Hilbert Dynamics in choosing position in BM/MWI

[cube137]

In General Relativity. Gravity is caused by curvature of spacetime.

In MWI and Bohmian Mechanics.. the position observable and position preferred basis is chosen. There must be a non-zero energy or some kind of dynamics that would lock the particular Hilbert space vectors into those special bases. What is this dynamics caused akin to gravity caused by the curvature of spacetime or akin to the non-zero value of the Higgs Field in the vacuum. You can't just say the position is chosen as the preferred basis in Bohmian Mechanics without any consequence or dynamics.

 

[bhobba]

Its caused by the radial nature of most interactions.

The reason is technical but is explained in detail here:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

 

[cube137]

Its caused by the radial nature of most interactions.

The reason is technical but is explained in detail here:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

But if the position observable and position preferred basis won't be selected as preferred in the environment, there won't even be any radial nature in particles in the environment. Imagine the vacuum of the Higgs. It's not zero but forced to choose a Vacuum Expectation Value. So in Hilbert Space (of environment), preferred basis of position is chosen ad hoc.. what is the corresponding dynamics causing it.. anyone?

 

[bhobba]

But if the position observable and position preferred basis won't be selected as preferred in the environment, there won't even be any radial nature in particles in the environment.

The basis is chosen in theory ie the position basis is implicit in the normal form of the Schrodinger equation. When expressed in that basis virtually all interactions turn out to be radial ie the V(x) in the Schrodinger equation. Its purely arbitrary what basis you chose to write your equations in - writing them in the position basis is what's usually done and you can easily see their radial nature.

Thanks
Bill

 

[cube137]

The basis is chosen in theory ie the position basis is implicit in the normal form of the Schrodinger equation. When expressed in that basis virtually all interactions turn out to be radial ie the V(x) in the Schrodinger equation. Its purely arbitrary what basis you chose to write your equations in - writing them in the position basis is what's usually done and you can easily see their radial nature.

Thanks
Bill

Does this normal form of the Schrodinger also the one use by Bohmian, Copenhagen and Many Worlds? Which doesn't use it? If they all use it.. then why is there a distinction between Bohmian, Copenhagen and Many Worlds?

 

[bhobba]

Does this normal form of the Schrodinger also the one use by Bohmian, Copenhagen and Many Worlds? Which doesn't use it? If they all use it.. then why is there a distinction between Bohmian, Copenhagen and Many Worlds?

There is the QM formalism that all interpretations have. The usual form of Schrodinger's equation is part of that formalism.

The diffference between interpretations hinges on things other than the formalism.

1. Copenhagen has the idea the state is like the Baysian interpretation of probability.
2. MW has the interpretation the state of the universe as very real, but when decoherence happens in the mixed state that results each outcome is a separate world. Everything simply evolves according to Schrodinger's equation. It uses the decision theory approach to probability
3. BM uses any interpretation of probability - the particle has actual position and velocity at all times - you use probabilities because according to QM you can't know initial conditions with certainty ie you can't know both position and momentum at the same time.

Interpretations are at least partially just arguments about of interpretations of probability:
http://math.ucr.edu/home/baez/bayes.html
'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'

Thanks
Bill

 

[cube137]

There is the QM formalism that all interpretations have. The usual form of Schrodinger's equation is part of that formalism.

The diffference between interpretations hinges on things other than the formalism.

1. Copenhagen has the idea the state is like the Baysian interpretation of probability.
2. MW has the interpretation the state of the universe as very real, but when decoherence happens in the mixed state that results each outcome is a separate world. Everything simply evolves according to Schrodinger's equation. It uses the decision theory approach to probability
3. BM uses any interpretation of probability - the particle has actual position and velocity at all times - you use probabilities because according to QM you can't know initial conditions with certainty ie you can't know both position and momentum at the same time.

