QM Interpretations: Most Popular & Why?

[Count Iblis]

I think that in the MWI, the Born rule can be derived from the weaker assumption that measuring an observable of a system that is in an eigenstate will yield the corresponding eigenvalue with certainty.

 

[Fredrik]

I think that in the MWI, the Born rule can be derived from the weaker assumption that measuring an observable of a system that is in an eigenstate will yield the corresponding eigenvalue with certainty.

That's what Wikipedia claims (here), and their reference for that is this 1968 article by James Hartle. I checked it out some time ago and he's clearly also assuming that the Hilbert space of a physical system is the tensor product of the Hilbert spaces of its subsystems. That's a very strong assumption. I don't have all the details figured out, but it seems to me that this assumption is essentially equivalent to assuming that the Born rule holds. The weak assumption that you mentioned is probably just the piece that needs to be added to make them completely equivalent.

 

[Fredrik]

...an internal sentient observer would be perfectly able to describe his own history and experience using, say, Copenhagen and wavefunction collapse, and treat everything about splitting of himself as Occam razor violating nonsense.

I still don't think that QM is anything more than a set of rules that tells us how to calculate probabilities of possibilities, but I think that using Occam's razor as an argument against the MWI makes about as much sense as using it against special relativity because it includes more than one inertial frame. If (the Dirac-von Neumann version of) quantum mechanics actually describes reality (which is hard to dismiss based only on Occam, considering that no other theory does a better job), this reality clearly must include many worlds. Even if some other version of QM is an accurate description of the world, then why would we consider it "simpler"? I don't think e.g. Bohm or a realist intepretation of the path integrals formulation is any simpler. The worlds are only "points of view" in the linear and deterministic evolution of a single point in a vector space, and I think the people who try to use Occam against the MWI have completely failed to understand this point.

I wonder if it's possible to set up an experiment that creates a superposition of a human being in different states.

I think every human is always in a superposition in most decompositions into subsystems, but the only decomposition that mattters to that human is the one that describes the universe as consisting of his memory and everything else, and in that decomposition, his memory states keep developing correlations with eigenstates of whatever he observes. Conscious experience is the development of such correlations. An important detail here is that the correlations form so quickly that the human won't ever notice that he failed to experience the time of decoherence.

This all depends on what you mean by "world". There's a definite branching of sentient beings and of classical worlds. There isn't any branching of the whole state of the universe in the big Hilbert space - that one simply evolves according to Schrodinger's equation.

Good point. I agree.

 

[Gerenuk]

What's the advantage of the MWI?
(What's the aim of any interpretation in general?)

To me it seems MWI makes an even more abstract mess than what we had before with "conventional" thinking.

 

[Fredrik]

What's the advantage of the MWI?

(What's the aim of any interpretation in general?)

It's a way to interpret QM as a description of what actually happens, instead of as nothing more than a set of rules that tells us how to calculate probabilities of possibilities. That's exactly what interpretations are about.

To me it seems MWI makes an even more abstract mess than what we had before with "conventional" thinking.

What do you consider conventional?

 

[Gerenuk]

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

Conventional I consider the Copenhagen interpretation I suppose.

Actually I do favour interpreting the set of rules of QM as to make the picture either more intuitive or so that one can grasp QM effects better in the mind or make the picture more well defined so that one has never doubt about what the result of a question might be. I cannot see MWI achieving either of these two. I also believe a good interpretation will give as a more correct and complete version of QM.

Admittedly I don't understand MWI fully, but that also shows that it doesn't simplify so much?

What is your opinion? Why do we need an interpretation and what should it achieve?
(I repeat that my opinion is that it should make QM either easier or extend it)

 

[zenith8]

Actually I do favour interpreting the set of rules of QM as to make the picture either more intuitive or so that one can grasp QM effects better in the mind or make the picture more well defined so that one has never doubt about what the result of a question might be. I cannot see MWI achieving either of these two. I also believe a good interpretation will give as a more correct and complete version of QM.

Hi Gerenuk,

Hmmm... you seem to be describing de Broglie-Bohm..

I found the following on-line lecture course helpful: http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

 

[Gerenuk]

Thanks a lot for the link. These kind of interpretation are actually really my favourite, but I also haven't studied them yet. So I've collected information and books and will study them soon.
My first impression was that the pilot wave is still a bit awkward.

Are there any less-known interpretations that are similar to that?

 

[zenith8]

Thanks a lot for the link. These kind of interpretation are actually really my favourite, but I also haven't studied them yet. So I've collected information and books and will study them soon.
My first impression was that the pilot wave is still a bit awkward.

Are there any less-known interpretations that are similar to that?

No there aren't - as far as I know.

Your impression that the de Broglie-Bohm pilot wave approach is awkward, I would respectfully suggest, is not true.

