Compatibility of MWI with probability of outcomes

[entropy1]

Can MWI account for the probabilities of outcomes? If MWI says all outcomes are realized, is the probability that an outcome occurs then not 100%? How is this explained with the entanglement of the measured object and the measurement apparatus?

 

[Halc]

If you're talking about the probability of a given possible outcome occurring in some world somewhere, then yes, sure, it is 100%. Unclear how entanglement is relevant here. If you measure two entangled particles in the same way, one world will get one correlated pair of measurements and other world will get the opposite correlated measurements. There will be no world where the two measurements come out uncorrelated, unless the measurements were not taken in exactly the same way, such as spin measured at slightly different angles.

 

[PeterDonis]

Can MWI account for the probabilities of outcomes?

If you mean, can the MWI account for the Born rule, there have been various attempts to derive the Born rule in the context of the MWI, but I don't think any of them have won general acceptance as being successful.

 

[Minnesota Joe]

Can MWI account for the probabilities of outcomes? If MWI says all outcomes are realized, is the probability that an outcome occurs then not 100%? How is this explained with the entanglement of the measured object and the measurement apparatus?

I think I understand best how Sean Carroll claims to derive the Born Rule in the Many World Interpretation (MWI) so I'll stick to that.

The rule he wants to use is a modified principle of indifference: "assign equal [epistemic] probability to branches when they have equal amplitudes". When a wavefunction doesn't have terms with equal amplitudes, you decompose the terms until it does. It turns out that the square of the amplitudes is equivalent to the epistemic probability assignment. So, supposedly, the Born Rule has been derived.

The amplitudes themselves can't be measured. Everyone only ever sees one result indicated by the measurement device in an experiment. But they remember past experiments--readings of the measurement device--and that also agrees with the Born Rule. Their memories suffer from a type of bias one might say. Other than that, I'm not sure that entanglement matters to the branch probability assignment.

Hopefully I'm characterizing his argument accurately, albeit briefly.There are many things that make me uneasy about MWI after reading and discussing it with people here.

 

[PeterDonis]

they remember past experiments--readings of the measurement device--and that also agrees with the Born Rule.

Yes, and Carroll's prescription does nothing at all to explain why that is the case.

 

[Minnesota Joe]

Yes, and Carroll's prescription does nothing at all to explain why that is the case.

Yes, I agree. Is that unique to Carroll? To me it seems like for MWI every observer is branch bound so their memories are necessarily biased without any explanation for why.

 

[PeterDonis]

Is that unique to Carroll?

As I said, I don't know of any derivation of the Born rule for the MWI that has won general acceptance.

To me it seems like for MWI every observer is branch bound so their memories are necessarily biased without any explanation for why.

I believe that is one of the issues that prevents many physicists from accepting the MWI, yes.

 

[Quanundrum]

If, as quite a lot of MWI supporters speculate, observers are tied to one branch since the inception of the universe, doesn't that explain this open question? I.E. every universe is isolated from all others, equivalent to other planets in a different spatial area of our universe?

 

[entropy1]

If you mean, can the MWI account for the Born rule, there have been various attempts to derive the Born rule in the context of the MWI, but I don't think any of them have won general acceptance as being successful.

If we can't reconstruct the Born rule, which is verified by experiment, in MWI, does that mean we have to expect that unitary evolution of the wavefunction, which seems a reasonable requirement, possibly won't hold?

 

[PeterDonis]

If we can't reconstruct the Born rule, which is verified by experiment, in MWI, does that mean we have to expect that unitary evolution of the wavefunction, which seems a reasonable requirement, possibly won't hold?

In the MWI, unitary evolution of the wave function is assumed to always hold. Not being able to reconstruct the Born rule is simply an open issue with that interpretation.

If you mean, does not being able to reconstruct the Born rule from unitary evolution alone mean that unitary evolution might not always hold, which in turn would suggest that QM itself might be only an approximate theory, not exactly correct, I personally think that's a possibility, yes, but I don't know that there are many physicists who agree.

 

[PeterDonis]

If, as quite a lot of MWI supporters speculate, observers are tied to one branch since the inception of the universe, doesn't that explain this open question?

No. The open question is about why we observe the Born rule to hold. That is an observation in one "branch" according to the MWI.

 

[entropy1]

If you mean, does not being able to reconstruct the Born rule from unitary evolution alone mean that unitary evolution might not always hold, which in turn would suggest that QM itself might be only an approximate theory,

I mean that either
1) We can't account for the probabilities of outcomes (MWI), or
2) We have to deal with the measurement problem (Copenhagen),
which don't seem small issues to me. So yes, this, to me, means that QM as a theory has issues. However, it is very, very accurate in making predictions, and people seem satified by that.

