## What is Many Worlds? What isn't Many Worlds?

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### Re: What is Many Worlds? What isn't Many Worlds?

After one measurement, your wavefunction contains 10 observers, unambiguously. That means each observer EXISTS with probability 1. Each observer has an amplitude associated with them, but no way to detect that amplitude. The common argument is that we have no reason to introduce a probability measure on this space. Probability of what?
Future computational history maybe?

I mean, if the universe didn't contain any operations that could combine to form computation at some scale, we wouldn't be here asking this question, so that has to be important somehow.

If you have an NDTM with observers in it, then two *different* observers can have memories of past observations that are in *literally* the same observations. Later on, both clearly exist separate from each other in the NDTM model. The model however, has clear distinction between branches, and so we are tempted to just draw the line there, but there can easily be analogue or continuous models that can encode an NDTM's operations (QM is perhaps even such a construct even at the smallest scales, we aren't sure yet) in which the "question what are we counting" becomes hazy. But the existence of the observer is still coming from the fact that it's modeling an NDTM, the fuzziness is just making things complicated (or perhaps, simpler) and... well... fuzzy. But even if no two observers ever become fully de-coupled in their possible interaction, there are still differing computational histories in the full description of the world (there are of course 'more' of them) and if there's a concept of history in a deterministic function, then surely there is also a concept of future. When an observer at T=n is multiple observers at T=n+k, then the observer at T=n cannot possibly be every observer at T=n+k, and must have some range of expectation for future past observations.

The only part that seems weird to me is explaining the actual probabilities we have been observing... why are they this, with undeniable repeatability, and not something else... or why this probability is coming from a term being multiplied by a complex number. I realize this is still one of the main objections to many worlds, I'm just saying I don't see why the existence of observers or having some probability associated with the wave function is strange. My gut reaction is actually that it shouldn't be using complex numbers at all, that they're just an abstraction over a deeper model that just works this way in the tests we've been able to bring to bear so far, which makes the probabilities observed and the complex factors reconcilable. We still don't have quantum gravity, and gravitons would be so much smaller than anything else that they might just reveal another layer of humdingery going on that the current model emerges from. That could (as in almost certainly is) just be my near complete ignorance of the field and general hopefulness talking however.
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WarDaft

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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:After one measurement, your wavefunction contains 10 observers, unambiguously.

Well, the problematic thing about assigning probabilities that way is that the wavefunction can contain those same observers before, too.

For example, if we have a computer hard drive with a bunch of possible 0s and 1s, and we prepare the hard drive by applying a potential towards "0," what we really have is a boltzmann distribution with some finite measure on all possible contents of the hard drive. Then if we write an image to it or something, we changed the wavefunction, but we didn't actually change the number of possible states. This total lack of time evolution makes it obvious that we don't recover our observations of the hard drive by counting the number of states.
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Charlie!

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### Re: What is Many Worlds? What isn't Many Worlds?

Well, the problematic thing about assigning probabilities that way is that the wavefunction can contain those same observers before, too.

If this problem existed, many worlds would be hopeless. Again- there are two separate problems.
1. How do we define 'observers' or 'worlds' within the wavefunction
2. What does it mean to assign probabilities to these observers?

If 1 can't be solved, the whole edifice collapses. In your harddrive example, even if your harddrive starts in an indeterminate state it will quickly decohere into a set of classical states of some 0s and 1s, and the probabilities will become classical- we won't have a super-position. In this case, the "measurement" is something the harddrive does to itself. After that, writing an image or whatever isn't a measurement.

And remember- we aren't assigning probabilities. All the observers exist. The statement "most of the observers that exist in the wavefunction don't see born probabilites" is a statement about the wavefunction at a given point in time. Its not probabilistic.
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### Re: What is Many Worlds? What isn't Many Worlds?

