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

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. 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

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

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

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

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

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

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 dont be irritated.Let say for fun.