I Determinism and causality in QM - a case

[entropy1]

I hope my thread won't be closed (too soon) and some forummers can shed their light over my question.

Let's suppose a deterministic universe. I assume all events have a cause, that everything is cause and effect. Then, given that the state of the universe at some instant is X, and this leads to event A, then, if instead event A did not happen, the state of the universe could not have been X, right?

But if we consider the MWI, then X can happen at t0, and then the universe can split in for instance branch L1 and branch L2, with A happening in L1 and not in L2, both being preceded by X. This seems to disagree with the previous case.

So how should we view this case?

 

[Nugatory]

Let's suppose a deterministic universe. I assume all events have a cause, that everything is cause and effect.

In other words, let's assume a universe that is not governed by quantum mechanics.
As far as we know, we don't live in such a universe so speculating about how one might behave is not going to be especially helpful, and any attempt to reconcile it with quantum mechanics will be inherently inconsistent.

[When posting in the main QM forum I often feel the need to apologize to the Bohmians. This is one of those times]

 

[PeterDonis]

given that the state of the universe at some instant is X, and this leads to event A, then, if instead event A did not happen, the state of the universe could not have been X, right?

No. You explicitly give a counterexample in your follow-up question.

if we consider the MWI, then X can happen at t0, and then the universe can split in for instance branch L1 and branch L2, with A happening in L1 and not in L2, both being preceded by X. This seems to disagree with the previous case.

No, it doesn't, because you have not carefully thought through what the "state of the universe" is in your two cases.

In your first case, you were implicitly assuming a classical universe in which the state of the universe, the thing that evolves deterministically, is identical with "what happens".

But in your second case, you were assuming the MWI, in which the state of the universe is not identical with "what happens". The state of the universe in the MWI, the thing that evolves deterministically, is a quantum state, which contains amplitudes for various different, mutually exclusive happenings. (Even this view requires choosing a basis, and different choices of basis can lead to different, mutually contradictory descriptions of the state in terms of the possible "happenings" it contains amplitudes for.)

So the logic you were using in your first case to deduce "if A does not happen, X could not have happened" from "if X happens, A will happen" simply doesn't apply to your second case.

 

[PeterDonis]

I assume all events have a cause, that everything is cause and effect.

In other words, let's assume a universe that is not governed by quantum mechanics.

Actually, the "cause and effect" assumption is irrelevant to the OP's scenario, and could simply be omitted.

However, I don't agree that "everything is cause and effect" is inconsistent with QM. I think it depends on which interpretation you adopt and what viewpoint you take on what "cause and effect" actually mean.

It is true that "cause and effect" don't appear anywhere in the basic rules of QM, as described for example in our Insights article on the subject, but the same is true in classical physics; "cause and effect" aren't anywhere in the basic rules there either. So I don't think one can say a particular scenario is inconsistent with either classical or quantum physics based on any assumptions about "cause and effect".

 

[entropy1]

In your first case, you were implicitly assuming a classical universe in which the state of the universe, the thing that evolves deterministically, is identical with "what happens".

But in your second case, you were assuming the MWI, in which the state of the universe is not identical with "what happens". The state of the universe in the MWI, the thing that evolves deterministically, is a quantum state, which contains amplitudes for various different, mutually exclusive happenings. (Even this view requires choosing a basis, and different choices of basis can lead to different, mutually contradictory descriptions of the state in terms of the possible "happenings" it contains amplitudes for.)

Very clear. Thank you.

 

[entropy1]

So the logic you were using in your first case to deduce "if A does not happen, X could not have happened" from "if X happens, A will happen" simply doesn't apply to your second case.

It seems to me that if it were true, we would have had determinism, following your deduction. So does that mean we don't have determinism, like @Nugatory says?

 

[Nugatory]

However, I don't agree that "everything is cause and effect" is inconsistent with QM.

It's the assumption of determinism that I'm objecting to - aside from the pro forma apology to the Bohmians I don't see how to eliminate nondeterminism from standard QM.

 

[PeterDonis]

It's the assumption of determinism that I'm objecting to - aside from the pro forma apology to the Bohmians I don't see how to eliminate nondeterminism from standard QM.

The OP assumed the MWI (and I realized that that means this thread belongs in the interpretations forum, so I have just moved it there). The MWI is deterministic; it's just that you have to be clear about what the "state" that evolves deterministically is. From the standpoint of the MWI, the "nondeterminism" in standard QM is only an appearance, just as the occurrence of a single outcome from a measurement is only an appearance.

