Many Worlds Interpretations and probabilities

[LeandroMdO]

Read Wallaces book:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Its very theorem, proof, theorem, proof in its style.

But the emphasis has shifted from observations to Histories.

Thanks
Bill

Okay. What are the axioms?

 

[bhobba]

Okay. What are the axioms?

As far as I can see simply the Schrodinger Equation.

Thanks
Bill

 

[Quantumental]

As far as I can see simply the Schrodinger Equation.

I feel like you are always talking with 2 tongues, on one hand you dismiss MWI because it's too weird, then you go onto say: nature is weird, therefore MWI doesn't have to explain itself, yet I don't believe it. Sometimes I am wondering if you are a hardcore MWI proponent that just troll for fun.

Re: axioms, you yourself literally say that the only way to accept something like Gleason or Decision Theory is to presume (another axiom) that nature just 'behaves like that'. That's not science.

Let's look at the most devoted MWI supporter out there: David Deutsch. Mr. Deutsch postulates (axiom alert) that there is an infinite amount of universes from start, he calls these 'fungible' meaning that there is no difference between them at all, there is literally no fact of the matter which of these infinite ones you are, yet there is an infinite of them. So in his reading of Everett if there is a 30% probability of something occurring, now 30% of the infinite worlds had this outcome while the 70% others had the other outcome, but if there is no fact of the matter of which world is which (fungibility) then how can it just magically split into a 3/7 formation? This is riddled in axioms and incoherence.

David Wallace, Simon Saunders, Alastair Wilson etc. has advocated for a slightly different approach where you start out with the wavefunction and all the worlds within it, but then they diverge instead of splitting, so in the aforementioned example there was initially 2 worlds, let's call them world A and world B, then A had the 30% outcome and 70% world had the other outcome. This is at least coherent, but begs the question: what made A evolve into the 30% outcome? What mechanism/property of that world from t0 determined this? Correct me if I am wrong, but this is also an axiom.

 

[bhobba]

I feel like you are always talking with 2 tongues, on one hand you dismiss MWI because it's too weird, then you go onto say: nature is weird, therefore MWI doesn't have to explain itself, yet I don't believe it. Sometimes I am wondering if you are a hardcore MWI proponent that just troll for fun.

I fail to see how any of those things are an issue. I find MWI too weird, but MWI adherent's don't. I don't dismiss it either - I just don't adhere to it - there is a difference.

Re: axioms, you yourself literally say that the only way to accept something like Gleason or Decision Theory is to presume (another axiom) that nature just 'behaves like that'. That's not science.

You get a weird prediction from a theory that is in accord with observation and accept it. That is science. I am being unscientific in rejecting it as too weird - you shouldn't do that - but I do. It called personal prejudices.

Let's look at the most devoted MWI supporter out there: David Deutsch. Mr. Deutsch postulates (axiom alert) that there is an infinite amount of universes from start,

I don't know what Deutch said, I learned from Wallace.

The prediction of MW, as espoused by Wallace is an exponentially increasing number of worlds, it's very very large, but not infinite. Its not an axiom either. The probability of experiencing a world is not an axiom - it simply asks a question. I will find myself in some world. I don't know which. What is the probability I will experience a certain outcome. Its like tomorrow I will experience some weather - I don't know what it will be but what is the probability it will be wet, cloudy, sunny or whatever. The issue with MW is when you consider all the other worlds why is it a different probability in other worlds - that is very counter intuitive - in fact downright weird. But its what the theory says.

I would suggest getting the book the Emergent Multiverse and actually studying it.

Thanks
Bill

 

[LeandroMdO]

I would suggest getting the book the Emergent Multiverse and actually studying it.

But that's the thing. If MWI had a precise formulation I wouldn't need to do that. I could get a list of axioms that define the theory and work from there.

Just the Schrödinger equation doesn't do at all. It's not clear that there are probabilities when evolution is purely deterministic. Yes, a pure state gets hopelessly entangled with the environment over time, but that by itself doesn't entitle me to write down a density matrix, discard off-diagonal elements, and interpret the diagonal as a probability distribution. For that, I need a probabilistic interpretation which is precisely what I'm trying to prove.

Even assuming some uncertainty, it doesn't follow from Gleason's theorem or anything else that frequencies of outcomes of repeated experiments converge to the Born rule derived probabilities, or any probability distribution at all.

 

[bhobba]

But that's the thing. If MWI had a precise formulation I wouldn't need to do that. I could get a list of axioms that define the theory and work from there.

It just one axiom as far as a I can see.

Of course you have to assume a question like what is the likelihood I will find myself in a particular world is meaningful. I think its a matter of taste if you consider such an axiom or not. In classical mechanics we define the velocity as the derivative of position, but obviously an axiom is such a derivative exists is needed, but nobody ever explicitly states it because its so damn obvious,

Thanks
Bill

 

[LeandroMdO]

It just one axiom as far as a I can see.

Of course you have to assume a question like what is the likelihood I will find myself in a particular world is meaningful. I think its a matter of taste if you consider such an axiom or not.

Not just likelihood. You have to prove that it is a probability. Assigning a weight to the branch is not enough, because a weight is just a number. It can mean anything. It could mean that "the branches on the left have |a|² units of beauty". The identification with actual frequencies needs to be stated explicitly, preferably as a consequence of an easily accepted axiom.

