B Do worlds of MWI ontologically have to exist?

stevendaryl

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A projection operator is an operator such that P^2 = P. A sequence of such operators is called a history. Its well defined. Its supposedly the stochastic theory of all such sequences. Obviously some will have zero or so close to zero probability so as to be of no value. There is a general theorem built from the Born Rule that gives that probability.
Yes, I know what a projection operator is. I asked how the projection operators are chosen.
 
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Yes, I know what a projection operator is. I asked how the projection operators are chosen.
I am confused - as I said there is no restriction - all are considered. Some are of no relevance, are inconsistent or for other reasons not worried about. The linked article gives some of the details eg about division into families and their consistency - it's part of the other name consistent histories.

Thanks
Bill
 
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stevendaryl

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I am confused - as I said there is no restriction - all are considered.
I know, I'm saying that without such a restriction, it isn't a stochastic theory. A stochastic theory tells the probability of a future state given the current state. Consistent Histories doesn't do that.
 
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Of course there are restrictions in order for a history to make sense eg they need to have a practicable probability, they are grouped into families and families must be consistent, have a Boolean structure that is classically logical etc. The exact detail I at one time knew more about - that was a bit ago now, and I cant recall many of those details, but the thesis I gave the link to seems to give the full details and reasoning on how they are used, as well as issues.

Thanks
Bill
 
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What ontologically have to exist, it's some different "sorts of reality", according to Gell-Mann:smile:
View attachment 233111
Your guess is as good as mine - we do not discuss what 'some sort of reality means' here - if that is what interests you go over to philosophy forums. Aside from the video I linked to previously Gell-Mann did another related one that may shed some further light on the issue:

Thanks
Bill
 
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stevendaryl

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I know, I'm saying that without such a restriction, it isn't a stochastic theory. A stochastic theory tells the probability of a future state given the current state. Consistent Histories doesn't do that.
I really can't make any sense of Consistent Histories as an interpretation. To me, it's basically Copenhagen bumped up a notch---rather than talking about single measurement outcome whose probability is given by the Born Rule, it shifts focus to an entire history whose probability is given by a more sophisticated version of the Born rule. I don't see how it's an interpretation, though.
 
There is a really interesting recent article on MWI in quanta magazine. It shows a fundamental flaw which is really hard to grasp. I think the author failed to realize that this flaw is not unique to MWI, it is just most obvious there. The basic problem is that most interpretations say that observations are random - but how do you tell something is random once you have observed it? If you know all fair dice rolls that have ever happened, how would you asses whether dice rolls are random? The basic model of randomness doesn't say anything about particular outcomes, only about "a tendency for many repetitions" and you cannot repeat the universe.
Well MWI is special on that in its simplest form it doesn't talk about probability but superposition amplitude. This has the same problem though: if everything that can happen does happen, even absurd (extremely improbable) things do happen in some "parallel world". But our world looks normal, not absurd. And it doesn't help to say absurd parallel worlds have a small amplitude because a parallel world cannot feel its own amplitude, so that doesn't explain why ours isn't absurd.
There are ways out of this. Kolmogorov complexity is a way to define what randomness can mean for a finite, unrepeatable sequence of observations. Maybe some process in nature suppresses all simple patterns in observations (except those that are always present - the laws of nature). The Boltzmann brain thought experiment suggests there should be - otherwise it's more likely to be a Boltzmann brain than to be a sentient being in a world with other sentient beings.
 
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Could one interpret MWI as the assertion that a measurement puts the observer in a superposition of worlds that are all to a certain degree real?

For example: if the measurement yields ##\frac{1}{\sqrt{5}}|w_{0}\rangle|W_{0}\rangle+\frac{2}{\sqrt{5}}|w_{1}\rangle|W_{1}\rangle##, could one say that ##\frac{2}{\sqrt{5}}|w_{1}\rangle|W_{1}\rangle## is 'more real' than ##\frac{1}{\sqrt{5}}|w_{0}\rangle|W_{0}\rangle##?
 

DarMM

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Could one interpret MWI as the assertion that a measurement puts the observer in a superposition of worlds that are all to a certain degree real?

For example: if the measurement yields ##\frac{1}{\sqrt{5}}|w_{0}\rangle|W_{0}\rangle+\frac{2}{\sqrt{5}}|w_{1}\rangle|W_{1}\rangle##, could one say that ##\frac{2}{\sqrt{5}}|w_{1}\rangle|W_{1}\rangle## is 'more real' than ##\frac{1}{\sqrt{5}}|w_{0}\rangle|W_{0}\rangle##?
I've seen the phrase "more real" used, so it would agree with how some see it.

