What is the current status of Many Worlds?

[PeterDonis]

Does the theory then actually say there are many 'worlds'

The term "worlds" refers to branches of the wave function. Heuristically, if two systems, $S$ and $M$, where $M$ is some kind of "measuring device" or "observer" and is assumed to be macroscopic, interact, they become entangled; the overall wave function might evolve from something like this:

$$
\Psi_\text{initial} = S_\text{prepared} M_\text{ready}
$$

To something like this:

$$
\Psi_\text{final} = S_\text{result A} M_\text{measured result A} + S_\text{result B} M_\text{measured result B}
$$

Each of the terms on the RHS of $\Psi_\text{final}$ is referred to as a "world". But the evolution from $\Psi_\text{initial}$ to $\Psi_\text{final}$ is unitary, so nothing is "created" or "destroyed"; all that happens is that two subsystems get entangled by a unitary interaction between them.

 

[PeterDonis]

I’ve never before heard anyone say the MWI branches aren’t real universes.

I didn't say that either.

Can you please provide links for more information about what you meant?

See post #40.

 

[bob012345]

The term "worlds" refers to branches of the wave function. Heuristically, if two systems, $S$ and $M$, where $M$ is some kind of "measuring device" or "observer" and is assumed to be macroscopic, interact, they become entangled; the overall wave function might evolve from something like this:

$$
\Psi_\text{initial} = S_\text{prepared} M_\text{ready}
$$

To something like this:

$$
\Psi_\text{final} = S_\text{result A} M_\text{measured result A} + S_\text{result B} M_\text{measured result B}
$$

Each of the terms on the RHS of $\Psi_\text{final}$ is referred to as a "world". But the evolution from $\Psi_\text{initial}$ to $\Psi_\text{final}$ is unitary, so nothing is "created" or "destroyed"; all that happens is that two subsystems get entangled by a unitary interaction between them.

Great but what is the relationship between $S_\text{prepared}$ and $S_\text{result A}, S_\text{result B}$? in terms of real systems? In other words, does each of $S_\text{result A}, S_\text{result B}$ contain all that was in $S_\text{prepared}$?

 

[PeterDonis]

Great but what is the relationship between $S_\text{prepared}$ and $S_\text{result A}, S_\text{result B}$? in terms of real systems? In other words, does each of $S_\text{result A}, S_\text{result B}$ contain all that was in $S_\text{prepared}$?

What do you mean by the phrase "all that was in"? What in the math does that phrase correspond to?

The states I wrote down are using perfectly straightforward notation from standard QM. There is nothing mysterious about them. $S$ and $M$ refer to different subsystems (i.e., different degrees of freedom), and the different subscripts refer to different possible states of those subsystems, considered in isolation. Which states those are, and what their intended physical interpretation is, should be obvious from the subscripts. $\Psi_\text{initial}$ is obviously a product state (i.e., separable), and $\Psi_\text{final}$ is obviously an entangled state; but $S$ and $M$ in both states refer to the same subsystems.

If what I wrote above does not answer your question, then there is an issue with your question; you are asking something that seems to be meaningful in vague ordinary language, but actually isn't when you try to pin it down to precise math.

 

[lukephysics]

You can write that binary formula for simple beam splitters with two outcomes but in reality there are so many splits every time step everywhere in the universe, and measurements are also happening everywhere constantly. It seems really hard to imagine this is a good way to erase the measurement problem like this even though it’s said to be the simplest interpretation of the math.

 

[bob012345]

What do you mean by the phrase "all that was in"? What in the math does that phrase correspond to?

I mean if $S_{prepared}$ was let's say a Uranium atom in some state and $M$ was a measurement system in some lab on some planet then are $S_{result A} , S_{result B}$ literally two different Uranium atoms in different 'worlds' or is this just a mathematical statement of a final wave-function over different outcomes. I'm trying to understand if this concept of different worlds co-existing is real or just a mathematical construct with no physical meaning.

 

[PeterDonis]

I mean if $S_{prepared}$ was let's say a Uranium atom in some state and $M$ was a measurement system in some lab on some planet then are $S_{result A} , S_{result B}$ literally two different Uranium atoms in different 'worlds' or is this just a mathematical statement of a final wave-function over different outcomes. I'm trying to understand if this concept of different worlds co-existing is real or just a mathematical construct with no physical meaning.

