Many Worlds Interpretation and act of measuring

[Quantumental]

Btw here is Kim Boström's most recent paper (just a few days old):
Quantum mechanics as a deterministic theory of a continuum of worlds
http://arxiv.org/pdf/1410.5653v4.pdf

 

[bhobba]

But then it is very misleading to suggest that MWI is "beauty incarnate" and "mathematical elegance".

Precisely why? For example what exactly is wrong with the decision theory analysis of Wallace that proves Born? I have gone through it in Wallace's book - The Emergent Multiverse and on page 475 has the Noncontextuality Theorem that he believes follows from any rational 'reward' function defined on the states. If its non-contextual then Gleason applies. Its a complex mathematical argument but I would like to know exactly what its flaw is. On page 189 he discusses why other possible ways of defining a rational 'probability' of outcomes is wrong. I believe its somewhat 'circular' in that if you go through them basically they are saying you can't reasonably define a decision type function on the space unless its basis independent - which is the essence of non-contextuality. But it's a rigorous elaboration of the idea.

Could you link?

Not off the top of my head - but this topic has been discussed many times before - I likely have posted it previously.

Thanks
Bill

 

[julcab12]

... Just a grain of doubt. Multiplicity is a predicted/recent phenomenon in cosmology. It is cause by the distortion of field or by gravitational lensing. A 'single object' will appear 'multiple' due to distortions and 'time' delay. Are there any similar effect in QM's vacuum or am i misunderstanding something on the vacuum effect?

http://newscenter.berkeley.edu/2015/03/05/distant-supernova-split-four-ways-by-gravitational-lens/

 

[rootone]

Gravitational lensing was predicted by GR, although I believe Einstein thought it would not be detectable.
It since turned out to be that it's very much detectable and highly useful.
The observation referred to in the link is a spectacular example, but it's not the first to be found.

I have not heard of any similar phenomena being predicted as a consequence of QM.

 

[bhobba]

Are there any similar effect in QM's vacuum or am i misunderstanding something on the vacuum effect?

What do you mean by he 'vacuum effect'?

The QFT vacuum is simply an artefact of the perturbation methods used and isn't really a teeming with particles popping in and out of existence as popularisations tell you.

A word of warning - just about anything you read outside a QFT textbook on QFT is likely wrong. Or to be more precise is a lot more nuanced than a literal reading.

Thanks
Bill

 

[atyy]

Precisely why? For example what exactly is wrong with the decision theory analysis of Wallace that proves Born? I have gone through it in Wallace's book - The Emergent Multiverse and on page 475 has the Noncontextuality Theorem that he believes follows from any rational 'reward' function defined on the states. If its non-contextual then Gleason applies. Its a complex mathematical argument but I would like to know exactly what its flaw is. On page 189 he discusses why other possible ways of defining a rational 'probability' of outcomes is wrong. I believe its somewhat 'circular' in that if you go through them basically they are saying you can't reasonably define a decision type function on the space unless its basis independent - which is the essence of non-contextuality. But it's a rigorous elaboration of the idea.

Wallace divides the probability problem in MWI into the "incoherence" and the "quantitative" problems. The derivation of the Born rule falls under the quantitative problem. Even if one were to grant the quantitative problem solved, it isn't clear that the incoherence problem is solved. Wallace favours an approach he calls "subjective uncertainty", but he indicates it is controversial (section 4.5 of http://arxiv.org/abs/0712.0149).

 

[bhobba]

but he indicates it is controversial

No argument that MW is controversial. No argument there is a factorisation problem that hasn't been settled. Other issues have been pointed out as well such as the assumption the environment is random.

My concern is precisely they are controversial. There seems to be this idea that because of that it must be wrong - it can't be beautiful mathematically (which it is) etc. They are controversial precisely because the issues haven't been settled and research is ongoing.

It seems to be rehashed over and over again eg:
https://www.physicsforums.com/threads/new-many-worlds-objections-right-wrong.781797/

As Kith said:
'Similar problems are also present in classical mechanics. The inital entropy problem is the question why was the initial entropy of the universe so low and the observer energy problem comes into play if we want measurements to be truly irreversible processes. For this, we need dissipation which contradicts the closed system assumption.'

I even recall one thread where it was shown the solution to a problem in classical mechanics crucially depended on a certain decomposition.

