MWI and interpretation of measurements

[entropy1]

I was wondering, if we have a measurement of, say, spin of an electron, which can yield spin-up and spin-down in the context of MWI, then the electron gets entangled with the measurement device, yielding the wave function $|Measurement_{spin-up}, Value_{spin-up} \rangle + |Measurement_{spin-down}, Value_{spin-down} \rangle$.

Now some terminology in populair science media speak of a "splitting of worlds", hence the name "Many Worlds Interpretation", because it seems that this wavefunction says there are two (both) outcomes, but in different contexts (worlds).

I think @PeterDonis told me, correct me if I'm wrong, that what is NOT happening is that a copy is made of the universe with each measurement, but that the "splitting" is done in the domain of Hilbert Space, where wavefunctions reside.

This suddenly became appealing to me. Something is happening with measurement that suggests that universe gets duplicated, but it is only in Hilbert space.

Is that correct?

 

[PeterDonis]

I think @PeterDonis told me, correct me if I'm wrong, that what is NOT happening is that a copy is made of the universe with each measurement

Correct.

but that the "splitting" is done in the domain of Hilbert Space, where wavefunctions reside.

According to the MWI, the wave function is all there is, so anything that happens has to happen to wave functions. But the term "splitting" doesn't really capture what is happening to the wave function.

Consider: you wrote down the wave function after measurement. But what is the wave function before measurement? It will be something like this:

$$
\ket{\text{Measurement}_{\text{ready}}} \left( \ket{\text{Value}_{\text{spin-up}}} + \ket{\text{Value}_{\text{spin-down}}} \right)
$$

This wave function also has two terms (if we expand out what is inside the parentheses); the only difference is that it is not entangled (the "measurement" and "value" degrees of freedom are separable). So all that is actually happening during the measurement is the entanglement; there is no "splitting", because the "value" degree of freedom in the wave function is already "split", as you can see in the above (both the "spin-up" and the "spin-down" terms are already there).

 

[entropy1]

So what does the WF after the measurement actually mean? What does it say about the outcome of the measurement, since measurement result and spin value are entangled?

To me it appears something like: "If we measure spin-up, the spin value was spin-up," and "If the spin value is spin-up, then we will measure spin-up", and the same for spin-down, however it seems to me nothing is revealed about what the outcome of the measurement actually is. But because in the human world we do get an outcome, the human world does not seem ontic, in contrast to Hilbert Space and the WF, who do seem ontic, which is the common understanding, right?

 

[StevieTNZ]

So what does the WF after the measurement actually mean? What does it say about the outcome of the measurement, since measurement result and spin value are entangled?

To me it appears something like: "If we measure spin-up, the spin value was spin-up," and "If the spin value is spin-up, then we will measure spin-up", and the same for spin-down, however it seems to me nothing is revealed about what the outcome of the measurement actually is. But because in the human world we do get an outcome, the human world does not seem ontic, in contrast to Hilbert Space and the WF, which is the common understanding, right?

One could go further with that entangled state and find an observable of the combined system + apparatus that will yield a result consistent with the two being in a superposition state. See "Sneaking a Look at God's Cards", pages 373-376 (chapter 15 for general information). See also Wigner's friend models.

 

[PeterDonis]

So what does the WF after the measurement actually mean?

According to the MWI, it means that the measured system and the measuring device are entangled, and each term in the entangled state represents a "world" in which the measuring device measured the measured system to have the corresponding value. Since each term in the entangled state is decohered, the "worlds" can never interfere with each other, so each term in the entangled state evolves thereafter as though it were the only term in the wave function. That is how the MWI accounts for the fact that we appear to observe measurements to have outcomes, even though, strictly speaking, neither the measured system nor the measuring device are in a definite state after the measurement, since they are entangled.

 

[PeterDonis]

One could go further with that entangled state and find an observable of the combined system + apparatus that will yield a result consistent with the two being in a superposition state.

Note, however, that every proposal that has been made for actually trying to do this (such as the various takes on the Wigner's friend scenario that have appeared in the literature) either assume that decoherence has not yet occurred--which invalides the interpretation of the separate terms in the after-measurement entangled states as "worlds"--or assume that decoherence can be reversed--which invalidates the whole concept of anything ever having an outcome or any irreversible record ever being made. (Most of the papers I have read in the second category then go on to blithely talk about measurements having outcomes and irreversible records being made, without ever appearing to notice the contradiction.)

