Many Worlds Interpretation and act of measuring

[Rodrigo Cesar]

"We can’t make a measurement without influencing what we measure.
before we look, there are only probabilities. When we open the box, they give way to a single actuality"

It would be more like this, all the time, Until we look?
http://upload.wikimedia.org/wikipedia/commons/9/91/Schrodingers_cat.svg
http://dimensions.rjdj.me/uploads/universe-multiverse-1024x768.png

 

[rootone]

The cat in the box is a visualisation of 'the measurement problem', we can't draw any conclusions from it.
'Multiverse' is one interpretation of QM among several, and it isn't an established fact.

Your original quote is reasonable enough - before something has been measured we don't know what it's measure is!, although we may have been able to establish a range of probabilities.
In the cat example it's life or death depends on the half-life of atomic decay - which is probabalistic.
If the cat is in the box for exactly the half life of the atom, then the probability of it being alive is exactly 50%

After the experiment is finished (box opened), then the measurement has been made.
We do know what happened. its no longer a possible outcome, it's a known outcome

 

[bhobba]

"We can’t make a measurement without influencing what we measure.
before we look, there are only probabilities. When we open the box, they give way to a single actuality"

That looks like a misunderstanding of Schroedinger's Cat.

You will find many threads on this forum discussing that thought experiment. The point though is in the standard Copenhagen interpretation QM is a theory about observations that occur in an assumed common sense classical world. In Schroedinger's Cat that observation occurs at the particle detector - everything is common sense classical after that. The purpose of the thought experiment was to show, while its obvious where you should put the observation, the theory doesn't force you to do that - in fact it says nothing about it. Then we have the issue of how does a theory explain the classical world when its assumed in the first place.

A lot of progress has been made in resolving those issues. If you are interested in the modern view the following, at the lay level, is a good source:
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

It would be more like this, all the time, Until we look?
http://upload.wikimedia.org/wikipedia/commons/9/91/Schrodingers_cat.svg
http://dimensions.rjdj.me/uploads/universe-multiverse-1024x768.png

Very picturesque. I don't know what the first is trying to depict, but the second one looks like Many Worlds. It's an interpretation and as such may or may not be true - but until there is a way to experimentally test it there is no way of telling. There are tons of other interpretations as well and they are all in the same boat.

Thanks
Bill

 

[Khashishi]

The key point of many worlds is that there are many versions of you. But you are only conscious of one of you. One version of you sees a living cat; another sees a dead cat. The universe contains a mixture of these different scenarios, but each version of you doesn't see this mixture.

 

[bhobba]

Mathematically, there's a superposition of yous.

That's precisely what MW says is not going on. The mixed state after decoherence is ∑pi |bi><bi|. Being a mixed state its no longer in superposition. Each |bi><bi| is interpreted as a world.

Nor are you entangled with the cat. The observation in Scrodinger's Cat occurs at the particle detector - that's where the splitting occurs in MW - in each world everything is common-sense from that point on - well as common-sensical as MW can be since decoherence is occurring all the time.

Thanks
Bill

 

[Khashishi]

edit: nevermind.
You say each |bi><bi| is interpreted as a world, but it's a superposition of states in the end. The result of decoherence is that the macroscopic world is only approximately diagonal with respect to the versions of you, to a very good approximation. The decoherence started back at the particle detector, so you are "well separated" from the other versions of you, but technically, it still is a grand superposition.

 

[bhobba]

You say each |bi><bi| is interpreted as a world, but it's a superposition of states in the end.

Do you understand the difference between a mixed state and a pure state? Mixed states are not in superposition - that's a concept applicable only to pure states and reflects their vector space structure when mapped to such - in reality they are operators.

Thanks
Bill

 

[Khashishi]

Yeah, I guess you are right...
I'll edit some of above to reduce confusion.

 

[bhobba]

Thanks.

In this stuff its always wise to be careful - its tricky enough even when you are.

Thanks
Bill

 

[Rodrigo Cesar]

"Very picturesque. I don't know what the first is trying to depict, but the second one looks like Many Worlds. "

I thought MWI was equal to multiverse, each universe would have other versions of these cats, but all cats in the same place? Where are the others, if we can see only 1? Invisible cats? As if they were ghosts?