1. How do we define 'observers' or 'worlds' within the wavefunction
Why isn't computational history satisfactory for this? I mean, rule 134 defines the entire 2d pattern instantaneously, but distant 'intelligent beings' can still be discerned in the universe. Granted there is potentially a continuum of realities if we do this, but it still defines observers, there's just a lot more.
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:In your harddrive example, even if your harddrive starts in an indeterminate state it will quickly decohere into a set of classical states of some 0s and 1s, and the probabilities will become classical
Okay. So for different sequences of 0s and 1s, we can grant for the sake of your argument that a bunch of other atoms that we don't care about get affected (though we could regenerate the same problem if we started caring about those atoms) and so the different 0 and 1 states become more different. But why would that mean they stop existing, or fitting the definition of "observer?"

And remember- we aren't assigning probabilities. All the observers exist. The statement "most of the observers that exist in the wavefunction don't see born probabilites" is a statement about the wavefunction at a given point in time. Its not probabilistic.
Well, the non-probabilistic statement is tautologically true. But I think it's only interesting if we make it probabilistic (e.g. "different observers have the same sort of symmetry that different sides of a die have, therefore they get equal probability"), because that's what implies that MW won't regenerate the Born rule.
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Charlie!

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### Re: What is Many Worlds? What isn't Many Worlds?

So for different sequences of 0s and 1s, we can grant for the sake of your argument that a bunch of other atoms that we don't care about get affected (though we could regenerate the same problem if we started caring about those atoms) and so the different 0 and 1 states become more different. But why would that mean they stop existing, or fitting the definition of "observer?"

Its not what we care about- its whats 'macro'. i.e. what is a strong measurement. Have you read any of the work on weak measurements?

Well, the non-probabilistic statement is tautologically true. But I think it's only interesting if we make it probabilistic (e.g. "different observers have the same sort of symmetry that different sides of a die have, therefore they get equal probability"), because that's what implies that MW won't regenerate the Born rule.

But we can make the statement "most observers in a wavefunction don't see Born probabilities" without invoking anything OTHER than the wavefunction. 'Most observers don't see Born probabilities' is the problem.
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:
So for different sequences of 0s and 1s, we can grant for the sake of your argument that a bunch of other atoms that we don't care about get affected (though we could regenerate the same problem if we started caring about those atoms) and so the different 0 and 1 states become more different. But why would that mean they stop existing, or fitting the definition of "observer?"

Its not what we care about- its whats 'macro'. i.e. what is a strong measurement. Have you read any of the work on weak measurements?

A little, but not enough that those two sentences answer my question for me Maybe I didn't make my "for the sake of argument" decoherence strong enough? Do you want the hard drive to be decohering not just into "internal" degrees of freedom (doesn't really change the point), but out into the environment (i.e. weak measurement)? That seems like a pain, but I'd claim that you get the same answer, if we don't measure time-evolving states.

Anyhow, if we totally idealize this memory storage unit, would you agree that if we initialize it with independent Boltzmann distributions (Say, P(0) = 1-10-14), every sequence of observations (each "observer's memory") fully exists in the sense you/Zurek intend both before and after any "actual" memories are formed?

SU3SU2U1 wrote:
Well, the non-probabilistic statement is tautologically true. But I think it's only interesting if we make it probabilistic (e.g. "different observers have the same sort of symmetry that different sides of a die have, therefore they get equal probability"), because that's what implies that MW won't regenerate the Born rule.

But we can make the statement "most observers in a wavefunction don't see Born probabilities" without invoking anything OTHER than the wavefunction. 'Most observers don't see Born probabilities' is the problem.

If I have a die that's loaded so that it lands on 6 50% of the time, most possible sequences of rolls aren't half sixes. But this isn't any sort of contradiction to the ordinary probability in this situation, because the die being loaded breaks the symmetry between the sequences of die rolls. "Most sequences of observations don't obey the Born probabilities" is in a similar situation - for this to contradict the Born probabilities, you'd need to show that the symmetry broken by the loaded die is unbroken in the MW formulation. This would also uniquely specify the probabilities (principle of indifference), so that's why I'm saying stuff about making it probabilistic.

