Single world or multiple worlds?

[entropy1]

In the Many Worlds Interpretation, I would formulate measurement something like this:

{Cat_alive + Cat_dead}[Observer] -> {Cat_alive}[Cat_alive_observed] + {Cat_dead}[Cat_dead_observed].

So does that mean that the cat and the observer are entangled after measurement?
Does this mean there are now two branches/worlds? Or:
Does this mean that we are in a single world but in an superposition of isolated outcomes?

Suppose the cat can have outcomes A and B, and the observer can have outcomes X and Y, where A=cat_alive, B=cat_dead, X=cat_alive_observed and Y=cat_dead_observed, then, after measurement, do we have two distinct branches in which in one A is correlated/entangled with X and in the other B is correlated/entangled with Y, and do these outcomes coexist in a single world? For, if two systems get entangled, that does not necessarily imply they multiplicate, right?

I am wondering because if "worlds would split", this would suggest enormous recources (energy, matter etc.).

 

[DrChinese]

1. So does that mean that the cat and the observer are entangled after measurement? Does this mean there are now two branches/worlds?

...

2. I am wondering because if "worlds would split", this would suggest enormous resources (energy, matter etc.).

1. Under MWI: Yes.

2. There are no resources required, as there is still just 1 wave function. That wave function has many very complicated terms, and each term is weighted very small (and essentially getting smaller as time passes).

I found this recent paper on MWI helpful: https://arxiv.org/pdf/2005.04812.pdf

 

[Quanundrum]

1. Under MWI: Yes.

2. There are no resources required, as there is still just 1 wave function. That wave function has many very complicated terms, and each term is weighted very small (and essentially getting smaller as time passes).

I found this recent paper on MWI helpful: https://arxiv.org/pdf/2005.04812.pdf

Did you become an Everettian in 2020

 

[DrChinese]

Did you become an Everettian in 2020

Apparently everything that can happen, will happen, as recent events appear to demonstrate. At least, in the world you and I occupy...

 

[Quanundrum]

Apparently everything that can happen, will happen, as recent events appear to demonstrate. At least, in the world you and I occupy...

As someone who's frequented this board off and on for the past ~15 years, this is actually interesting. What convinced you that the objections (primarily probability related) were not sufficient to render its compelling nature moot?

 

[DrChinese]

As someone who's frequented this board off and on for the past ~15 years, this is actually interesting. What convinced you that the objections (primarily probability related) were not sufficient to render its compelling nature moot?

Ha, it may sound like I changed my view per my comments in this thread, but... It's more that I have been trying to do a better job of understanding MWI. After all, it is a viable interpretation. I have been reading a recent paper by Biao Wu, here's the abstract:

"This is a tutorial for the many-worlds theory by Everett, which includes some of my personal views. It has two parts.The first part shows the emergence of many worlds in a universe consisting of only a Mach-Zehnder interferometer. The second part is an abridgment of Everett’s long thesis, where his theory was originally elaborated in detail with clarity and rigor. Some minor comments are added in the abridgment in light of recent developments. Even if you do not agree to Everett’s view, you will still learn a great deal from his generalization of the uncertainty relation, his unique way of defining entanglement (or canonical correlation), and his formulation of quantum measurement using Hamiltonian."

https://arxiv.org/pdf/2005.04812.pdfPS I still lean to interpretations such as Relational Blockworld. In that interpretation: Alice and Bob's future measurement settings are explicitly part of the overall context in a Bell test (or any quantum system). Therefore they naturally reproduce the quantum statistics without requiring an FTL influence (although the system is extended in spacetime). It is acausal, and there are no other hidden variables.

 

[entropy1]

1. Under MWI: Yes.

2. There are no resources required, as there is still just 1 wave function. That wave function has many very complicated terms, and each term is weighted very small (and essentially getting smaller as time passes).

Couldn't you just say that there is still a single universe/world, and that the result of the measurement is still a superposition, just in such a way that the outcomes are orthogonal and diverge macroscopicly? That the worlds may be very different depending on the outcomes, but that that is the way the superposition is constituted?

 

[entropy1]

I was thinking that if we as humans make choices, the environment adapts to the choice. If we can generalize this rule, it seems logical in a way that the environment adapts to the (measurement) outcome in MWI.

 

[PeterDonis]

Couldn't you just say that there is still a single universe/world

That is what he said. He said there is just one wave function.

the result of the measurement is still a superposition

It's an entangled state: the measurement is an interaction that entangles the measured system with the measuring device.

Whether or not the state is a "superposition" depends on what basis you choose. That is true of any quantum state, whether it's entangled or not. So "superposition" does not really pick out the key feature of the state after a measurement, which is entanglement.

the worlds

If there is only a single universe/world, then your use of the plural here is incorrect.

if we as humans make choices, the environment adapts to the choice. If we can generalize this rule, it seems logical in a way that the environment adapts to the (measurement) outcome in MWI.

This does not seem to me to have any relationship to the MWI in particular; it's just a vague general statement that things interact with each other.

 

[entropy1]

It's an entangled state: the measurement is an interaction that entangles the measured system with the measuring device.

Whether or not the state is a "superposition" depends on what basis you choose. That is true of any quantum state, whether it's entangled or not. So "superposition" does not really pick out the key feature of the state after a measurement, which is entanglement.

