I Quantum entanglement in the MWI

[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.

 

[PeterDonis]

It doesn't need a new concept of probability. It is sufficient to identify a subsystem in which "which-branch" information is not available.

Please give a reference. I strongly doubt you will be able to give one that expounds this point of view and is generally accepted as correct, since this is still an open issue with the MWI (as I have already said several times now).

 

[gentzen]

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'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.

Are you sure that we are talking about a Vaidman paper here? Like

https://arxiv.org/abs/1501.02691

(Bell Inequality and Many-Worlds Interpretation) or https://arxiv.org/abs/1602.05025 (All is Psi)? Or the SEP article https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds/?

 

[Morbert]

This paper might be relevant
https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1039&context=philosophy_articles

In the MWI there is a well-defined alternative strategy that weights descendants in proportion to their absolute squared amplitudes (or equivalently, their measures of existence). It is attractive because it ensures consistency with the situations in which majority vote is legitimate: every D-world can be split into two equal amplitude worlds with amplitude equal to the A world.

 

[Morbert]

As an aside: Does Vaidman or anyone explain how to exclude worlds with zero weights when pursuing these equal-amplitude terms? E.g. If we can rewrite a term $\sqrt{\frac{2}{3}}|\psi\rangle$ as $\sqrt{\frac{1}{3}}|\psi\rangle + \sqrt{\frac{1}{3}}|\psi\rangle$ what stops us from rewriting $0|\psi\rangle$ as $|\psi\rangle - |\psi\rangle$

 

[kered rettop]

Please give a reference. I strongly doubt you will be able to give one that expounds this point of view and is generally accepted as correct, since this is still an open issue with the MWI (as I have already said several times now).

A reference for what? I am pointing out a flaw in your argument.

 

[PeterDonis]

A reference for what?

For your claim that I quoted.

I am pointing out a flaw in your argument.

No, you were making a positive claim, which needs a reference.

 

[pines-demon]

As an aside: Does Vaidman or anyone explain how to exclude worlds with zero weights when pursuing these equal-amplitude terms? E.g. If we can rewrite a term $\sqrt{\frac{2}{3}}|\psi\rangle$ as $\sqrt{\frac{1}{3}}|\psi\rangle + \sqrt{\frac{1}{3}}|\psi\rangle$ what stops us from rewriting $0|\psi\rangle$ as $|\psi\rangle - |\psi\rangle$

Following the world weight idea, why would this be an issue? Zero would be zero worlds, it does not matter how you write the state.

 

[PeroK]

Are you sure that we are talking about a Vaidman paper here?

I'm not sure now. I thought someone posted a paper by Vaidman that had a summary of the probability argument. I can't find it now. Then, I watched the PBS video, which seemed to explain the very points in the paper.

Like

(Bell Inequality and Many-Worlds Interpretation) or https://arxiv.org/abs/1602.05025 (All is Psi)? Or the SEP article https://plato.stanford.edu/archives/fall2021/entries/qm-manyworlds/?

It wasn't those papers I was thinking of. Sorry, maybe I dreamt it!

 

[PeroK]

As an aside: Does Vaidman or anyone explain how to exclude worlds with zero weights when pursuing these equal-amplitude terms? E.g. If we can rewrite a term $\sqrt{\frac{2}{3}}|\psi\rangle$ as $\sqrt{\frac{1}{3}}|\psi\rangle + \sqrt{\frac{1}{3}}|\psi\rangle$ what stops us from rewriting $0|\psi\rangle$ as $|\psi\rangle - |\psi\rangle$

I can boil down my argument to this:
If you are doing a Markov chain in a equally likely scenario (coin toss, roll of a die etc.), then you can drop the probabilitity calculations at every branch and just count the final outcomes. I've often used this trick myself. Three rolls of a die, means $6^3 = 216$ equally likely outcomes and you simply count how many add up to 17, say, and that's your final probability: $N(17)/216$.

A Markov chain is usually interpreted as a model of all the possibilities in a probabilistic setting. Only one line through the chain will actually happen. But, of course, it could be interpreted as an MWI-type model of everything that happens.

But, you can only replace probabilities with counting if everything has the same equal likelihood at every stage. For example, suppose we toss a coin to get us started. If it's heads we toss it again. If it's tails we roll a die. That gives us 8 final outcomes. But, these outcomes are not equally likely anymore. Even though each branch was an equally likely split. If we tried the MWI interpretation, we would find six worlds where the first toss was a tail and only two where it was a head. This won't do.

To fix this, we would have to split the second coin toss into six worlds: three being a head and three a tail. Now, we do have twelve equally likely final outcomes.

To do this counting trick for Markov chains requires some sleight of hand to keep the number of outcomes representative of the probabilies. And, in general, this counting trick cannot be made to work in all scenarios.

This idea, I believe, is at the heart of the idea that "probability is an illusion from the number of worlds" presented in these papers. They complicate the matter by reference to observers and macroscopic devices. But, these complications effectively obscure the fundamental problems with the idea:

1) You would need a superdeterministic sleight of hand to keep the number of worlds in all cases aligned with the quantum mechanical probabilities.

2) There is an immediate problem with any branching that is itself not an equally likely model. Addition of angular momentum using the Clebsch-Gordan coefficients is one example where the fundamental branching is not equally likely.

I just don't see how one could possibly pull off this trick in general.

 

[kered rettop]

For your claim that I quoted/

No, you were making a positive claim, which needs a reference.

Well, that's the trouble, you see. I don't think I did make a positive claim. I took considerable care to make my point without doing so. Which is why I am asking you, in the nicest possible way, to tell me exactly what claim you think I made. It's no good just throwing my post back at me verbatim, saying "it's in there".