Another explanation used in modern derivations of the Born rule in MWI is that there are an infinity of worlds and the ##\frac{2}{\sqrt{5}}## represents the volume in world space of all the worlds with the ##|w_1, W_1\rangle## outcome, i.e. 80% experience it.
 
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The basic model of randomness doesn't say anything about particular outcomes, only about "a tendency for many repetitions" and you cannot repeat the universe.
Oh yes it does - its called the Kolmogrov axioms and the strong law of large numbers that follows from those axioms:
https://en.wikipedia.org/wiki/Law_of_large_numbers

You can't say anything about a single observation, other than the possible outcomes you can get - but in a large ensemble of systems prepared exactly the same way (technically the same state) the same observation performed on them all will yield results as per the strong law of large numbers.,

And yes that you cannot observe the universe is an issue with interpretations of QM.

Thanks
Bill
 

stevendaryl

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You can't say anything about a single observation, other than the possible outcomes you can get - but in a large ensemble of systems prepared exactly the same way (technically the same state) the same observation performed on them all will yield results as per the strong law of large numbers.
I wouldn't say "will yield results..." I would say "will probably yield results..." (with probability approaching 1).
 
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To me, it's basically Copenhagen bumped up a notch---rather than talking about single measurement outcome whose probability is given by the Born Rule, it shifts focus to an entire history whose probability is given by a more sophisticated version of the Born rule.
What it tries do do is as detailed at the start of the thesis I posted:
Its from 'Pioneering work by Griffiths, extended among others by Omnes, Gell-Mann and Hartle, has led to a new formulation of quantum mechanics in which no observer or quantum-classical divide is required and wave function collapse does not occur. This interpretation is known as ‘consistent histories’.

It is supposed to fix the issue in Copenhagen of what is a measurement - everything is quantum from the start - no collapse - just a quantum state. A book explaining it at the intermediate level has kindly been made available by Griffiths:
http://quantum.phys.cmu.edu/CQT/index.html

I read it about 10 years ago now, liked it but it seemed a bit too contrived so didn't go deep into it. That's the thing about all these interpretations - you cant really know the deep detail of them all, only a general outline. I did study the Emergent Multiverse in its entirety and its a bit more advanced, and interestingly actually similar in many ways to Decoherent Histories

Thanks
Bill
 
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In addition, one should look to more recent work, like the Pusey-Leifer theorem concerning operational time symmetry, which show Many Worlds would have to be fine tuned to avoid disagreeing with QM.
Just wondering to which result this is referring?
https://arxiv.org/abs/1607.07871 "Is a time symmetric interpretation of quantum theory possible without retrocausality?" maybe?

I think in that result they say it doesn't apply to Everett (MWI) or Bohm (although I may be misreading it, or we're talking about different things here....it gets confusing to me). If that is the paper you're referring to I may just need to study it more.
 

stevendaryl

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What it tries do do is as detailed at the start of the thesis I posted:
Its from 'Pioneering work by Griffiths, extended among others by Omnes, Gell-Mann and Hartle, has led to a new formulation of quantum mechanics in which no observer or quantum-classical divide is required and wave function collapse does not occur.
I don't think it actually accomplishes that, though.
 

DarMM

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Just wondering to which result this is referring?
https://arxiv.org/abs/1607.07871 "Is a time symmetric interpretation of quantum theory possible without retrocausality?" maybe?

I think in that result they say it doesn't apply to Everett (MWI) or Bohm (although I may be misreading it, or we're talking about different things here....it gets confusing to me). If that is the paper you're referring to I may just need to study it more.
So a symmetry can show up in three ways in a theory let's say.
  1. Ontologically, that is it really is a genuine fundamental symmetry of the theory
  2. Dynamically, where the symmetry is not naturally present but becomes effectively true because of some effect of evolution over time. An example might be where some liquid freezes into a crystal. The fundamental molecular laws don't have lattice displacement symmetries, but the crystals do.
  3. Fine-tuning, where the initial conditions are chosen so that the symmetry looks like it is true, but they aren't. An example would be a pencil being perfectly set up to balance on its tip. This situation is perfectly circularly symmetric, but the laws and the pencil itself are not by default. The "tuning" part refers to how the symmetry would be destroyed by the slightest perturbation of the situation
So there is a symmetry in QM called Operational Time Symmetry. What they prove in that paper is that if you don't have retrocausal or acausal theories, then Operational Time Symmetry can't be Ontological, i.e. can't be a fundamental symmetry. Now this is an observed symmetry in experiments, so you do have to explain it. By dropping Retrocausality then, you only have recourse to showing it arises dynamically or via fine-tuning.