(The Bohmian interpretation, as you note, is also deterministic, but in that interpretation, the "state" is basically the same as in classical physics, and can be equated with "what happens" in the OP's logic.)

 

[PeterDonis]

does that mean we don't have determinism

No. The MWI is deterministic. See my response to @Nugatory just now.

 

[entropy1]

No. The MWI is deterministic. See my response to @Nugatory just now.

The wavefunction may be deterministic, but if you adopt that, you have to accept that ALL possible measured outcomes are realized. Subjectively that is not the case; you then have a single probable outcome.

 

[PeterDonis]

if you adopt that, you have to accept that ALL possible measured outcomes are realized

Which is exactly what the MWI says, and you said you were assuming the MWI for this discussion.

Subjectively that is not the case

And according to the MWI, that subjective appearance is only an appearance. You're the one that picked the MWI for this thread; that means you need to use it.

 

[entropy1]

You're the one that picked the MWI for this thread; that means you need to use it.

So the logic you were using in your first case to deduce "if A does not happen, X could not have happened" from "if X happens, A will happen" simply doesn't apply to your second case.

I think you deduction holds, but as I said, I think it suggests my second case, in which I adopt MWI for sake of reason, is not deterministic as a consequence of your reply. And that has to do, in my view, with the difference between the objective and subjective approach in this matter. We have the wavefunction on one side, and measurement outcomes on the other side. Objectively, we have determinism of the wavefunction.

 

[PeterDonis]

I think it suggests my second case, in which I adopt MWI for sake of reason, is not deterministic as a consequence.

No, it doesn't. It means you are refusing to actually adopt the MWI and use what it actually says.

that has to do, in my view, with the difference between the objective and subjective approach in this matter.

Determinism is never subjective, so it makes no sense to use a subjective approach to address a question about determinism.

Objectively, we have determinism of the wavefunction.

In the MWI, yes. Which means the MWI, as I have said, is deterministic, since, as above, the objective approach is the only one that makes sense when addressing a question about determinism.

 

[entropy1]

In the MWI, yes. Which means the MWI, as I have said, is deterministic, since, as above, the objective approach is the only one that makes sense when addressing a question about determinism.

MWI does have an objective and a subjective aspect. It says about the subjective aspect that only a single outcome is observed by the observer.

 

[entropy1]

No, it doesn't. It means you are refusing to actually adopt the MWI and use what it actually says.

So the logic you were using in your first case to deduce "if A does not happen, X could not have happened" from "if X happens, A will happen" simply doesn't apply to your second case.

Wait, I think we are in fact agreeing that in the second part of the case "if A does not happen, X could not have happened" does not hold. That is in fact what I am saying there.

"If X happens, A will happen" is determinism to me. So if it doesn't apply, either the wavefunction or the measurement outcomes are not deterministic, and it must be the latter I think.

It all is so ingenious

 

[PeterDonis]

MWI does have an objective and a subjective aspect. It says about the subjective aspect that only a single outcome is observed by the observer.

No, that's not what the MWI says. The MWI says that the concept of "observer" that you are implicitly using is invalid.

Here is a correct description of what happens to an "observer" when a measurement is made, according to the MWI:

Before measurement: "O-before" has not observed any result, and "S" (the system to be measured) is in some prepared state.

After measurement: The joint system is in an entangled state which is a combination of "O-after-observed-outcome-1" $\otimes$ "S-1" (the "outcome 1" state of the system S) and "O-after-observed-outcome-2" $\otimes$ "S-2" (the "outcome 2" state of the system S).

Now, what does the term "observer" refer to in the above?

If it refers to "O-before", then that observer has not observed any outcome.

If it refers to either "O-after-observed-outcome-1" or "O-after-observed-outcome-2", then each of these "observers" has observed a single outcome, but neither one is "the" observer, and neither one is "the same observer" as "O-before". There simply is not any "observer" with a single continuous identity before and after measurement in this sense.

If it refers to the subsystem (set of degrees of freedom) to which the "O" states refer, then that subsystem does not have a definite state after the measurement and so has not observed any definite outcome.

 

[PeterDonis]

I think we are in fact agreeing that in the second part of the case "if A does not happen, X could not have happened" does not hold.

No. I am saying that that statement is not even well-defined if we adopt the MWI, because the underlying notion of "happening" that the statement is using is not well-defined if we adopt the MWI. A statement can't be either true or false if it isn't well-defined to begin with.

