, what is the link between "The independence tests fail" and "Therefore, all local hidden variables are ruled impossible"?

Sorry for all the questions but I've struggled with this for a long time and I'm frustrated that I feel no closer to really understanding QM.

There are multiple issues here. You need to get to the point where you can see that there are no local realistic solutions. That is a consequence of Bell. Attempt to construct a dataset and you will see that there are no possibilities of "variable influences" which are strictly local. I can show you the rules for this if you like. Once you play around a bit, the difficulty becomes pretty clear.

Next, you need to see that the quantum formalism explains everything that is actually observed. It also makes predictions for behavior, which has allowed all kinds of experiments to be constructed. There are about 25 new ones a month being reported for the past 10 years or so.

Last, you need to realize that interpretations are somewhat akin to religions. Believe what you like. As you might skip religions that involve human sacrifice, I would recommend skipping any interpretation which is local realistic (this is just an analogy so please don't take this as a literal comparison).

 

[SeventhSigma]

How do we define the difference between a local and nonlocal variable? In the die example, would the features I described be local?

(For instance, in the example of a human rolling a die, maybe I am failing to account for the randomness because I am neglecting the initial state of the die, the force I throw it, the distance it drops, the rotations it undergoes, etc.)

And yes I'd love to see the rules for differentiating these things

 

[DrChinese]

Doesn't Aharanov's formulation of Time Symmetric Quantum Mechanics add another little spin on this. I believe his idea was that if there appeared to be missing information, via hidden variables, or what have you, perhaps this is because we are looking for it in the wrong place - the present! Anyhow, that's what led to his two vector formulation of QM, with one of the wave vectors "propagating" from the future to the present.


Anyhow, seems like on the surface this might allow for locality without the use of hidden variables? I've never heard that explicity stated though, in the little bit of reading I have done on TSQM.

Yes, and in fact I think that is the easiest way to picture what happens from a physical perspective. No FTL! But it is a little weird.

 

[DrChinese]

How do we define the difference between a local and nonlocal variable? In the die example, would the features I described be local?

(For instance, in the example of a human rolling a die, maybe I am failing to account for the randomness because I am neglecting the initial state of the die, the force I throw it, the distance it drops, the rotations it undergoes, etc.)

Yes, those are local. A non-local variable would be something like "net spin of Mars at this time". Normally, you would expect Mars to only be able to influence us as to how it was a few minutes ago.

 

[SeventhSigma]

But both are ultimately still "influencing variables" no? It's just that one is a lot less obvious than the other and may have a negligibly small effect. Do we say it's only non-local because its effects are typically modeled as being in accordance to some non-instantaneous rate of influence (say, gravity or c)? If this is true, then does entanglement directly clash with the notion of c? How can non-local variables with instant influence be compatible with the notion that no information can travel faster than c? Is this a different "form" of information? Does wavefunction collapse not fall within the standard confines of information transmission?

 

[DrChinese]

How can non-local variables with instant influence be compatible with the notion that no information can travel faster than c? Is this a different "form" of information? Does wavefunction collapse not fall within the standard confines of information transmission?

Quantum nonlocality is actually not a counterexample to special relativity. Relativity=you measure the speed of light as c in any reference frame, light being the mediator of the electromagnetic force. QL=You measure entangled particles at any location and observe the HUP. One does not preclude the other. (However, they do seem to be at odds on the surface.)

 

[SeventhSigma]

Is that basically saying that entangled particles can communicate instantly and that it uses some mechanism that isn't bound by c in the way that gravity/light/EM waves are?

 

[DrChinese]

Is that basically saying that entangled particles can communicate instantly and that it uses some mechanism that isn't bound by c in the way that gravity/light/EM waves are?

I am not an expert on it, but in the Bohmian/dBB interpretations: the instantaneous positions of all other particles in the universe are factored into the setup. This in turn explains the apparent "random" action.

Of course, this is one of several interpretations and some do not require action at a distance. In time symmetric interpretations, the future influences the past and there is no non-local component per se.

 

[DrChinese]

Again, I strongly recommend you get to the point where you acknowledge there are no local realistic solutions. If you still question this point, you have not really come very far because you will think it is a matter of opinion. It really isn't. There are hundreds of experiments local reality cannot explain.

 

[mquirce]

An unworthy cent from a layman is permited? :
1-The mater of whatever particle is eterne.
2- Not the field create particles but field are property of particles spread in space.
3 - Hence : the conjugate particle whenever is going find there the presence of its budy.
Please don't be irritated.Let say for fun.

 

[SeventhSigma]

Again, I strongly recommend you get to the point where you acknowledge there are no local realistic solutions. If you still question this point, you have not really come very far because you will think it is a matter of opinion. It really isn't. There are hundreds of experiments local reality cannot explain.

I am still struggling to understand what it means for a solution to be local and realistic. Under Bell's Theorem we basically see that independence is shown to be false. That is to say, if realism were true and our observations had no impact on the state of the particles, we'd expect certain probabilities to arise that do not.

