I Quantum entanglement in the MWI

[kered rettop]

No, it isn't, because you can have wave function collapse even in cases where you are not measuring an entangled system. For example, if I measure the spin of a single free electron that isn't entangled with anything, I still have wave function collapse (in an interpretation where there is such a thing) when I detect the electron in one or the other output arm of the Stern-Gerlach device.

Didn't I mention this? Must have edited it out thinking it was too obvious to be worth saying. Life being short and all that. Yes, obviously, the words do mean different things and you can't break the entanglement of a system that is not entangled because that would be silly. But they still refer to the same putative physical process.

 

[Nugatory]

Ah, just when I thought I was following you! What's wrong with "we have two particles"?

In the math we don’t have two particles. We have one quantum system described by one wave function, it just so happens that the two possible measurements (spin/polarization at one detector, spin/polarization at the other) we might perform on this system happen at different places. Because of the spatial separation our classical intuition demands that we think in terms of two distinguishable particles in two different places… and it’s a short step from there to spooky action at a distance and all the other entanglement misunderstandings that show up in our B-level threads.

 

[pines-demon]

Conjecture: It does not matter what terminology you use to describe entanglement, there is always one interpretation in which your description is wrong.

Corollary: you might use math to avoid this problem, but you will still get criticism for how you call or describe your equations and variables.

Of course this does not exclude being wrong in all interpretations.

 

[Morbert]

That doesn't break entanglement, it just spreads it out to include the pointer degrees of freedom. (And then to include the environment degrees of freedom, once you take decoherence into account.) I already posted about this.

I am referring to the entanglement in the microscopic system. E.g. Consider a two-particle system in the Bell state $|\Phi^+_{12}\rangle\langle\Phi^+_{12}|$ and a joint (and ideal and nondestructive) spin measurement represented by $\frac{\hbar^2}{4}\sigma^1_x\sigma^2_z$ (I.e. a measure of spin-x on particle 1 and spin-z on particle 2). If we include the pointer degrees of freedom, a unitary evolution through the measurement process and a trace over the pointer degrees of freedom will yield the two-particle system in the unentangled state $\rho_1\otimes\rho_2$.

[edit]- Rewrote last bit, which was unclear

 

[PeterDonis]

I am referring to the entanglement in the microscopic system

Unitary evolution doesn't break that either. The microscopic entanglement will no longer be maximal, because other degrees of freedom are involved, but it doesn't go away either.

a trace over the pointer degrees of freedom

Throws away precisely the information you need to see that the entanglement between the microscopic degrees of freedom is still there. To properly evaluate this question you need to look at the actual pure state of the entire system; you can't trace out anything.

 

[kered rettop]

In the math we don’t have two particles.

Correct me if I'm wrong, but don't we have a sum of products like |H>|V> + |V>|H> ?
If not two particles, what do the kets refer to?
Or would you say that |H>|V> + |V>|H> is actually wrong and we should always write |HV> + |VH>?

We have one quantum system described by one wave function, it just so happens that the two possible measurements (spin/polarization at one detector, spin/polarization at the other) we might perform on this system happen at different places. Because of the spatial separation our classical intuition demands that we think in terms of two distinguishable particles in two different places… and it’s a short step from there to spooky action at a distance and all the other entanglement misunderstandings that show up in our B-level threads

Not only there.

I tend to think of the system as two particles largely because I can definitely prepare two photons which do not behave as a single unit, and also an entanglement which behaves as two photons in every respect
except, arguably, the entangled property. So rather than adopt a really weird ontology for the little hard lumps I look to the "get-outs" of Bell's Theorem.

 

[Morbert]

@PeterDonis I don't know if our disagreement is substantive. I.e. I don't want to argue over the specifics of "to break" so I'll leave it there.

 

[RUTA]

TL;DR Summary: Does the MWI explain "spooky action at a distance"?

As far as I know, we don't understand the apparent faster-than-light "communication" between a measured particle and one entangled to it. Does the Many Worlds Interpretation explain this? Does it have anything else to say about entanglement?

MWI doesn't explain entanglement in terms of concepts fundamental to quantum mechanics because MWI simply assumes the quantum formalism is fundamental. And, it really doesn't resolve the mystery of entanglement because there is still a nonlocality associated with entanglement in MWI. It's easy to see this nonlocality in entangled spin measurements. Suppose Alice and Bob are switching very fast between measurement options so that Alice's(Bob's) outcome is spacelike related to Bob's(Alice's) setting. Sometimes Alice and Bob happen to choose the same setting and sometimes they choose different settings. When they choose the same setting the wavefunction splits into the two possible outcomes (possible worlds), i.e., uu and dd, and when they choose different settings the wavefunction splits into all four possible outcomes (possible worlds), uu, ud, du, and dd. How does the wavefunction know the possibilities? Here is what Vaidman writes in SEP https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds/:

Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A “world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.

