How many worlds is Many Worlds talking about?

[bushmonk]

TL;DR Summary

There are many options available for, say, a radioactive atom to disrupt the atoms around it when it decays. Is there a separate world for each option?

For clarity, consider a very orderly crystal with a single radioactive atom at a specific location. It decays by alpha emission. When the alpha particle is emitted, it disrupts the location of nearby atoms and then comes to rest and forms a stray helium atom. It would seem that there is a moderately large number of possibilities. The alpha particle might go left and disrupt the location of the nearest atom on the left, and then proceed in a more or less leftward path, each collision and disruption being one of the options that Shrodinger's equation permits, with a certain probability and subject to what has already been disrupted. There are many directions that the alpha particle can go. Furthermore, the alpha emission could occur sooner or later.
According to the Many Worlds Interpretation:
1. Does the situation generate new worlds or are the worlds already presumed to exist?
2. Is there a separate world for each possible set of disruptions?
3. Is there a separate set of worlds for each instant.
4. If there is a separate set of worlds for each instant, is there some constraint that would limit "instant" to being finitely small rather than infinitely small.
5. If the alpha particle has indeed been emitted, are there yet other worlds in which it has not yet done so.

 

[PeterDonis]

According to the Many Worlds Interpretation:
1. Does the situation generate new worlds or are the worlds already presumed to exist?

It depends on what you mean by "worlds". In the MWI, the physical reality is the wave function and only the wave function, and there is only one wave function. So in that sense there is only one "world".

However, when a measurement, or more generally an event causing decoherence, takes place, the wave function develops multiple branches, one for each possible result of the event. In this case, there would be one branch for each possible configuration of alpha particle + crystal after the emission. (There would also be a "no emission" branch--see the response to 5. below.) These decoherent branches are what are usually described as "worlds" in the MWI.

2. Is there a separate world for each possible set of disruptions?

To the extent that different possible disruptions cause decoherence, yes. See above.

3. Is there a separate set of worlds for each instant.

No. The "worlds", as above, are branches of the wave function, which evolves and forms branches over time, but the worlds are not "snapshots" at some instant of time; they are just the branches as they develop over time.

5. If the alpha particle has indeed been emitted, are there yet other worlds in which it has not yet done so.

As soon as any decoherence is caused by the emission, yes, it becomes a separate decoherent branch from "no emission". Or, in wave function terms, yes, there will be a branch of the wave function in which no alpha particle has been emitted and everything is still in the initial state, although the probability associated with this branch will decrease over time.

 

[Quantumental]

The jury is still out on this. Just 2 weeks ago this paper was published: https://arxiv.org/abs/2310.06755 which has implications if shown to apply

 

[gentzen]

The jury is still out on this. Just 2 weeks ago this paper was published: https://arxiv.org/abs/2310.06755 which has implications if shown to apply

Do you have an own opinion on the paper? Would you like to discuss it a bit? I have not studied it in detail yet, but I noticed that they use the decoherent histories formalism

Formalism. To access the decoherence of branches for L ≫ 1 it is natural to use the consistent or decoherent histories formalism, see Refs. [12–17] for reviews. We are aware of controversies about its use in relation to interpretations of quantum physics (see, e.g., Ref. [18]). In relation to our work, we reject this criticism as we only use the mathematical framework and do not postulate the consistency or decoherence of histories (instead, we study their emergence based solely on the Schrödinger equation). Seen from that perspective, little controversy remains about the fact that decoherent histories capture an essential aspect of classicality, even though they might not capture all aspects. In particular, various researchers have established a close connection between decoherent histories and the formation of stable records or memories—an important prerequisite to identify classical branches that could support observers [19–26].

but cite neither On maximum number of decoherent histories by Lajos Diósi nor Properties of Consistent Histories by Fay Dowker and Adrian Kent. Those would have been important to have certain "basic expectations" of how their L (length of history) and D (dimension of Hilbert space) interact. I looked which parameter combinations they study:

First, in Figs. 2 (a) and (b) we consider a short history of length L = 25 and compare two system sizes: D = 250 and D = 25000. We confirm that decoherence is much stronger for larger system size, in unison with Ref. [28, 29]. Moreover, we have q(n) ≈p(n) for D = 25000, but see significant deviations for D = 250 owing to the strong influence of finite size effects.