Some manner of branch counting always seems to be implied. If you tell me that you have |a|² branches on one side and |b|² branches on the other it doesn't take much work for me to accept that the probability of finding myself in the former side is |a|², and all I really had to assume is that my experience corresponds to one branch (which is an axiom, but a much weaker one). But then proponents of many worlds turn around and say that the number of worlds isn't well-defined/meaningful, that branch-counting is misguided, and that probabilities come from someplace else. If that's so, the connection with frequencies must be justified. One cannot use a branch-counting intuition to establish something, and then discard branch counting.

In classical mechanics we define the velocity as the derivative of position, but obviously an axiom is such a derivative exists is needed, but nobody ever explicitly states it because its so damn obvious.

It is explicitly stated: it's part of Newton's first law. The common wording of it does some extra work that excludes noninertial frames, but the meat of it is the idea that the state of motion doesn't change without reason. This excludes discontinuous changes in position and velocity (assuming no infinite forces, which is a much milder assumption).

It's also worth noting that even if it were obvious, the emergence of probabilities in MWI certainly isn't, or there'd be a consensus in its favor already; this conversation wouldn't happen because we'd both happily accept many worlds.

 

[bhobba]

Not just likelihood. You have to prove that it is a probability.

You mean to say, for example, you can't assume tomorrow there is a probability it will rain or not. As far as I can see that's all they are doing. You will have a number of copies after. You will not know about any of the others. What is the probability the copy you are experiencing gets a certain outcome. Most would say that's not an assumption even though it is.

Regarding Newtons first law by mentioning acceleration you are assuming position is twice differentiable - that is an implicit but unstated assumption. Should it be stated as an axiom? I think modern versions of classical mechanics based on sympletic geometry do just that - but is really only used by mathematicians of the pure variety. Such things are purely a matter of taste and semantics which I think is the silliest thing I know to argue about.

The classic example though would have to be good old Euclidean geometry. Would you consider Euclid's axioms valid? If so exactly what did Hilbert do when he gave his axioms? Again its a matter of taste as to what level of rigor you want.

Thanks
Bill

 

[bhobba]

Here is an article that I found that examines the isssue of axiomatics in what I consider a fair way - giving points for and against:
https://arxiv.org/pdf/gr-qc/9703089.pdf

The only issue I have is it was written in 1989.

I learned MW from Walllace's book which is very recent, written in 2012, so things have likely moved on a lot since 1989.

As far as I can see modern MWI is simply decoherent histories with each history being in a separate world. I think its likely if you have issues with one, you have the same issue with the other - not always of course but they seem to have so much in common it would be likely.

I will state my own preference - Decoherent Histories is way better than MW - but that is, as I try to explain to some, just a preference, it doesn't mean anything.

Thanks
Bill

 

[LeandroMdO]

You mean to say, for example, you can't assume tomorrow there is a probability it will rain or not.

In a sense that's right. The statement "there is an 80% chance of rain tomorrow" is a bit meaningless unless it is qualified. For instance, you can say that, historically, there has been rain at your location 8 out of 10 March 23rds, and you expect the trend to continue in the future. Or you may have a model of the climate, that when fed today's atmospheric data, produces rain in 24 hours in 8 out every 10 model runs.

If you did your job right, you will see your predictions of this type be confirmed by experiment which will then justify the shorthand "there's a 80% probability of rain tomorrow". But the precise meaning of probability in this context is clear: I have a frequentist definition that came from my use of a model that I can, in fact, run many times.

When it comes to many worlds, I don't see such a frequentist approach working unless there's a branch counting argument, which people such as Wallace explicitly advise against. It is then illegitimate to refer to the measure obtained from Gleason's theorem as a probability; it is best termed a weight. Then more work is required to find the physical meaning of these weights.

Regarding Newtons first law by mentioning acceleration you are assuming position is twice differentiable - that is an implicit but unstated assumption. Should it be stated as an axiom? I think modern versions of classical mechanics based on sympletic geometry do just that - but is really only used by mathematicians of the pure variety. Such things are purely a matter of taste and semantics which I think is the silliest thing I know to argue about.

I don't require the axioms to be stated with mathematical rigor, necessarily, but I want them to elucidate what assumptions are being made. I think it's clear, if implicit, that Newton's first law implies differentiability properties for classical paths. The issue with MWIs is that they don't say anything, explicitly or implicitly.

EDIT:

Here is an article that I found that examines the isssue of axiomatics in what I consider a fair way - giving points for and against:
https://arxiv.org/pdf/gr-qc/9703089.pdf

Yes, I'm familiar with that paper. I agree with him that "I'm uncomfortable with the idea of many worlds" is not a valid objection, and that the program is worthwhile. I also agree with him that it's still not clear what all these not obviously equivalent versions of MWI are saying. It's possible that things have moved on since then, but if we take a look at more recent papers, e.g.

https://arxiv.org/abs/1405.7907

and its rejoinder by A. Kent

https://arxiv.org/abs/1408.1944

The situation doesn't appear to be any better resolved.

 

[Blue Scallop]

https://www.physicsforums.com/threads/why-mwi-cannot-explain-the-born-rule.364063/

Dense reading.. but how does BM deal with the amplitudes and probability and how does it derive the Born Rule?

 

[Demystifier]

Dense reading.. but how does BM deal with the amplitudes and probability and how does it derive the Born Rule?

BM is discussed in many other threads. This thread is about MWI.