These are issues not confined to MW but crop up all over the place. I think far too much weight is given to them personally - they are issues - but not the big deal some want to make out they are.

Thanks
Bill

 

[atyy]

These are issues not confined to MW but crop up all over the place. I think far too much weight is given to them personally - they are issues - but not the big deal some want to make out they are.

What's your take (and anyone else who wants to comment) on Zurek's comment in http://arxiv.org/abs/1412.5206: "Quantum Darwinism shows why only such redundantly recorded pointer states are accessible to observers|it can account for perception of `quantum jumps'. However, full account of collapse involves 'consciousness', and may have go beyond just mathematics or physics."

I assume he is talking about it within his Existential Interpretation, which I have never understood, but it seems to be some variant of MWI.

 

[julcab12]

What do you mean by he 'vacuum effect'?

The QFT vacuum is simply an artefact of the perturbation methods used and isn't really a teeming with particles popping in and out of existence as popularisations tell you.

A word of warning - just about anything you read outside a QFT textbook on QFT is likely wrong. Or to be more precise is a lot more nuanced than a literal reading.

Thanks
Bill

..? A yes, maybe or no is fine with me. I'm referring to the vacuum where particle is observed in a state of superposition. But anyways i did found some insights; http://arnold-neumaier.at/physfaq/topics/vacfluc.

"... They are not changes in time. Instead, they describe uncertainties about what one gets when one tries to measure something. They describe the fluctuations in the measurement results when one repeats them under identical conditions - not fluctuations in what is measured... Fluctuations have a much better ontological status than virtual particles. Their properties are indeed computable nonperturbatively, hence are properties of the system under study and (unlike virtual particles) not only of the approximation method used. They are properties of the system, whether or not somebody measures it. In this
sense they exist independent of measurement, like a tree exists no matter whether someone looks at it."

...There much be a reason/evaluation on why they're taking this very literal -- Multiples as series of individual system/world = MWI. Non relativistic QM-- time and space are treated differently, with position being an operator and not time while QFT treats space and time on equal footing. GR- cosmology on the other hand has a natural intuitive solution to an OBSERVATION of 'multiplicity' -- distortion on the field causing it to appear multiple despite of being only 1 object. I might be making a weak comparison here but I want to understand also; why it can't happen to the very small?

"Time in QM is a label wrt to which things change.. Time is not a property of Quantum system so it makes no sense to promote it to an operator..Position of a particle however is a particular property of the system so it is an observable & hence an operator.. Time on the other hand is a universal property independent of any system..In fact this the beginning of Quantum Field theory where you demote position to a label to bring time & position on equal footing to get a Lorentz invariant theory."

 

[bhobba]

What's your take (and anyone else who wants to comment) on Zurek's comment in http://arxiv.org/abs/1412.5206: "Quantum Darwinism shows why only such redundantly recorded pointer states are accessible to observers|it can account for perception of `quantum jumps'

I would have to reacquaint myself with the detail of Quantum Darwinism to comment. But overall my take on Quantum Darwinism is it starts at the wrong end of the problem. It assumes states, Schroedinger's equation, unitary evolution etc to derive observations and the Born rule. Without delving into if it succeeds, I prefer the other way of attacking it - starting with observations as the primitive and deriving the other stuff.

However, full account of collapse involves 'consciousness', and may have go beyond just mathematics or physics."

Taking the modern interpretation of collapse as why do we get any outcomes at all we have interpretations like BM that do not require conciousness to explain it so obviously it's an incorrect statement.

Thanks
Bill

 

[bhobba]

I'm referring to the vacuum where particle is observed in a state of superposition.

The usual terminology would be frame - which in standard QM is assumed to be an inertial frame. But it is generally assumed unless for some reason you want it explicit.

Time is not a property of Quantum system so it makes no sense to promote it to an operator..Position of a particle however is a particular property of the system so it is an observable & hence an operator.. Time on the other hand is a universal property independent of any system..In fact this the beginning of Quantum Field theory where you demote position to a label to bring time & position on equal footing to get a Lorentz invariant theory."

That is basically true (although a bit philosophically waffley for my taste). Although I would use observable - rather than property.