Go read my post #43 again, particularly the last paragraph. $S$ refers to the degrees of freedom that correspond to the Uranium atom. That's all there is to it as far as the math is concerned. Everything else is just standard QM applied to entangled states. If that doesn't answer your question, that means there is an issue with the question; it seems to you to be asking something meaningful, but it actually isn't.

 

[PeterDonis]

It seems really hard to imagine this is a good way to erase the measurement problem like this even though it’s said to be the simplest interpretation of the math.

Many physicists would agree with you, since many physicists do not agree with the MWI.

 

[bob012345]

Go read my post #43 again, particularly the last paragraph. $S$ refers to the degrees of freedom that correspond to the Uranium atom. That's all there is to it as far as the math is concerned. Everything else is just standard QM applied to entangled states. If that doesn't answer your question, that means there is an issue with the question; it seems to you to be asking something meaningful, but it actually isn't.

I have spent quite a bit of time trying to figure out how to respond to that third paragraph. I think I asked a reasonable question. I think you understand it.

 

[PeterDonis]

I think I asked a reasonable question.

Then you are wrong. See below.

I think you understand it.

You think incorrectly. Your question can't be understood because it is not well-defined. I know it seems to you that it is, but it isn't. That is why physicists don't use vague ordinary language; they use math. Again, you need to look at the math, not try to reason about the MWI in vague ordinary language. It won't work.

 

[PeterDonis]

you need to look at the math, not try to reason about the MWI in vague ordinary language. It won't work.

Btw, the fact that I am insisting on correct descriptions of what the MWI actually says does not mean I agree with the MWI. As a matter of personal opinion, I don't. As I think I remarked in another thread a while ago about interpretations, one needs to be even more careful about correctly stating what an interpretation says if one disagrees with it.

 

[PeterDonis]

I have spent quite a bit of time trying to figure out how to respond to that third paragraph.

If you're still having trouble with it, try taking a step back and asking yourself this question: in the state $\Psi_\text{final}$ that I wrote down, the $S$ and $M$ subsystems are entangled. What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

 

[bob012345]

Then you are wrong. See below.You think incorrectly. Your question can't be understood because it is not well-defined. I know it seems to you that it is, but it isn't. That is why physicists don't use vague ordinary language; they use math. Again, you need to look at the math, not try to reason about the MWI in vague ordinary language. It won't work.

Then help me ask the correct question! You are the mentor not me!

 

[PeterDonis]

Then help me ask the correct question! You are the mentor not me!

I've already given you a couple of suggestions.

 

[Demystifier]

Why isn’t predicting market prices also talked about as many worlds?

Because we know what's the ontology of market prices, which is not the many world ontology. We know that the price PDF is just a map, not the territory.

 

[Demystifier]

Do you have a reference for this formulation?

See e.g.
https://plato.stanford.edu/entries/qm-bohm/#QuanPote
https://arxiv.org/abs/1704.08017 (especially Eq. (1) and Sec. 8)
https://www.mathematik.uni-muenchen.de/~duerr/Survey.pdf (especially Eqs. (2) and (3))

 

[PeterDonis]

See e.g.
https://plato.stanford.edu/entries/qm-bohm/#QuanPote
https://arxiv.org/abs/1704.08017 (especially Eq. (1) and Sec. 8)
https://www.mathematik.uni-muenchen.de/~duerr/Survey.pdf (especially Eqs. (2) and (3))

Thanks!

 

[bob012345]

I've already given you a couple of suggestions.

Fine. I'll figure it out elsewhere. Thanks.

 

[PeterDonis]

Fine. I'll figure it out elsewhere.

You mean, you've read all my posts and you don't see any suggestions? How about, for example, answering the question I posed in post #47?

 

[bob012345]

You mean, you've read all my posts and you don't see any suggestions? How about, for example, answering the question I posed in post #47?

What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

That you don't know what state each system is in until you measure it? I'm not asking about standard QM. I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math. If it is just math then why are physicists like DeWitt saying such misleading nonsense like every interaction branches the universe?

 

[PeterDonis]

That you don't know what state each system is in until you measure it?

No. That's not even true; if you prepare a system in a particular state, you know it's in that state.