Well, or you could show that the symmetry is broken in a way that doesn't give you the Born probabilities, but that would be really weird.
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Charlie!

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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:But we can make the statement "most observers in a wavefunction don't see Born probabilities" without invoking anything OTHER than the wavefunction.

To make this statement, you have to add the assumption that there is something which you can count, or you have to propose a method to define "one observer" in a wave function in an exact way. This counting is an assumption you use in every post. And as long as you put this in, you will always keep this counting problem.
A similar statement for Copenhagen is: "Most possible results are far away from Born probabilities". It is true. But why should we repeat this over and over again?
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### Re: What is Many Worlds? What isn't Many Worlds?

To make this statement, you have to add the assumption that there is something which you can count, or you have to propose a method to define "one observer" in a wave function in an exact way.

There are exact ways built into the wavefunction- Zureck's pointer states are one way to do it. Also- if you can't separate the wavefunction into distinct "worlds" the whole edifice of many worlds does not work.

Lets invoke many minds for a second- if I want to define the probability my mind transitions to a specific world, I first need a way to define those worlds. If this step is insurmountable, then your claim is that many worlds can't work, yet I don't think this is the implication you want?
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### Re: What is Many Worlds? What isn't Many Worlds?

Define the probability that your mind transitions to an integral over a (small) volume in phase space? It is proportional to the integrated amplitude squared.
You can treat every "blob" as a collection of a lot of very similar, interacting worlds, without breaking anything. There is nothing special about the blobs. They are just some regions with high amplitude, surrounded by regions with lower amplitude.

>> Also- if you can't separate the wavefunction into distinct "worlds" the whole edifice of many worlds does not work.
Just your counting does not work. But that is a pointless discussion here, as it seems.
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### Re: What is Many Worlds? What isn't Many Worlds?

You can treat every "blob" as a collection of a lot of very similar, interacting worlds, without breaking anything.

How are you defining a world?

I'm defining a 'world' the way that Everett, DeWitt, Deusch and Wallace do (have you read the literature I referenced?). This is more or less analogous to Zureck's pointer states- a linear subspace of the wavefunction that contains a unique macro-state and evolves independently of the rest of the wavefunction (where independently means that effects from other worlds become arbitrarily small in finite time).

Also, that doesn't solve the problem- in your picture observers only live in your 'collection of very similar interacting worlds', so you still have the issue that most of the observers in the wavefunction don't see born probabilities. Its a general feature of how the wavefunction evolves. Of course, you can follow Weismann and modify Schroedinger to kill off subsets of observers.

Define the probability that your mind transitions to an integral over a (small) volume in phase space?

This is a non-sensical question. Minds are associated with observers in distinct states, not general-regions of phase space.
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### Re: What is Many Worlds? What isn't Many Worlds?

mfb wrote:>> Also- if you can't separate the wavefunction into distinct "worlds" the whole edifice of many worlds does not work.
Just your counting does not work. But that is a pointless discussion here, as it seems.

I have been following this thread, and I have to agree that this discussion seems rather pointless. You seem to think that this counting that SU3SU2U1 has been talking about is something he came up with. It is not, it is part of the Many Worlds Interpretation. The point he is trying to make is that in the Many Worlds Interpretation, there is inherently this counting problem. It seems like you are missing this point because the Many Worlds Interpretation is not what you think it is.

SU3SU2U1 is discussing Many Worlds Interpretation, while you seem to be discussing your own interpretation which is different from the Many Worlds Interpretation. If you wish to discuss your own interpretation (perhaps in another thread), I invite you to formalize it so that we are actually talking about the same thing.
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### Re: What is Many Worlds? What isn't Many Worlds?

Charlie! wrote:Anyhow, if we totally idealize this memory storage unit, would you agree that if we initialize it with independent Boltzmann distributions (Say, P(0) = 1-10-14), every sequence of observations (each "observer's memory") fully exists in the sense you/Zurek intend both before and after any "actual" memories are formed?