 

[kered rettop]

MWI doesn't explain entanglement in terms of concepts fundamental to quantum mechanics because MWI simply assumes the quantum formalism is fundamental. And, it really doesn't resolve the mystery of entanglement because there is still a nonlocality associated with entanglement in MWI. It's easy to see this nonlocality in entangled spin measurements. Suppose Alice and Bob are switching very fast between measurement options so that Alice's(Bob's) outcome is spacelike related to Bob's(Alice's) setting. Sometimes Alice and Bob happen to choose the same setting and sometimes they choose different settings. When they choose the same setting the wavefunction splits into the two possible outcomes (possible worlds), i.e., uu or dd, and when they choose different settings the wavefunction splits into all four possible outcomes (possible worlds), uu, ud, du, or dd. How does the wavefunction know the possibilities? Here is what Vaidman writes in SEP https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds/:

Easy! The two-electron wave function does not split so it does not need to know.

When it interacts with the detector, the resultant entanglement does know the setting.

 

[pines-demon]

MWI doesn't explain entanglement in terms of concepts fundamental to quantum mechanics because MWI simply assumes the quantum formalism is fundamental. And, it really doesn't resolve the mystery of entanglement because there is still a nonlocality associated with entanglement in MWI. It's easy to see this nonlocality in entangled spin measurements. Suppose Alice and Bob are switching very fast between measurement options so that Alice's(Bob's) outcome is spacelike related to Bob's(Alice's) setting. Sometimes Alice and Bob happen to choose the same setting and sometimes they choose different settings. When they choose the same setting the wavefunction splits into the two possible outcomes (possible worlds), i.e., uu and dd, and when they choose different settings the wavefunction splits into all four possible outcomes (possible worlds), uu, ud, du, and dd. How does the wavefunction know the possibilities? Here is what Vaidman writes in SEP https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds/:

What do you mean by "how the wavefunction knows the possibilities?" The possible outcomes are clear if you write the state, it depends on the settings. The state is just following Schrödinger's equation.

Also, what does even Vaidman mean when he says that a "World is a nonlocal concept". Is it just that an observer in a world predicts non-local probabilities? Or does he mean something related to the concept of World by itself?

 

[PeterDonis]

the wavefunction splits

More precisely, the entanglement spreads to include the detector (and then to include the environment once we take decoherence into account). There is no "split"; the possibilities you refer to are already there in the wave function, they just don't include the detector and the environment until after the measurement.

 

[PeterDonis]

what does even Vaidman mean when he says that a "World is a nonlocal concept"

He means that the wave function includes entangled degrees of freedom that are spatially separated.

 

[gentzen]

Also, what does even Vaidman mean when he says that a "World is a nonlocal concept". Is it just that an observer in a world predicts non-local probabilities? Or does he mean something related to the concept of World by itself?

His text immediately continues with nonlocal correlations after his „world is a nonlocal concept“. Therefore, he doesn‘t mean that the concept of world would be inherently nonlocal. Just that it allows nonlocality.

 

[Morbert]

Also, what does even Vaidman mean when he says that a "World is a nonlocal concept". Is it just that an observer in a world predicts non-local probabilities? Or does he mean something related to the concept of World by itself?

Re/ a world as a concept: According to Vaidman, the only physical process is a universal wavefunction evolving according to a relativistic generalization of the Schroedinger equation , and he describes a world as a "human concept which is supposed to help explaining our experience" i.e. a concept relating the universal wavefunction to our experiences. The decomposition of the wavefunction into states tracking our experiences, where all macroscopic objects are localized, is not privileged over any other decomposition.

Re/ a world as nonlocal: Vaidman notes that the entanglement/nonseparability of the wavefunction means the worlds each observer conceptualizes will have connections, and these connections give the illusion of action at a distance
https://arxiv.org/abs/1501.02691

What makes this situation [the GHZ experiment] nonlocal is that while all four different local options are present for all observers, i.e., there are four Everett worlds for Alice, and separately for Bob and for Charley, we do not have 64 worlds. Specifying Everett worlds of two observers fixes the world of the third. This connection between local worlds of the observers is the nonlocality of the MWI.

[...]