There is an alternative, but it doesn't help you any. See below.

"If X happens, A will happen" is determinism to me.

And this is true in the MWI, for the correct concept of "happening" in the MWI. In the MWI, what "happens" in terms of determinism is the wave function. And the wave function obeys both of your statements: if the wave function is X, it will be A, and if it is not A, it could not have been X. So the MWI is deterministic by your definition, if we use this notion of "happening".

However, you are refusing to use the correct notion of "happening" for the MWI, and trying to apply a different notion of "happening" that is well-defined in your other case (classical physics), but is not well-defined if we adopt the MWI. And in that case, my first comment at the start of this post applies.

Either way, no, we do not agree.

 

[entropy1]

And this is true in the MWI, for the correct concept of "happening" in the MWI. In the MWI, what "happens" in terms of determinism is the wave function. And the wave function obeys both of your statements: if the wave function is X, it will be A, and if it is not A, it could not have been X. So the MWI is deterministic by your definition, if we use this notion of "happening".

However, you are refusing to use the correct notion of "happening" for the MWI, and trying to apply a different notion of "happening" that is well-defined in your other case (classical physics), but is not well-defined if we adopt the MWI. And in that case, my first comment at the start of this post applies.

So the logic you were using in your first case to deduce "if A does not happen, X could not have happened" from "if X happens, A will happen" simply doesn't apply to your second case.

"If X happens, A will happen" is determinism to me. So if it doesn't apply, either the wavefunction or the measurement outcomes are not deterministic, and it must be the latter I think.

We were talking past each other: you was referencing exclusively to the wavefunction and I wasn't making the distinction, which I should have.

I thought I had posted a reply concerning this, but apparently not in this thread. My view is that MWI is deterministic considering the wavefunction, but the measurement outcomes, in my view, are not necessarily.

I guess it depends on the way you look at it. I feel there has to be a sort of objective/subjective distinction, that is, the wavefunction (objective) and the measured outcomes (subjective), and those related.

Either way, no, we do not agree.

We might, though. I understand what you are trying to say to me.

 

[PeterDonis]

you was referencing exclusively to the wavefunction

That's because, in the MWI, the wave function is all that there is. There is nothing else. So the only thing you can reference if you're talking about the MWI is the wave function.

My view is that MWI is deterministic considering the wavefunction, but the measurement outcomes, in my view, are not necessarily.

Yes, the measurement outcomes are deterministic in the MWI. The MWI says that all possible outcomes occur, every time, as a deterministic fact. The outcomes are all part of the wave function after measurement, which, as I have said and you have agreed, evolves deterministically in the MWI.

I feel there has to be a sort of objective/subjective distinction, that is, the wavefunction (objective) and the measured outcomes (subjective)

No, the measurement outcome is not subjective in the MWI. The measurement outcome is an objective fact about each branch of the entangled wave function of the total system after measurement.

I understand what you are trying to say to me.

I'm not sure you did. See above.

 

[entropy1]

@PeterDonis , I understand exactly what you are saying. I feel we have a difference of conception. Of course you can claim that MWI is deterministic, because it is. But the measurement outcomes we observe are not ALL measurement outcomes at once. We observe a single outcome with the probability given by the Born rule.

 

[PeterDonis]

I understand exactly what you are saying.

I continue to doubt that you actually do, since you keep making statements that are simply wrong if the MWI is assumed. See below.

I feel we have a difference of conception.

I agree in the sense that I have a correct conception of what the MWI actually says, and you have an incorrect one. See below.

We observe a single outcome with the probability given by the Born rule.

Not in the MWI. In the MWI, there is no single "we" after the measurement in the sense you are using the term. There are multiple copies of "we" after the measurement, one in each branch, and each copy of "we" observes a different outcome. So any statement that assumes there is only a single "we", as yours does, is simply wrong if the MWI is assumed.

Also, since all outcomes occur in the MWI, it is meaningless to talk about the "probability" of a particular outcome. In fact, a consistent explanation for the Born Rule in the MWI is one of the primary outstanding issues with that interpretation. So if you want to say you question whether the MWI is correct because it can't account for the Born Rule, that's fine. But that's not what you are saying; what you are saying is simply a wrong description of what the MWI says.

 

[entropy1]

So any statement that assumes there is only a single "we", as yours does, is simply wrong if the MWI is assumed.