 

[PeterDonis]

I don't think I did make a positive claim.

Here is what you said:

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.

That's a positive claim. Either give a reference to back it up or retract it.

It's no good just throwing my post back at me verbatim, saying "it's in there".

Um, yes, it is. What I quoted was all of your post except the first sentence, which just said you were disagreeing with me. If you don't think that two declarative assertions by you are a positive claim, then I am very confused about what language you think you are speaking.

 

[kered rettop]

That's a positive claim. Either give a reference to back it up or retract it.

Neither of those is going to happen, are they?

 

[PeterDonis]

Neither of those is going to happen, are they?

If not, then the subject is off topic for this thread and I will delete both of our posts that refer to it.

 

[kered rettop]

I just don't see how one could possibly pull off this trick in general.

Would it help to recognise that there is a difference between dividing a world-state using arithmetic and dividing it by means of decoherence?

With arithmetic, the amplitude is divided by a real number, N, to produce N identical micro-world-states. Phase is retained: the micro-world-states are coherent. So they are indistinguishable and it doesn't make any sense to assign probability to them individually. Though if you did, it would be original/N^2. However, when you add a bunch of them together, they interfere constructively.

Decoherence works the opposite way. The process leads directly to N orthogonal micro-world-states. You can calculate the required probabilities using the Born Rule and there is no interference. Obviously the amplitudes are not original/N but original/sqrt(N).

Edit - It seems to me that what you call fundamental branching doesn't enter into any of this.

 

[PeterDonis]

You can calculate the required probabilities using the Born Rule

But in the MWI, there is no accepted derivation of the Born Rule. And if you adopt it as an extra assumption, you can't then use it to justify a concept of probability in the MWI; that would be arguing in a circle.

 

[kered rettop]

But in the MWI, there is no accepted derivation of the Born Rule. And if you adopt it as an extra assumption, you can't then use it to justify a concept of probability in the MWI; that would be arguing in a circle.

No, the context was arguments based on world-counting, specifically about how to count worlds correctly. One criterion, pointed out by the previous poster, PeroK, is that world-counting must sucessfully reconcile amplitudes with probabilities. The correct probabilities are given by the Born Rule. The Born Rule is thus an objective of the argument, it has no place as an assumption of the argument. That's why I said "required probabilities".

 

[PeterDonis]

the context was arguments based on world-counting

Which means the MWI. Which means you can't just take the Born Rule as given.

The Born Rule is thus an objective of the argument

Are you claiming that this argument is a valid derivation of the Born Rule in the MWI? On what basis? Do you have a reference?

 

[PeterDonis]

One criterion, pointed out by the previous poster, PeroK, is that world-counting must sucessfully reconcile amplitudes with probabilities. The correct probabilities are given by the Born Rule.

In the context of the MWI, before you can even get to this point, you have to justify how the concept of "probability" even makes sense.

 

[kered rettop]

In the context of the MWI, before you can even get to this point, you have to justify how the concept of "probability" even makes sense.

If by "you", you mean the formulator of the candidate argument, then sure, of course they do.

 

[PeterDonis]

If by "you", you mean the formulator of the candidate argument, then sure, of course they do.

Where do they do that?

 

[kered rettop]

Which means the MWI. Which means you can't just take the Born Rule as given.

Oh I see what you mean. Yes, I was assuming that the desired probabilies would be the Born Rule. I should have left it at "desired probabilites" and left it to the formulators or PeroK to decide and justify what they should be.

 

[kered rettop]

Where do they do that?

Oh good grief!
"do have to justify" not "do justify"!!!

 

[kered rettop]

Are you claiming that this argument is a valid derivation of the Born Rule in the MWI?

No.

 

[PeroK]

Would it help to recognise that there is a difference between dividing a world-state using arithmetic and dividing it by means of decoherence?

Take Schrodinger's cat as an example. But, instead of the 50-50 probability of decay, make it 10%. There should only be two decohered worlds. The fundamental branching of the radioactive sample is fundamental to the experiment. And, yet, there would have to be 9 times as many decohered worlds with a live cat than a dead one. Unless that ratio is driven by an initial weighted or probabilistic branching, how can it be otherwise conjured?

Moreover, the probabilistic explanation is simple. The sample has a probability of $p$ to decay; the probability the cat dies is $p$.

 

[kered rettop]

Moreover, the probabilistic explanation is simple. The sample has a probability of $p$ to decay; the probability the cat dies is $p$.

It depends what you mean by simple. Introducing probability as a primitive complicates the fundamentals of the theory. It may simplify the development of the theory. Occam's Razor vs Shut Up And Calculate.

 

[PeroK]

It depends what you mean by simple. Introducing probability as a primitive complicates the fundamentals of the theory. It may simplify the development of the theory. Occam's Razor vs Shut Up And Calculate.

I don't see how what is proposed can claim the moral high ground and insinuate a shut up and calculate accusation against a probabilistic theory. You need a constructive argument to support the MWI counting process. Throwing mud in the form of cheap soundbites doesn't cut it.

 

[PeterDonis]

Oh good grief!
"do have to justify" not "do justify"!!!

Sorry, I misinterpreted your post.

 

[kered rettop]

I don't see how what is proposed can claim the moral high ground and insinuate a shut up and calculate accusation against a probabilistic theory.

Hardly a theory. Just the status of probability.

You need a constructive argument to support the MWI counting process.

Somebody might. I don't, since I am not advocating anything.

Throwing mud in the form of cheap soundbites doesn't cut it.

Oh, it's much worse than that. I have only just realized what you've been talking about. Even if I'd used a phrase which you found acceptable, my point would have been invalid. SUAC isn't so bad in the context of my misundertanding.

And yes, this means that my suggestion won't be helpful either.