Getting to the Heart of Entanglement and Locality in Plain English

[jeffn1]

I understand two particles can be entangled even though they are many millions of miles away.

I understand a simple example of this is a "quantum singlet state":

Singlet State: This is the precise quantum state where two entangled particles have a total spin of zero. Because the total spin must balance out, measuring one particle as spin-up means the other must instantly be spin-down.

I understand that if we measure/disturb/observe one of the entangled particles, we know that the other entangled particle will have the opposite spin.

I understand that, if we do this with one particle, nothing will apparently happen to the other particle. However, when the other particle is measured, it will confirm the opposite spin.

Making this even more interesting, I believe that if we measure/disturb/observe the local particle and then measure/disturb/observe the nonlocal particle, it will confirm the opposite spin, even though, if something were transmitted from the local particle to the nonlocal particle, it could not have reached the nonlocal particle based on the speed of light.

I also understand none of this can be used for faster-than-speed of light communication for reasons that have been discussed in this forum and elsewhere.

I can see two types of explanations:
1. The entangled particles would have always had these two spins when measured. So, when we measure/disturb/detect one of the particle, it is revealing the spin of the local particle. And since the particles are entangled, we also immediately know the spin of the nonlocal particle. This explanation seems very similar to the right and left glove metaphor. I think this type of analysis would be considered a "hidden variable" interpretation (?).
2. The entangled particles did not always have their relative spins. The act of measuring/disturbing/observing the local particle ends the entangled state. In this case, we have to confront the fact (as I understand it) that the nonlocal particle millions of miles away (when measured within less time than the speed of light would require to reach it) shows the opposite spin.

In this cases would a (poor) metaphor of a conveyor belt be helpful? (Even though I think we are dealing with excitations in a universal quantum field.). The conveyor belt stops and immediately stops changes in the spin of the nonlocal particle. The notion would be this is not inconsistent with the speed of light because breaking the entanglement at its source immediately stops changes to the spin. I thought Bill/Bhoppa gave some analogy along these lines? (Sorry I am not explaining it well).

Well, I am hoping this post can stay up a bit to get input.....

 

[.Scott]

Hello @jeffn1 :
First, look up the Bell Inequality experiments. If you don't understand them, post your confusion here and I will attempt to sort it out.

I can see two types of explanations:
1. The entangled particles would have always had these two spins when measured. So, when we measure/disturb/detect one of the particle, it is revealing the spin of the local particle. And since the particle are entangled, we also immediately know the spin of the nonlocal particle. This explanation seems very similar to the right and left glove metaphor. I think this type of analysis would be considered a "hidden variable" interpretation (?).

No. The notion of "hidden variables" can only be considered an "interpretation" if it can be used to make the same predictions as the QM calculations. I think most in Physics consider the success of "Bell Inequality" experiments - including ones that make the measurements dependent on demonstrably non local events (such as light from galaxies on opposite sides of the sky) - to put "hidden variables" closer to the trash bin than to a real "interpretation".

If you measure both particles along the same axis, you will discover they have opposite spins. In that way, measurements will be consistent. That spin state is independent of other states. So if you "disturb" the particle without affecting the spin state, you haven't started the experiment. Also, if you measure the spin along different axis, you may still find a correlation between the remote and local measurements.

2. The entangled particles did not always have their relative spins. The act of measuring/disturbing/observing the local particle collapses the wave function (or causes a branching in the MWI?). In this case, we have to confront the fact (as I understand it) that the nonlocal particle millions of miles away (when measured within less time than the speed of light would require to reach it) shows the opposite spin.

I am no great fan of MWI, but if you use that interpretation, then in the simplest sense the "first measurement" would split the universe and the second measurement would be consistent with the first because it would be consistent with the universe where that measurement is taken. Of course, there isn't necessarily a "first" and "second" (the measurements might be space-like events). But we can repair that by simply saying that the universe split ahead of time (before either measurement) in preparation for those expected measurements. But that means that two copies of the "hidden variables" were create - one for each universe. This can also be repaired (for example, by abandoning the notion of hidden variables but still trying to differentiate the two child universes another way) - but you probably get the sense of why I am no MWI fan.

