Why does nothing happen in MWI?

[PeterDonis]

Obviously the whole of quantum mechanics is based on the idea that a state evolves

In the Schrödinger picture, yes. Not in the Heisenberg picture: in that picture, states don't change at all; all the time evolution is in the operators.

 

[bhobba]

Obviously the whole of quantum mechanics is based on the idea that a state evolves, the dynamics are typically described by Schrödinger's Equation and the Hamiltonian requires analysis of particular physical laws.

But just as obviously factoring this into cats, people etc etc is not part of those laws. That's the crucial issue. The claim is its this extra structure that's responsible for decoherence.

Thanks
Bill

 

[Derek Potter]

Sure - but you talked about an observer state. The observer, since its entangled with what's being observed, is NOT in superposition - and obviously so.

Thanks
Bill

Well, when fighting on several fronts sometimes a little sloppiness creeps in.

 

[Derek Potter]

But just as obviously factoring this into cats, people etc etc is not part of those laws. That's the crucial issue. The claim is its this extra structure that's responsible for decoherence.

Yes. Without actual physical processes to make the state evolve, there would be no decoherence.

I don't know why such an obvious, if unstated, assumption is crucial. Has someone changed the definition of MWI so that it works without physics?

 

[PeterDonis]

I am beginning to think someone has changed the definition of MWI so that it works without physics.

Well, you're the one that brought up Schwindt's paper , so it's his definition of "MWI" that we're discussing. His definition is basically, that "MWI" means "the universe has a pure state vector that is subject to unitary evolution" and that's it. Anything else (factorization, etc.) is "additional structure", and the "MWI", on his interpretation, doesn't include that additional structure.

That definition of "MWI" probably isn't the one a lot of physicists are implicitly using when they talk about the MWI. But I do think it's a valid question where the "additional structure" comes from; I don't think you can just say "it's in the state vector" and be done with it.

 

[Derek Potter]

Well, you're the one that brought up Schwindt's paper , so it's his definition of "MWI" that we're discussing. His definition is basically, that "MWI" means "the universe has a pure state vector that is subject to unitary evolution" and that's it. Anything else (factorization, etc.) is "additional structure", and the "MWI", on his interpretation, doesn't include that additional structure.
That definition of "MWI" probably isn't the one a lot of physicists are implicitly using when they talk about the MWI. But I do think it's a valid question where the "additional structure" comes from; I don't think you can just say "it's in the state vector" and be done with it.

I didn't exactly" bring up" Schwindt's paper, the thread was started by me asking for help in understanding it.
Now, if you add "unitary evolution" to the state vector postulate, you introduce time dependence and if you introduce time dependence you must say what the dependency is and if you say what it is then you can say how a state evolves. You can then identify which factorizations result in interactions with stable entanglements - a.k.a. observations. The additional structure is the form of the unitary evolution. I cannot believe that Schwindt would have forgotten about that. And from the fact that his claim seems only to apply to the whole universe and not to smaller systems I would think this general discussion about factorization is off the point.

 

[PeterDonis]

if you introduce time dependence you must say what the dependency is and if you say what it is then you can say how a state evolves

Yes, agreed; but "evolves" here just means one state vector for the universe with norm 1 turns into another state vector for the universe with norm 1.

You can then identify which factorizations result in interactions with stable entanglements - a.k.a. observations. The additional structure is the form of the unitary evolution.

This part I'm not sure about. As above, unitary evolution tells you how the state vector of the whole universe evolves, but that in itself contains no information about anything other than one state vector of norm 1 turning into another state vector of norm 1. Or, to put it another way, any such unitary evolution can be written in a basis in which nothing happens; that's the point of the "Nirvana" theorem Schwindt talks about.

his claim seems only to apply to the whole universe and not to smaller systems

I don't think that's true. His claim is that the pure state vector that appears in unitary evolution is a state vector of the whole universe, because, according to the MWI (as he interprets it), that's the only "pure" state that really is pure.

 

[Derek Potter]

Yes, agreed; but "evolves" here just means one state vector for the universe with norm 1 turns into another state vector for the universe with norm 1.

Which now sits askew on whatever basis you previously set it square on. Ergo every damn thing you could ever want to know about it is now different.

This part I'm not sure about. As above, unitary evolution tells you how the state vector of the whole universe evolves, but that in itself contains no information about anything other than one state vector of norm 1 turning into another state vector of norm 1. Or, to put it another way, any such unitary evolution can be written in a basis in which nothing happens; that's the point of the "Nirvana" theorem Schwindt talks about.