What I had in mind was the fact that if two subsystems are entangled, then neither subsystem even has a well-defined state by itself. Only the whole entangled system does. See further comments below.

I'm not asking about standard QM.

If you don't understand what standard QM says about a particular scenario, you can't possibly expect to understand what any interpretation says about it. You have to understand the basics of standard QM--the math and the predictions--before you can understand any interpretation.

I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math.

Not at all. The many worlds view says that the wave function is real. It does not say it is "just math".

So, if you have an electron and a measuring system entangled with two separate states as you showed in post #36, does MWI say there is some physical reality such as separate 'worlds' or is that merely a mathematical contrivance for computation purposes?

The MWI says that the wave function is real. That's all it says about what is "real". The "worlds" it talks about are all part of the wave function (as I've already described, they are the individual terms in an entangled state). Does that answer your question?

Instead of continuing to belabor the same question, let's go back to what I said above about entangled states. If we have an electron and a measuring device, and they are entangled, neither one has any well-defined state by itself. Only the total system of electron plus measuring device does.

However, according to the MWI, we can give a relative interpretation to the individual terms in the entangled state. For example, if we have measured an electron's spin, we can say that the electron has the state "spin up" relative to the state "measured spin up" of the measuring device, and vice versa; and we can say that the electron has the state "spin down" relative to the state "measured spin down" of the measuring device, and vice versa. In fact, the original name for what is now called the "many worlds" interpretation, in the paper and Ph.D. thesis by Hugh Everett that introduced it, was the "relative state" interpretation; the name "many worlds" was introduced and popularized later, mainly by DeWitt, whose claims about it were very different (and much more extreme) than Everett's original ones. It was DeWitt and others who shared his views who started using the term "worlds" to describe the individual terms in the entangled wave function after measurement.

 

[bob012345]

No. That's not even true; if you prepare a system in a particular state, you know it's in that state.

I was not speaking of prepared states.

What I had in mind was the fact that if two subsystems are entangled, then neither subsystem even has a well-defined state by itself. Only the whole entangled system does. See further comments below.

I am not a mindreader.

If you don't understand what standard QM says about a particular scenario, you can't possibly expect to understand what any interpretation says about it. You have to understand the basics of standard QM--the math and the predictions--before you can understand any interpretation.

I only said I wasn't asking about standard QM but the MWI version not that I had no standard QM background.

Not at all. The many worlds view says that the wave function is real. It does not say it is "just math".The MWI says that the wave function is real. That's all it says about what is "real". The "worlds" it talks about are all part of the wave function (as I've already described, they are the individual terms in an entangled state). Does that answer your question?

Yes. I have no more question beyond what then is such a wave function physically if it is real and what does it mean to be in an entangled state for a real macroscopic wave-function. Are there many me's after all if I am in an entangled state? I do not expect an answer.

Instead of continuing to belabor the same question, let's go back to what I said above about entangled states. If we have an electron and a measuring device, and they are entangled, neither one has any well-defined state by itself. Only the total system of electron plus measuring device does.

However, according to the MWI, we can give a relative interpretation to the individual terms in the entangled state. For example, if we have measured an electron's spin, we can say that the electron has the state "spin up" relative to the state "measured spin up" of the measuring device, and vice versa; and we can say that the electron has the state "spin down" relative to the state "measured spin down" of the measuring device, and vice versa. In fact, the original name for what is now called the "many worlds" interpretation, in the paper and Ph.D. thesis by Hugh Everett that introduced it, was the "relative state" interpretation; the name "many worlds" was introduced and popularized later, mainly by DeWitt, whose claims about it were very different (and much more extreme) than Everett's original ones. It was DeWitt and others who shared his views who started using the term "worlds" to describe the individual terms in the entangled wave function after measurement.

Ok. It's rather late and I'm tired so I'm signing off for tonight. Thanks for the discussion!

 

[PeterDonis]

Are there many me's after all if I am in an entangled state?

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

 

[PeterDonis]

I am not a mindreader.

You shouldn't need to be to answer the question I asked about subsystems in entangled states. It's basic QM.

 

[Jarvis323]

My take is that there is what MWI says, and then there is what people claim that MWI implies.

I understand it could be a misconception, but I am trying to reason through it. Am I correct to say a real inaccessible world is identical mathematically and logically to an imaginary or hypothetical branch from the reference point of our branch?