It's simply that in standard QM time is a parameter, position an observable, but relativity requires they be treated on the same footing so position was demoted to also a parameter. Promoting time to an observable was also tried but ran into severe technical difficulties so was abandoned. It wasn't waffle like 'Time is not a property of Quantum system so it makes no sense to promote it to an operator.' Time is what a clock measurers, position is what rulers measure - calling them properties or whatever has nothing to do with physics

Thanks
Bill

 

[kith]

Regarding the definition of the worlds in the MWI, I tend to think that there's a trade-off between defining rigorously what a world is and the extent to which these worlds interact.

If we define the worlds by decoherence-induced splitting as usual, it isn't clear what exactly a world is and when exactly the splitting occurs because decoherence is only approximate. But because of FAPP irreversibility, the worlds can be viewed as non-interacting.

On the other hand, the papers which Quantamental linked to in posts #50 and #51 have a rigorous definition of what the worlds are: namely the possible classical configurations of the universe. But these worlds can't be non-interacting even FAPP because the superposition principle of QM has observable effects.

In older threads on the MWI, Frederik talked about yet another precise definition for the worlds: "every one-dimensional subspace of the universal Hilbert space is a world". The interaction between worlds is even more clear here because only the usual QM language is used.

 

[kith]

I have a question. Some MWI advocates described Bohmian Mechanics as "Everett in denial". If this is the case, and given that there is high confidence with Bohmian Mechanics at least for non-relativistic physics, couldn't Bohmian Mechanics solve the problems of MWI, eg. simply asserting that all BM worlds are real and exist?

Demystifier stressed a number of times that dBB depends on decoherence. If this is true, it isn't clear to me how dBB may remove the ambiguity of the splitting process from the MWI. Wouldn't you need to introduce something which specifies when the off-diagonal elements of the density matrix are small enough?

Only disregarding the splitting process altogether seems to work.

PS: I still plan to reply to you in the other thread. What you wrote felt just a bit too extensive to write a quick comment in passing. Instead, comments like the one above, which did seem like I could do them quick in passing, took me more time than I expected. ;-)

 

[bhobba]

Demystifier stressed a number of times that dBB depends on decoherence. If this is true, it isn't clear to me how dBB may remove the ambiguity of the splitting process from the MWI.

That's the other issue I have with the factorisation problem supposedly invalidating MW. A number of interpretations make use of decoherene eg DBB (as you mention) but also my ignorance ensemble and even Consistent Histories (its required to enforce that interpretations consistency condition). If its invalided by factorisation then we are in deep do do.

I know in the link I gave it was said those other interpretations by the assumption of macro objects called observational devices have a natural way around it, but decoherence is now beyond that eg as I often mention a few stray photons is enough to decohere a dust particle and give it a definite position. That goes out the door.

Thanks
Bill

 

[atyy]

That's the other issue I have with the factorisation problem supposedly invalidating MW. A number of interpretations make use of decoherene eg DBB (as you mention) but also my ignorance ensemble and even Consistent Histories (its required to enforce that interpretations consistency condition). If its invalided by factorisation then we are in deep do do.

I know in the link I gave it was said those other interpretations by the assumption of macro objects called observational devices have a natural way around it, but decoherence is now beyond that eg as I often mention a few stray photons is enough to decohere a dust particle and give it a definite position. That goes out the door.

I think the cut in dBB is subjective, so it doesn't need decoherence to place the cut.

 

[jimmylegss]

I have zero idea where you got that from.

I saw a poll that was took at some conference, it may have even been a string theory one, and that most definitely was NOT the view of most physicists - Copenhagen was still the most favoured one.

Brian Green, for example, ascribes to Qbism (interesting discussion as well):


However MW is one of the most popular interpretations - as I said its mathematical elegance is striking.

Thanks
Bill

Hey maybe you can help me on this , but around the 56-57 minute mark, the guy second to the right is arguing that MW intepretation takes out the pure randomness. But that still means pure randomness exists in our universe, since we cannot look into other universes. So technically that means it is still random for us what will happen?

 

[rootone]

I haven't watched the video yet, but have it marked as worth looking at.
Einstein famously said that he did not believe 'God plays dice with the Universe', (often mistaken as evidence of his views on religion).
My view, not being a mathematical rock star, is that there always will be things we just cannot fathom out, (yet), but that doesn't mean it's random, just that we don't know how it happens.
Brownian motion?, well it can be described in math, but hey it can be seen as well, - that doesn't explain very much.