Well the exact meaning of the Nirvana theorem is what I was asking about. I'm imagining the state vector pinned down and the basis running all over the place around it, in which case the Nirvana basis would be time-dependent. But states are supposed to be basis-independent so the state would appear to be unchanging in any basis... huh, that's got to be silly! Or could we say that the appearence of activity is purely the result of the Nirvana basis swinging around? Seems like playing with words, but I'm out of my depth.

 

[atyy]

Derek Potter, since there is no branching in your MWI, isn't your MWI really BMW, as we discussed before?

So we just take all variants of BM to be real, and in each variant, all Bohmian worlds are real?

I'm pretty sure there's one world in which BMW does use Vorsprung durch Technik.

 

[Derek Potter]

Derek Potter, since there is no branching in your MWI, isn't your MWI really BMW, as we discussed before?
So we just take all variants of BM to be real, and in each variant, all Bohmian worlds are real?
I'm pretty sure there's one world in which BMW does use Vorsprung durch Technik.

I think it will be simplest if I just agree :)

 

[PeterDonis]

Which now sits askew on whatever basis you previously set it square on.

Not necessarily. That's the point of the Nirvana theorem. See below.

the exact meaning of the Nirvana theorem is what I was asking about.

As I understand it, the theorem says that, given a state and a Hamiltonian, we can always find a basis in which the unitary evolution induced by the Hamiltonian does nothing but phase rotate the state. In this basis, called the "Nirvana basis", nothing happens, since phase rotation does not change any physical observables.

I don't actually understand all the ins and outs of how the theorem is proved, so I may be missing something; but that's how it looks to me.

 

[craigi]

Derek,

Try to answer the following, in the conext of the MWI, to see where the problem arises.

Consider that we prepare an arbitrarily large, isolated, quantum system. Think about what happens happens within that system. Can it undergo decoherence, while isolated from the outside world? Decoherence with what? Can a meaningful measurement be made within it, while isolated from the outside world?

If yes, then how do we determine how the classical system (or environment) emerges, which the quantum subsystems can decohere with and be measured by?

If no, then how did the first classical system (or environment) emerge?

 

[Derek Potter]

Derek,
Try to answer the following, in the conext of the MWI, to see where the problem arises.

Consider that we prepare an arbitrarily large, isolated, quantum system. Think about what happens happens within that system. Can it undergo decoherence, while isolated from the outside world?
Yes

Decoherence with what?
You said "within". That means you have factorized it so the question becomes can one subsystem be decohered by another.

Can a meaningful measurement be made within it, while isolated from the outside world?
Yes

If yes, then how do we determine how the classical system (or environment) emerges, which the quantum subsystems can decohere with and be measured by?
If no, then how did the first classical system (or environment) emerge?
I don't know how we determine how, in fact I'm not sure what the question means. I can tell you how the classical system emerges. It emerges due to entanglement of the two subsystems. This then evolves into an improper mixture through decoherence.

 

[Derek Potter]

As I understand it, the theorem says that, given a state and a Hamiltonian, we can always find a basis in which the unitary evolution induced by the Hamiltonian does nothing but phase rotate the state. In this basis, called the "Nirvana basis", nothing happens, since phase rotation does not change any physical observables.

Well I'd still like to know what such a Nirvana basis looks like as I have a distinct feeling, nothing more, that the title "Nothing happens in the Universe of the Everett Interpretation" may be a slight extrapolation.

 

[PeterDonis]

I'd still like to know what such a Nirvana basis looks like

Section 3 of the paper has the key equations. He considers both a time-independent "Nirvana" factorization (in which each branch of the induced superposition phase rotates at its own frequency, but the branches don't interact) and a time-dependent one (in which each branch does not change at all).

 

[Ilja]

But what does it mean that there is a factorization in which nothing happens? What are the non-interacting subsystems like?

It means that MWI is inadequate to describe our world, because in our world something happens. Thus, MWI in this factorization is definitely false. If, now, MWI in another factorization is true, that means, MWI is incomplete without defining also the factorization, as part of the physical structure.

I have made a similar argument that the structures which MWI officially accepts are not sufficient to define physics in http://arxiv.org/abs/0901.3262

 

[Ilja]

I don't know why such an obvious, if unstated, assumption is crucial. Has someone changed the definition of MWI so that it works without physics?

MWI is supposed to be an interpretation of the most fundamental physical theory. Thus, there is no physics except the physics defined and explicitly described by MWI, or MWI does not describe what it claims to describe.