If the wave function is real, with all of its terms, then the other worlds are real. If the wave function is not real, but just mathematics, then those other terms can still be in the wave function, yet only represent hypothetical imaginary worlds.

They may be mathematically equivalent within a limited view/context. Obviously they are logically distinguished, however, they are opposing statements of what is true. And thus, the structures of logic that follow these statements are not the same.

You may wonder whether it can ever be fruitful to try to work out logical deductions that depend on the truth values of these statements. Some people think that the ability to compare mathematics and logic with physical experiment hit a dead end here. In that case, perhaps the mathematics and logic that depend on these truth values aren't something physicists need to be concerned with. But a lot of mathematicians and philosophers could care less. And everyday people, as well as some physicists, don't mind pondering the logical implications of these kinds of statement either.

The motivation to do this, regardless of perceived experimental limitations, for QM specifically, is that the logic of QM is weird. Of course people want to try and wrap their minds around what kind of possibilities there might be for our reality given what we can learn from QM.

 

[lukephysics]

Schrodingers equation says there are many worlds, but can’t there be an equally explanatory equation that drops the many worlds since they seem unnecessary?

I guess none of this matters really anyway since schrodingers and qm works anyway.

 

[Jarvis323]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels. And if I could probe your mind, maybe I'd see some wrinkles where this state lives. If we say the wave function is real, it is already a statement about something that is a level of abstraction beyond (or below) just the mathematics. So isn't looking at the mathematics to understand what MWI means only half the picture.

 

[vanhees71]

In the financial case, only one of the possible outcomes in the PDF actually occurs. In many worlds, all of the possible outcomes occur.

Can you tell me, how to get into that very universe, where the content of my account is spontaneously doubled by some event on the stock market? SCNR.

 

[vanhees71]

What does standard QM say about the states of individual subsystems that are entangled? (The "subsystems" could just be two electrons, instead of an electron and a measuring device.)

If you have a quantum system that can be separated in two subsystems $A$ and $B$ the Hilbert space of the system is described as the product of the two Hilbert spaces of the subsystems $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. Let $|u_j \rangle \in \mathcal{H}_A$ and $|v_k \rangle \in \mathcal{H}_B$ be complete orthonormal systems (CONSs) then $|w_{jk} \rangle=|u_j \rangle \otimes |v_k \rangle$ are a CONS in $\mathcal{H}$.

If the quantum system is prepared in some state $\hat{\rho}$ then the states of the subsystems are described by the reduced statistical operators $\hat{\rho}_A$ and $\hat{\rho}_B$, defined by taking the partial traces over the respective other subsystem:
$$\hat{\rho}_A = \sum_{j,k,l} |w_{kj} \rangle \langle w_{kj}|\hat{\rho}|w_{lj} \rangle |u_k \rangle \langle u_l |$$
and analogously for $\hat{\rho}_B$.
If you know the state of the complete system all subsystems take unique states defined by these "reduced statistical operators".

Take, as a simple example, the spin-singlet state of a system of two spins 1/2. Then
$$\hat{\rho}=|\Psi \rangle \langle \Psi|$$
with
$$|\Psi \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|-1/2,1/2 \rangle).$$
It's a simple exercise to find that for this "Bell state" the subsystems are maximally indetermined, i.e., the corresponding particles are precisely unpolarized,
$$\hat{\rho}_A=\hat{\rho}_B=\frac{1}{2} \hat{1}.$$

That you don't know what state each system is in until you measure it? I'm not asking about standard QM. I'm asking if there is any reality to all this multiple worlds view or is it just math. Seems to me you are saying it is just math. If it is just math then why are physicists like DeWitt saying such misleading nonsense like every interaction branches the universe?

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

 

[Jarvis323]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

For me, this line of thinking is highly confusing. The entire goal of philosophy is to make things not fuzzy. The thing that changed in the renaissance wasn't separating philosophy from science, it was to establish concrete philosophical foundations for science. This was also the time when we began to established concrete philosophical foundations for mathematics. The revolution in science was due to a breakthrough in philosophy, not an abandonment of it.

 

[WernerQH]

This is an enigma to me too, but usually when physicists enter the terrain of fuzzy philosophy, "misleading nonsense" is likely to occur (just an observation ;-)). For me the greatest progress of the thinking of mankind was the idea to strictly separate the "hard sciences" from the fuzzy "humanities" in the renaissance when modern natural sciences started to be developed.