 

[bhobba]

I thought MWI was equal to multiverse,

The multiverse is applicable to a number of different ideas not just MW eg eternal inflation.

Thanks
Bill

 

[Edward Wij]

Before I thought Many World was silly because in the atomic orbital like hydrogen atom, the electron has an almost infinity of position eigenstates.. so it's silly to think each position eigenvalue has its own words.. so many worlds only occurred after any measurement? How does this work in the electron orbital?

But then, if each electron position eigenvalues in the orbitals don't have separate worlds.. then what's the use of many worlds to explain QM?

Sean Carrol is convincing us many worlds may be the easiest thing to consider because the alternative is the anger interpretation (bohmians) or in denial of reality (the bellantinians).

 

[bhobba]

Before I thought Many World was silly because in the atomic orbital like hydrogen atom, the electron has an almost infinity of position eigenstates.. so it's silly to think each position eigenvalue has its own words.

That's not what it says. It says when you observe it the possible outcomes become separate worlds. You generally don't observe electrons in orbitals.

Sean Carrol is convincing us many worlds may be the easiest thing to consider because the alternative is the anger interpretation (bohmians) or in denial of reality (the bellantinians).

Its beauty incarnate mathematically. Like all interpretations make up your own mind.

I love mathematical beauty - but its too weird for me.

We also have the new Consistent Histories interpretation:
http://quantum.phys.cmu.edu/CQT/index.html

Many people consider it Copenhagen done right and MW without the many worlds. It does this by not even having observations - instead it is the stochastic theory of what are called histories. Each history roughly corresponds to a separate world (roughly is because the histories are course grained). There is only one history so you don't have the many worlds and there is no observation so the measurement problem is bypassed.

The link I gave details this well so I won't be going into it - if you are interested read the link.

Thanks
Bill

 

[Rodrigo Cesar]

Sean Carrol is convincing us many worlds may be the easiest thing to consider because the alternative is the anger interpretation (bohmians) or in denial of reality (the bellantinians).

Denial of reality? what? lol

 

[Rajkovic]

MWI the easiest thing? lol this idea is the most nonsense I've ever seen, mathematically beautiful, realistically bull****.. Sean Carrol must be smoking some Mushrooms

 

[Rodrigo Cesar]

MWI the easiest thing? lol this idea is the most nonsense I've ever seen, mathematically beautiful, realistically bull****.. Sean Carrol must be smoking some Mushrooms

It's not so strange, I think MWI would be more like that? Everytime we make a new decision, a new universe is created?

(someone correct if I'm wrong)

 

[rootone]

MWI the easiest thing? lol this idea is the most nonsense I've ever seen, mathematically beautiful, realistically bull****.. Sean Carrol must be smoking some Mushrooms

Well there is a saying 'beauty lies in the eye of the beholder''
* shudders *
Let's not start bringing consciousness into it though.

 

[Quantumental]

Its beauty incarnate mathematically. Like all interpretations make up your own mind.

Except for the preferred basis and born rule problems that has yet to be solved ;p It' really not as mathetmatically beautiful when you look at the contrived attempts at solving these problems that come from David Wallace, Max Tegmark, David Deutsch, Sean Carroll. They add so many axioms that it's really no more elegant than Bohm

 

[craigi]

It's not so strange, I think MWI would be more like that? Everytime we make a new decision, a new universe is created?

(someone correct if I'm wrong)

In the MWI the different worlds 'exist' in an abstract mathematical space, Hilbert Space. So don't take this visualisation too literally.

 

[craigi]

MWI the easiest thing? lol this idea is the most nonsense I've ever seen, mathematically beautiful, realistically bull****.. Sean Carrol must be smoking some Mushrooms

Not only Sean Carrol. The MWI is 'believed' by most leading cosmologists and string theorists.

The MWI was conceived of by Hugh Everett and had we stuck with his original name for it, the Relative State Formulation, then reactions like this every time someone new is introduced to it, would be far less common.

 

[Rodrigo Cesar]

In the MWI the different worlds 'exist' in an abstract mathematical space, Hilbert Space. So don't take this visualisation too literally.