Yes, lets assume the harddrive is big enough that it will decohere quickly (obviously true for something as big as a brain or harddrive). You initialize it, and it will split into many different worlds, each with their own amplitude. If you've checked the harddrive,there is a copy of you in each harddrive-world.

Now, if I go and write something to the harddrive, the world I live in (with my copy of the harddrive) will split again depending on the distribution of what I've written.

SU3SU2U1 wrote:
Well, the non-probabilistic statement is tautologically true. But I think it's only interesting if we make it probabilistic (e.g. "different observers have the same sort of symmetry that different sides of a die have, therefore they get equal probability"), because that's what implies that MW won't regenerate the Born rule.

"Most sequences of observations don't obey the Born probabilities" is in a similar situation - for this to contradict the Born probabilities, you'd need to show that the symmetry broken by the loaded die is unbroken in the MW formulation. This would also uniquely specify the probabilities (principle of indifference), so that's why I'm saying stuff about making it probabilistic.

But each observer exists. Imagine on a table you have two dice with the number 1 showing each with the number 1/8 written on the table next to them and 5 more dice each showing the numbers (2,3,4,5,6) each next to the number 3/20. Now, I can make the statement 'most of the dice are showing 1' very easily. How would I go about investigating whether the number next to them reflects any kind of bias in the dice?

Edit: How can we make the argument that each number represents 'how real' the dice are?
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:How are you defining a world?

I avoid the word "world" due to that reason. I like your** "blob", but if you* think in a finite number of worlds which do not have any difference (in terms of "more real" mentioned before), you* run in the counting problem mentioned before.

*with the general meaning, not as a single person (@JWalker)
**that is SU3SU2U1's word as far as I can tell

>>have you read the literature I referenced?
I did.

>> (where independently means that effects from other worlds become arbitrarily small in finite time).
Which is not what I asked for .

Define the probability that your mind transitions to an integral over a (small) volume in phase space?

This is a non-sensical question. Minds are associated with observers in distinct states, not general-regions of phase space.

These distinct states are just special regions of phase-space.

You seem to think that this counting that SU3SU2U1 has been talking about is something he came up with.

No, I don't think that. But I do agree that counting does not work (unless something somehow modifies the evolution of the wave function, as mentioned). So where is the point to discuss this over and over again?
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### Re: What is Many Worlds? What isn't Many Worlds?

What about the example given though? If you have a machine/system that writes down the rolls of a normal dice, what happens about the universe/world/blob where the dice lands on 6 every time? Those universes are going to be what? In my mind, those universes will show that their is a break in reality. As a separate measurement (say balance/etc) would show it's an unbias die. Yet the results show it always rolls a 6.

However, we live in a universe where we do not get these results. We get the Borne probabilities, right? So you need a way to show why we are not in the universe where every die (bias or not, 6 sided 2 sided, 12 sided or 102 sided) does not all roll 6s. Because in MW theory, those universes exist... Yet I have seen no reply as to why we do not find ourselves in that universe.
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### Re: What is Many Worlds? What isn't Many Worlds?

@Technical Ben: Why are you not born in Germany? (If you happen to be born there: Why not in the UK?)
You know that humans exist which are born there. But "you live in a universe where you are not born there".
This does not account for any probability or anything else. It is just the general idea.

Maybe there are observers which are confused like hell because all 1000000 photons hit detector 1 and none hit detector 2, even if they calculated that both events have the same probability/amplitude.
But most observers (in the symmetric case, counting is fine ) will observe roughly 500000 photons in both detectors.
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### Re: What is Many Worlds? What isn't Many Worlds?

I like your** "blob", but if you* think in a finite number of worlds which do not have any difference (in terms of "more real" mentioned before), you* run in the counting problem mentioned before.

The problem is- how do you formalize more real?