Is there any possibility of action at a distance in the framework of the MWI? Obviously, at the level of the physical universe that includes all the worlds, local action cannot change anything at remote locations. However, a local action splits the world, which is a nonlocal concept, and local actions can bring about splitting to worlds that differ at remote locations. Thus, an observer for whom only his world is relevant has an illusion of an action at a distance when he performs a measurement on a system entangled with a remote system.

 

[pines-demon]

As we are talking about MWI. One thing that does not click to me appears when discussing entanglement that is not a symmetrical Bell state. What about other kinds of entanglements?

Suppose we have the state:
$$|\Psi\rangle = \sqrt{\frac34}|00\rangle+\frac{1}{2}|11\rangle$$

How does a world "split" in order to make the percentages right? Note that even with repeated measurements, the answer seems to be 2 at each split. Is there some kind of densities of worlds?

 

[PeterDonis]

How does a world "split" in order to make the percentages right?

The "splitting" (which is not a good term, see my previous post on this) does not depend on the coefficients of the terms; there is just one "world" for each term.

The "weights" of the worlds (the coefficients of each term) and what they mean is an open issue with the MWI. Various MWI proponents have expressed viewpoints on it, but AFAIK none of them has gotten general acceptance.

 

[kered rettop]

As we are talking about MWI. One thing that does not click to me appears when discussing entanglement that is not a symmetrical Bell state. What about other kinds of entanglements?

Suppose we have the state:
$$|\Psi\rangle = \sqrt{\frac34}|00\rangle+\frac{1}{2}|11\rangle$$

How does a world "split" in order to make the percentages right?

The amplitude of the world-states must be the same as that of the parent components in the entanglement, namely $$ \sqrt{\frac34} and \frac{1}{2}$$

Note that even with repeated measurements, the answer seems to be 2 at each split.

There's only one split. The 00 world for instance is |00> and nothing else so it can't be split by a second measurement.

Is there some kind of densities of worlds?

Of course. The amplitudes determine the probabilities via the Born Rule: 3/4 and 1/4 in your example.

 

[PeterDonis]

Of course. The amplitudes determine the probabilities via the Born Rule: 3/4 and 1/4 in your example.

"Of course" is somewhat optimistic as regards the MWI, since how to account for the Born Rule (and indeed how to formulate a meaningful concept of probability at all) in the context of the MWI is a key open issue.

 

[PeroK]

"Of course" is somewhat optimistic as regards the MWI, since how to account for the Born Rule (and indeed how to formulate a meaningful concept of probability at all) in the context of the MWI is a key open issue.

As far as I can see, Vaidman's argument amounts to a bit of hand waving and saying that probability is an illusion. The examples (in the various recent threads on this) always involve equally likely basic events, where to some extent probability can be waved away. It's not clear, however, that an event like radioactive decay can be explained in this way. The basic events of decay or not decay over a given time period are generally not equally likely. I don't see how probability or a weighting of worlds in the model can be avoided.

 

[Motore]

Here is a (pop sci) video, arguing for a Principle of indiference as a possible solution of the derivation of the Born rule in MWI. I know is pop sci but you have a link to a pdf by Taha Dawoodbhoy (that is itself a derivation of the concept from Zurek and Carroll) that explains it in more detail.

 

[PeroK]

Here is a (pop sci) video, arguing for a Principle of indiference as a possible solution of the derivation of the Born rule in MWI. I know is pop sci but you have a link to a pdf by Taha Dawoodbhoy (that is itself a derivation of the concept from Zurek and Carroll) that explains it in more detail.

I think I understand the argument. The idea is that all quantum states can be broken down to a number of equally likely basic states. This reduces probability to counting the states and - due to the equal likelihood - the emergent probabilities are explained without probabilities in the fundamental branching. This is a relatively simple argument.

Let's take the example of radioactive decay, where (say) the probability of decay in the next second is 0.1. The argument is that somewhere buried in the weak interaction is a process with 10 equally likely outcomes: 9 of which entail no decay; and, only one of which entails decay. Then, you have 9 worlds with no decay after a second and only one world where you have decay. All the non-equally-likely probabilities emerge from this fundamental non-probabilistic or equally-likely fundamental branching.

A similar argument would apply to scattering processes, where you would postulate a set of fundamental equally-likely interactions (buried somewhere in the theory), that eventually produce unequal probability amplitudes for different scattering angles.

In summary:

The basic idea is quite simple.

