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.....

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.

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".

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/

[I will read your linked publications!]

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".

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.

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".

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.

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.

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.

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.

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.

I do think it's important to understand and keep clear the distinction between making predictions and comparing them with experiment, and things that aren't that. "Cause", to me, falls into the latter category.

Even then, "cause" is not quite the same kind of thing as, for example, "electron". We can point to particular mathematical objects in our theoretical models and say that they describe an "electron", a real thing. It's not so clear how that works with "cause", at least not if you want to try to include whatever it is that produces Bell inequality violating correlations in the category of "cause".

Proximate cause is used in tort law to say that something that never would have been expected should not legally be considered a cause (triggering liability). AI gives this description/example: Proximate cause acts as a legal limitation, asking whether the link between the action and the result is close and direct enough to be fair.

The big case establishing this concept if Palsgraf v. Long Island Railroad (Cardozo): In Palsgraf, a man dropping a package of fireworks while boarding a train caused a distant scale to fall on a woman. It is somewhat related to the scientific concept of the "butterfly effect" which highlights how a tiny, seemingly harmless action can trigger an unpredictable chain of massive consequences.

But, sorry went off on a tangent there.....

But, I think, as you suggest, in science the notion of cause probably requires some type of interpretive model. And in quantum physics right now, things are unsettled with competing "interpretations".

But, as you also (rightly) suggest (maybe even "say"), physicists can accomplish a lot based on knowing the mathematical tools at hand without considering an interpretation ("the story", as you denote it). :)

So, assuming you meant "ends the entanglement", then, as Peter noted, different interpretations (or theories) have different perspectives on what that means. This is, in my view, roughly why Peter keeps saying (something like) there's no cause-effect relationship here but you keep thinking there is. You have a mental model of what "ending entanglement" means that goes beyond what the raw formalism of QM says.

Now talking on a tangent. For example, if you demand an ontological ##\psi## (and complete in the sense of EPR) and that collapse is an objective fact of the matter, you run into Einstein's objections from the 1927 Solvoy conference that your theory would have to be nonlocal. You can see Section 7.1 of https://arxiv.org/abs/quant-ph/0609184 for a brief overview.

Einstein's out was to say the wave function is epistemic, incomplete, and about ensembles of particles.

Note that for the above argument, there is no entanglement at all.

So, a preliminary question for you: what do you think the wave function is? Is it a bookkeeping device for us to run calculations or is it a thing that exists in the world? Or something else? These are, of course, interpretational questions.

We have many no-go theorems that carve out (reject) portions of the space of interpretations, but not enough and not in a way that yields one agreed upon interpretation (or theory).

For example, John Bell made the case, in his paper "The Theory of Local Beables" that if you have a certain sense (a reasonable one, but not one without controversy) of local causality then violations of his inequalities means no locally causal theory can reproduce all of QM, and therefore, the world is non-local. But this requires additional machinery (assumptions and theory crafting), and it's not the majority view (afaik) among physicists today. There are certainly many physicists who think the world is local because relativity tells us it is.

Many discussions on this topic are really different people using different definitions of the same words and talking past each other. (This includes plenty of past PF threads.) That's one reason why, IMO, it's important to understand the math and the experimental predictions without having to use any of those words. Otherwise you keep mixing the basic theory--the machinery that makes the predictions--with interpretation.

Yes, "cause" is an interesting concept; more slippery than one might initially think. In law there are two legal concepts "but for" causation and "proximate" causation. "But for" causation seems to be the relevant one for science.

Proximate cause is used in tort law to say that something that never would have been expected should not legally be considered a cause (triggering liability). AI gives this description/example: Proximate cause acts as a legal limitation, asking whether the link between the action and the result is close and direct enough to be fair.

The big case establishing this concept if Palsgraf v. Long Island Railroad (Cardozo): In Palsgraf, a man dropping a package of fireworks while boarding a train caused a distant scale to fall on a woman. It is somewhat related to the scientific concept of the "butterfly effect" which highlights how a tiny, seemingly harmless action can trigger an unpredictable chain of massive consequences.

But, sorry went off on a tangent there.....

But, I think, as you suggest, in science the notion of cause probably requires some type of interpretive model. And in quantum physics right now, things are unsettled with competing "interpretations".

But, as you also (rightly) suggest (maybe even "say"), physicists can accomplish a lot based on knowing the mathematical tools at hand without considering an interpretation ("the story", as you denote it). :)

The math and experimental predictions (for two state systems) given by QM are generally quite clean and simple. The algebra can sometimes be a bit of a grind but it's worthwhile to do it oneself at least once, e.g. to calculate ##\langle \hat{a}\cdot\vec{\sigma}\otimes\hat{b}\cdot\vec{\sigma}\rangle=-cos(\theta_{ab})## starting from ##|\Psi\rangle=\frac{1}{\sqrt{2}}(|01\rangle-|10\rangle)##.

The math on the hidden variables side is not too bad either (depending on version).