Things start to change drastically for long histories with L = 250 as shown in Figs. 2 (c) and (d).

The parameter combinations L=250 and D=25000 will be dominated by the bound derived by Lajos Diósi in the paper above. (Me, Morbert and Fra had some discussion (for example here and here) on the meaning of that bound, and how problematic it is for consistent histories. (But please ignore those discussion for the moment, my question is just whether you like to discuss the paper you brought up a bit.)

 

[bushmonk]

No. The "worlds", as above, are branches of the wave function, which evolves and forms branches over time, but the worlds are not "snapshots" at some instant of time; they are just the branches as they develop over time.

A surprising statement to me. I gather that the amplitude of the un-decayed atom gradually decreases and the amplitude of the various decoherent branches gradually increase with time. This raises a couple of questions:
1. How does MWI set t = 0 for this case.
2. Suppose that at a certain time, the decay is observed to take place. How does the MWI handle this new information. It would seem that if the wave equation is all there is, the particular branch represented by the disruption in the crystal would continue to gradually increase in amplitude, but by now we know that the event has already occurred.
Thanks in advance.

 

[PeterDonis]

1. How does MWI set t = 0 for this case.

t = 0 is assumed to be the initial preparation of the atom in the undecayed state.

2. Suppose that at a certain time, the decay is observed to take place.

If you suppose this, you are not using the MWI. The MWI says that all possible outcomes take place. That includes decays at all possible times that a decay could happen. If you suppose that the decay takes place only once, at one particular time, you are using some other interpretation of QM, not the MWI.

 

[PeterDonis]

That includes decays at all possible times that a decay could happen.

Note that many treatments of this case using the MWI will not say this; they will say there are only two branches of the wave function, the "undecayed" branch and the "decayed" branch, whose relative amplitudes change over time. If the atom started out alone in the universe, this would be true, because there would be no way of distinguishing a decay at one time from a decay at another. But in our actual universe, decays at different times will have different effects on other parts of the universe, and as soon as you include those other parts in your model, you will end up with what I described.

 

[bushmonk]

If you suppose that the decay takes place only once, at one particular time, you are using some other interpretation of QM, not the MWI.

I am not assuming that the decay takes place only once. Only that I have observational access to one decoherent branch, and in that branch the decay has taken place. The decay in other branches may or may not have taken place.

I am far from assuming that the decay only occurs once. But it only occurs once in the branch to which I have observational access. My initial query (post #1) was that MWI included not only all possible disruptions of the crystal as different decoherent branches but also that the time of occurrence generated additional sets of decoherent branches. So if I observed that in my branch the decay occurred at noon and disrupted the crystal in a certain way, then at the same time (12 noon) every other possible disruption occurred in other branches and further, the same set of possible disruptions would occur at 12:01 PM in still other worlds.

In post #2 you replied to my query, " Is there a separate set of worlds for each instant" with

No. The "worlds", as above, are branches of the wave function, which evolves and forms branches over time, but the worlds are not "snapshots" at some instant of time; they are just the branches as they develop over time.

Then in post #6, you said,

The MWI says that all possible outcomes take place. That includes decays at all possible times that a decay could happen.

You clarified the seeming contradiction in post #7

Note that many treatments of this case using the MWI will not say this; they will say there are only two branches of the wave function, the "undecayed" branch and the "decayed" branch, whose relative amplitudes change over time. If the atom started out alone in the universe, this would be true, because there would be no way of distinguishing a decay at one time from a decay at another.

This was very clear. The absence of a physical difference in outcomes is matched by the absence of a theoretical difference.
Further:

But in our actual universe, decays at different times will have different effects on other parts of the universe, and as soon as you include those other parts in your model, you will end up with what I described.

So if there is a physical difference in outcomes, MWI will generate new worlds at new times but not if there is no physical difference.