 

[kith]

If we can't reconstruct the Born rule, which is verified by experiment, in MWI, does that mean we have to expect that unitary evolution of the wavefunction, which seems a reasonable requirement, possibly won't hold?

That's kind of a semantic question. That unitary evolution is supposed to always hold is the defining characteristic of the MWI (the "many worlds" are secondary). If it doesn't hold, you simply have another interpretation.

 

[entropy1]

That's kind of a semantic question. That unitary evolution is supposed to always hold is the defining characteristic of the MWI (the "many worlds" are secondary). If it doesn't hold, you simply have another interpretation.

Ok. But as for yet, we can't have both the Born rule and unitary evolution in QM. This is significant, I think, with repect to its explanatory power.

 

[PeterDonis]

we can't have both the Born rule and unitary evolution in QM

Sure we can; that's exactly what basic QM, independent of any interpretation, does.

What we don't have is a way to derive the Born rule from unitary evolution. But we don't need one if we just adopt the Born rule as an additional postulate, which is what basic QM does.

 

[entropy1]

What we don't have is a way to derive the Born rule from unitary evolution. But we don't need one if we just adopt the Born rule as an additional postulate, which is what basic QM does.

But how is it reconsilable to have the Born rule but still have all outcomes realized? What does the Born rule mean in that way?

 

[PeterDonis]

how is it reconsilable to have the Born rule but still have all outcomes realized? What does the Born rule mean in that way?

It means observers in each branch observe relative frequencies of outcomes that are consistent with the rule.

 

[entropy1]

It means observers in each branch observe relative frequencies of outcomes that are consistent with the rule.

To me, the problem occurs something like this: In MWI, we assume all outcomes happen, and in separate realities so to say (loss of interference). If we have for instance P(A)=0.1 and P(B)=0.9, then we don't have outcome A for 10% real and outcome B for 90% real. In each subjective reality, the outcome is 100% real. (This looks like some similarity with collapse, where a single outcome becomes 100% real). So we can't prefer the frequencies of outcomes because (we assume that) all outcomes occur!

 

[PeterDonis]

If we have for instance P(A)=0.1 and P(B)=0.9, then we don't have outcome A for 10% real and outcome B for 90% real.

You're looking at the wrong frequencies. The MWI says the Born rule is observed in the relative frequencies of A and B results in a single branch after a large number of measurements.

 

[entropy1]

You're looking at the wrong frequencies. The MWI says the Born rule is observed in the relative frequencies of A and B results in a single branch after a large number of measurements.

I am not sure that I understand you. In the example I gave, B should, over a large number of measurements, happen more often than A. In MWI, to me that seems improbable at least, because A and B happen equally often. You could argue that the experience of measuring outcome B happens more often than the experience of measuring outcome A, that is, the subjective experience of the thread you are in, but that is not true, because ALL experiences happen with every measurement.

What do you mean with "single branch"?

 

[PeterDonis]

In the example I gave, B should, over a large number of measurements, happen more often than A.

Yes.

In MWI, to me that seems improbable at least, because A and B happen equally often.

No. In terms of the overall wave function, A and B both happen every single time, and there is no "equally often" about it; "equally often" would imply that half the time only A happens, and half the time only B happens, but in the MWI, both happen every time.

You could argue that the experience of measuring outcome B happens more often than the experience of measuring outcome A, that is, the subjective experience of the thread you are in

What you call "the thread you are in" is what I mean by "single branch". The argument you describe here is basically the argument that purports to derive the Born rule in the MWI. The problem is that, taken literally, it's obviously false: there will be many branches in which the relative frequencies of experiencing A and B will be different from the ones that the Born rule gives. Arguments have been made that, over a large enough number of measurements, the branches in which the experienced results differ measurably from the ones the Born rule gives will be a "set of measure zero" or something like that. Those arguments have not generally been considered convincing by physicists who don't accept the MWI.

Note that your use of the words "experience" and "subjective" is not really appropriate here. A measurement outcome is observed in each branch, and this is perfectly objective: if you restrict attention to just that branch, you can predict future measurement outcomes in that branch by treating the observed outcome as the preparation of a new wave function, i.e., you can ignore all other branches and just use the wave function you would use if only that one branch existed. (In other words, you can do what the standard math of QM, independent of any interpretation, tells you to do.)