Sorry my ignorance, but What is an abstract mathematical space? where are the other cats, I can't understand it
I just wonder if the reality remains the same, we live in a UNIverse only, and even if MWI is true, It has nothing to do with our Universe, we can see only 1 outcome, the others are in others Universes, etc,etc.. Invisible for us..?
If this is true , we move on, nothing special or mystic about it..

 

[bhobba]

Denial of reality? what? lol

Yea - there is a lot of confusion about this stuff. To deny reality you need first to figure out what reality is and have everyone agree - as I say - good luck with that.

Thanks
Bill

 

[bhobba]

Sorry my ignorance, but What is an abstract mathematical space? where are the other cats, I can't understand it

The mathematical formulation of QM requires an abstract mathematical space called a Hilbert space:
http://en.wikipedia.org/wiki/Hilbert_space

These days in math space and set are generally synonymous and set is rather an abstract idea.

Some harp on such math can't be reality bla bla bla. The modern view of the math is the following:
http://arxiv.org/pdf/quant-ph/0101012.pdf

It's simply an extension of probability theory to allow continuous transformations between so called pure states which, if you think about it, is what's required to model physical systems. If a system transforms to a state after 1 second it went through another state after 1/2 second. This is the generalised probability view of QM. It explains the math very elegantly. What it means of course is where interpretations come in - but the math is no more or less abstract than ordinary probability theory.

I just wonder if the reality remains the same, we live in a Universe only, and even if MWI is true, It has nothing to do with our Universe, we can see only 1 outcome, the others are in others Universes, etc,etc.. Invisible for us..?If this is true , we move on, nothing special or mystic about it..

Forget this reality stuff. There is no agreement on what that is. Physical theories describe it without getting into exactly what it's describing. Guys like me believe that's the best we can do. There is nothing in QM that FORCES anyone to adopt a weird mystical new age inspired view of reality. That's what common sense people need to take from it. However there is no way of proving, without experimental support, the weird views of QM are incorrect - its in the nature of science. Also weirdness is in the eye of the beholder.

Thanks
Bill

 

[bhobba]

Not only Sean Carrol. The MWI is 'believed' by most leading cosmologists and string theorists.

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

 

[bhobba]

Except for the preferred basis and born rule problems that has yet to be solved

As I have pointed out to you before the issue has yet to be resolved one way or the other. Certain key mathematical theorems are lacking.

I have seen papers where for simple models it is shown the results do NOT depend on the factorisation. They however need to be extended, and that hasn't been done yet.

Thanks
Bill

 

[craigi]

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

Greene is undecided about the MWI.

Polls are conducted regularly by Tegmark, but perhaps the most thorough poll was conducted by Raub.

Unfortunately the opinion of the average phycisist isn't helpful because the standard undergrad education only covers the CI and most postgrads won't revisit this.

 

[Rajkovic]

All phycisists says that Many Worlds = Multiverse, BUT for Sean Carrol, multiverse is different from MWI
http://www.preposterousuniverse.com...many-worlds-and-the-multiverse-the-same-idea/

"The cat is neither alive nor dead; it is in a superposition of alive + dead. At least, until we observe it ..at the moment of observation the wave function “collapses” , both possibilities continue to exist, but “we” (the macroscopic observers) are split into two, one that observes a live cat and one that observes a dead one. There are now two of us, both equally real, never to come back into contact."

What he is saying is that at the moment I observe, another universe is created, in this another Universe my "other me" observes the cat alive, and here in our real Universe my "real me" is seeing it dead..right?
this has so many implications , like " we create universes wherever we look, we are gods " or " immortality "
This idea is easily debunked.

 

[bhobba]

Unfortunately the opinion of the average phycisist isn't helpful because the standard undergrad education only covers the CI and most postgrads won't revisit this.

That's true. Most physicists are not concerned with foundational issues.

The link I gave is a careful round table discussion on interpretations - he may be undecided on it but his vote there goes for Qbism.

Polls on this are occasionally posted here and while MW is certainly not backwater (conciousness causes collapse most definitely is) Copenhagen is still king.

Thanks
Bill

 

[craigi]

That's true. Most physicists are not concerned with foundational issues.