Tell you what. You don't have to go through the full Cambridge de Broglie-Bohm course. I note that the guy recently added a popular lecture to the bottom of his slides page. Why don't you read that (should take half an hour) then, if you still think it's awkward, we can talk.. (the many worlds guys have had their four pages).

 

[Fredrik]

Why do we need an interpretation and what should it achieve?

We don't need one, but it would be nice to have one, if it really does describe what actually happens.

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

I do too.

I also believe a good interpretation will give as a more correct and complete version of QM.

A correct interpretation would certainly do that, but I doubt that there is such a thing.

Conventional I consider the Copenhagen interpretation I suppose.

I don't think there's a universally accepted definition of the Copenhagen interpretation, but most people would say that it asserts that the laws of QM do not apply to measuring devices(!) even though it applies to the components they're made of(!), and that measurements "collapse" wave functions into eigenstates. The problem with this is that it's complete rubbish that no one has ever believed is true. The first assumption introduces an obvious inconsistency into the theory, and the second implies that we have not one, but two rules that specify how systems change with time. That makes another inconsistency possible.

I would say that the MWI must be defined by the assumption that QM actually describes something, and that all that stuff about "worlds" follows logically from that assumption. (Those logical arguments are quite complicated, as you can see in my posts above). We may not like it, but it's certainly better than the version of the Copenhagen interpretation that I described above.

 

[Hurkyl]

Hmm, then I personally prefer the set of rules without the complicating extension like MWI around it.

The main epistemological point of MWI is that it is essentially the only interpretation that is not an extension.

The extra "complication" is mainly because it looks different. Also, it's partly because it does not use any extensions -- like collapse -- that could be used to simplify things.

 

[Hurkyl]

For Fredrik:

There may be a higher-level difference in how we picture QM.

I prefer something more like the C*-algebra picture. The main thing is the algebra of observables. Quantum states are functions that map observables to complex numbers that satisfy certain properties. (we might call the value of such a function the "expected value" of the observable on the state)

For any particular state, we can apply the GNS construction to create a Hilbert space in which our state is represented by a ket. The Born rule simply comes from the definition of what it means for a ket to represent a quantum state -- i.e. that \rho(O) = \langle \rho | O | \rho \rangle.

While the ket picture is useful for some calculations, it obscures what's happening when we want to restrict to subsystems or whatever.

 

[hamster143]

That's what Wikipedia claims (here), and their reference for that is this 1968 article by James Hartle. I checked it out some time ago and he's clearly also assuming that the Hilbert space of a physical system is the tensor product of the Hilbert spaces of its subsystems. That's a very strong assumption. I don't have all the details figured out, but it seems to me that this assumption is essentially equivalent to assuming that the Born rule holds. The weak assumption that you mentioned is probably just the piece that needs to be added to make them completely equivalent.

Perhaps I'm missing your point, but how could the Hilbert space of a physical system NOT be the tensor product of its subsystems? That seems axiomatic to me.

using Occam's razor as an argument against the MWI makes about as much sense as using it against special relativity because it includes more than one inertial frame. If (the Dirac-von Neumann version of) quantum mechanics actually describes reality (which is hard to dismiss based only on Occam, considering that no other theory does a better job), this reality clearly must include many worlds.

The observer is never able to experience a splitting of himself, because he's always in a state of definite memory. In places where MWI says that the observer is split, the observer instead observes wavefunction collapse. So, from the point of view of the observer, those "other" states of him are unobservable and do not exist. From his point of view, the Occam-minimal, positivist interpretation is Copenhagen and not MWI. Even if MWI is the proper description of the totality of the universe.

It would be more interesting to design an experiment that "proves" to an observer that he did, in fact, split, but, short of quantum suicide, nothing good comes to mind.

 

[Fredrik]

Perhaps I'm missing your point, but how could the Hilbert space of a physical system NOT be the tensor product of its subsystems? That seems axiomatic to me.

There's more than one way to use two Hilbert spaces to construct a third. We use the tensor product because we want to make sure that the probability of obtaining two specific results in two independent measurements on two non-interacting systems is the product of the two probabilities assigned by the Born rule. See this post for a few more details about this, and this one for more about the tensor product in general.

 

[Fredrik]

I prefer something more like the C*-algebra picture.

I think I will too when I have learned it. I have bought the books already. 1, 2. I just need to get through them. It looks like it will take a long time. I'm going to finish another book (3) before I get deep into these two.

Nothing in your summary was new to me, but it covers most of what I know already, which is just the "big picture" and none of the details. One of the things I feel that I do understand is that there isn't a huge difference between the C*-algebra formulation and the Dirac-von Neumann (Hilbert space) formulation. It avoids superselection rules, but those aren't relevant here since we can consider a quantum theory that doesn't have any. It may be a better starting point for derivations of rigorous theorems, but that doesn't seem to be very important here either. It's prettier, but...you get the idea.