And this incompleteness is, of course, the point. It claims to be complete, argues, in particular, that dBB theory contains unnecessary additional things, a claim which would be nonsensical if MWI would not describe physics completely.

 

[Derek Potter]

MWI is supposed to be an interpretation of the most fundamental physical theory. Thus, there is no physics except the physics defined and explicitly described by MWI, or MWI does not describe what it claims to describe.

And this incompleteness is, of course, the point. It claims to be complete, argues, in particular, that dBB theory contains unnecessary additional things, a claim which would be nonsensical if MWI would not describe physics completely.

Of course MWI defines and describes all the necessary physics. The state is not merely a static ray in Hilbert space, it moves around, driven by a differential equation featuring the Hamiltonian. There's the physics that allows the state to evolve.

 

[Derek Potter]

It means that MWI is inadequate to describe our world, because in our world something happens. Thus, MWI in this factorization is definitely false. If, now, MWI in another factorization is true, that means, MWI is incomplete without defining also the factorization, as part of the physical structure.

I have made a similar argument that the structures which MWI officially accepts are not sufficient to define physics in http://arxiv.org/abs/0901.3262

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post? Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

 

[atyy]

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post? Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

But if your view is BMW, then in a sense what you and Ilja are saying are the same. He is complaining about the lack of extra structure. Is it clear that your stability condition for something to become observable isn't "extra structure", especially when you consider how to implement it in detail?

 

[Derek Potter]

But if your view is BMW, then in a sense what you and Ilja are saying are the same. He is complaining about the lack of extra structure. Is it clear that your stability condition for something to become observable isn't "extra structure", especially when you consider how to implement it in detail?

It would help if there was some sort of prior agreement about what is meant by structure. Regardless of Nirvana frames it seems Ilja regards factorization as part of the physics. Factorization is a mathematical technique that applies to tensors and requires no more physics than addition. Of course my tensor theory is rubbish so I have to say if factorizability does not follow from "a vector space equipped with an inner product" then the usual "Postulate 1" of QM should be amended to include the extra structure.

Your point about stability - similarly. There is still no complete consensus about when a measurement can be said to be complete. Impatient types who insist on adding a postulate to cover the present uncertainty will no doubt also insist that the postulate is extra physics. I would take a more conservative approach. Use any criterion you like and give the result a different name each time. This doesn't add anything to the physical structure, it just defines the scenario you want to analyse. We are free to do this because MWI claims to eliminate postulates about observations and instead derive them. So instead of importing poorly-defined "observations" into the structure from everyday life, we now have complete freedom to invent different types of measurement and see which ones MWI predicts.

 

[atyy]

Use any criterion you like and give the result a different name each time. This doesn't add anything to the physical structure, it just defines the scenario you want to analyse.

So you end up with the subjective criterion of the observer. Is this any different from Copenhagen? Doesn't this leave the measurement problem open?

 

[Ilja]

Our world? You expect a Many Worlds picture to single out the very world where you are reading this post?

Of course, the aim of any physical theory is to predict and explain what happens in the world which I observe. It is free to add something I do not observe, if there is some necessity for this. But if it does not explain anything, it can be simply rejected, and we can go back to the Bible which explains at least something - by unexplainable decisions of some guy named God.

Of course you don't, yet you expect it to single out factorizations that allow things to happen - and not only that, you demand that this singling out be part of the physical structure. But MWI does not have to do any such thing, it is quite sufficient to show that factorizations are possible which result in things happening. It is logically obvious the "our world" must be one of those. The fact that Nirvana factorizations are possible does not invalidate the fact that Samsara factorizations are also possible.

But then we are back to a theory which explains nothing. I do not need any theory to know that our particular world is logically possible - else if would be impossible for me to live in it.

 

[Derek Potter]

Of course, the aim of any physical theory is to predict and explain what happens in the world which I observe. It is free to add something I do not observe, if there is some necessity for this. But if it does not explain anything, it can be simply rejected, and we can go back to the Bible which explains at least something - by unexplainable decisions of some guy named God. .

Actually God's decisions are explained throughout the Bible - in Biblical terms. It probably isn't a good idea to jump on the fashionable bandwaggon of holding up Biblical belief as a model of irrationality. Some people might get offended. It is also against forum rules. And it might annoy God. MWI also explains itself - the particular world you experience is one of many. MWI does not single out any particular world and then put "you" in it. You are in every world. All worlds are equally real, you seem to be expecting MWI to single out one world to be more real than the others. You are free to make up an interpretation that does this, and it will certainly require extra structure, but it will not be MWI.