The link I gave is a careful round table discussion on interpretations - he may be undecided on it but he his vote there goes for Qbism.

Polls on this are occasionally posted here and while MW is certainly not backwater (conciousness causes collapse most definitely is) Copenhagen is still king.

Thanks
Bill

Again, almost all physicists are frequentists. From a mathematical perspective Bayesianism is much more common than for the typical physicist.

QBism will be much more difficult for physicists to accept than the MWI.

 

[bhobba]

this has so many implications , like " we create universes wherever we look, we are gods " or " immortality "
This idea is easily debunked.

Its weird, and I don't ascribe to it - but it can't be debunked.

If it has aspects that appeal you may like Consistent Histories - its sometimes described as MW without the many worlds. I probably have given a link to it before, but here it is again:
http://quantum.phys.cmu.edu/CQT/index.html

Thanks
Bill

 

[bhobba]

Again, almost all physicists are frequentists. From a mathematucal perspective Bayesianism is much more common than for the typical physicist. QBism will be much more diificult for physicists to accept than the MWI.

Yes. If you ask them they will probably say Copenhagen, but if you pin them down you will find its really Ballentine's Ensemble because they don't really understand Copenhagen has a subjective view of probabilities. That's because beginning texts like Griffiths don't explain the nuances of it and only some graduate texts like Ballentine delve deeper.

Thanks
Bill

 

[Rajkovic]

Its weird, and I don't ascribe to it - but it can't be debunked.

If it has aspects that appeal you may like Consistent Histories - its sometimes described as MW without the many worlds. I probably have given a link to it before, but here it is again:
http://quantum.phys.cmu.edu/CQT/index.html

Thanks
Bill

It can't be debunked to a certain point until some new experiment put an end to all of this (hope that day comes soon)

which theory fits the best to you Bill? do u think these doubts will be solved soon?

I will read it, thx

 

[atyy]

Yes. If you ask them they will probably say Copenhagen, but if you pin them down you will find its really Ballentine's Ensemble because they don't really understand Copenhagen has a subjective view of probabilities. That's because beginning texts like Griffiths don't explain the nuances of it and only some graduate texts like Ballentine delve deeper.

Copenhagen simply has many flavours, and a frequentist view of probability is also a flavour of Copenhagen. Ballentine's Ensemble is not new, and he should not get credit for work that is wrong where it is novel, and simply an orthodox flavour of Copenhagen where it is correct.

I should also note that Ballentine's Ensemble (1998, p46) does have a subjective notion of the state because he uses a conceptual ensemble that does not exist, except in his mind: "Thus, although the primary definition of a state is the abstract set of probabilities for the various observables, it is also possible to associate a state with an ensemble of similarly prepared systems. However, it is important to remember that this ensemble is the conceptual infinite set of all such systems that may potentially result from the state preparation procedure, and not a concrete set of systems that coexist in space."

 

[bhobba]

Copenhagen simply has many flavours, and a frequentist view of probability is also a flavour of Copenhagen. Ballentine's Ensemble is not new, and he should not get credit for work that is wrong where it is novel, and simply an orthodox flavour of Copenhagen where it is correct.

Yes there are many variants of Copenhagen, but when I mention it I mean something along the lines of the following:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.htm

Note point 1.
A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system.

Frequentists have a differing view.

Thanks
Bill

 

[atyy]

Yes there are many variants of Copenhagen, but when I mention it I mean something along the lines of the following:
http://motls.blogspot.com.au/2011/05/copenhagen-interpretation-of-quantum.htm

Note point 1.
A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system.

Frequentists have a differing view.

Thanks
Bill

Even if one used a purely subjective definition of the state, that doesn't mean that one is using a Bayesian interpretation of probability. Frequentists and Bayesians differ about the interpretation of Kolmogorov's axioms, which has no concept of the quantum state. So even if one considers the state "subjective", the probability obtained from the Born rule can be Frequentist.

 

[julcab12]

... I'm always getting reminded to be very critical, skeptic and careful. MWI is no exemption. So i'll leave a note to these guys.

 

[atyy]

... I'm always getting reminded to be very critical, skeptic and careful. MWI is no exemption. So i'll leave a note to these guys.