I disagree because subjectively we experience something different than objectively. I, in this branch, don't experience other branches. They withdraw from my experience in this branch. If you are fine with the notion that other branches ARE experienced, that is where I don't even disagree, it is just that my way of viewing is one too.

So if you want to say you question whether the MWI is correct because it can't account for the Born Rule, that's fine.

Although that is a serious issue, I'm not claiming that.

In short: I don't disagree with you that MWI is deterministic, but I would rather include the distinction between objective and subjective. I think we disagree there. But I have to say you make a strong case of course. I will study it further.

 

[PeterDonis]

I, in this branch, don't experience other branches.

While this is true, it doesn't change what I said. Remember we are assuming here that the MWI is true. That means we have to adopt the MWI's viewpoint, not yours. And in the MWI's viewpoint, this...

If you are fine with the notion that other branches ARE experienced

...is not just a "notion" or "another way of viewing it", it is a fact. It is not open to subjective interpretation. It is not a "viewpoint" that you can choose whether or not to take. It is reality. That is what the MWI says.

it is just that my way of viewing it is one too.

Not if the MWI is assumed to be true. See above.

I would rather include the distinction between objective and subjective.

The way you are doing it, you can't, if the MWI is assumed to be true. See above.

 

[entropy1]

So tell me, @PeterDonis , is your experience objective or subjective?

 

[entropy1]

If you are fine with the notion that other branches ARE experienced,

...is not just a "notion" or "another way of viewing it", it is a fact.

I am not claiming anything and not even disagreeing, I am stating an axiom.

If you are fine with the notion that other branches ARE experienced,
that is where I don't even disagree, it is just that my way of viewing is one too.

 

[PeterDonis]

I am stating an axiom.

"Other branches are experienced" is an axiom if we assume the MWI is true, yes.

But "my way of viewing it is one too" is not an axiom if we assume the MWI is true.

 

[PeterDonis]

So tell me, @PeterDonis , is your experience objective or subjective?

Before I can even answer this, since we are assuming the MWI is true, you need to give me definitions of "objective" and "subjective" that are well-defined if the MWI is true.

 

[entropy1]

Before I can even answer this, since we are assuming the MWI is true, you need to give me definitions of "objective" and "subjective" that are well-defined if the MWI is true.

This may be not so "well-defined", but I think that probably in the different "worldthreads", we observe different measurement outcomes, so that the experience of all subsequent outcomes differ in each thread, a thread being a macro-outcome paired with a micro-outcome? Although I am not so sure that all subsequent outcomes in each thread should differ that much from those in another thread.

But what do I know? Have I mentioned that? No point in doing this, right?

 

[PeterDonis]

This may be not so "well-defined", but I think that probably in the different "worldthreads", we observe different measurement outcomes, so that the experience of all subsequent outcomes differ in each thread, a thread being a macro-outcome paired with a micro-outcome? Although I am not so sure that all subsequent outcomes in each thread should differ that much from those in another thread.

As to your last statement here, that will depend on the measurements being made.

How does any of this relate to "objective" or "subjective"?

 

[PeterDonis]

No point in doing this, right?

You're the one that asked the question.

 

[entropy1]

How does any of this relate to "objective" or "subjective"?

Subjectively, we observe a single outcome. In a different thread we observe a different outcome. This difference is a difference in subjective experience, I dare to venture.

 

[PeterDonis]

Subjectively, we observe a single outcome. In a different thread we observe a different outcome. This difference is a difference in subjective experience, I dare to venture.

A difference in subjective experience of what?

Normally, when we talk about "subjective experience", we mean something like: you and I both observe the same objective event or situation, but we have different experiences of it, subjectively.

But in this case, we have two "copies" of the same person experiencing two different outcomes in two different branches. They are not observing "the same objective event or situation" at all; they are each observing different objective events or situations--different branches. So "subjective experience" in the usual sense doesn't even apply: it's not two different people, it's two "copies" of the same person, and they're not observing the same objective thing, they're observing different objective things.

 

[entropy1]

Normally, when we talk about "subjective experience", we mean something like: you and I both observe the same objective event or situation, but we have different experiences of it, subjectively.