But anyway- we all appear to be on the same page now I hope? To recap- Many worlds requires
1. a way to define 'worlds' or 'observers' or 'branches' or 'blobs' within the wavefunction

and this problem is solved by decoherence (an 'branch' is a linear subset of the wavefunction that evolves independently of the rest of the wavefunction)

2. when we define worlds in this way, we can make the unambiguous statement "most branches of the wavefunction will not have observed Born probabilities." This statement is troubling for the many worlds paradigm- it means that we need some way to say 'oh, but those worlds aren't us!' or minimally 'those worlds aren't likely to be us.' There are lots of ways to try and deal with this problem- but many worlds as-it-exists doesn't give us a handle on it.

Many minds asks us to interpret the probabilities defined by something like Gleason's theorem as weights of 'how much of our mind' follows down each branch. This formalizes what it could mean for a branch to be 'more real'. This is almost certainly the reasoning that most people are intuiting when they say "you only need the wavefunction."- but you don't, they are adding in a super-set of brains.
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:(an 'branch' is a linear subset of the wavefunction that evolves independently of the rest of the wavefunction)
Don't you mean "almost independently"? (the interaction gets very small in short period of time, but it doesn't fall to zero, right?)
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### Re: What is Many Worlds? What isn't Many Worlds?

Almost zero things ever get down to exact zero.
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### Re: What is Many Worlds? What isn't Many Worlds?

mfb wrote:@Technical Ben: Why are you not born in Germany? (If you happen to be born there: Why not in the UK?)
You know that humans exist which are born there. But "you live in a universe where you are not born there".
This does not account for any probability or anything else. It is just the general idea.

Maybe there are observers which are confused like hell because all 1000000 photons hit detector 1 and none hit detector 2, even if they calculated that both events have the same probability/amplitude.
But most observers (in the symmetric case, counting is fine ) will observe roughly 500000 photons in both detectors.

Nope. I'd expect everyone to be born in Germany if we had MW. I'm asking, if we have MW why do we not see everyone being born in Germany? It's just as likely under MWI to have all dice roll a 6 forever as it is for us to get normal distribution?

So the basic question is, why does a dice prefer a normal distribution over any of the other results?

(I'm guessing what the answer is, but I'll save my reply till it's clear. )
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### Re: What is Many Worlds? What isn't Many Worlds?

Don't you mean "almost independently"? (the interaction gets very small in short period of time, but it doesn't fall to zero, right?)

I mean that the influence from the rest of the wavefunction becomes arbitrarily small in finite time.
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### Re: What is Many Worlds? What isn't Many Worlds?

So it's zero at some point. Not almost zero, but actually zero.

I don't think that's experimentally verifiable. I also can't think of any 'nice' functions that smoothly slope down to and become zero. Sure we can engineer one fairly easily, but it would be hard to argue that it just drops out of the equations.
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### Re: What is Many Worlds? What isn't Many Worlds?

Technical Ben wrote:I'm asking, if we have MW why do we not see everyone being born in Germany?

Why should we? There are many other countries in the world.
There are 1 billion humans on earth which happen to be born in china. And only 1 human which was born in town X in hospital Y at time Z. Let's assume we don't have other humans on earth, so this single one is something special. This human could ask "wtf, why am I this single human and not one of the 1 billion in china?".
Could you give him an answer?
I think it is the wrong way to approach this issue. Begin with the fact that 1 billion were born in china and 1 in XYZ. It is totally natural that this single human will wonder what happened, while 1 billion humans don't do that.

It's just as likely under MWI to have all dice roll a 6 forever as it is for us to get normal distribution?

With a fair die, all sequences have the same probability/amplitude. This is independ on the interpretation. 1 million "6" in a row just looks much more interesting than most of the other sequences. And therefore, most of the observers will see something close to "each number with 1/6 probability, without correlation".
If you manipulate it, you still have all observers, but their worlds have a different amplitude.
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### Re: What is Many Worlds? What isn't Many Worlds?

mfb wrote:
It's just as likely under MWI to have all dice roll a 6 forever as it is for us to get normal distribution?

With a fair die, all sequences have the same probability/amplitude. This is independ on the interpretation. 1 million "6" in a row just looks much more interesting than most of the other sequences. And therefore, most of the observers will see something close to "each number with 1/6 probability, without correlation".
If you manipulate it, you still have all observers, but their worlds have a different amplitude.