In this cases would a (poor) metaphor of a conveyor belt be helpful?

I think of it this way:
1) the pair share a single state;
2) the measurement of that state can occur at either particle or with both of them;
3) the results must not challenge the speed-of-light limit on information transfer; and
4) because the two measurements are correlated but random, that speed limit is enforced.

 

[jeffn1]

I didn't think Bell inequalities experiments ruled out nonlocal hidden variables. I thought Bohmian Mechanics is a nonlocal hidden variable interpretation.

 

[Matterwave]

I can see two types of explanations:
1. The entangled particles would have always had these two spins when measured. So, when we measure/disturb/detect one of the particle, it is revealing the spin of the local particle. And since the particle are entangled, we also immediately know the spin of the nonlocal particle. This explanation seems very similar to the right and left glove metaphor. I think this type of analysis would be considered a "hidden variable" interpretation (?).
2. The entangled particles did not always have their relative spins. The act of measuring/disturbing/observing the local particle ends the entangled state. In this case, we have to confront the fact (as I understand it) that the nonlocal particle millions of miles away (when measured within less time than the speed of light would require to reach it) shows the opposite spin.

Very roughly speaking yes. Bell's theorem ruled out a class of models called local hidden variable models. In my mind, I map your point 1 as pointing in the direction of hidden variables and your point 2 as pointing in the direction of locality vs non locality. But there's some call outs:

1. The notion of hidden variables is not as simple as "revealing the spin" would suggest. You have to account for example for contextuality of measurement. There is a no-go theorem (Bell-Kochen-Specker) attached to this as well.
2. Bell thought his result was strong enough to prove non-locality but this is a (highly) contested point. There are some loopholes. For example, "super determinism".

In this cases would a (poor) metaphor of a conveyor belt be helpful?

I don't understand this metaphor.

Some interesting resources:

Bertlemann's socks essay from Bell:
https://cds.cern.ch/record/142461/files/198009299.pdf

SEP entry on Bell's theorem which actually lays out his arguments (and their different versions) pretty well: https://plato.stanford.edu/entries/bell-theorem/

 

[jeffn1]

Thank you! The conveyor belt analogy (I suspect others have created a better one) is that the pre-detection environment is "in flux". But, a detection performed at different points in time would result in different spins (so there is no predetermined hidden spin(s)). But, once the measurement/detection is made, the conveyor belt stops (please ignore real world macroscopic issues, like momentum). If you conceive the quantum field as all connected, I think you can take the position that stopping the "flux" (potential change in spin, if measured) locally automatically stops any change in spin immediately for the nonlocal particle as well without violating GR. The analogy (which might not withstand scrutiny involving a real conveyor belt) is that stopping the conveyor belt at the source (locally) immediately stops the conveyor belt nonlocally.

[I will read your linked publications!]

 

[.Scott]

I didn't think Bell inequalities experiments ruled out nonlocal hidden variables. I thought Bohmian Mechanics is a nonlocal hidden variable interpretation.

John Bell's 1964 paper described tests to decide whether quantum mechanics could be explained by adding "local hidden variables" to restore classical causality and locality.
You could phrase Bohmian Mechanics as a "nonlocal hidden variable interpretation", but I wouldn't leave out that "nonlocal".

2. Bell thought his result was strong enough to prove non-locality but this is a (highly) contested point. There are some loopholes. For example, "super determinism".

Yes. Super-determinism is why I said it was "closer to the trash bin" rather than in it. For me, super-determinism begs the question "What would the grand logic be that makes the Bell Inequality work?". In other words, I'll grant you super-determinism, but where does that leave us? And the answer to that may not be "nowhere". There might be direction from there. But I think we need to see what the presumed "super determinism" has left us with before we can figure out what it is.