My view was that the measurement outcome would be a subjective experience of the measurement made. I don't claim that this subjectivity is bound to a single human observer. All observers in a worldthread agree on the measured outcome. So you say the measured outcome is objective and real, but that all other outcomes in the different worldthreads are too. Perhaps I should use the word "experience" instead of "subjective". Experience is subjective. The significance of that is, I think, that a single measurement spawns several outcomes, so that we have different experiences by different people of the same measurement, objectively as well as subjectively. But the ones in different worldthreads can't compare notes.

it's two "copies" of the same person,

Some "me" could be in thread A while of copy of me is in thread B. But you could symmetrically say some "me" is in thread B while a copy is in thread A. So, they are both "me", just with different experiences. Either that, or I have been replaced by something different altogether, which is what I understand you assert.

 

[PeterDonis]

Some "me" could be in thread A while of copy of me is in thread B. But you could symmetrically say some "me" is in thread B while a copy is in thread A.

No, neither of these is correct. Both "copies" are referring to the same subsystem--the same set of degrees of freedom--and neither one has any more claim than the other to be "the original" vs. "the copy". As you say, the situation between them is symmetric.

Either that, or I have been replaced by something different altogether, which is what I understand you assert.

No. The quantum subsystem representing "you"--the particular set of degrees of freedom that is "you"--has not changed.

However, before measurement there was only one branch, and the quantum subsystem representing "you" had a definite state. After measurement, there are two branches, and the quantum subsystem representing "you" is entangled with the system that was measured, so "you" are no longer in a definite state at all; only the total system, comprising both "you" and the system being measured, has a definite state. The "copies" of "you" in the two branches are "pieces" of the total state, so the difference between them and "you" before measurement is that the "you" before measurement has a definite state, while the "copies" after measurement do not.

 

[PeterDonis]

we have different experiences by different people of the same measurement

No, we don't. We have different experiences by the same person (the same set of degrees of freedom) of the same measurement--different for each "copy" of that person in each branch.

 

[entropy1]

No, we don't. We have different experiences by the same person (the same set of degrees of freedom) of the same measurement--different for each "copy" of that person in each branch.

That is what I am saying.

I thought you were claiming the copies were different persons. Must have misread you.

 

[entropy1]

the difference between them and "you" before measurement is that the "you" before measurement has a definite state, while the "copies" after measurement do not.

Then they better hurry getting a definite state, for there may be another measurement coming.

That is the shortest way to make my point about that in this thread. Having said that, you have the mathematical knowledge that I lack mostly. So maybe we should burry the hatch here.

 

[PeterDonis]

Then they better hurry getting a definite state

They can't. The only way to do that would be to reverse their entanglement with the measured system, and decoherence means that's not possible.

there may be another measurement coming

And that measurement will just add further entanglement to the entanglement that already exists. It won't remove any. Which means it won't put any subsystem back into a definite state.

That is the shortest way to make my point about that in this thread.

And that point is wrong. See above.

 

[entropy1]

How do you explain your remark below then:

the "you" before measurement has a definite state

 

[PeterDonis]

How do you explain your remark below then

We were assuming it. In effect, we were assuming that the measurement we were discussing was the first measurement "you" had ever made.

Of course this assumption is highly unrealistic in practice. This is one reason why it's so difficult to really apply what the MWI actually says. If we take what the MWI says at face value, it means no subsystem of the universe now is in a definite state, taken by itself; only the whole universe, as a single huge joint quantum system, has any definite state at all.

 

[entropy1]

We have different experiences by the same person (the same set of degrees of freedom) of the same measurement--different for each "copy" of that person in each branch.

So you say that all possible experiences are experienced. But still the experience is a series of single experiences (outcomes). So I wondered if the worlds in MWI could reflect possible threads/experiences, but that the observer navigates by adhering to a particular possibility, if you understand what I mean. That way, we have free will as well as determinism (WF). Now this is not mainstream I think, but if you can point out where I go wrong, I would be grateful.

 

[PeterDonis]

I wondered if the worlds in MWI could reflect possible threads/experiences, but that the observer navigates by adhering to a particular possibility

No. that's not what the MWI says. The MWI says that all of the branches are equally real. Trying to pick out any particular branch as somehow being "the one the observer navigates to" contradicts what the MWI says.

this is not mainstream I think

Certainly not. It's personal speculation on your part, which is off limits for PF.

 

[entropy1]

Certainly not. It's personal speculation on your part, which is off limits for PF.

I don't agree. I said in advance that it is probably not mainstream science. I just wanted to know where I was wrong. So one could say that MWI makes a claim about what is real, or to what degree. Which clears the issue up. It also avoids the zombie-problem. I should have thought of that. But perhaps to avoid that, it makes the claim about reality. And of course the math clearly does.