It is also useful to see (and discuss) the assumptions in mathematical form. E.g. the factorizability assumption (in notation from the SEP entry cited in post #4):

$$
p_{ab}(s,t|\lambda)=p^1_a(s|\lambda)p^2_b(t|\lambda)
$$

The fact that ##b## does not appear as a subscript on ##p^1## and ##a## does not appear on ##p^2## is what we would say in English "Alice's outcome(s) does not depend on Bob's measurement setting and vice versa".

For the interested reader, what does the fact that ##p^1## contains no conditioning on ##t## mean?

So, assuming you meant "ends the entanglement", then, as Peter noted, different interpretations (or theories) have different perspectives on what that means. This is, in my view, roughly why Peter keeps saying (something like) there's no cause-effect relationship here but you keep thinking there is. You have a mental model of what "ending entanglement" means that goes beyond what the raw formalism of QM says.

Now talking on a tangent. For example, if you demand an ontological ##\psi## (and complete in the sense of EPR) and that collapse is an objective fact of the matter, you run into Einstein's objections from the 1927 Solvoy conference that your theory would have to be nonlocal. You can see Section 7.1 of https://arxiv.org/abs/quant-ph/0609184 for a brief overview.

Einstein's out was to say the wave function is epistemic, incomplete, and about ensembles of particles.

Note that for the above argument, there is no entanglement at all.

So, a preliminary question for you: what do you think the wave function is? Is it a bookkeeping device for us to run calculations or is it a thing that exists in the world? Or something else? These are, of course, interpretational questions.

I tend to think the concept of "phase transition" may be helpful here (e.g., rapid change from water to ice, etc.). An analogy to cosmic microwave background might be helpful too. As you guys know (you're real physicists!), the tiny temperature fluctuations (anisotropies) in the CMB—mapped in detail by space missions like COBE, WMAP, and the ESA's Planck Mission—reveal the density seeds that eventually grew into galaxies and large-scale cosmic structures.

I suspect, in a similar way, I suspect tiny differentials in energy moving at the speed of light at a quantum level "resolve" to the location of a particles when they are measured.

(Back to "phase transitions", there are some scientists who believe Cosmic Inflation preceded the Big Bang and the Big Bang was the product of a phase transition.)

We have many no-go theorems that carve out (reject) portions of the space of interpretations, but not enough and not in a way that yields one agreed upon interpretation (or theory).

It can, but you need to be explicit with your definition of causality.

For example, John Bell made the case, in his paper "The Theory of Local Beables" that if you have a certain sense (a reasonable one, but not one without controversy) of local causality then violations of his inequalities means no locally causal theory can reproduce all of QM, and therefore, the world is non-local. But this requires additional machinery (assumptions and theory crafting), and it's not the majority view (afaik) among physicists today. There are certainly many physicists who think the world is local because relativity tells us it is.

[PS: Peter Donis is gonna kill me. Hah!;)]

I tend to think the concept of "phase transition" may be helpful here (e.g., rapid change from water to ice, etc.). An analogy to cosmic microwave background might be helpful too. As you guys know (you're real physicists!), the tiny temperature fluctuations (anisotropies) in the CMB—mapped in detail by space missions like COBE, WMAP, and the ESA's Planck Mission—reveal the density seeds that eventually grew into galaxies and large-scale cosmic structures.

I suspect, in a similar way, I suspect tiny differentials in energy moving at the speed of light at a quantum level "resolve" to the location of a particles when they are measured.

It is also your own home-brewed QM interpretation, which is also off limits here. Not to mention a bad idea to begin with. There is 100 years' worth of literature on QM interpretations. Please don't try to roll your own.

The simplest explanation is in line with Ballentine.

In an experiment that involves the creation of photon pairs, spin measurements are made at opposite positions.

Subsequently photons are detected and a pattern emerges.
Just like a pattern emerges in a double split experiment. This pattern can be derived with quantum mechanics, the probabilities can be calculated.

But back to the entanglement; at one end, you do not find a photon with spin up and the next one measured with spin down.

Instead, You find a photon out of a pair with this one having spin up and the partner having spin down.
And the next one you have found a photon out of a pair with this one having spin down and the partner far away has spin up.

It is not possible to tell in advance what it will be for the next one, but the probabilities are known.

There is no causality between the measurements and it is unimportant in which order measurements of a specific pair had been made. It is unimportant how far away they are.
You always find a pair out of the ensemble. No problem with locality either.

It becomes more complicated when the measurement angle in the device is rotated. There is actually not much one can know of the spin of an electron or photon. The only thing to work with is the spin impulsmoment in the z-direction, i.e. the spin up and spin down.
The distribution of the probabilities by (difference in) angle in the measurement, the larger pattern, can be calculated starting with Pauli-spin-matrices ..

But one pair will do this and the next pair will do that and so the pattern builds up.

No problem with locality either.

So indeed the context was mainly Ballentine.