While the ket picture is useful for some calculations, it obscures what's happening when we want to restrict to subsystems or whatever.

OK, that's a statement I haven't heard before. How does the C*-algebra formulation deal with subsystems, and how is it relevant? Does it imply that something I said is wrong?

By the way, I'm quite fascinated by the fact that there are so many different approaches that lead to essentially the same thing. The Dirac-von Neumann approach defines a mathematical structure (a complex separable Hilbert space) to represent the states of a physical system. The C*-algebra approach defines a mathematical structure (a non-abelian C*-algebra) to represent the observables, and the quantum logic approach defines a mathematical structure (a something something orthomodular lattice that something something ) to represent experimentally verifiable statements. OK, I know even less about quantum logic than about C*-algebras, but I've bought a book about that too. 4. If I can get through all of these by the end of 2010, I'll be quite pleased with myself.

 

[hamster143]

There's more than one way to use two Hilbert spaces to construct a third. We use the tensor product because we want to make sure that the probability of obtaining two specific results in two independent measurements on two non-interacting systems is the product of the two probabilities assigned by the Born rule. See this post for a few more details about this, and this one for more about the tensor product in general.

In order for the tensor product construction to work, all we need is for the two Hilbert spaces to be orthogonal, which is automatically true in all interpretations of QM as long as two systems are non-overlapping.

 

[Fredrik]

In order for the tensor product construction to work, all we need is for the two Hilbert spaces to be orthogonal, which is automatically true in all interpretations of QM as long as two systems are non-overlapping.

The subsystems aren't represented by orthogonal subspaces. For example, if you take the tensor product of a 2-dimensional and a 3-dimensional Hilbert space, the result is 6-dimensional, not 5-dimensional. The choice to use the tensor product is definitely non-trivial.

(I'm going to bed now, so I won't be writing any more replies for at least 8 hours).

 

[Dmitry67]

Returning to the Born rule… I am keeping to have some kind of internal dialog with myself, and can't escape this trap. May be someone can help me. As a reminder, I like MWI, but the Born rule… personally, I think for MWI it must be interpreted differently. So:

“I am driving to work. But there is a branch where (because my brain malfunctioned) I killed/attacked people and ended in a jail/got killed”
“Yes, such branch exists, but the probability is very very low”
“But our sense of “being real” does not depend of “intensity” of a branch!”
“How is it possible?”
“Generate 1000 random decimal digits and read this number. Now you are on one of 10^1000 branches. Do you feel 10^1000 times less real after you did it?”
“Definitely not. Then intensity is not important. Even if we have Frequent event (90%) and Rare event (10% probability), and we make 100 tries, then all combinations are possible, like FFFFFFFFFFFF… (100 Fs), and RRRRRRRRR (100Rs which is also rare). All 2^100 branches must exist! There are 2^100 observers observing all these branches”
“Lets make that experiment. I bet we get about 85-95Fs and 5-15Rs. What is a prediction of MWI?”
“Hmmmm…. Everything is possible…”
I am blocked at this point.

 

[Dmitry67]

P.S.
If anyone claims that Born rule is proven in MWI first I need to know, how Born rule is defined, because there is NO probability MWI. It must be defined is other terms, like, total number of observers observing X divided by the total number of observers in some subbranch on a given basic...

 

[Fra]

What is your opinion? Why do we need an interpretation and what should it achieve?
(I repeat that my opinion is that it should make QM either easier or extend it)

I think this is a motivated question. I posed the same in post 43, where I gave my view.

(I guess an addition would be to note that my interpretation is also somewhat related to the version of MWI called "many minds" instead of many worlds; which is basically the idea that the different worlds are simply the different views the actual observers have that populate our one universe. The problems with this appoach, are then solved by letting the popultion and thus worlds evolve - in this picture the different worlds do interact; which is why it's better seen as many minds rather as many worlds, and from where I see it, this view gives a very good stance for expansion and unification of current theory - in line with my "pet views")

Edit: To respond again in little more detail to the point with my preffered view - it apparently holds the potential of unification since INTERACTIONS can probably be inferred from the rational player analogy (where in economy the dynamics of the economical system is inferred from the assumption of each player acting rationally) where each subsystem of the universe acts originally at will, but an evolution where selection for rational actions takes place. This is my motivation for my view. It is a vision, not finished theory, but the rationality for my preference lies in that I see it as a very natural and promising stance for extending current models and solving some of the open problems.

What the point is with the regular standard MWI I don't know. I don't see it either :)

/Fredrik

 

[Fra]

How about this?

“Definitely not. Then intensity is not important. Even if we have Frequent event (90%) and Rare event (10% probability), and we make 100 tries, then all combinations are possible, like FFFFFFFFFFFF… (100 Fs), and RRRRRRRRR (100Rs which is also rare). All 2^100 branches must exist! There are 2^100 observers observing all these branches”
“Lets make that experiment. I bet we get about 85-95Fs and 5-15Rs. What is a prediction of MWI?”
“Hmmmm…. Everything is possible…”
I am blocked at this point.

