The splitting into worlds in MWI

[entropy1]

If we have binary decoherence at spacetime location X, as far as I understand, we almost instantly have a splitting into two worlds.

Now if we have a different location Y, about a lightyear apart from X, then the decoherence hasn't reached Y before a year has passed.

So for Y, the split hasn't happened yet.

And also, where are the two worlds created from if they would emerge at X?

Is this a valid issue?

Observing this issue among other issues concerning the Many Worlds, I have a hard time accepting Many Worlds.

 

[PeterDonis]

If we have binary decoherence at spacetime location X, as far as I understand, we almost instantly have a splitting into two worlds.

The "splitting of worlds" does not have a spatial location. It happens in configuration space, the space in which the wave function "lives" (since it's just a description of what happens to the wave function under decoherence), not ordinary space. As such, it is not something that can be localized in ordinary space, nor is it something that can be viewed as "traveling" in ordinary space.

 

[akvadrako]

I would say all the splitting is local. The splitting in many-worlds happens via decoherence which happens via interactions, and the interactions are local. Worlds are agent-relative things, so when Bob makes a measurement, that doesn't split Alice until that information reaches her. This isn't evident in every formulation, but there is a program of developing models where it becomes more clear.

The changing face of nonlocality (arXiv:2003.03395, Ch. 9) gives a decent overview of this research. One of the earliest approaches is the Deutsch-Hayden picture (most recently presented here and perhaps more simply in arXiv:2012.11189).

Another of the better developed approaches is called Parallel Lives. One co-author, Paul Raymond-Robichaud, went on to show that any theory that conforms to the no-signalling principle has a local-realistic model and recently published an example of such a model for QM.

Both of these approaches provide local-realistic models for no-collapse QM, though with different ontologies than what some assume many-worlds is about. If one were to argue they constitute different interpretations, I would say that the history of the interpretation shows it isn't about a specific ontology.

 

[PeterDonis]

Worlds are agent-relative things

Not in the standard MWI. As I noted in post #2, the "splitting" in the standard MWI happens in configuration space, since it's just a description of unitary evolution of the wave function in the presence of the measurement interaction. When subsystems are entangled, as in the Alice and Bob example, the "splitting" of the wave function affects both subsystems, not just one, and cannot be localized in ordinary space since that is not the space in which the "splitting" is happening.

If one were to argue they constitute different interpretations

This is what I would argue about the lines of research in the references you give, yes. (At least some of them--one simply points out that the MWI does not have to violate the locality assumption of Bell's Theorem in order to violate the Bell inequalities, because it already violates the "single world" assumption of that theorem. Which is perfectly true, and has been well known for some time, but does not in itself provide a definition of "locality" that applies to MWI world splitting.)

 

[akvadrako]

When subsystems are entangled, as in the Alice and Bob example, the "splitting" of the wave function affects both subsystems, not just one, and cannot be localized in ordinary space since that is not the space in which the "splitting" is happening.

It can be true that in some pictures of MWI the splitting happens in both subsystems and in other pictures it's localized in ordinary space, while both are equivalent pictures of reality. It's just they are from different perspectives or have different underlying ontologies.

This is what I would argue about the lines of research in the references you give, yes.

Yes, it's a matter of definition of what constitutes MWI / Everett / etc..., which is basically about history or language. But what the approaches share with Everett's original thesis is significant: at least there is no collapse, the wave-function is real (ontic), and agents split into multiple copies.

I think these approaches, which are actually formally equivalent (I read today), and are now a couple decades old, are the modern approach to MWI. Even if the name should be different, the prominent supporters do include these within their definition of MWI, for example Deutsch and Wallace. Though not all of them, for example Vaidman. So when someone asks about many-worlds, I think this program should be included.

 

[PeterDonis]

what the approaches share with Everett's original thesis is significant: at least there is no collapse

Agreed.

the wave-function is real (ontic)

I'm not sure I agree with this as you state it, since in the Heisenberg picture formulation that is described in several of your references, the wave function basically carries no information at all; all of the relevant information is in the operators. But I would agree that "the thing that plays the same role as the wave function" in these formulations is ontic.

agents split into multiple copies.

Agreed.