This seems to be satisfactory. Setting t = 0 at 11:00 AM when I first look at the crystal and observe that in my branch the atom has not decayed, dismisses as irrelevant all the previous branches in which it has decayed. We can set the amplitude of the un-decayed atom at 1 and of the branches at 0. No theoretical or observational contradiction here because going forward the results are the same as if we set t = 0 at 10:00 AM.

So in the end, MWI generates an enormous but not necessarily infinite set of worlds in a finite period of time.

 

[PeterDonis]

I am not assuming that the decay takes place only once.

Yes, you are, when you say "at a certain time, the decay is observed to take place". See further comments below.

it only occurs once in the branch to which I have observational access.

Wrong. "You" are in every branch; the quantum degrees of freedom that the word "you" (when I use it, or "I" when you are speaking of yourself) refers to have "observational access" to all of the branches. Those degrees of freedom are entangled with the degrees of freedom representing the atom and its decay products, so the overall quantum state is an entangled superposition of terms like "atom has not decayed, you observe that atom has not decayed", "atom decayed at t = 1 second, you observed atom to decay at t = 1 second", "atom decayed at t = 2 seconds, you observed atom to decay at t = 2 seconds", etc.

My initial query (post #1) was that MWI included not only all possible disruptions of the crystal as different decoherent branches but also that the time of occurrence generated additional sets of decoherent branches.

The possible times (plural) of occurrence generate additional branches, yes.

in my branch

There is no such thing as "my branch". As above, "you" are in all the branches.

if there is a physical difference in outcomes, MWI will generate new worlds

More precisely, if there are multiple decoherent outcomes that are physically distinguishable, MWI says there is a branch of the wave function corresponding to each outcome.

Setting t = 0 at 11:00 AM when I first look at the crystal and observe that in my branch the atom has not decayed, dismisses as irrelevant all the previous branches in which it has decayed.

No, it doesn't. You have to prepare the atom in the un-decayed state at t = 0. Just looking at the crystal is not enough, because if you haven't explicitly done a preparation process at t = 0 that puts the atom exactly in the un-decayed state, then there will be another branch of the wave function in which the atom did decay at 11:00 AM, or whatever instant you are calling t = 0, and you observed that.

in the end, MWI generates an enormous but not necessarily infinite set of worlds in a finite period of time

Unless the possible set of outcomes is discrete, an infinite set of branches of the wave function will be generated in a finite period of time. For example, if the possible decay times of the atom form a continuous set, then there will be a continuous infinity of branches corresponding to each of the possible decay times.

 

[kered rettop]

The "worlds" are distinguished phenomenally, i.e. you have a dead-cat world and a living-cat world. But when you relate that to decomposing the wave function you can
1 stick with a very coarse-grained decomposition, making just two worlds or
2 go to the finest-graining by taking it it all the way down to every microscopic interaction with the environment, where there will be a ridiculously large number.
Of course you can have the best of both worlds, so to speak, by bundling the microstates together to give the two coarse-grain worlds.
So how many worlds? Your choice. Possibly vast, maybe even infinite. How many classes of world? In general as many macroscopically distinct states as can arise. Two in this case.
Everything else is semantics.

 

[kered rettop]

TL;DR Summary: There are many options available for, say, a radioactive atom to disrupt the atoms around it when it decays. Is there a separate world for each option?

For clarity, consider a very orderly crystal with a single radioactive atom at a specific location. It decays by alpha emission. When the alpha particle is emitted, it disrupts the location of nearby atoms and then comes to rest and forms a stray helium atom. It would seem that there is a moderately large number of possibilities. The alpha particle might go left and disrupt the location of the nearest atom on the left, and then proceed in a more or less leftward path, each collision and disruption being one of the options that Shrodinger's equation permits, with a certain probability and subject to what has already been disrupted. There are many directions that the alpha particle can go. Furthermore, the alpha emission could occur sooner or later.
According to the Many Worlds Interpretation:
1. Does the situation generate new worlds or are the worlds already presumed to exist?
2. Is there a separate world for each possible set of disruptions?
3. Is there a separate set of worlds for each instant.
4. If there is a separate set of worlds for each instant, is there some constraint that would limit "instant" to being finitely small rather than infinitely small.
5. If the alpha particle has indeed been emitted, are there yet other worlds in which it has not yet done so.