 

[StevieTNZ]

There is discussion in "Quantum Mechanics and Experience" by David Albert that once the environment becomes involved, the original observable for the system + apparatus would be the wrong one to measure. It would then be the observable of system + apparatus + environment (aka the rest of the world).

 

[PeterDonis]

There is discussion in "Quantum Mechanics and Experience" by David Albert that once the environment becomes involved, the original observable for the system + apparatus would be the wrong one to measure. It would then be the observable of system + apparatus + environment (aka the rest of the world).

Yes, that's true, decoherence means the system + apparatus gets entangled with the environment. And since there is no way to measure any observable that includes the entire universe, since there is no "outside" of the universe from which to measure it, that would make decoherence irreversible.

 

[StevieTNZ]

Yes, that's true, decoherence means the system + apparatus gets entangled with the environment. And since there is no way to measure any observable that includes the entire universe, since there is no "outside" of the universe from which to measure it, that would make decoherence irreversible.

I guess the discussion poses interesting thought, for it is "in principle". For example, the interpretation I adhere to (consciousness causes 'wave function collapse'), the outside of the universe will be consciousness. It is heavily correlated to brains, but personally I believe (as do some others, authors I can't remember off the top of my head) consciousness is not a by-product of brain activity. That's my view anyway. It is independent of the brain. But this is starting to stray off topic, which is MWI, so I'll stop there.

 

[Demystifier]

This suddenly became appealing to me. Something is happening with measurement that suggests that universe gets duplicated, but it is only in Hilbert space.

Is that correct?

It is correct.

But to better understand it, ask yourself this: If the splitting was not in the Hilbert space, but in some other space, then what space could that be?

The main assumption of MWI is that there is no any other space except the Hilbert space. The only well-established interpretation of QM that explicitly denies that assumption is the Bohmian interpretation, which assumes that there is also the space of particle positions (or field configurations, in the case of QFT). By contrast, Copenhagen-like interpretations do not talk explicitly about any other space except the Hilbert space. So I repeat my question, when you thought that splitting could have been in some other space, what specific space did you have in mind?

 

[entropy1]

when you thought that splitting could have been in some other space, what specific space did you have in mind?

Well, I'm not an expert but I guess that would be spacetime, as we perceive it by our senses. But I agree that on a more fundamental level it may be Hilbert space.

However, I suspect the state after measurement could represent a lack of predictive power or a lack of representative power. In MWI the WF is seen as ontic. I don't know if that is required though.

It seems to me MWI is what you get if you insist on determinism (Unitary evolution), and Copenhagen is what you get if you don't insist on determinism. The splitting into worlds in MWI may be a concession that has to be made in order to deal with actual randomness in the (quantum) world, is my take on it.

even though, strictly speaking, neither the measured system nor the measuring device are in a definite state after the measurement, since they are entangled.

I think that's right. The measurement outcome and the measured value depend on each other, right? This is the kind of randomness that, in my view, could reconsile MWI with Copenhagen.

The statement the state after measurement makes in MWI, in my view, is: "You will measure the correct value, but we don't know in advance which value", or: "Something else than the SE determines the measurement outcome", or: "The value of the observable and the outcome of the measurement are correlated/entangled", or: "You will have an outcome, but it just as well could have been a different outcome". The question is: are the terms simultaneously true, or are they mutually exclusive after measurement, because if the terms represent a superposition, then they don't seem to have a definite value.

You can superimpose states to make up a definite single state, so that a single state can be seen as a superposition of states, and a superposition of states can add up to a single state. With measurement, the state can either collapse to a single outcome, or it can keep being in superposition and yield outcomes in superposition. But the state having been measured is the same one in both cases.

So it still seems a matter of interpretation.

 

[PeterDonis]

the measurement outcome and the measured value depend on each other, right?

The measurement outcome is the measured value.

This is the kind of randomness

There is no randomness whatever in the MWI. Everything is completely deterministic. The measurement outcome is not random because all possible outcomes occur, each one in its own branch of the wave function.

The statement the state after measurement makes in MWI, in my view, is

Your view is wrong. See my statement above about the lack of randomness in the MWI.