Interpretations are at least partially just arguments about of interpretations of probability:
http://math.ucr.edu/home/baez/bayes.html
'It turns out that a lot of arguments about the interpretation of quantum theory are at least partially arguments about the meaning of the probability!'

Thanks
Bill

Have you not heard about the problems of how to define preferred basis (like positions) in Many worlds? how do you connect this with what you mentioned above?

 

[bhobba]

Have you not heard about the problems of how to define preferred basis (like positions) in Many worlds? how do you connect this with what you mentioned above?

Yes.

Many are BS, but some are legit eg the so called factorization problem. Decoherence explains it in all interpretations including many worlds with a few caveats such as the factorization issue I mentioned. IMHO much too much is made out of that and similar issues, but it is legit.

You will find a discussion in the textbook I gave before - but it is not at the beginner level - unfortunately the questions you are asking are not answerable at the beginner level except in very broad terms.

If you want to understand MW you must study its detail:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Unfortunately it is an advanced I level text - meaning upper undergraduate with at least a first proper course in QM.

Thanks
Bill

 

[PeterDonis]

In General Relativity. Gravity is caused by curvature of spacetime.

Yes, but this is a classical theory, not a quantum theory. It is not relevant to the question you are asking in this thread.

Imagine the vacuum of the Higgs. It's not zero but forced to choose a Vacuum Expectation Value.

Yes, but that's true in any basis.

 

[cube137]

The basis is chosen in theory ie the position basis is implicit in the normal form of the Schrodinger equation. When expressed in that basis virtually all interactions turn out to be radial ie the V(x) in the Schrodinger equation. Its purely arbitrary what basis you chose to write your equations in - writing them in the position basis is what's usually done and you can easily see their radial nature.

Thanks
Bill

But in Many Worlds how is the position basis chosen when the wave function "must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilitie"? are you saying the following is BS? Please comment this.

https://arxiv.org/abs/quant-ph/0110148

"This section identifies the core basis problem. The essential point is that if the universe has been evolving since the big bang in accordance with the Schrödinger equation, then it must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilities. Indeed, the planet Earth would not have a well-defined location, nor would the rivers and oceans, nor the cities built on their banks. Due to the uncertainty principle, each particle would have had a tendency to spread out. Thus various particles with various momenta would have been able to combine and condense in myriads of ways into bound structures, including measuring devices, whose centers, orientations, and fine details would necessarily be smeared out over continua of possibilities. The quantum state would be, to first order, a superposition of a continuum of slightly differing classical-type worlds with, in particular, each measuring device, and also each observing brain, smeared out over a continuum of locations, orientations, and detailed structures. But the normal rules for extracting well-defined probabilities from a quantum state require the specification, or singling out, of a discrete set (i.e., a denumerable set) of orthogonal subspaces, one for each of a set of alternative possible experientially distinguishable observations. But how can a particular discrete set of orthogonal subspaces be picked out from an amorphous continuum by the action of the Schrödinger equation alone?"

 

[bhobba]

But in Many Worlds how is the position basis chosen when the wave function "must by now be an amorphous structure in which every device is a smeared-out cloud of a continuum of different possibilitie"? are you saying the following is BS?

Partially BS, partially the factorization problem.

You have started a B level thread for at least an I level issue.

The answer of how that basis is singled out is as I told you before. Its detail can be found in the standard reference I gave.

The reference you gave is at least I level, probably A level - it can't be discussed at the B level.

You just have to take the word of the experts here - the solution is well known.

If not then you have 2 options:

1. Learn the technicalities yourself and study the references I gave.

2. Get Dr Stapp to come and argue his case here.

The other thing I need to mention is the modern version of MW you will find in Wallace is based on the idea of history which clarifies many (but not all) issues. I suspect Stapp has not gone into its detail. The thing is this, MW is basically Consistent Histories without the Many Worlds. You prove one wrong - down goes the other. Consistent Histories is basically the modern version of Copenhagen that fixes a blemish it has. In Copenhagen QM is a theory about observations that appear in an assumed commonsense classical world. How such a world emerges from a theory that assumes it in the first place is an issue. Consistent Histories and other modern interpretations based on decoherence fixes that - not entirely - some issues still remain, but most think they are nothing to really worry about.