1 Different components of the global wave function evolved into the worlds. So no, the worlds have not always existed, their precursors had.
2 Yes.
3 Yes, if there is possibility of another interaction.
4 Not unless you add one to the theory. That would be problematical because it would probably mean that the universe stops evolving once we reached the threshold.
5 Of course. Got a dead Schroedinger cat on your hands? Fear not, Felix is alive and well in another world.

 

[bhobba]

I think one needs to be careful what one means by world:


If you take Gell-Mann's view then you end up with decoherent histories.

Like Gell-Mann I think it is basically decoherent histories without the strange metaphysical baggage, which, IMHO, just makes the fundamental idea of QM without actual meaasurements wieird. As usual just my view - I could be wrong.

Thanks
Bill

 

[kered rettop]

I think one needs to be careful what one means by world.

If you take Gell-Mann's view then you end up with decoherent histories.

Like Gell-Mann I think it is basically decoherent histories without the strange metaphysical baggage, which, IMHO, just makes the fundamental idea of QM without actual meaasurements wieird. As usual just my view - I could be wrong.

Thanks
Bill

Was that a response to me, Bill? I don't know enough about decoherent histories to comment.

 

[Morbert]

If you take Gell-Mann's view then you end up with decoherent histories.

Like Gell-Mann I think it is basically decoherent histories without the strange metaphysical baggage, which, IMHO, just makes the fundamental idea of QM without actual meaasurements wieird. As usual just my view - I could be wrong.

"Oxford Everettians" (Wallace, Saunders, Deutsch, Greaves etc) support application of decoherent histories formalism in an Everettian framework. Though they would make a stronger metaphysical commitment than Gell-Mann suggests: Histories are actually existing branches.

The formalism has some features attractive to MWI proponents: sharp definition of worlds, applicable to relativistic theories, sharp posing of interesting metaphysical questions (e.g. overlapping vs diverging branches). But also some features possibly unattractive to MWI proponents: No unique branching structure, no unique answer to the question "How many worlds is Many Worlds talking about?", quasiclassicality is no longer privileged.

 

[gentzen]

Was that a response to me, Bill? I don't know enough about decoherent histories to comment.

At least the decoherent histories formalism has coarse-graining built-in from the start, and seems to "confirm" your statements below:

The "worlds" are distinguished phenomenally, i.e. you have a dead-cat world and a living-cat world. But when you relate that to decomposing the wave function you can
1 stick with a very coarse-grained decomposition, making just two worlds or
2 go to the finest-graining by taking it it all the way down to every microscopic interaction with the environment, where there will be a ridiculously large number.

For your following statements, it is less obvious how well they "fit" with decoherent histories:

Of course you can have the best of both worlds, so to speak, by bundling the microstates together to give the two coarse-grain worlds.
So how many worlds? Your choice. Possibly vast, maybe even infinite. How many classes of world? In general as many macroscopically distinct states as can arise. Two in this case.
Everything else is semantics.

Talking of "the microstates" slightly violates the spirit of DH. And the "simplest" DH formalism doesn't work too well with infinity. (Sean Carroll tried to go the other way for MWI regarding infinity, and investigated how well it could work in Finite-Dimensional Hilbert Spaces.)

 

[bhobba]

Was that a response to me, Bill? I don't know enough about decoherent histories to comment.

It was a general comment about Many Worlds. There is a basic semantic difficulty with the idea, as alluded to by Gell-Mann. That is what one means by a different world. Is it a parallel world like ours and just as real, or is it treating all possible worlds equally? I think the issue is semantic and at rock bottom, just philosophical., which we don't discuss here.

I like the Decoherent Histories formulation, although I hold to the Ensemble interpretation formally. Surprisingly, the best book I have read on Decoherent Histories is The Emergent Multiverse by David Wallace, which is about Many Worlds. One simply thinks of the many worlds as many possible worlds - not actual worlds. Only one of the possible worlds is experienced by us as real.

Another name for Decoherent Histories is Consistent Histories:
https://quantum.phys.cmu.edu/CHS/histories.html

Thanks
Bill

 

[kered rettop]

Thank, Bill. I'll try to give that book a look.