This type of argument only works because of the nice numbers that pop out of an even probability measure like what fair dice provide.

Instead, take my thought experiment from before - set up 6 identical experiments, each with a 90% chance of producing an "A" on their detector, and 1% each chance of producing the digits 0-9 on their detector. (Assume that the difference in the 11 outcomes is due to a single quantum variable, for simplicity.) Run them all.

Basic probability says that you have a hair over 50% chance to see 6 As, and the chance of seeing 6 digits (of any kind) is 1 in a million. If you count worlds, though, there are about 1.7million worlds, in which 1 million of them (a bit over 50%) see 6 digits. Only *one* world sees six As. The two situations have *completely* reversed - now "most" observers see the most unlikely events.
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:
Don't you mean "almost independently"? (the interaction gets very small in short period of time, but it doesn't fall to zero, right?)
I mean that the influence from the rest of the wavefunction becomes arbitrarily small in finite time.
So you are saying that the answer to my question is "yes"?

Ie, you are agreeing that the influence from the rest of the wavefunction never falls to zero in any finite period of time?
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### Re: What is Many Worlds? What isn't Many Worlds?

Based on SU's earlier posts, I think that's a yes.
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### Re: What is Many Worlds? What isn't Many Worlds?

So you are saying that the answer to my question is "yes"?

Ie, you are agreeing that the influence from the rest of the wavefunction never falls to zero in any finite period of time?

Yes, but it becomes arbitrarily small- which is as good a definition of 'zero' as you'll find in physics. I was just giving you the definition of independent I was using.
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### Re: What is Many Worlds? What isn't Many Worlds?

mfb, how do "most of the observers" observe borne probabilities (the die not rolling 6 every time)? Because, if we have a MW set of universes, the majority do not observe a normal distribution. How do "amplitudes" help? Do we get "more" universes with high amplitudes? Hence others counter argument on the "more real" problem?
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### Re: What is Many Worlds? What isn't Many Worlds?

As long as we're being technical with our definitions, what's an observer?

Sure theres plenty of intuition on this, but theres also plenty of (not necessarily correct) intuition as to what a 'world' is, and I feel as if theres related issues there. Are there a discrete number of observers? A finite number? Is the number 'large', or might it be 1 or even 0?

The above might be getting rather close to the realm of unanswerable philisophical questions, but if an argument is being made about 'most observers', then that suggests that that's a meaningful thing to think about, and it's not the case theres just one observer ('me') observing everything simultaniously. (I don't claim to have an explanation for what that means, but it doesn't seem like a totally unsalvagable notion.)

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### Re: What is Many Worlds? What isn't Many Worlds?

Technical Ben wrote:mfb, how do "most of the observers" observe borne probabilities (the die not rolling 6 every time)? Because, if we have a MW set of universes, the majority do not observe a normal distribution. How do "amplitudes" help? Do we get "more" universes with high amplitudes? Hence others counter argument on the "more real" problem?

Please specify what exactly you mean, otherwise it gets confusing because there are multiple experiments hanging around in the posts.

>> Do we get "more" universes with high amplitudes?
No, but universes which contribute more to the total measure of the universe.

For further questions about this, I refer to the thread up to this post. Sorry, this repetition of questions and arguments is really pointless, and I won't participate in this any more.
mfb

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### Re: What is Many Worlds? What isn't Many Worlds?

Dopefish wrote:As long as we're being technical with our definitions, what's an observer?

Sure theres plenty of intuition on this, but theres also plenty of (not necessarily correct) intuition as to what a 'world' is, and I feel as if theres related issues there. Are there a discrete number of observers? A finite number? Is the number 'large', or might it be 1 or even 0?

The above might be getting rather close to the realm of unanswerable philisophical questions, but if an argument is being made about 'most observers', then that suggests that that's a meaningful thing to think about, and it's not the case theres just one observer ('me') observing everything simultaniously. (I don't claim to have an explanation for what that means, but it doesn't seem like a totally unsalvagable notion.)