Let's play with idea of the many observer view rather than many world view? (or just think of MWI, but where there is a physical basis for each world, which is an subjective view)

If we instead acknowledge that each observer, actually sees a different statistical basis, and thus has acquired different priors. No finite real inside observer have something we can call complete statistical basis, or a "fair sampling".

This explains (assuming the observer is rational) why the different observers in a given population act differently. Each observers rationally act upon his own history only.

I think it's central to ask what is the point of "making a prediction"? Clearly the rational action of one observer, depends on the expected future. "anything is possible" would be a useless constraint. But otoh, a particular observer would not infer that anything is possible, since the distinguishable state space of a given observe is truncated.

I'm not sure if this makes sense to you, but I don't see this as as problem. But then I don't have the degree of realist desire you have :)

/Fredrik

 

[Fra]

Quite relevant to what I tried to convey relates to what user=Fredrik (not Fra) said about his impression of MWI

The same as the axioms for the statistical interpretation (Link), plus the additional assumptions that it makes sense to consider the Hilbert space of the universe (even though it includes yourself), and that a state vector in that Hilbert space is a representation of all the properties of a physical system (the omnium). (The statistical interpretation doesn't assume that, and it never includes the observer in the Hilbert space).

According to my way of reasoning, these two ideas does not even mix consistently.

IMHO a possible corrected version of something close to it, but still very different is to consider a kind of holographic picture where each observer encodes an image of it's own environment (the remainder of the universe). But obviously each observers has encoded a different version of the universe, and more so, only the OBSERVABLE part of the universe. This should even constrain the size of the observable universe, and relate it to the observers complexity in a kind of holographic spirit.

A kind of statistical interpretation can still be maintained, but it's of subjective nature - which is no problem per see.

And instead of a an very ambiougs and unclear infinite superposition of universes, we instead have a set of interacting VIEWS of worlds, represented by a population of observers in our one evolving universe (since the observes aren't static).

/Fredrik

 

[Demystifier]

I think that in the MWI, the Born rule can be derived from the weaker assumption that measuring an observable of a system that is in an eigenstate will yield the corresponding eigenvalue with certainty.

The problem with such an additional assumption is that it destroys all the beauty of pure MWI without that assumption. This is because such an assumption raises questions that cannot be answered within MWI:
What does it mean "to measure"?
Are measurements and/or observers described by the Schrodinger equation?
Or are they something external?
In short, with this additional assumption, MWI is not much different from the Copenhagen interpretation.

On the other hand, without that assumption (or a similar one) MWI is really beautiful and elegant, but unfortunately - physically empty. It's physically empty because it cannot explain the emergence of the Born rule - the crucial part of standard QM without which QM is physically empty.

So there are only 2 possibilities:
1. Abandon MWI completely, or
2. Accept MWI but add something additional that will destroy a part of its beauty.

If you choose 2., then you can add something that will make it either vague (like the assumption above), or not vague. The price for choosing something not vague is that it will probably look somewhat ad hoc. The best known example of non-vague but ad hoc assumption that can be added to MWI in order to recover the Born rule is - the Bohmian particle trajectories.

Personally, I find the last choice most appealing because this "ad hoc" assumption does not look to me so much ad hoc at all. Unfortunately, there is no objective quantitative measure of "ad hocness", so I cannot present a proof that the Bohmian trajectories are not so much ad hoc as many think that they are. I can present arguments, but not the proof.

In short, I believe that pure MWI is correct, but not complete. A possible completion of MWI is provided by the Bohmian interpretation.

 

[Fredrik]

the Born rule… personally, I think for MWI it must be interpreted differently.

...like, total number of observers observing X divided by the total number of observers in some subbranch on a given basic...

We can and should interpret it differently, but I don't know if there's a way to interpret it the way you're suggesting. There are several different ways to derive the Born rule's assignment of probabilities from the assumption that the Hilbert space of the omnium can be decomposed into a tensor product of Hilbert spaces of subsystems (and some minor technical assumption such as the one Count Iblis mentioned). We can also prove the converse. This suggests that in the MWI, we should think of the Born rule as the assumption that these decompositions are allowed. The actual probability assignment should be thought of as a result derived from that axiom. Just don't forget that the this decomposition axiom is very non-trivial.

The decompositions are not only allowed, they're what turns the model into a theory. In the MWI, Hilbert space with the Schrödinger equation and without the Born rule, is a perfectly valid mathematical model of reality, but it's not a theory because it doesn't make any predictions about results of experiments. An experiment is an interaction between subsystems, so we can't even begin to think about predictions until we have decomposed the omnium into the appropriate subsystems. The most useful way seems to be to decompose the omnium into the tensor product of "the system" and "the environment". The observer is part of the environment.