 

[.Scott]

Thank you! The conveyor belt analogy (I suspect others have created a better one) is that the pre-detection environment is "in flux". But, a detection performed at different points in time would result in different spins (so there is no predetermined hidden spin(s)). But, once the measurement/detection is made, the conveyor belt stops ...(please ignore real world macroscopic issues, like momentum). If you conceive the quantum field as all connected, I think you can take the position that stopping the "flux" (potential change in spin, if measured) locally automatically stops any change in spin immediately for the nonlocal particle as well without violating GR. The analogy (which might not withstand scrutiny involving a real conveyor belt) is that stopping the conveyor belt at the source (locally) immediately stops the conveyor belt nonlocally.

We only need to deal with special relativity (SR) for this one.
Right away, we have this problem with that "immediately". Those two measurement events can be either "time like" or "space like".
If they are "time like", then one measurement happened before the other and it can create a signal that will reach the other measurement before it happens. Such a signal would be a "local effect". It could travel at light speed and there is no cause/effect issue.
If the measurements events are "space like", then which one appears to have happen first is dependent on your frame of reference. If you are speeding along in one direction, measurement "A" might look like it happened first. In that same case, someone coming at you in the opposite direction could see "B" happen first. But it doesn't matter because neither A nor B can signal its measurement to the other in time to affect the others measurement. They are too far away from each other and their measurements are being made too close in time for either one to signal the other - something that all observers would agree with no matter their reference frame.

Clearly, we want to address ourselves to the "space like" situation. In such a case, which measurement stops the belt? Neither one is unambiguously first.

If we decide that the signal is "nonlocal", then we also don't need to worry which one is measured first because there will never be a time or place when they are unable to exchange information.

But I would call that "the same state".

 

[Matterwave]

Yes. Super-determinism is why I said it was "closer to the trash bin" rather than in it.

I am (purely) curious to know if you would consider "non-locality" (in the sense that Bohmian Mechanics is non local) as a "legitimate out" for Bell's theorem, a loophole, or if it's simply untenable due to relativity, or something else?

 

[PeterDonis]

I thought Bohmian Mechanics is a nonlocal hidden variable interpretation.

It is, but the hidden variables are unobservable particle positions. They are not anything like "the direction of spin". When you measure a particle's "spin", BM says that you're actually measuring particle positions and then telling a story about how they indirectly indicate "spin".

The nonlocality comes from the fact that the wave function, which is part of the equation of motion of the particles, depends, if it is entangled, on all of the positions of the entangled particles. And measuring a particle means making it interact with a measuring device, which affects its position, and in turn affects the equation of motion of all other particles that are entangled with it.

 

[Matterwave]

Thank you! The conveyor belt analogy (I suspect others have created a better one) is that the pre-detection environment is "in flux".

What's this mean? Is it your next sentence?

But, a detection performed at different points in time would result in different spins (so there is no predetermined hidden spin(s)).

A little hard to know exactly what you mean by this. Are you suggesting the spin state evolves in time?

But, once the measurement/detection is made, the conveyor belt stops (please ignore real world macroscopic issues, like momentum). If you conceive the quantum field as all connected, I think you can take the position that stopping the "flux" (potential change in spin, if measured) locally automatically stops any change in spin immediately for the nonlocal particle as well without violating GR.

I can't parse what this means. I'm unable to map this to any actual physics unfortunately.

The analogy (which might not withstand scrutiny involving a real conveyor belt) is that stopping the conveyor belt at the source (locally) immediately stops the conveyor belt nonlocally.

Same for this.

 

[.Scott]

I am (purely) curious to know if you would consider "non-locality" (in the sense that Bohmian Mechanics is non local) as a "legitimate out" for Bell's theorem, a loophole, or if it's simply untenable due to relativity, or something else?

Bohemian Mechanics (MB), as I understand it, says that the particle's trajectory can be affect "instantaneous" across long spatial distances. This makes it non-local - which is exactly what the Bell Inequality argues for. So it's not a "loophole", it's completely allowed.

To go on, I have always noted that after the measurement, there is always a way of describing the particle as following a specific trajectory. If (per BM) the trajectory can be affected across large spatial distances, then (per SR) how could you possibly stop it from doing the same thing across time.
I notice that BM insists on being "deterministic" and says that the reason the results are apparently "random" is due to a lack of knowledge of the "exact initial positions". I also like determinism (mostly because leaving things to pure random chance is very much NOT in the spirit of scientific exploration). But, since in some cases we need to loose information to avoid FTL communication, I would have the randomness based on something that cannot be foreseen "in principle" rather than "in practicality".