Carroll does not claim MWI is without problems. He gives a list of serious issues in the MWI approach about which consensus has not been reached in http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/.

"The fierce austerity of EQM is attractive, but we still need to verify that its predictions map on to our empirical data. This raises questions that live squarely at the physics/philosophy boundary. Why does the quantum state branch into certain kinds of worlds (e.g., ones where cats are awake or ones where cats are asleep) and not others (where cats are in superpositions of both)? Why are the probabilities that we actually observe given by the Born Rule, which states that the probability equals the wave function squared? In what sense are there probabilities at all, if the theory is completely deterministic? These are the serious issues for EQM ..."

 

[stevendaryl]

There is a slight difference between the problems of MWI and the problems of other interpretations. With MWI, the problem is purely about how to interpret the theory. The theory itself is unambiguous, it seems to me (just a state vector evolving continuously and unitarily). But in the case of other interpretations of QM, the problems are about additions to (or exceptions to) unitary evolution. Bohm's theory has additional "elements of reality", namely definite particle locations at all times. Von Neumann's "collapse" interpretation has an additional type of state change--collapse following an observation.

 

[rootone]

In the MWI the different worlds 'exist' in an abstract mathematical space, Hilbert Space. So don't take this visualisation too literally.

That is where the problem lies.
Not with the interpretation as a concept, but with the presentation of it as being literal, by some folks.
I'm not having a go at Carrol in particular, but I do think people like Greene, Tegmark, and Kaku could be deemed 'guilty' of encouraging misunderstanding among the general public.
Some of whom then go on to quote them on mystical woo type sites.

 

[atyy]

There is a slight difference between the problems of MWI and the problems of other interpretations. With MWI, the problem is purely about how to interpret the theory. The theory itself is unambiguous, it seems to me (just a state vector evolving continuously and unitarily). But in the case of other interpretations of QM, the problems are about additions to (or exceptions to) unitary evolution. Bohm's theory has additional "elements of reality", namely definite particle locations at all times. Von Neumann's "collapse" interpretation has an additional type of state change--collapse following an observation.

I'm not sure it is so different. From what I understand, Carroll's concern is whether MWI matches experiment.

 

[stevendaryl]

Even if one used a purely subjective definition of the state, that doesn't mean that one is using a Bayesian interpretation of probability. Frequentists and Bayesians differ about the interpretation of Kolmogorov's axioms, which has no concept of the quantum state. So even if one considers the state "subjective", the probability obtained from the Born rule can be Frequentist.

I'm always bothered by frequentist versus bayesian arguments. To me, the differences just amount to different ways of talking about the same things. There is really no substantive difference.

In my opinion, frequentism is just a collection of rules-of-thumb for dealing with probability. It isn't an interpretation of probability. To say that probability means frequency is nearly vacuous. Any real experiment is only conducted a finite number of times, so the concept of relative frequency in the limit of infinitely many trials seems irrelevant. Now, what you can do, with a finite number of trials, is to compute the probability that the observed relative frequency is different from the theoretically predicted probability, and you can argue that for a large enough number of flips of an unbiased coin, the difference between the relative frequency of heads and 1/2 will be vanishingly small, with a probability close to 1. But that latter part--"with a probability close to 1"--is using some theoretical notion of probability that is NOT given a frequentist meaning.

In a real experiment, you never do anything more than a finite number of times, so what happens in an infinite number of trials seems irrelevant. Of course, frequentists have ways of dealing with that situation, involving measures of the level of significance. But as I said, those techniques seem like ad hoc rules of thumb---they aren't actually justified by any frequentist understanding of probability.

 

[julcab12]

Carroll does not claim MWI is without problems. He gives a list of serious issues in the MWI approach about which consensus has not been reached in http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/.
.."

No objections. But i was wondering since he strongly stated. " The potential for multiple worlds is always there in the quantum state, whether you like it or not." Would we be able to get a different viewpoint on that manner? "Yes! It appears we are detecting seemingly series of different state + classical time. We should make a basic assumption from it -- Multiples". BUt wait! How about Time? Would it have any effect on that scale -- Like a gravitational time dilation/ distortion or/ lensing that causes things to appear decohered. Think of like visual slices of possible outcomes. It should have decoherance of time not just a decoherence of state.