What you said about probability is how I was thinking about the MWI before this thread. That's actually the main reason why I felt that the MWI was complete nonsense. I have never seen anyone even try to define the "branches", or to quantitatively define probability in terms similar to what you're talking about, and without that, I felt that the MWI was at best a few "loosely stated ideas about what sort of things are happening". (And that really was the most positive way I could describe it. Most of the time I wouldn't be so kind).

Edit: I don't fully understand any of the derivations of the Born rule's assignment of probabilities from the decomposition assumption + minor technicalities. It's possible that someone who does would think that this approach does explain how to think about probabilities in a way that's similar to what you describe.

 

[Demystifier]

There are several different ways to derive the Born rule's assignment of probabilities from the assumption that the Hilbert space of the omnium can be decomposed into a tensor product of Hilbert spaces of subsystems (and some minor technical assumption such as the one Count Iblis mentioned).

Such as?
(I ask for a reference where such a derivation can be seen.)

Edit: Now I have seen your edit in which you admit that you do not fully understand any of such derivations.

 

[vanesch]

I agree fully with your analysis (especially that you need *some kind of Born rule* to turn MWI into something observable).

I'm starting to come around a little bit about the MWI. For a long time, it just seemed more nonsensical the better I understood it, but it's been going in the other direction while I've been writing my posts in this thread. I still think the terminology is confusing at best and idiotic at worst, and the same goes for the statements that MWI proponents make about the MWI, but I think it's possible to make sense of some of their ideas.

These are some of my thoughts:

. . .

The way I look upon MWI is that in the "omnium" the state of the omnium contains several terms with several "classical brain states", and by the Born rule, I'm aware of one of them. What's somewhat clear is that I can't at the same time have an wareness of "several classical brainstates" and have an illusion of "free will" because that would imply that I could act differently as a function of comparisons of "different brain states", and hence, the evolution of the state of the omnium would not be linear (superposition wouldn't hold). So any awareness and illusion of free will must automatically include the point that you can only be aware of "one" classical state at once. I can't be aware of the dead cat and the live cat simultaneously. So there must be SOME rule that tells me which awareness I'm about to experience, and we can just say that it is the Born rule.

And there it stops for me, this is good enough. As to the question of what ARE classical brain states, well, you could delve into those brain states which are more or less robust against decoherence and so on, but it doesn't matter. This is an unsolved problem in any case, because also in a Copenhagen, of a statistical ensemble interpretation, at a certain point you must DEFINE what are the pointer states, the states of "awareness", the possible outcomes of "observation".

I agree that it is not satisfying entirely to have to "stop there", but it has the advantage of being able to treat everything in the lab under unitary evolution, without having to ask "what's a measurement ?". It has also the advantage of not having to say that there's some objective physical action by "consciousness", and that there is no "transition from quantum to classical at some point".
In the end, you still don't know exactly how and where the probabilities come from, that's true, but at least you can have some intuition of what "physically happens" - at least in the omnium - this in contradiction to the "ensemble" interpretation where there's no "physical hold-on" to give you a relationship between the calculations and "the physical world".

You can say that the way I see this MWI thing is that it generates "ensembles of states of awareness". This is somewhat unorthodox in MWI, because a pure MWI adherent still thinks that you can obtain the Born rule from the unitary evolution alone. There are arguments in favor of that view, but I don't think any of them is conclusive - so I don't see the problem of introducing a Born rule for awareness.

The big points are that as long as you consider the wavefunction, you do give it some physical ontological reality within the omnium, and it evolves strictly according to unitary evolution. That's for me the essence of the MWI idea. It implies that all instruments, and all observers, end up physically by being in an entangled superposition with "all possible outcomes" in some "real" kind of way. It allows for "physical intuition". That's good enough for me, to give me a picture of what quantum mechanics is about.

 

[Demystifier]

Vanesch, would you agree that the Bohmian interpretation can be viewed as an attempt to make a completion or refinement of MWI, by providing a possible origin of the Born rule in MWI?

 

[vanesch]

What you said about probability is how I was thinking about the MWI before this thread. That's actually the main reason why I felt that the MWI was complete nonsense. I have never seen anyone even try to define the "branches", or to quantitatively define probability in terms similar to what you're talking about, and without that, I felt that the MWI was at best a few "loosely stated ideas about what sort of things are happening". (And that really was the most positive way I could describe it. Most of the time I wouldn't be so kind).

I would say that the difficulty here is that suddenly, one requires of a physical theory to solve a lot of philosophical issues which have been recognized since ages as being difficult (or even unsolvable) issues, like what is "awareness", and "why am I "I" " and questions like that. The only reason being that now, in MWI, these considerations enter into the theory in a non-negligible way. That doesn't make their philosophical consideration less difficult. So in as much as in classical physics, we don't know the answer really to "why am I experiencing *my* body" and things like that, but we don't care because it doesn't seem to have the slightest incidence on "the physics", in MWI it does seem to play a role, but we still don't know the answer. Let's pretend we do, in MWI as much as in classical physics, no ?