It seems some people desperately try to make sense of MWI. Using stict logical deduction, it is of course possible to "derive" an infinity of absurd conclusions from just one nonsensical assumption.

 

[bob012345]

Suppose we have a two-electron system with electrons A and B in the singlet state:

$$
\frac{1}{\sqrt{2}} \left( \ket{A}_\text{up} \ket{B}_\text{down} - \ket{A}_\text{down} \ket{B}_\text{up} \right)
$$

Are there "many" electron A's and "many" electron B's in this state?

Whatever your answer is to this question, the answer will be the same to the question you asked that is quoted above.

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons. You seem to be saying to regard the MWI wavefunction in the same way. That makes sense to me. Going back and forth further about what MWI adherents really believe is counterproductive at this point. I found an essay by a Princeton physicist;

https://arxiv.org/pdf/1801.08587.pdf

Thanks for the discussion!

 

[PeterDonis]

If you want to ask this kind of question, why not go further and ask if there are any electrons in this state. All there are that I see are arrangements of black pixels.

"Electron" in this case is simply a name for the degrees of freedom referred to by the symbols $A$ and $B$. So of course there are electrons in this state. There are "electron A" degrees of freedom, and "electron B" degrees of freedom. They're right there in the wave function.

Of course when we write down a wave function like this, we are usually making some implicit assumption about how the degrees of freedom in the state correspond to measurements--for example, we might relate the "electron A" degrees of freedom to some measurement made by Alice, and the "electron B" degrees of freedom to some measurement made by Bob. That is not a matter of any particular QM interpretation; it's a matter of the basic math and how it relates to measurements. If you can't relate the math to measurements in some way, you can't test the theory's predictions.

isn't looking at the mathematics to understand what MWI means only half the picture.

For any interpretation, as I said, there has to be a grounding in the math. Otherwise it isn't an interpretation of QM to begin with.

For the MWI in particular, there is a sense in which "the math is all there is", because the central claim of this interpretation is that the wave function is real, and it's the only thing that's real. But I agree that advocates of the MWI have to do more than just point at the wave function to explain why they think the interpretation makes sense.

 

[PeterDonis]

My answer is no, of course not. I would not regard this wavefunction as involving two A electrons and two B electrons. The wavefunction is over states of the electrons.

That is my view as well.

You seem to be saying to regard the MWI wavefunction in the same way.

Yes. And then the challenge for MWI advocates is to explain how this can possibly be consistent with our experiences, since when we observe or measure something we experience a definite result having occurred. The MWI has to say that all of the possible results occurred, but it's not clear to start with what that means, since in an entangled state like the ones we have been looking at, it seems like nothing has "occurred"--neither subsystem is in a definite state at all.

The original "relative state" viewpoint explained this by saying that, for each subsystem, each of the possible results occurs relative to the corresponding result for the other subsystem. So it would say that in the singlet state, two results have occurred: "electron A up, electron B down" and "electron A down, electron B up". (Actually, since the development of decoherence theory, even a "relative state" interpretation would no longer say this, since no decoherence has occurred for two electrons in the singlet state. But it would still work for any case that does involve decoherence, which certainly includes any macroscopic measurement or any observation by a human.) This is still a change in the meaning of the term "occurs", since it no longer corresponds to a subsystem having a definite state period--now it only requires the subsystem to have a relative state with respect to another subsystem with which it is entangled.

The "many worlds" viewpoint, however, wants to make a stronger claim, one that seems to amount to there actually being multiple "copies" of each subsystem, one in each "world"--but, as we've seen, if we take such statements literally they are obviously false since that's not how entangled states in QM work. So the "many worlds" viewpoint still has to fall back on something like a "relative state" formulation when challenged, while trying to make the stronger-sounding "many worlds" claims whenever it can get away with it. As you can see from this description of mine, I am not a many worlds proponent myself (as I've already said).

 

[AndreiB]

Wave function is fundamental but not ontic, in the same sense in which Hamiltonian in classical mechanics is fundamental but not ontic.

Why is the Hamiltonian fundamental in classical mechanics? Newton was fine without it. Is Bohm's interpretation fine without the wave function?