I What is the current status of Many Worlds?

[CelHolo]

I’m talking about financial markets where you are predicting the position of a market. You only have a PDF of the position of the market, and when you measure it it collapses to 1. Same as the wave function. Why isn’t predicting market prices also talked about as many worlds?

You could do it, i.e. consider a classical probability distribution as a "real wave" and thus that each price "occurs in some world", it's just historically very few people have done so.

 

[bob012345]

Many worlds is the kind of thinking that happens when physicists don't get out enough. I mean how can we laugh at cranks trying to make energy out of nothing while postulating that the universe does the same by infinite amounts at every instant?

 

[PeterDonis]

how can we laugh at cranks trying to make energy out of nothing while postulating that the universe does the same by infinite amounts at every instant?

There is no "creation of energy" in many worlds. The term "many worlds" is in fact misleading since no "worlds" are created; the wave function just evolves unitarily all the time, so nothing is ever created or destroyed.

 

[bob012345]

There is no "creation of energy" in many worlds. The term "many worlds" is in fact misleading since no "worlds" are created; the wave function just evolves unitarily all the time, so nothing is ever created or destroyed.

Thanks. Does the theory then actually say there are many 'worlds' however that is defined in existence already, thus other copies of each of us?

 

[lukephysics]

Peterdonis I’ve never before heard anyone say the MWI branches aren’t real universes. Quite the opposite. Can you please provide links for more information about what you meant?

 

[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.