 

[stevendaryl]

To me, there are legitimate criticisms of MWI, having to do with the issues of how to interpret probability for a deterministic system, and how to count worlds, and so forth. But the most common complaint about MWI is about the "many worlds" aspect--the idea that when something happens due to random chance--Schroedinger's cat either dies or doesn't, depending on a random quantum event--there is a world in which the cat lives and a world in which the cat dies. People complain that this is "multiplying entities" in violation of occam's razor. But it's hard for me to see how to get just one world without ADDING something to the quantum formalism (such as a special status for "measurements")

 

[atyy]

In my opinion, frequentism is just a collection of rules-of-thumb for dealing with probability. It isn't an interpretation of probability. To say that probability means frequency is nearly vacuous. Any real experiment is only conducted a finite number of times, so the concept of relative frequency in the limit of infinitely many trials seems irrelevant. Now, what you can do, with a finite number of trials, is to compute the probability that the observed relative frequency is different from the theoretically predicted probability, and you can argue that for a large enough number of flips of an unbiased coin, the difference between the relative frequency of heads and 1/2 will be vanishingly small, with a probability close to 1. But that latter part--"with a probability close to 1"--is using some theoretical notion of probability that is NOT given a frequentist meaning.

Is the latter part in the law of large numbers really not given a Frequentist meaning? It would seem consistent to apply the Frequentist meaning there too. It would be nearly vacuous as you say, or at least circular. But I think it is as vacuous as physics - what is a charge? It is a thing on which an electric field exerts a force. What is an electric field? It is a thing which exerts a force on a charge. It is saved because we somehow have conventions as to what operations in real life correspond to certain dynamics of the mathematical objects.

 

[stevendaryl]

Is the latter part in the law of large numbers really not given a Frequentist meaning? It would seem consistent to apply the Frequentist meaning there too. It would be nearly vacuous as you say, or at least circular. But I think it is as vacuous as physics - what is a charge? It is a thing on which an electric field exerts a force. What is an electric field? It is a thing which exerts a force on a charge. It is saved because we somehow have conventions as to what operations in real life correspond to certain dynamics of the mathematical objects.

The law of large numbers says (in a quantitative way) that the probability that relative frequency for many repeated events differs significantly from the probability of a single event goes to zero as the number of repetitions goes to infinity. So using the law of large numbers to justify a frequentist interpretation of probability seems circular, as you say. I don't have any problem with circular definitions, but if you're using a circular definition, then you're not really defining the concepts, you're just axiomatizing them. So you're basically treating "probability" as an undefined term. If that's what you're doing, then it's not really frequentist, it's just abstract probability, which doesn't distinguish between frequentism and Bayesianism.

The only real source of disagreement between frequentists and Bayesians, it seems to me, is over whether it is meaningful to talk about probability of something that only happens once (or a small number of times). But the blunt fact is that EVERYTHING only happens once or a small number of times (for some definition of "small"). We always have a limited collection of samples. So the frequentist disdain for talking about probabilities on a small sample space really to me makes it impossible to do anything with probabilities (except through ad hoc means, such as cut offs and levels of significance, etc., which are not justified by the frequentist interpretation, as I already said).

 

[atyy]

The law of large numbers says (in a quantitative way) that the probability that relative frequency for many repeated events differs significantly from the probability of a single event goes to zero as the number of repetitions goes to infinity. So using the law of large numbers to justify a frequentist interpretation of probability seems circular, as you say. I don't have any problem with circular definitions, but if you're using a circular definition, then you're not really defining the concepts, you're just axiomatizing them. So you're basically treating "probability" as an undefined term. If that's what you're doing, then it's not really frequentist, it's just abstract probability, which doesn't distinguish between frequentism and Bayesianism.

The reason the Frequentist interpretation does more than just rename probability is that it is an operational definition, ie. it's a way of converting the abstract Kolmogorov axioms into statements about real operations.