Therefore, what is the reason behind the probabilities we see as are described by QM? In a state where we have, say, three attributes and two experiments run at the same time such that the attributes were entangled, we'd expect at least a 1/3 lowerbound when in fact we see a 1/4 lowerbound when different attributes are selected. This means that somehow our observation influences the experiment's outcome. We have 100% correlation between states when we observe directly entangled attributes and less correlation than we'd expect when we choose different aspects of those particles to observe. To me, this sounds like a local variable (observation) influencing the outcomes.

How is this "influence" indicative that there aren't variables inherent in our system that are affecting the outcome that we aren't aware of?

 

[DrChinese]

I am still struggling to understand what it means for a solution to be local and realistic. Under Bell's Theorem we basically see that independence is shown to be false. That is to say, if realism were true and our observations had no impact on the state of the particles, we'd expect certain probabilities to arise that do not.

Therefore, what is the reason behind the probabilities we see as are described by QM? In a state where we have, say, three attributes and two experiments run at the same time such that the attributes were entangled, we'd expect at least a 1/3 lowerbound when in fact we see a 1/4 lowerbound when different attributes are selected. This means that somehow our observation influences the experiment's outcome. We have 100% correlation between states when we observe directly entangled attributes and less correlation than we'd expect when we choose different aspects of those particles to observe. To me, this sounds like a local variable (observation) influencing the outcomes.

How is this "influence" indicative that there aren't variables inherent in our system that are affecting the outcome that we aren't aware of?

Good, you are following nicely.

To answer: if I set Alice and Bob to the SAME angle, then I always get the same/expected result. So there isn't anything happening at one end that isn't happening at the other. If you are a local realist, you just say: "hey, that's because Alice and Bob each had the info to give the result independently. Sorta like if you and I have the same copy of a book. If Alice says turn to page 240, and Bob says turn to page 240, we will both have the same first word. So no surprise in that.

But that means there are no variables other than the book. But in fact, the correlation rate is based ONLY on the angle between. For the analogy: we get the same first word as a function of the difference in our page numbers. However, there are no sets of pages which produce the QM expected results.

So if Alice needs to know what page Bob is asking about, the model is not local. If there are no datasets in which the QM results are replicated, it is not realistic.

 

[SeventhSigma]

Aaahhhhh, that makes a lot more sense -- thank you. I understand now why there aren't local hidden variables. So basically we say that it's probably a nonlocal phenomenon because Alice needs to know what page Bob is talking about (although how would MWI allow for local nonreal explanations?). I suppose then the open-to-interpretation question is the nature of that nonlocal relationship?

 

[DrChinese]

Aaahhhhh, that makes a lot more sense -- thank you. I understand now why there aren't local hidden variables. So basically we say that it's probably a nonlocal phenomenon because Alice needs to know what page Bob is talking about (although how would MWI allow for local nonreal explanations?). I suppose then the open-to-interpretation question is the nature of that nonlocal relationship?

Yes that is correct. We don't have any significant insight on that... yet.

Now suppose we have one single particle. The HUP says if you narrow its momentum enough, its position is completely uncertain. Technically, it could be anywhere in the universe! And would/could interact with other particles as such. So that is a kind of nonlocality, right? That is the same quantum nonlocality as with entangled pairs. The difference relates to the shape and nature of the nonlocal effect.

Hey, I don't understand it either.

 

[SeventhSigma]

Is it possible that particles experience nonlocal effects "through space" between two particles in the same way that a wormhole is typically envisioned to "bind two points in space" like a piece of paper folded against itself?

I feel like trying to understand the universe is like being a character stuck in a video game environment and being unable to ever pierce through to see the underlying code, let alone the hardware itself.

 

[JesseM]

Aaahhhhh, that makes a lot more sense -- thank you. I understand now why there aren't local hidden variables. So basically we say that it's probably a nonlocal phenomenon because Alice needs to know what page Bob is talking about (although how would MWI allow for local nonreal explanations?). I suppose then the open-to-interpretation question is the nature of that nonlocal relationship?

When you say "Alice needs to know what page Bob is talking about", what do you mean by that? "Needs to" in order for what? The Bell type experiment is like if Alice and Bob were repeatedly sent 3-page books on each trial, and on each trial they turned to one of the three pages at random and noted the first word--they don't need to know what page the other one chooses to do this experiment. But when they later get together and compare results, they find that on any trial where they both turned to the same page, they found the same word. A local realistic explanation of this would be that they were each sent identical books that had identical predetermined first words on each of the three pages, a nonlocal explanation would be that Bob's book could somehow "choose" what word to show him when he turned to a certain page based on FTL knowledge of which page Alice had looked at on that trial (and what she had found).

 

[SeventhSigma]

When you say "Alice needs to know what page Bob is talking about", what do you mean by that? "Needs to" in order for what? The Bell type experiment is like if Alice and Bob were repeatedly sent 3-page books on each trial, and on each trial they turned to one of the three pages at random and noted the first word--they don't need to know what page the other one chooses to do this experiment. But when they later get together and compare results, they find that on any trial where they both turned to the same page, they found the same word. A local realistic explanation of this would be that they were each sent identical books that had identical predetermined first words on each of the three pages, a nonlocal explanation would be that Bob's book could somehow "choose" what word to show him when he turned to a certain page based on FTL knowledge of which page Alice had looked at on that trial (and what she had found).

Yes, we're in agreement -- by "needs to know what page Bob is talking about" I mean the nonlocal explanation you described at the end of your post.