 

[entropy1]

both happen every time.

Yes, that is what I mean; each measurement spawns ALL outcomes, right? wouldn't you call that equally often? Namely each outcome once with each measurement? 100% chance for each outcome - not 0.1 or 0.9. So to me that means that you can't steer on making B happen more often than A, not even subjectively.

Note that your use of the words "experience" and "subjective" is not really appropriate here. A measurement outcome is observed in each branch, and this is perfectly objective

There are two cases to observe here I think: the objective fact that in MWI ALL outcomes occur per measurement, and the subjective fact of experiencing only one of them at the time.

But I get more convinced that there must be a problem with MWI, but I also hate to compromise on unitarity.

 

[PeterDonis]

each measurement spawns ALL outcomes, right?

If you look at the whole wave function, yes.

wouldn't you call that equally often?

No, for the reason I already gave. But this is a matter of choice of words, not physics.

However, you also need to be careful not to let your choice of words lead you into mixing up different concepts. See below.

100% chance for each outcome

There is no "chance" involved at all. Everything is completely deterministic.

to me that means that you can't steer on making B happen more often than A

You are mixing up two different concepts.

If you look at the whole wave function, every outcome happens every time. But no individual branch will ever observe this. "Every outcome happens every time" means that every time the measurement is made, a branch will exist for every outcome, in which that outcome happens. But in each branch, only the outcome observed in that branch happens. If you look at the whole wave function, you could just as well say that no outcome happens--the whole wave function is entangled and does not describe any definite outcome.

If you look at one branch of the wave function, there will be some relative frequency of B and A as observed in that branch. That relative frequency will be an observed fact in that particular branch. But this is a different concept from any concept of "outcome" in the wave function as a whole.

the subjective fact of experiencing only one of them at the time

No, that's not a subjective fact, it's an objective fact. Consider just one measurement:

Before the measurement, the overall wave function describes one branch, with one system to be measured, one measuring device, and one observer who will observe the measuring device's result, all in definite states.

After the measurement, the overall wave function describes two branches, the "A" branch and the "B" branch, each one containing a "copy" of the system to be measured, a "copy" of the measuring device, and a "copy" of the observer. In each branch, taken by itself, the system, the device, and the observer are all in the state described by the observed result, "A" or "B". But the whole wave function is entangled; each branch is a term in an entangled superposition, and the wave function as a whole describes the three subsystems--system, device, observer--as not being in any definite state at all, but being entangled with each other, in the same way that two qubits created from a common source with opposite spins are entangled with each other: neither has any definite spin on its own.

All of these are objective facts about the wave function: there is nothing subjective at all.

 

[PeterDonis]

I get more convinced that there must be a problem with MWI, but I also hate to compromise on unitarity

Unfortunately, that's pretty much the choice one is faced with, since the MWI is exactly what you get if you absolutely refuse to compromise on unitarity.

 

[Minnesota Joe]

But how is it reconsilable to have the Born rule but still have all outcomes realized? What does the Born rule mean in that way?

Carroll has suggested that the Born Rule is the credence a rational observer assigns to one outcome or another occurring--to the observer finding herself in one branch/universe or another--after the measurement is complete, but before she looks at the detector reading. I guess that would be part of the meaning he wants to assign it.

 

[PeterDonis]

Carroll has suggested that the Born Rule is the credence a rational observer assigns to one outcome or another occurring--to the observer finding herself in one branch/universe or another--after the measurement is complete, but before she looks at the detector reading.

I'm not sure this makes sense, though. Carroll's suggestion requires that there is a meaningful sense in which the universe has already branched, but the observer has not yet looked at the detector reading; as I understand it that's how he justifies interpreting the squared modulus of the amplitude of the wave function for the branch as a probability/credence with the standard ignorance interpretation. But the branching process includes the observer looking at the detector reading--until everything is entangled with the measured system, including the observer himself, the branching process is not complete. So I don't think Carroll's justification works.

 

[Minnesota Joe]

I'm not sure this makes sense, though. Carroll's suggestion requires that there is a meaningful sense in which the universe has already branched, but the observer has not yet looked at the detector reading; as I understand it that's how he justifies interpreting the squared modulus of the amplitude of the wave function for the branch as a probability/credence with the standard ignorance interpretation. But the branching process includes the observer looking at the detector reading--until everything is entangled with the measured system, including the observer himself, the branching process is not complete. So I don't think Carroll's justification works.