 

[Fredrik]

What does it mean "to measure"?

To decompose the omnium into the tensor product of "the system" and "the environment", and give the interaction sufficent time to allow correlations to form between eigenstates of a self-adjoint operator on the system's Hilbert space and pointer states of the environment. (Which observable that is is defined by the environment)

Don't ask me exactly what a pointer state is. I need to study decoherence theory in greater detail first. My intuitive understanding of pointer states includes the notion that every pointer state has every observer in a well-defined memory state. So memories of results of experiments are correlated with the actual results.

Are measurements and/or observers described by the Schrodinger equation?

Yes, definitely. The problem is just that the description includes all possible measurement results without any sort of probability assignment. (See my previous post).

So there are only 2 possibilities:
1. Abandon MWI completely, or
2. Accept MWI but add something additional that will destroy a part of its beauty.

I don't think that the Born rule (which we can state as the axiom that a tensor product decomposition is allowed + some minor technicality) destroys the beauty. Without it, the model doesn't even look like it has anything to do with the real world. It's just a vector space with an equation that describes the shape of a curve in it. But I think it's extremely cool that the additional axiom both turns the model into a theory that agrees with experiment with an amazing accuracy, and also tells us a bunch of things about the real world that we would never have expected to find in a theory that has any chance of being right.

 

[vanesch]

Vanesch, would you agree that the Bohmian interpretation can be viewed as an attempt to make a completion or refinement of MWI, by providing a possible origin of the Born rule in MWI?

Yes, you can say that. The bohmian view gives you an "objective" token that can assign probabilities to branches, which are derived ultimately from "initial conditions", as in classical statistical mechanics.

I said already several times that if it weren't for the difficulty the Bohmian view has with the *spirit* of relativity, it would be my favorite interpretation, free of all the philosophical difficulties that come with MWI - or at least, we could again do as if we didn't need to think about them to do physics.

 

[Fredrik]

Such as?
(I ask for a reference where such a derivation can be seen.)

Edit: Now I have seen your edit in which you admit that you do not fully understand any of such derivations.

I was thinking about Zurek's derivation based on the concept of "envariance", and Hartle's derivation, which is what Count Iblis is talking about. This article claims to cover Zurek's method better than he did. I have only taken a very quick look at it. If you don't like it, I'm sure there's a reference to Zurek's original article in it. Hartle's derivation is discussed here. There's a link to his article in #3.

 

[Demystifier]

I said already several times that if it weren't for the difficulty the Bohmian view has with the *spirit* of relativity, it would be my favorite interpretation, free of all the philosophical difficulties that come with MWI

Yes, I remember you said that. But I also remember that, when I drawn your attention to a paper that formulates Bohmian mechanics in a completely relativistic spirit without a preferred foliation, you were not interested in styding the details. Perhaps you will now, so I will try again:
arXiv:0811.1905 [Int. J. Quant. Inf. 7 (2009) 595]
For further developments see also
arXiv:0904.2287 [to appear in Int. J. Mod. Phys. A]

 

[Dmitry67]

Yes, you can say that. The bohmian view gives you an "objective" token that can assign probabilities to branches, which are derived ultimately from "initial conditions", as in classical statistical mechanics.

I said already several times that if it weren't for the difficulty the Bohmian view has with the *spirit* of relativity, it would be my favorite interpretation, free of all the philosophical difficulties that come with MWI - or at least, we could again do as if we didn't need to think about them to do physics.

Strange that you did not mention the problem with the initial conditions: while in BM they are infinitely complex, in MWI the initial state of the 'omnium' can be very simple.

For me it is a part of the beauty of MWI. I will never believe that God had positioned all these BM particles so 13 billions years after that I would type this very post.

 

[vanesch]

Yes, I remember you said that. But I also remember that, when I drawn your attention to a paper that formulates Bohmian mechanics in a completely relativistic spirit without a preferred foliation, you were not interested in styding the details. Perhaps you will now, so I will try again:
arXiv:0811.1905 [Int. J. Quant. Inf. 7 (2009) 595]
For further developments see also
arXiv:0904.2287 [to appear in Int. J. Mod. Phys. A]

I will try to read it, but I have to say that I've a bit lost interest in the interpretational issues. Not totally, but it is less on my mind than it was a few years ago. Probably I'm growing mentally old

 

[Dmitry67]

Fredrick,

What was your opinion about Max Tegmark's MUH before and after your trip to the MWI world?

I mean, if there is nothing else except the evolution of omnium, and that evolution is deterministically defined by 1 or more equations, what is Universe but a solution to these equations?