 

[bhobba]

But that still means pure randomness exists in our universe, since we cannot look into other universes.

Your reasoning for such a statement escapes me.

MW is a deterministic theory - but of a slightly novel type. The theory itself doesn't determine which world you will experience - all you can do is come up with a reasonable argument to determine the likelihood. It may seem, for example, that since there is no reason to choose one world over another you would have equal probability of being in any world. It turns out however that leads to issues. That and similar ideas don't work properly. IMHO that's because it really needs to be basis independent in which case Gleason's theroem applies. But that is just my view. You can find the detail in the book I mentioned by Wallace. Be warned - the math is of the non-trivial type.

Thanks
Bill

 

[bhobba]

Brownian motion?, well it can be described in math, but hey it can be seen as well, - that doesn't explain very much.

The math describes what we see.

Thanks
Bill

 

[rootone]

The math describes what we see.

Thanks
Bill

and we can describe what we see as math ...

 

[bhobba]

and we can describe what we see as math ...

You can describe it in English?

Thanks
Bill

 

[rootone]

Not in a way that I can be sure to have communicated an idea well.

 

[bhobba]

Not in a way that I can be sure to have communicated an idea well.

Then you are starting to glimpse the issue. Math is a language highly suited to some things and ordinary language to other things. What is chosen depends on the situation. For Brownian motion how do you express the diffusion equation in English? For an experimental set-up to check if its correct how do you express that in math?

Thanks
Bill

 

[craigi]

Hey maybe you can help me on this , but around the 56-57 minute mark, the guy second to the right is arguing that MW intepretation takes out the pure randomness. But that still means pure randomness exists in our universe, since we cannot look into other universes. So technically that means it is still random for us what will happen?

Yes. Although all possibilities are realized in the MWI we only observe the normal probabalisitic outcomes of QM.

An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.

 

[bhobba]

Yes. Although all possibilities are realized in the MWI we only observe the normal probabalisitic outcomes of QM.
An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.

That is incorrect. Its got nothing to do with an observer but for some reason you keep harping on it.

I have Wallaces text on the subject - The Emergent Multiverse. I have read the text - there is no mention of observer. I have looked at the index - there is no mention of observer. But beyond that I understand the interpretation and it has nothing to do with an observer.

As I have explained many times succinctly the interpretation is dead simple. After decoherence you have a mixed state. Each part is interpreted as a world. No observer used, required, or part of the interpretation.

Thanks
Bill

 

[rootone]

This conversation reminds me of Piet Hein, not exactly a mainstream scientist, or philosopher either.
"The universe may be as great as they say. But it wouldn't be missed/ if it didn't exist."
and some other interesting comments.
http://en.wikiquote.org/wiki/Piet_Hein

 

[bhobba]

This conversation reminds me of Piet Hein

As a mathematician and scientist he would understand that modern science isn't particularly concerned with philosophical musings.

Thanks
Bill

 

[rootone]

Yes, but I do like his poetic way of presenting scientific ideas,

Another one.

The road to wisdom? — Well, it's plain
and simple to express:
Err
and err
and err again
but less
and less
and less.

 

[bhobba]

Yes, but I do like his poetic way of presenting scientific ideas,

Highly amusing. But this isn't a forum where such is discussed. Mentioning it as an aside is probably ok - but its not what we are on about here.

Thanks
Bill

 

[rootone]

Fair enough. I am here to learn.

 

[craigi]

That is incorrect. Its got nothing to do with an observer but for some reason you keep harping on it.

I have Wallaces text on the subject - The Emergent Multiverse. I have read the text - there is no mention of observer. I have looked at the index - there is no mention of observer. But beyond that I understand the interpretation and it has nothing to do with an observer.

As I have explained many times succinctly the interpretation is dead simple. After decoherence you have a mixed state. Each part is interpreted as a world. No observer used, required, or part of the interpretation.

Thanks
Bill

Bill,

This is a well documented and a widely understood implication of the interpretation. I have provided reference on this subject matter to you previously. Do I really need to do it again?

The fact that Wallace chooses not to discuss it in the book that you read doesn't imply that it is not relevant and it certainly does not imply that it is incorrect.