But that does not mean I then adopt MWI.

 

[PeterDonis]

I said in advance that it is probably not mainstream science. I just wanted to know where I was wrong.

None of this contradicts the assertion that your proposal was personal speculation. That assertion by me was not an invitation to argue the point; it was a reminder to you of the forum rules, from a forum moderator.

one could say that MWI makes a claim about what is real, or to what degree.

Yes.

that does not mean I then adopt MWI

As far as your own personal beliefs, independent of this thread, go, that's fine. I'm not a fan of the MWI myself.

But in this particular thread, you said you were assuming the MWI. That means that, for purposes of discussion in this thread, you have to adopt the MWI, even if you don't actually believe it's true. You can't say you assume the MWI for discussion of a given scenario and then not adopt it for discussion of that scenario.

 

[entropy1]

Is it fair to suppose that, in MWI, if a human makes choice A, it is just as much determined than if they make choice B? What I mean is that if the choice is free, by free will, it is nevertheless still compatible with determinism, from the viewpoint of MWI? Or should we say that all choices are made and that there is therefore no real choice, just determinism? This is my key point I think.

 

[mattt]

Is it fair to suppose that, in MWI, if a human makes choice A, it is just as much determined than if they make choice B? What I mean is that if the choice is free, by free will, it is nevertheless still compatible with determinism, from the viewpoint of MWI? Or should we say that all choices are made and that there is therefore no real choice, just determinism? This is my key point I think.

Whatever your conception of "Free Will", it is "compatible" with dBB-QM ("single-world" and deterministic) if and only if it is "compatible" with MW-QM ("many worlds" and deterministic").

What most people conceive as "free will" is incompatible with any deterministic model though...

 

[PeterDonis]

Is it fair to suppose that, in MWI, if a human makes choice A, it is just as much determined than if they make choice B?

Before you can answer any such questions in the context of the MWI, you have to decide whether "making a choice" involves a quantum measurement--something that causes entanglement and decoherence and therefore leads to "branching" of the wave function.

If "making a choice" does not involve a quantum measurement, then as far as the MWI is concerned, it doesn't involve any branching and so "which choice is made" would be deterministic, since the MWI is deterministic and the deterministic result from the MWI is that only one choice is made (no branching).

If "making a choice" does involve a quantum measurement, then it is meaningless to ask whether "which choice is made" is deterministic, because the MWI says that all choices are made; that is the deterministic prediction of the MWI.

 

[PeterDonis]

What most people conceive as "free will" is incompatible with any deterministic model

A compatibilist (of which there are many; we have had some previous PF threads on this) would say this is because most people have not carefully thought through what "free will" actually means. If they did, they would realize that having free will in any meaningful sense requires, if not exact determinism, at least a very, very good approximation to it. Otherwise you can't depend on your free will choice determining what happens.

 

[mattt]

A compatibilist (of which there are many; we have had some previous PF threads on this) would say this is because most people have not carefully thought through what "free will" actually means. If they did, they would realize that having free will in any meaningful sense requires, if not exact determinism, at least a very, very good approximation to it. Otherwise you can't depend on your free will choice determining what happens.

I know what you mean, and I agree with it. It's simply that I don't like to use the term "free will" for that.

I would prefer to use another word for that, given that historically it was conceived with a different meaning (mostly in dualism and similar belief systems) than the better one you have in mind.

 

[entropy1]

Before you can answer any such questions in the context of the MWI, you have to decide whether "making a choice" involves a quantum measurement--something that causes entanglement and decoherence and therefore leads to "branching" of the wave function.

If "making a choice" does not involve a quantum measurement, then as far as the MWI is concerned, it doesn't involve any branching and so "which choice is made" would be deterministic, since the MWI is deterministic and the deterministic result from the MWI is that only one choice is made (no branching).

If "making a choice" does involve a quantum measurement, then it is meaningless to ask whether "which choice is made" is deterministic, because the MWI says that all choices are made; that is the deterministic prediction of the MWI.

Your position is clear. Compatibalist free will works fine with determinism. But if I had the option to choose A and also the option to choose B, I think a quantum measurement must be involved, for that is (in the context of MWI) the only mechanism that makes more than one future possible.

The point I want to make is that in my example choice A and B are both possible, however some choice will be made between them if we view it subjectively. If you insist to view it objectively in the context of MWI, then you can say both choices are made, so really there is no choice made, so free will, if it exist, has to be compatibalist. Do you agree?