 

[Demystifier]

I was thinking about Zurek's derivation based on the concept of "envariance", and Hartle's derivation, which is what Count Iblis is talking about. This article claims to cover Zurek's method better than he did. I have only taken a very quick look at it. If you don't like it, I'm sure there's a reference to Zurek's original article in it. Hartle's derivation is discussed here. There's a link to his article in #3.

Thanks!

 

[Demystifier]

Strange that you did not mention the problem with the initial conditions: while in BM they are infinitely complex, in MWI the initial state of the 'omnium' can be very simple.

That is not strange at all, for two reasons:
First, this alleged advantage of MWI is not something widely known. In fact, you seem to be the only guy who uses this argument. Or do you know anybody else?
Second, you have never proved that it is really true that a complex universe can really emerge from a very simple initial state. In fact, at another thread you admitted that it was not so obvious as you thought it were.

Third, I have a challenge for you. Give me a relatively clear argument that a simple MWI initial condition can lead to a complex universe, and I will turn your argument (whatever it will be) into an analogous and equally clear argument that a simple Bohmian initial condition can also lead to an equally complex universe.

 

[Hurkyl]

I will never believe that God had positioned all these BM particles so 13 billions years after that I would type this very post.

As opposed to picking infinitely many values to set an initial wavefunction?

If it makes you feel better, the position of all those particles is just a single point in a 36 billion dimensional vector space -- much smaller than the Hilbert space the wavefunction is chosen from.

 

[Dmitry67]

1
First, this alleged advantage of MWI is not something widely known. In fact, you seem to be the only guy who uses this argument. Or do you know anybody else?

2
Second, you have never proved that it is really true that a complex universe can really emerge from a very simple initial state. In fact, at another thread you admitted that it was not so obvious as you thought it were.

3
Third, I have a challenge for you. Give me a relatively clear argument that a simple MWI initial condition can lead to a complex universe, and I will turn your argument (whatever it will be) into an analogous and equally clear argument that a simple Bohmian initial condition can also lead to an equally complex universe.

1 Yes, and I am trying to understand why

2 Well, we don't know the equations of the superstring/loop gravity near the Big bang, so it is diffucult to do it right now

3 Do you remember your own analogy: MWI is a tree, but without an ant? The root of a tree is very simple, the complexity is on the leaves. Or what do you mean by 'Simple Bohmian condition'? In BM information is conserved (if we include hidden variables), so it was the same at BB.

On the contrary, in MWI the final state is not pre-coded.
Say, I make a cat experiment. Cat dies, I cry. I repeat experiment again, cat dies, I commit suicide. But if the second cat is alive, I feel relieved. But if the very first cat was alive, I (would) lose interest to science, make a sturtup, and end being a millionaire.

Is all that complexity 'encoded' in the state of the neutron used in the cats experiment? No of course. The relatively simpel state evolved into a tree of different final states

 

[Dmitry67]

As opposed to picking infinitely many values to set an initial wavefunction?

If it makes you feel better, the position of all those particles is just a single point in a 36 billion dimensional vector space -- much smaller than the Hilbert space the wavefunction is chosen from.

What if these infinitely many values at the BB are defined by very simple equation we don't know yet?

 

[MaxwellsDemon]

When I hear all these complex discussions concerning various interpretations, I can't help but think of King Alfonso X who upon studying the Ptolemaic universe stated, "If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler."

 

[Demystifier]

3 Do you remember your own analogy: MWI is a tree, but without an ant?

Yes I do.

The root of a tree is very simple, the complexity is on the leaves.

You probably mean the complexity is on the branches, not leaves. However, it is important to emphasize that each particular branch must be complex by itself, because otherwise no complexity would be perceived (by "frogs").

Or what do you mean by 'Simple Bohmian condition'?

I said that I will turn YOUR argument on MWI into my argument on BM. So you must first say what do YOU mean by "The root of a tree is very simple". I have some idea what does it mean, but the crucial point of my challenge to you is that I base my arguments on YOUR arguments. In other words, I want to beat you by your own weapon. Otherwise, my arguments will not be sufficiently convincing to you. (This is like the famous case when Bohr beat Einstein by using argument based on General Relativity. Later it turned out that this Bohr's argument was not valid, but at that time it served the purpose to convince Einstein.)

In BM information is conserved (if we include hidden variables), so it was the same at BB.

In MWI information is also conserved (if we include the whole wave function), so it was the same at BB. [That's what I call beating you by your own weapon.]

On the contrary, in MWI the final state is not pre-coded.

Yes it is (if, as I said, we include the whole wave function - the bird view).

 

[Demystifier]

What if these infinitely many values at the BB are defined by very simple equation we don't know yet?

What if Bohmian initial values at the BB are also defined by very simple equation we don't know yet?
[I continue with beating you by your own weapon, including your typos.]

 

[Fredrik]

What was your opinion about Max Tegmark's MUH before and after your trip to the MWI world?