There is no observer role in wavefunction collapse in the MWI, since collapse does not take place. However, the observer splits into different worlds upon decoherence. Some worlds may and some worlds may not contain the observer. It is well known that Everett was extremely clear about this. Regardless of whether Wallace wrote about it, I find it very hard to imagine that he doesn't accept it. The fact that you choose not to accept it reflects your own prejudice on interpretational issues.

 

[julcab12]

After decoherence you have a mixed state. Each part is interpreted as a world. No observer used, required, or part of the interpretation.

Bill

... I am one of the " Maybe it is true but I'm not convinced -- yet ". Simply because i don't take 'multiplicity-overlaps' very lightly or direct especially on the part where we assign eigenstates on each point -- equivalent of a multiple real state/space; Model wise? Yes! it is helpful as a build up to a theory but I view it as strange -- unless we have sufficient evidence that each part is really a world, -- although i must agree that the interpretation is direct, simplest and workable (at least to some extent). I am more comfortable in viewing the multiple effect or any in particular as distortions of the field. IMO The collapse/interference is real to me while the decoherence is just an effect created by field distortions or any effect causing the collapse to appear decohered. I'm trying to understand the reason behind why we took this 'pointer'/direct approach. Imagine the problem it will cause if the same is used in cosmology. Without that field effect. We could be counting multiple supernova when in fact it is only one.

http://apod.nasa.gov/htmltest/gifcity/nslens_effects.html
http://hubblesite.org/newscenter/archive/releases/2015/08/full/

 

[bhobba]

This is a well documented and a widely understood implication of the interpretation. I have provided reference on this subject matter to you previously. Do I really need to do it again?

Yes you do. I can recall nothing you have posted doing that.

Wallace is an acknowledged expert on the interpretation and his text a definitive reference. If he doesn't include it the VERY strong odds are its a crock. But it goes beyond that. I spent quite a bit of time studying it to understand the interpretation and can say it has nothing to do with observers - nothing.

The issue isn't if the world contains observers - of course if they do they will be split and copied with each observation just like everything is - that's utterly obvious - the issue is if it in anyway affects the interpretation. It doesn't - and obviously so.

However, if, as required by forum rules, you have a peer reviewed physics paper (not a philosophy one) that shows otherwise post it. Also rather than me going through the paper you should be able to present a précis of the argument.

Thanks
Bill

 

[bhobba]

... I am one of the " Maybe it is true but I'm not convinced -- yet ". Simply because i don't take 'multiplicity-overlaps' very lightly or direct especially on the part where we assign eigenstates on each point -- equivalent of a multiple real state/space; Model wisehttp://hubblesite.org/newscenter/archive/releases/2015/08/full/

Before going any further I need to check you understand exactly what is being said. Can you explain to me the difference between a superposition and a mixed state? In general can you explain why a state is a positive operator rather than an element of a vector space?

Thanks
Bill

 

[bhobba]

http://apod.nasa.gov/htmltest/gifcity/nslens_effects.html
http://hubblesite.org/newscenter/archive/releases/2015/08/full/

BTW we are discussing MW not astronomy or cosmology.

Don't be fooled by incorrect comments that the multiverse of the many worlds interpretation is the same as the multiverse in cosmology (eg eternal inflation) - it isn't.

Although there has been speculation linking the two:
http://arxiv.org/abs/1105.3796

Thanks
Bill

 

[julcab12]

Before going any further I need to check you understand exactly what is being said. Can you explain to me the difference between a superposition and a mixed state?

Thanks
Bill

The common understanding is that --Worlds, or branches of the universal wavefunction, split when different components of a quantum superposition "decohere" from each other. Decoherence refers to the loss of coherency or absence of interference effects between the elements of the superposition. For two branches or worlds to interfere with each other all the atoms, subatomic particles, photons and other degrees of freedom in each world have to be in the same state, which usually means they all must be in the same place or significantly overlap in both worlds, simultaneously.

 

[bhobba]

Decoherence refers to the loss of coherency or absence of interference effects between the elements of the superposition.

Not quite - it refers to a superposition being converted to a mixed state - but to understand it you need to know what those terms mean. Since you didn't reply to my query about that I can only assume you haven't come across it before. Unfortunately with this stuff it can only be detailed in the math.