If I stay with MWI, then suppose, if we have a two-dimensional measurement basis, that the measured particle entangles with the measurement device. Then, in my somewhat simple view, we should have something like this:
{↑ + ↓}[Observer] -> {↑}[↑_observed] + {↓}[↓_observed].
Since we must measure either ↑ or ↓, the expression of the entanglement should (to my understanding) be something like above, right? And it looks (in my view) like a superposition. This equation is not something I invented myself! I got it from Demystifier but I think it is pretty much general as a formulation in MWI.

The basis is determined by the measurement device. We can't take a different one. I don't know how it is in case of position or momentum, in which the number of possible outcomes is infinite.

So my question to you I guess is if there is a different expression than the above that conforms to MWI?

 

[PeterDonis]

the expression of the entanglement should (to my understanding) be something like above, right?

Yes.

And it looks (in my view) like a superposition.

It looks like a superposition in the basis you wrote it in. But there will always exist a basis in which it is not a superposition.

The fact that the state is entangled, however, is basis independent.

 

[PeterDonis]

The basis is determined by the measurement device.

No, it isn't. Remember we're talking about the MWI, so it's unitary evolution all the time. Unitary evolution has no preferred basis.

What is true is that the basis you wrote the state down in is the basis that makes sense to us humans. But nature doesn't care what makes sense to us humans.

 

[PeterDonis]

I don't know how it is in case of position or momentum, in which the number of possible outcomes is infinite.

Not really, because it's not actually possible to measure an exact position or momentum state; any real measurement will have a finite number of possible outcomes because of finite measurement resolution. But of course there will typically be a lot more than just two.

 

[entropy1]

It looks like a superposition in the basis you wrote it in. But there will always exist a basis in which it is not a superposition.

No, it isn't. Remember we're talking about the MWI, so it's unitary evolution all the time. Unitary evolution has no preferred basis.

What is true is that the basis you wrote the state down in is the basis that makes sense to us humans. But nature doesn't care what makes sense to us humans.

Ok. But don't the states [↑_observed] and [↓_observed] have to make up part of the expression of the (possible) outcome(s) in this case?

 

[entropy1]

{↑}[↑_observed] + {↓}[↓_observed].

So if I understand you correctly, this expression is the particle (property) entangled with the observed outcome?

It's an entangled state: the measurement is an interaction that entangles the measured system with the measuring device.

So the question here is: can this entangled state be expressed in different basises?

For example: $\sqrt{\frac{1}{3}}[↑][↑observed] + \sqrt{\frac{2}{3}}[↓][↓observed]$?

 

[PeterDonis]

don't the states [↑_observed] and [↓_observed] have to make up part of the expression of the (possible) outcome(s) in this case?

In the basis that makes sense to us humans, they do. But, as I said, there will be some basis in which the final entangled state of the system is not a superposition, and in that basis, the expression describing the state will look different. It won't make sense to us humans, but again, nature doesn't care what makes sense to us humans.

can this entangled state be expressed in different basises?

Of course it can. Any state can be expressed in any basis. The choice of basis in QM is like the choice of coordinates in relativity: it is just a convenience for us humans.

 

[PeterDonis]

For example: $\sqrt{\frac{1}{3}}[↑][↑observed] + \sqrt{\frac{2}{3}}[↓][↓observed]$?

That's not the same state in a different basis. That's a different state in the same basis.

 

[entropy1]

Yes.

Anyway, my initial question was if there must be a generation of multiple worlds in MWI by measurement, or that there could be single world. Looking at the equation I suggest, you seem to agree the right hand side (bold) can represent a situation in a single world, containing represented entanglement, am I right?

{↑ + ↓}[Observer] -> {↑}[↑_observed] + {↓}[↓_observed].

 

[PeterDonis]

my initial question was if there must be a generation of multiple worlds in MWI by measurement, or that there could be single world

You need to define what you mean by "world". Until you have done that, your question is not well-defined and cannot be answered.

 

[entropy1]

You need to define what you mean by "world". Until you have done that, your question is not well-defined and cannot be answered.

Maybe a definition could be that a world is that what is observed. In that case there seem to be two worlds after measurement following my example. But since you are saying that the basis used in the example can be different, I start wondering if there actually are the two worlds the equation is suggesting.

I happen to think the wavefunction is the thing that is real, and what is observed is not (necessarily). In that case I suspect the right hand side of my example equation, representing a wavefunction, is real as a whole.

Do you disagree?

NOTE: Do we need an observer in MWI?

 

[PeterDonis]

Maybe a definition could be that a world is that what is observed

That doesn't really help because you then have to define what "observed" means.

In that case there seem to be two worlds after measurement following my example.

The definition of "world" you are implicitly using here is not quite "what is observed", but "a particular term in the wave function when it is written in the $\uparrow, \downarrow, \uparrow \text{observed}, \downarrow \text{observed}$ basis".

since you are saying that the basis used in the example can be different, I start wondering if there actually are the two worlds the equation is suggesting

Any definition of "world" along the above lines would have to be basis-dependent, yes. The usual argument is that the basis given above is picked out by some physical characteristic of the system, but specifying exactly what that characteristic is turns out to be a so far unsolved problem.

I think the wavefunction is the thing that is real

The MWI says this, yes.

and what is observed is not (necessarily)

The MWI does not view "observation" as any kind of special thing; it's just part of the unitary evolution of the wave function. But this doesn't make observation "not real" in MWI terms.