But then we are back to a theory which explains nothing. I do not need any theory to know that our particular world is logically possible - else if would be impossible for me to live in it.

What's that got to do with anything at all? The question isn't whether you exist but how MWI explains it.

 

[Demystifier]

Why should MWI have to justify the mathematical axiom of choice? See https://en.wikipedia.org/wiki/Axiom_of_choice

The set-theoretic axiom of choice has nothing to do with that.

 

[Demystifier]

I didn't exactly" bring up" Schwindt's paper, the thread was started by me asking for help in understanding it.

So do you now understand it better?

 

[Derek Potter]

So you end up with the subjective criterion of the observer.

If photons have subjective states then yes, why not?

Is this any different from Copenhagen?

Copenhagen means different things to different people. I dare say it could absorb MWI and Harry Potter if it wanted to. But if you mean "does defining observations and measurements before arguing whether MWI explains them, maintain the quantum/classical cut?", then I guess the answer's obvious: it depends on the definition.

Doesn't this leave the measurement problem open?

The measurement problem *is* open. There is no consensus definition of a measurement. That's hardly MWI's fault.

There's an important principle here. Well-formed theories rest on suppositions without which the theory cannot be built up. QM is (said to be) a theory about observations - an observation postulate is required to ground the maths in consensus reality. It is there, intact and unexplained, imported from everyday experience. It hides a massive assumption: that there are measurements and that the prosaic model of someone using a tape measure and noting down the results actually means something.

MWI, however, removes the observation postulate. Instead, measurements are derived or described. But this means that the orthodox assumptions come to the surface. The tape measure is, rather appropriately, replaced by entanglement, it seems we can describe the physical process quite well in this quasi-operational way. The noting down of results is however, less clear. Is leaving a permanent record a sufficient or necessary condition? etc. Quantum erasure highlights the nee3d to be consistent in what you want MWI to explain.[/QUOTE]

 

[Demystifier]

The state is not merely a static ray in Hilbert space, it moves around, driven by a differential equation featuring the Hamiltonian.

But there is a basis in which it does not move around. The basis in which only the phase changes.

Perhaps it is easier to understand it in a classical analog:

Consider a 3-dimensional universe containing nothing but one classical pointlike particle moving around. Does anything happen in such a universe? You can consider the system in coordinates (the classical analog of basis) comoving with the particle. In these coordinates the particle does not move. So nothing happens in the universe with one particle.

How about the 3-dimensional universe with two particles? Now there is relative motion of two particles, so one may think that something really happens in the case of two particles. However, the mathematics of two particles in 3 dimensions is the same as mathematics of one particle in 6 dimensions. So mathematically, we may say that we still have one particle, only in 6 dimensions. So from that point of view nothing happens even with two particles, because they are mathematically equivalent to one particle.

How to avoid the conclusion that nothing happens in a universe with two particles? Only by saying that physically we really do have two particles (in 3 dimensions) and not one particle (in 6 dimensions). But we cannot say that only from the mathematical structure of classical mechanics. There must be some additional structure involved, something which tells us that two particles in 3 dimensions is not the same as one particle in 6 dimensions. So pure classical mechanics cannot explain why something happens.

Likewise, pure quantum mechanics (the Schrödinger equation and nothing else) also cannot explain why something happens.

 

[Derek Potter]

The set-theoretic axiom of choice has nothing to do with that.

Wikipedia - Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.
The question was If all you have is the pure state vector of the entire universe, how do you pick out the "cat" subspace? If your answer is, "well, I pick some particular basis...", then what justifies picking out that particular basis?
Seems to me the axiom is needed otherwise we can't select one space out of a collection (one in this case) of bins full of factorizations. But outside of its normal home it is so obvious that needs no recognition. Or so I thought until the question was raised. But of course if you were to insist that the axiom does not apply, I would not mind - the point still stands: why should MWI have to justify my being able to consider a cat if the existence of cats has already been established?. Come to think of it, that might be a better way of putting it.

 

[Demystifier]

Seems to me the axiom is needed otherwise we can't select one space out of a collection

The axiom of choice guarantees that you can select one member of the collection. But the physical question is - which one? The axiom of choice does not answer that crucial physical question, so that's why it is irrelevant in this context.

From the set-theoretic point of view, let me also note that the axiom of choice is really important only when there is an infinite number of collections, and you want to select one member from each of the collections. In the case of a finite number of collections, the axiom of choice is trivial.