For two branches or worlds to interfere with each other all the atoms, subatomic particles, photons and other degrees of freedom in each world have to be in the same state, which usually means they all must be in the same place or significantly overlap in both worlds, simultaneously.

No. For them to interfere it means if P is the state <bi|P|bj> is not zero for i not equal to j where |bi> is the basis singled out by decoherence. These are called interference terms or off diagonal elements. Decoherence is considered to have occurred if that is so small it's way below detectability and can be taken as zero. This is a genuine issue with MW and decoherence in general. It depends on the non-detectability of off diagonal interference effects which is a technological moving target. The general unstated assumption is they quickly fall so low that it can never be detected. That of course is a debatable assumption and could form the basis of a new thread if anyone wants to pursue it - although it has been discussed a number of times before.

Thanks
Bill

 

[julcab12]

BTW we are discussing MW not astronomy or cosmology.

Don't be fooled by incorrect comments that the multiverse of the many worlds interpretation is the same as the multiverse in cosmology (eg eternal inflation) - it isn't.

Although there has been speculation linking the two:
http://arxiv.org/abs/1105.3796

Thanks
Bill

-- I'm perfectly aware of that and understand the incompatibility (Besides, I've been reading and contemplating it for years now). I just wanted to understand the QM's perspective on multiplicity and why should be taken or designated as a direct pointer's view. I have no luck in googling the subject so I'm asking an experts opinion. Technically, why should we consider a representation of 'A' as real-multi space operator

.

The link i provided is just supplement on the principle involved that is apparent in nature -- that a multiplicity can also be interpreted as distortions causing it to appear multiple. -- Oh, I'll read the link soon.

 

[bhobba]

Technically, why should we consider a representation of 'A' as real-multi space operator

.

I have zero idea what you mean by a real-multi space operator.

Thanks
Bill

 

[julcab12]

ut to understand it you need to know what those terms mean. Since you didn't reply to my query about that I can only assume you haven't come across it before. Unfortunately with this stuff it can only be detailed in the math.

I only have the general idea. Can you please provide a link on the subject? Much appreciated! I only have this link

http://farside.ph.utexas.edu/teaching/qmech/Quantum/node40.html.. But there are no explanation on why it is pointing to a multiples. Well It assumes that"

acts a multiple of the original wavefunction (Simply bec. it is looking to be that way- multiples). These special wavefunctions are called eigenstates, and the multiples are called eigenvalues. -- Meaning we assign a variable that act as a multiple and not as far as explaining why it should be the case.

No. For them to interfere it means if P is the state <bi|P|bj> is not zero for i not equal to j where |bi> is the basis singled out by decoherence. These are called interference terms or off diagonal elements. Decoherence is considered to have occurred if that is so small it's way below detectability and can be taken as zero. This is a genuine issue with MW and decoherence in general. It depends on the non-detectability of off diagonal interference effects which is a technological moving target

Can you provide me a link to elaborate this claim. Thanks!

 

[julcab12]

I have zero idea what you mean by a real-multi space operator.

Thanks
Bill

Consider a general real-space operator

. When this operator acts on a general wavefunction

the result is usually a wavefunction with a completely different shape. However, there are certain special wavefunctions which are such that when

acts on them the result is just a multiple of the original wavefunction. These special wavefunctions are called eigenstates, and the multiples are called eigenvalues...

 

[bhobba]

Can you provide me a link to elaborate this claim. Thanks!

Its very basic. The textbook that explains with just a first course in QM (which usually doesn't cover it) it is the following:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

The following also covers it, but not in the same depth:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill

 

[bhobba]

Consider a general real-space operator

. When this operator acts on a general wavefunction

the result is usually a wavefunction with a completely different shape. However, there are certain special wavefunctions which are such that when

acts on them the result is just a multiple of the original wavefunction. These special wavefunctions are called eigenstates, and the multiples are called eigenvalues...

Yes - your point being?

Here is even more detail on exactly what's going on (see post 137):
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

It is a foundational axiom of QM, in fact the foundational axiom because Born's Rule can be derived from it, that the outcomes of observations can be mapped to a POVM which leads to what you said above, as the above link explains.

In MW what happens is you have a mixed state ∑pi |bi><bi| after decoherence. The interpretation is each |bi><bi| is a separate world. MW also has a decision theory argument that shows the pi is the probability of experiencing the world with |bi><bi|. Note - despite what Gragi says that probability has nothing to do if an observer is actually in the world or not any more than if you have a machine that throws a dice the probability changes depending on if someone observes it or not.