Yes, that is a good point and I'm not sure it makes sense either. It's clear from the wavefunction that what you said has to be true, so I think I read it, charitably, as an abstraction. It's the credence we imagine we would assign if we could or something like that. I need to resist this "god's eye" view temptation it seems.

 

[entropy1]

But the branching process includes the observer looking at the detector reading--until everything is entangled with the measured system, including the observer himself, the branching process is not complete.

COULD you say that the outcome is not determined until observed, and NOT EVEN determined AFTER that because we have the superposition of ALL outcomes?

To be speculative : if P(A)=0.2, P(B)=0.3 and P(C)=0.5, and we measure outcome A, could it be that the universe behaves for 20% as if A happened, for 30% as if B happened, and for 50% as if C happened?

Outcome A then is not 100% "true", it is just a value in a list of outcomes converging to an average ratio of 0.2.

 

[Minnesota Joe]

That reminds me of something I wonder about very much: IF the branching process is not complete until X happened (making an observation), COULD it be that the OUTCOME is not yet DETERMINED until X happened? And to extend that: COULD the observer for a part determine the outcome? (Or is the observer/observation correlated with the measurement?)

MWI is a deterministic theory, though. So smooth, unbroken evolution of the universal wavefunction according to the Schrodinger Equation determines everything, including what the observers do.

Or are you talking about orthodox QM now?

 

[entropy1]

MWI is a deterministic theory, though. So smooth, unbroken evolution of the universal wavefunction according to the Schrodinger Equation determines everything, including what the observers do.

Or are you talking about orthodox QM now?

Determinism can involve retrocausality I think. Or rather, correlation, as a combination of causality and retrocausality.

 

[Minnesota Joe]

Determinism can involve retrocausality I think. Or rather, correlation, as a combination of causality and retrocausality.

In the Many Worlds Interpretation? In any case, wouldn't it still be determinism? So the outcomes necessarily follow from the initial conditions. I'm sorry, maybe I don't understand what you are driving at.

 

[entropy1]

In the Many Worlds Interpretation? In any case, wouldn't it still be determinism? So the outcomes necessarily follow from the initial conditions. I'm sorry, maybe I don't understand what you are driving at.

Ok, let me be clearer: IF A -> B, or: "IF A THEN B", then you could say A and B are causally linked. But they are also retrocausally linked, because the equivalent assertion is: NOT-B -> NOT-A, or: "IF NOT B THEN NOT A". The rule is deterministic, but the values are left to fill in. If you fill in A, B follows, but if you fill in (NOT-)B, (NOT-)A follows. The question remains: who determines what?

 

[Minnesota Joe]

Ok, let me be clearer: IF A -> B, or: "IF A THEN B", then you could say A and B are causally linked. But they are also retrocausally linked, because the equivalent assertion is: NOT-B -> NOT-A, or: "IF NOT B THEN NOT A". The rule is deterministic, but the values are left to fill in. If you fill in A, B follows, but if you fill in (NOT-)B, (NOT-)A follows. The question remains: who determines what?

I'm still not sure what you mean. "If A then B, A, therefore B" concludes something quite different than, "If not-B then not-A, not-B, therefore not-A". They contradict each other on the common reading, since it is not possible that (A & not-A). They can't both be true. If, instead, you are referring to conditions on the wavefunction being specified at $t_1$ compared to some later $t_2$, then they have to be consistent with each other. You should be able to derive the first conditions from the second conditions and visa versa, just using the Schrodinger equation.

 

[entropy1]

If, instead, you are referring to conditions on the wavefunction being specified at $t_1$ compared to some later $t_2$, then they have to be consistent with each other. You should be able to derive the first conditions from the second conditions and visa versa, just using the Schrodinger equation.

Then I think you are talking about A <-> B, or (A -> B) AND (B -> A), which is equivalent to NOT-A <-> NOT B. I distinguish the rule and the values. You may think of fixed rules, but who fills in which values? I think that in the deterministic view of QM, MWI, this is solved by yielding all possible outcomes (all possible values). But I have to say I am not a physicist.

 

[Minnesota Joe]

Then I think you are talking about A <-> B, or (A -> B) AND (B -> A), which is equivalent to NOT-A <-> NOT B. I distinguish the rule and the values. You may think of fixed rules, but who fills in which values?

Who or (I'm more inclined to say) what sets the initial conditions for the universal wavefuction is irrelevant to the point. After they are set, everything is determined by the Schrodinger equation. That includes our actions and observations. I'm talking about MWI in particular of course. Something analogous would follow for other deterministic theories of QM, but the equations would be different. Do you disagree with what I've written?