The only real source of disagreement between frequentists and Bayesians, it seems to me, is over whether it is meaningful to talk about probability of something that only happens once (or a small number of times). But the blunt fact is that EVERYTHING only happens once or a small number of times (for some definition of "small"). We always have a limited collection of samples. So the frequentist disdain for talking about probabilities on a small sample space really to me makes it impossible to do anything with probabilities (except through ad hoc means, such as cut offs and levels of significance, etc., which are not justified by the frequentist interpretation, as I already said).

The cut-offs and levels of significance are additional ad hoc criteria, but the Bayesian interpretation also has ad hoc things, like how one chooses the prior. So it is largely a matter of taste where one puts the ad hoc stuff. The real difference is that Frequentists at the meta-level don't mind being incoherent, whereas Bayesians believe in coherence. So in practical situations, one can apply Bayesian statistics while violating at at the philosophical level by being incoherent (ie. by saying that Bayesian statistics are just a tool).

*When I say Bayesian, I actually mean de Finetti's beautiful theory of coherence. I don't accept Jaynes's ugly objective Bayes philosophy.

 

[Quantumental]

As I have pointed out to you before the issue has yet to be resolved one way or the other. Certain key mathematical theorems are lacking.

But then it is very misleading to suggest that MWI is "beauty incarnate" and "mathematical elegance". Copenhagen is also very simple, as long as you don't worry about explaining collapse. So it Bohm, minus the non-locality etc. etc. I feel that MWI is getting a lot of unearned praise simply for existing as an idea that hasn't been fleshed out, or rather every time it's attempted to be fleshed out it's fatal flaws shine through.

At this moment in time, due to it's severe flaws, we have absolutely no reason to assume that these will just "work themselves out" anymore than we have a good reason to think that Bohm will somehow do away with it's problems with relativity.

I have seen papers where for simple models it is shown the results do NOT depend on the factorisation. They however need to be extended, and that hasn't been done yet.

Could you link?

 

[atyy]

At this moment in time, due to it's severe flaws, we have absolutely no reason to assume that these will just "work themselves out" anymore than we have a good reason to think that Bohm will somehow do away with it's problems with relativity.

At present, the standard model does not need exact relativity. For example, QED needs an high energy cutoff. Some advocate a lattice regularization, which violates special relativity, eg. Capitani, http://arxiv.org/abs/hep-lat/0211036: "In principle all known perturbative results of continuum QED and QCD can also be reproduced using a lattice regularization instead of the more popular ones." So if one accepts relativity as only approximate, Bohmian Mechanics does not necessarily have problems with relativity. As I understand, the main problem with Bohmian Mechanics is chiral fermions, but there is no theorem ruling that out yet, and plenty of recent work on it: eg. http://arxiv.org/abs/0709.3658, http://arxiv.org/abs/0912.2560.

 

[atyy]

At this moment in time, due to it's severe flaws, we have absolutely no reason to assume that these will just "work themselves out" anymore than we have a good reason to think that Bohm will somehow do away with it's problems with relativity.

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?

http://arxiv.org/abs/0712.0149 "A potentially more serious flaw arises from the so-called “Everett-in-denial” objection to realism (Deutsch 1996; Zeh 1999; Brown and Wallace 2005). ... Advocates of the Everett interpretation claim that, (given functionalism) the decoherence-defined quasiclassical histories in the unitarily evolving physically real wavefunction describe — are — a multiplicity of almost-identical quasiclassical worlds; if that same unitarily-evolving physically real wavefunction is present in DBB (or any other hidden-variable theory) then so is that multiplicity of physically real worlds, and all the hidden variables do is point superfluously at one of them."

 

[Quantumental]

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?

Actually this is very similar to the ideas that have been presented by several different researchers in the last years, all independent of each other.
Charles Sebens, who did the paper with Sean Carroll on their Born Rule in MWI proposal posted his main theory of many interacting worlds on Seans blog late last year: http://www.preposterousuniverse.com...racting-worlds-approach-to-quantum-mechanics/

Then almost at the same time another team of quantum foundation researchers posted a very similar proposal as can be seen here:
Quantum Phenomena Modeled by Interactions between Many Classical Worlds
http://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.041013

Finally Kim Joris Boström's Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
http://arxiv.org/abs/1208.5632 Is touching on the same.