You can superimpose states to make up a definite single state, so that a single state can be seen as a superposition of states, and a superposition of states can add up to a single state.

This just means the word "superposition" is the wrong word to use to describe the state after measurement. The correct word is "entangled"; whether or not a state is entangled is a definite property of the state and does not depend on any choice of basis.

So it still seems a matter of interpretation.

There is no "matter of interpretation" whatever about any of the things I have said above about the MWI. All of those statements are unequivocal claims of the MWI. Of course the MWI is just one interpretation of QM, but there is no "matter of interpretation" about what it says. The only issues I can see are with your understanding of what the MWI actually says.

 

[PeterDonis]

The statement the state after measurement makes in MWI

Is: All possible outcomes occur. In the particular state you wrote down in the OP, the state, according to the MWI says: "the spin up outcome occurs, in the entangled branch in which the measuring device registers spin up; and the spin down outcome occurs, in the entangled branch in which the measuring device registers spin down".

 

[entropy1]

The measurement outcome is the measured value.

The value of the pointer is the measurement outcome, and spin is the measured value, in this case.

There is no randomness whatever in the MWI. Everything is completely deterministic. The measurement outcome is not random because all possible outcomes occur, each one in its own branch of the wave function.

Then I must have misunderstood your remark:

even though, strictly speaking, neither the measured system nor the measuring device are in a definite state after the measurement, since they are entangled.

You speak of (not being in) a "definite" state. So I if I understood you correctly earlier on, the state of the combined system is in a definite state, right? It seems to me if we have A and B entangled, and the values of A and B are not definite on their own, but are definite together, that we have a dependence between A and B.

The statement the state after measurement makes in MWI, in my view, is:

Your view is wrong. See my statement above about the lack of randomness in the MWI.

I should have been more careful in my formulation. I ment to identify the equivalence between MWI and Copenhagen, because they yield the exact same results. We don't measure all possible outcomes, even though they may all occur. MWI claims that that is what happens. Well, Copenhagen doesn't. So there may be a difference between what some interpretation claims and what actually happens, right?

This just means the word "superposition" is the wrong word to use to describe the state after measurement. The correct word is "entangled"; whether or not a state is entangled is a definite property of the state and does not depend on any choice of basis.

Ok. I have to investigate that.

There is no "matter of interpretation" whatever about any of the things I have said above about the MWI. All of those statements are unequivocal claims of the MWI. Of course the MWI is just one interpretation of QM, but there is no "matter of interpretation" about what it says. The only issues I can see are with your understanding of what the MWI actually says.

Here I mean a matter of which interpretation you prefer. (eg. Copenhagen/MWI/etc)

Is: All possible outcomes occur.

Well, Copenhagen is a valid interpretation also, right? So what is actually happening may be a matter of interpretation.

I think I should have included "... and comparison with Copenhagen" in the title of this thread.

 

[PeterDonis]

You speak of (not being in) a "definite" state.

Yes, because if a state is entangled, neither of the subsystems are in a definite state, only the full joint system is. This is a basic fact about QM and has nothing whatever to do with randomness.

It seems to me if we have A and B entangled, and the values of A and B are not definite on their own, but are definite together, that we have a dependence between A and B.

Not "dependence", entanglement. Entanglement is what it is. It is not something else. Trying to use other words when entanglement is the fact of the matter is only going to cause confusion.

there may be a difference between what some interpretation claims and what actually happens, right?

Of course if an interpretation is wrong, then what it claims will be different from what actually happens. Since the MWI and Copenhagen make contradictory claims about what actually happens, it is impossible for them both to be right; at least one must be wrong. (It is also possible that they are both wrong.)

I think I should have included "... and comparison with Copenhagen" in the title of this thread.

If that is what you meant, then yes, you certainly should have. However, your OP in this thread says nothing about Copenhagen, only about the MWI. If you want to compare the two, you should start a new thread with a new OP that clearly states the comparison you want to make.

 

[entropy1]

If that is what you meant, then yes, you certainly should have. However, your OP in this thread says nothing about Copenhagen, only about the MWI. If you want to compare the two, you should start a new thread with a new OP that clearly states the comparison you want to make.

I had not foreseen the discussion would go that way, so I'll forgive myself.