 

[jeffn1]

What's this mean? Is it your next sentence?


A little hard to know exactly what you mean by this. Are you suggesting the spin state evolves in time?


I can't parse what this means. I'm unable to map this to any actual physics unfortunately.


Same for this.

I think forget about the conveyor belt analogy (and thank you for thinking about it). I don't think it was very good because it is too removed and different from entangled particles.

But, I suppose all I was trying to say was that, if the detection/measurement/merely stops any further correlation in spins and the two particle each are left with opposing spins, this does not seem to require the transmission of anything (beyond the speed of light or otherwise). It simply ends the correlation immediately and the (formerly) entangled particles are left with the spin that follows the dis-entanglment. That was the intended point of the (somewhat weak) conveyor belt analogy. [I appreciate your effort to make sense out of my non-physicist language].

I guess I still am not convinced why causality should not apply to this. I do not think there is much dispute that the measurement/detection causes the particles to dis-entangle. But, I think the causality does not require faster-than-speed-of-light (or any other) communication. I will keep looking into it.

 

[PeterDonis]

I guess I still am not convinced why causality should not apply to this.

Causality normally implies ordering: the cause has to come before the effect. But with measurements on a pair of entangled particles, the ordering doesn't matter: the results are the same no matter which one is measured first. That makes it very hard to see how the usual concept of causality could apply.

I do not think there is much dispute that the measurement/detection causes the particles to dis-entangle.

Only in interpretations where collapse is a real process. In an interpretation like the MWI, the entanglement doesn't go away; it just gets spread to the measuring devices as well as the particles.

 

[jeffn1]

Causality normally implies ordering: the cause has to come before the effect. But with measurements on a pair of entangled particles, the ordering doesn't matter: the results are the same no matter which one is measured first. That makes it very hard to see how the usual concept of causality could apply.


Only in interpretations where collapse is a real process. In an interpretation like the MWI, the entanglement doesn't go away; it just gets spread to the measuring devices as well as the particles.

Thank you, Peter. Maybe the confusion stems from what we are defining as "the cause". I tend to think the detection/measurement/interaction of either particle causes both particles to dis-entangle. Is that helpful?

 

[PeterDonis]

I tend to think the detection/measurement/interaction of either particle causes both particles to dis-entangle.

Again, whether the particles "dis-entangle" depends on the interpretation of QM that you adopt. In the MWI, they don't.

Also, saying that the particles "dis-entangle" assumes an interpretation where the wave function describes individual quantum systems. In a statistical/ensemble interpretation, such as Ballentine's, that is not the case.

Also, even if you are using an interpretation where neither of the above issues apply, if the measurements are spacelike separated, there is no invariant fact of the matter about which one occurs first. So it's not possible to say that either measurement "causes" the disentanglement in the usual sense of "cause".

My question would be, why do you care about "cause"? You don't need to answer any of the questions you're asking about "cause" in order to do the actual physics--make the predictions and compare them with experiment.

 

[jeffn1]

Again, whether the particles "dis-entangle" depends on the interpretation of QM that you adopt. In the MWI, they don't.

Also, saying that the particles "dis-entangle" assumes an interpretation where the wave function describes individual quantum systems. In a statistical/ensemble interpretation, such as Ballentine's, that is not the case.

Also, even if you are using an interpretation where neither of the above issues apply, if the measurements are spacelike separated, there is no invariant fact of the matter about which one occurs first. So it's not possible to say that either measurement "causes" the disentanglement in the usual sense of "cause".

My question would be, why do you care about "cause"? You don't need to answer any of the questions you're asking about "cause" in order to do the actual physics--make the predictions and compare them with experiment.

Ahh, that's a deeper question. I am not doing "actual physics", but I do want to understand science. Is it fair to say you are in the Niels Bohr school of thought? ;)