Thanks
Bill

 

[stevendaryl]

That is incorrect. Its got nothing to do with an observer but for some reason you keep harping on it.

I'm sure that what I'm about to say is exactly on-topic, but to me, observers are relevant in MWI in the following sense:

• MWI is a completely deterministic theory.
• Yet, from the subjective view of an observer, the universe seems non-deterministic.

So observers come into play simply because of the need to explain why things appear the way they do. Without observers, there is no reason to introduce probability into the theory at all.

It's not that observers necessarily involve any different physics than any other system, it's just that they are the systems that have a point of view that needs explaining.

 

[stevendaryl]

Not quite - it refers to a superposition being converted to a mixed state - but to understand it you need to know what those terms mean.

At this point, I'm not sure what objections are legitimate, and what objections are quibbling. But in MWI, there is never a conversion to a mixed state. Instead, the wave function is FAPP (for all practical purposes) in a mixed state if it is impossible to observe interference between the different elements of the superposition. Mathematically, this means something like: the density matrix becomes that of a mixed state after "environmental degrees of freedom" are traced out.

 

[bhobba]

So observers come into play simply because of the need to explain why things appear the way they do.

I can't follow that at all.

Probabilities enter due to a decision theory rational agent argument - this is a Bayesian view - namely what would a rational agent assign the probability to be where its a subjective thing. Its got nothing to do if observers are in the world or not.

Thanks
Bill

 

[stevendaryl]

I can't follow that at all.

Probabilities enter due to a decision theory rational agent argument

And some people use the word "observer" instead of "decision theory rational agent". The notion of a "decision theory rational agent" is a way to formalize those aspects of an "observer" that are relevant to reasoning about probability.

 

[bhobba]

And some people use the word "observer" instead of "decision theory rational agent". The notion of a "decision theory rational agent" is a way to formalize those aspects of an "observer" that are relevant to reasoning about probability.

If that's what they mean then they should state it. However its obvious that is not affected by if there are actual observers in the world or not. In particular the following is false - 'An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.' That a rational agent decides on a particular probability has nothing to do if there are observers in the world or not, or even if the rational agent is in the world or not. Its simply what the rational agent would conclude if they were experiencing it. Whether they actually do is obviously irrelevant any more than it would be relevant if a machine flipped a coin and a rational agent decided it had a 50-50 chance of being heads or tales.

Thanks
Bill

 

[julcab12]

The interpretation is each |bi><bi| is a separate world

Of course. You can create a model dependent on that axiom simple because it is essential within the demand of the framework. But it can be utterly indistinguishable whether each individual system is in an eigenstate of some multiple hilbert spaces , or each individual system is in a superposition state with huge constraint like MWI. I'm not saying i ignore the superposition. Almost everything I've read about QM invovles a crude formalism of separation and interpretation -- "That is how the system literally looks like. It appears multiple, let's assign each multiple state to be real create worlds pragmatic to ours. Let's make it independent to any specific interpretation and built something within that framework -- It works!". Ok here's an image of 4 supernovas in single frame must be 4 distinct supernovas. Actually we can create a model within that premise and can still work..Well, Lensing will tell you it's not the case anyways..

 

[stevendaryl]

If that's what they mean then they should state it. However its obvious that is not affected by if there are actual observers in the world or not.

By "actual observers" do you mean human beings (or intelligent aliens, or whatever)? I certainly agree with that; you can substitute a mechanical device for a human, and get the same "appearance" of probability. Or do you mean that the decision-theoretic notion of probability doesn't require any rational agents to exist, only that IF they existed, THEN they would do ... (whatever).

In particular the following is false - 'An exception occurs when a singnificant fraction of possible outcomes do not contain the observer.' That a rational agent decides on a particular probability has nothing to do if there are observers in the world or not, or even if the rational agent is in the world or not. Its simply what the rational agent would conclude if they were experiencing it. Whether they actually do is obviously irrelevant any more than it would be relevant if a machine flipped a coin and a rational agent decided it had a 50-50 chance of being heads or tales.

Okay, so you do mean the counterfactual: if such agent did exist, then it would behave in such and such a way.