I have always liked that suggestion. What has changed is just that I previously didn't think it was possible to interpret this particular mathematical structure (Hilbert space) as a description of a physical system that we're a part of. Now I think it's possible.

I mean, if there is nothing else except the evolution of omnium, and that evolution is deterministically defined by 1 or more equations, what is Universe but a solution to these equations?

It's too soon to say. I mean, we're still not even able to explicitly construct a Hilbert space and operators on it for the standard model, and it's possible that QM needs to be modified to be fully compatible with gravity.

 

[Hurkyl]

OK, that's a statement I haven't heard before. How does the C*-algebra formulation deal with subsystems, and how is it relevant?

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

e.g. interested in spin? Then we can look at the algebra generated by the spin observables. Other experiments? Maybe we should restrict to just those observables localized to the laboratory.

Since a state is a function, it automatically restricts to a function on the subalgebra (and the restriction remains a state).

In other words, a state is a function that maps observables to complex numbers... and when looking at a subsystem, the restricted state is just the same map (but with the restricted domain) from observables to complex numbers.

The point I was trying to make (I think) was that dealing with subsystems doesn't require invoking Born's rule or trying to make any sort of statement about (seemingly arbitrary) factorizations of a Hilbert space.

 

[Fredrik]

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

e.g. interested in spin? Then we can look at the algebra generated by the spin observables.

And for each such subalgebra, the GNS construction gives us a representation of observables as bounded operators on a Hilbert space, right? What's the relationship between these Hilbert spaces and the Hilbert space that corresponds to the huge C*-algebra we started with? Is the latter a tensor product of the former?

 

[Fra]

If we start with the algebra of all observables that can be "observed" in the entire universe, then we can (in principle) write down the subalgebra of those observables that relate to the subsystem of interest.

I do not question the connection between algebras defined by operators, and the corresponding sets/structure space.

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I know many people refer to this GNS reconstruction and seem to somehow feel better there, but I do not find this more plausible, than just accepting other axioms. It mainly suggest a connection between operations and representations. But they both come together IMO.

/Fredrik

 

[Hurkyl]

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I confess that I'm not aware of any way in which this differs from dealing with subsystems in any other physical theory. Would you elaborate?

 

[Hurkyl]

And for each such subalgebra, the GNS construction gives us a representation of observables as bounded operators on a Hilbert space, right? What's the relationship between these Hilbert spaces and the Hilbert space that corresponds to the huge C*-algebra we started with? Is the latter a tensor product of the former?

Don't forget GNS takes a state as input too! Your question seems a little off -- but since I only have a shallow understanding of the subject, I don't have a good guess what the right question to ask is.

So two notes:
. Every representation of the big algebra is automatically a representation of the subalgebra.
. (Once I'm sure what we're asking) I imagine the tensor product factorization is somewhat unlikely... but I expect there is no essential difference whether or not a factorization exists, so it's useful to look at the algebraically simpler case.

 

[Fra]

The question is, wether there is any physical leap here, but making use on an "in principle" argument, that as far as I see it, can never be physicall realized, and is not a plausible premise to me.

I confess that I'm not aware of any way in which this differs from dealing with subsystems in any other physical theory. Would you elaborate?

If we are talking about existing mature "theories", then I think you have a point.

But since my opinon as expressed earlier in this thread, is that to me these interpretational questions are justified only to the extent that they make a difference to extending the theory. Also your argument isn't a theory IMO, it's more a supposed possible plausible argument for motivating parts of it, and I just think it isn't that plausible after all.

So my opinion, implies that I think that QM needs revision. Not because it doesn't make sense for most of particle and atomic physics, but becaues we still have several issues, including gravity, that is not on par with this framework, and because there are IMHO clearly identifiable highly questionable assumptions in it's construction or axiomatisation.

What I mean specifically in the comment above is that I think a real observer, can not in a way that makes sense to me at least never simultaneously relate to all possible observables in the universe. This means that a justified argument, instead should acknowledge this and see how this changes the inference.

I think the result would be that the notion of a large state space of the universe, or a large set of possible measurements, from which one can shave out the observables and measurements state space seen by any subsystem is making the mistake byt not acknowledging where THIS very inference lives. As I see it, this inference must be executed by a third real observer. And in general an observer is bounded.

The implications of this, would then suggest a new direction to be explore. Namely one where the QM framework with hilber spaces and operators, rather is a result of evolution, but not in the decoherence sense, but in a more intrinsic sense where there is no outside description of it. It would be an evolving law.

What I HOPE to eventually understand, but which isn't yet developed, is why the specific representations and structures of operators incl commutators in QM is the way is is, from a fitness perspective. I've always had as a for me plasible working hypothesis that QM logic is a result of a kind of data compression. Where the information state space (hilbert state space) can be understood as the state space of an encoded observations, that is preferred since it provides a more memory/cost effective basis for actions.

/Fredrik