There's no question that probabilities could be produced by a fundamental uniform or equally likely discrete branching into all possible outcomes. Although, I can see some issues with discrete branching when you look at all possible interactions at the same time. Using infinite branching at the fundamental level, I imagine the numbers could be made to work out. Even if discrete branching cannot be made to work across all interactions simultaneously.

The bigger problem, IMO, is justifying the idea of this equal branching on a fundamental level. It's not clearly supported by the mathematics of scattering processes and Feynman diagrams etc. That said, the path-integral formulation may, in fact, be quite close to this idea.

 

[PeroK]

PS I was just looking at the Clebsch-Gordan table yesterday. If we take that at face value, then fundamental unequal amplitudes appear naturally out of the mathematics of group representation theory. This is a striking (and not to be underestimated) piece of evidence for the fundamental nature of probabilities.

To make the MWI argument work fully it would be necessary to have an underlying mathematical theory where the coefficients in the Clebsch-Gordan table emerged from some sort of equally-likely counting process.

As far as I understand it, the group theory that generates the C-G table is already based on irreduciblity in group theory. At first sight, that could not be generated by a simplistic underlying mathematical formulation.

If I were to put a question to Vaidman it would be this: justify the Clebsch-Gordan table mathematically using equally-likely branching.

 

[PeterDonis]

There's no question that probabilities could be produced by a fundamental uniform or equally likely discrete branching into all possible outcomes.

Yes, there is a question, because in the MWI, time evolution, including whatever "branching" occurs, is always unitary, and unitary means deterministic. There is no randomness whatever and nothing is unknown. That is why there is an open issue with the MWI about coming up with a meaningful concept of probability: because all known concepts of probability require randomness and/or unknown information.

 

[PeterDonis]

This is a striking (and not to be underestimated) piece of evidence for the fundamental nature of probabilities.

Only if you already have an interpretation that gives you a meaningful concept of probability from amplitudes.

 

[PeroK]

That is why there is an open issue with the MWI about coming up with a meaningful concept of probability: because all known concepts of probability require randomness and/or unknown information.

You can get round it in the special case where all events are equally likely. In that special case, probability reduces to counting outcomes. This is the point that Vaidman is pushing. You can't distinguish between randomness of a single outcome and the number of worlds with that outcome.

The problem arises when not all fundamental outcomes are equally likely. The PBS video was quite good actually, because he was much more explicit about this issue. If, say, you have a biased coin that has 2/3 probability of landing heads, then you need to postulate a more fundamental set of three outcomes, two of which result in a head and only one in a tail. Then, you can proceed by counting outcomes again instead of using probabilties.

You could do this on a Markov chain, for example. The Markov chain in a way is an MWI-type structure, as it shows every possible event. You usually need to include the probabilities of each branch. But, if every branch has equally likely outcomes, you can drop the explicit probabilities and just count the final outcomes. That's the idea, at least.

 

[PeroK]

Only if you already have an interpretation that gives you a meaningful concept of probability from amplitudes.

The point is that, IMO, it disrupts the premise of the Vaidman paper that you can reduce everything to equally likely outcomes. That's what Vaidman's idea relies on.

 

[PeterDonis]

This is the point that Vaidman is pushing.

Yes, but that doesn't mean what he's pushing is generally accepted. It isn't. As I have said, this is an open issue with the MWI that does not have an accepted solution.

 

[PeroK]

Yes, but that doesn't mean what he's pushing is generally accepted. It isn't. As I have said, this is an open issue with the MWI that does not have an accepted solution.

It's not just not accepted: IMO, it's wrong! He's trying to pull the wool over our eyes by pretending that everything is fundamentally composed of equally likely outcomes (really equal amplitudes). That should sound wrong and the Clebsch-Gordan table is an example of where it cannot be justified.

I'm talking here about what is specifically in the Vaidman paper. This issue of fundamentally equal amplitudes is a necessary assumption, not explicity stated in his paper.

 

[PeterDonis]

It's not just not accepted: IMO, it's wrong!

Welcome to the wonderful world of MWI discussions. As with any QM interpretation discussion, there is no way to resolve this issue; it comes down to different opinions for different people.

 

[kered rettop]

Yes, there is a question, because in the MWI, time evolution, including whatever "branching" occurs, is always unitary, and unitary means deterministic. There is no randomness whatever and nothing is unknown. That is why there is an open issue with the MWI about coming up with a meaningful concept of probability: because all known concepts of probability require randomness and/or unknown information.

It doesn't need a new concept of probability. It is sufficient to identify a subsystem in which "which-branch" information is not available. This can be personified as an observer who is ignorant of the branch in which they are embedded.