If you choose dynamically you really have to prove this occurs and you would be letting in the fact that before the relevant dynamical process took place (e.g. the freezing of the liquid above) the symmetry would not be present. Since it is a symmetry of QM, this would mean Many-Worlds would disagree with standard QM at some point in the early history of the universe and hence cosmological observations could disprove it.

Choosing fine-tuning arguments is considered artificial, as basically the multiverse in MWI would have to have started off in precisely the correct state to make it look as though Operational Time Symmetry was a fundamental symmetry, when it isn't.

They discuss Bohmian Mechanics and Many-Worlds in the last section of the paper.
 
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Is a superposition itself ontologically consisting of multiple realities? Or is a superposition occuring in one and the same reality? (And is the separation into worlds the result of decoherence then?)
 
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I've seen the phrase "more real" used, so it would agree with how some see it.
What is the difference between real, more real, very real, and really real?

Cheers
 

DarMM

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What is the difference between real, more real, very real, and really real?

Cheers
I honestly don't know what is meant by the phrase, I could never make sense of it, which is why I mentioned the world volume explanation of the coefficients, as that makes more sense to me.
 
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I honestly don't know what is meant by the phrase, I could never make sense of it, which is why I mentioned the world volume explanation of the coefficients, as that makes more sense to me.
The term reality should be used very sparingly and in very obvious ways in physics. Even then you rub into issues best discussed, not here, but in philosophy. As I have posted before it used to bore Richard Feynman so much during a class he took on it at MIT he purchased a little drill and spent his time in class drilling little holes in his shoes he was so bored. He had to write an essay on consciousness. In typical Feynman style he did experiments on himself while falling to sleep and wrote up his experiences. No discussion of what consciousnesses was - just some observations on it in regard to dreaming and being semi awake. We now know about various brain states etc like alpha state and certain practices like Tai Chi promote being in such a state. That's how Tai CHi masters do these unbelievable things eg:

They are in alpha state where you react quicker.

But what is consciousnesses? Who knows - we can do experiments, training etc - but ultimately who knows. Science is strange like that. You start out wanting to answer all these deep questions, but its a chimera - you end up answering something else that is interesting - but does not answer things like consciousness, reality etc.

Thanks
Bill
 
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They discuss Bohmian Mechanics and Many-Worlds in the last section of the paper.
Thanks for the detailed reply, and, of course, you're right about their conclusion in the paper. I was a little confused because they were saying they deal with those two theories at the end. Honestly I still find some of the arguments in that paper hard to follow, not with the math but just with all of the definitions they put forth and how those concepts are used to prove their points. But, anyway, that's another thread for another day, so I'll just leave it at that! :wink:
 
But it [MWI] does not explain why each observer sees only one alternative, and why different observers usually agree on the alternative seen.
MWI does explain why each observer sees only one outcome, and why all observers agree on all outcomes; this was the whole point of Everett's thesis. Each observer gets split by the outcome event, with each observer, in their own world, seeing just one of the outcomes. It is not an assumption but the consequence of the dynamics of quantum theory. Strictly undergraduate stuff - nothing advanced. And all observers, within each world, agree on their observations for the same reason.
 

DarMM

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A. Neumaier

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this was the whole point of Everett's thesis. Each observer gets split by the outcome event, with each observer, in their own world, seeing just one of the outcomes. It is not an assumption but the consequence of the dynamics of quantum theory.
No.

I had studied Everett's thesis. It contains nothing dynamical except for the dynamics of the wave function. All branches are there all the time; just their contents changes. When does a split happen, given only the Schrödinger equation? The Schrödinger equation does not distinguish between times with events and times without events - it does not even have a concept of event. These questions are swept under the carpet.

A proper logical definition would say what an observer is in terms of the deterministic time-dependent wave function (since there is nothing else), and what the stochastic dynamics of each observer's observables is, again in terms of the deterministic wave function. It would specify what it means that some part of the universe (an observer) observes another part of the universe (the observed).
 
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If you send a photon through a beamsplitter, it becomes in superposition of traveling several paths at once. Nevertheless there still is only one photon traveling those paths. So if we measure the photon, we detect it in one place and only once.

So I was wondering if the superposition of worlds leads to such a situation: the measurement is the detection of a quantum, so that it appears only once; in one of the worlds. The other worlds get probability 0 of detecting it.

So in that sense collapse is a result of quantization?

It seems strange to me that the quantum that gets measured suddenly multiplies itself to be able to be detected in ALL worlds!
 

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