An observer is any system complex enough to trigger decoherence, I think - in other words, something capable of causing a significant world-split.

Yes, there's not just one observer, at least not in a human-meaningful sense. One *can* argue that there's a single "me" spread across the phase space, but most of "me" is too separated to meaningfully interact with the rest of "me", so that's not a very useful definition. In practice, I (along with every other sufficiently complex system) exist in a large number of worlds as independent entities that experience independent realities.
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### Re: What is Many Worlds? What isn't Many Worlds?

I'd prefer to just focus on observable operators. Nice and hermitian, local, form an algebra. "Observer" is much more pesky a notion. Observable operator, now that's something you can anchor a theory on!
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### Re: What is Many Worlds? What isn't Many Worlds?

I'd prefer to just focus on observable operators. Nice and hermitian, local, form an algebra. "Observer" is much more pesky a notion. Observable operator, now that's something you can anchor a theory on!

Unfortunately then, you can't make many worlds happen. All we get from decoherence is diagonal density matrices, which give us diagonal operators values.

To make predictions in many worlds we need definitions for 'relative states', 'observers','worlds', 'blobs' or whatever your preferred nomenclature is. We have to interpret a diagonal density matrix as a sum of classical 'worlds.'

An observer is any system complex enough to trigger decoherence, I think - in other words, something capable of causing a significant world-split.

In the sense I've been using it, I've been using "each observer" as a synonym for "each branch of the wavefunction." In this case, I'm formalizing branch as a linear subset of the wavefunction that evolves independently (where independently is defined above) of the rest of the wavefunction.

Question for the interested reader- if I change basis (say from spin z to spin x, or position to momentum) can I change the number of branches in the wavefunction?
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:
I'd prefer to just focus on observable operators. Nice and hermitian, local, form an algebra. "Observer" is much more pesky a notion. Observable operator, now that's something you can anchor a theory on!

Unfortunately then, you can't make many worlds happen.

Perhaps, if by 'unfortunately' you mean 'hosannah.'
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### Re: What is Many Worlds? What isn't Many Worlds?

Huh?
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### Re: What is Many Worlds? What isn't Many Worlds?

SU3SU2U1 wrote:Question for the interested reader- if I change basis (say from spin z to spin x, or position to momentum) can I change the number of branches in the wavefunction?

No. If you measure the z-direction (I think this what you think of?), you get a superposition of "spin x up" and "spin x down" with well-defined phases in between for both branches (or other amounts for spins different from 1/2 of course). Your basis is just a mathematical tool, not a physical property of the system.

Something new .
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### Re: What is Many Worlds? What isn't Many Worlds?

Technical Ben wrote:Huh?

I was expressing my deep elation at dismissing MW. It is awful stuff.

And mfb, you misunderstand. Switching from a spin-x to spin-y is not something you'd expect to change the number of branches. Going from spin-x to position or momentum, hmm?

SM knows very well that choice of basis is a coordinate artifact without physical significance. It would be interesting to know if MW supporters are willing to assign the same ontological status to "number of branches of the universe."
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### Re: What is Many Worlds? What isn't Many Worlds?

doogly wrote:I was expressing my deep elation at dismissing MW. It is awful stuff.

Aw, cmon It's really useful for picturing entanglement. You don't have to have any changes propagating faster than light, because the measurement is a change to the measuring apparatus, not to the particles.
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### Re: What is Many Worlds? What isn't Many Worlds?

Oh sweet Dirac's ghost, what do you take me for? Of course I'm not picturing anything superluminal during entanglement. If that were the case, other interpretations of quantum mechanics would not simply be interpretations, but would be modifications of the fundamental physics (hi Bohm!) and we can't have that.
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### Re: What is Many Worlds? What isn't Many Worlds?

Come now, that's not true. Superluminal effects that don't allow superluminal information transfer are still quite compatible with physics.
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