You will find the state of play here (it's a B level reference):
https://www.amazon.com/dp/0691004358/?tag=pfamazon01-20

BTW Stapp, while a legit scientist and researcher, is well known to hold views outside the mainstream.

Thanks
Bill.

 

[Demystifier]

So in Hilbert Space (of environment), preferred basis of position is chosen ad hoc.. what is the corresponding dynamics causing it.. anyone?

In MWI, the preferred basis problem is much more serious than in other interpretations
https://www.physicsforums.com/threads/many-worlds-proved-inconsistent.767809/

For instance, in BM one can pick the position as a preferred observable simply because it leads to results which agree with observations. In principle one can do that even in MWI, but this breaks the spirit of MWI.

 

[bhobba]

In MWI, the preferred basis problem is much more serious than in other interpretations

Its the legit Factorization problem I mentioned before.

Its worse in MW because it does not explicitly assume the existence of structure like other interpretations do.

I have never however seen exactly why the same issue doesn't occur in Decoherent Histories which as far as I can see doesn't either.

If you read Walllace's book its all based on Histories - not structure.

Thanks
Bill

 

[Demystifier]

I have never however seen exactly why the same issue doesn't occur in Decoherent Histories which as far as I can see doesn't either.

Good point!

 

[bhobba]

Good point!

Yes. If you read the book Understanding QM, which basically elucidates decoherent histories, I gave the link to (it's at the beginner level) it points out a number of key theorems are missing. The factorization problem is one of them. We need theorems to elucidate exactly what happens with different factorizations - if so under what conditions - its a minefield that needs more work.

I don't think at this stage it can be used to rule out MW, Decoherent Histories etc, but more work is required.

Thanks
Bill

 

[Demystifier]

If you read Walllace's book its all based on Histories - not structure.

You mean Omnes, not Wallace, right?

 

[bhobba]

You mean Omnes, not Wallace, right?

Yes - sorry for not being clear.

Although Wallace gives the modern version of MW it is not at the B level and not suitable for the OP.

Thanks
Bill

 

[bhobba]

Just to show the OP this emergence of a classical world is NOT universally accepted as not possible (in fact I am pretty sure most scientists are like me and think saying it must be like that is BS) see:
http://rsta.royalsocietypublishing.org/content/370/1975/4566

Is the above right? Who knows - we need a lot more work here which is why articles like Stapp annoy the bejesus out of me and confuse beginners unnecessarily IMHO.

Thanks
Bill

 

[cube137]

Yes. If you read the book Understanding QM, which basically elucidates decoherent histories, I gave the link to (it's at the beginner level) it points out a number of key theorems are missing. The factorization problem is one of them. We need theorems to elucidate exactly what happens with different factorizations - if so under what conditions - its a minefield that needs more work.

I don't think at this stage it can be used to rule out MW, Decoherent Histories etc, but more work is required.

Thanks
Bill

Hi Mr. Hobba. I finally received this book "Understanding Quantum Mechanics" by Roland Omnes that you recommended. But I couldn't find the topic about Factorization (which was why I bought it). Can you please review your book when you have time and please share what pages are they in. Also I tried to find the pages where it says key theorems are missing. I couldn't find them either. I think you mistaken it for another book?

 

[bhobba]

Hi Mr. Hobba. I finally received this book "Understanding Quantum Mechanics" by Roland Omnes that you recommended. But I couldn't find the topic about Factorization (which was why I bought it). Can you please review your book when you have time and please share what pages are they in. Also I tried to find the pages where it says key theorems are missing. I couldn't find them either. I think you mistaken it for another book?

Sorry. I can see how my wording would indicate he did mention the factorization problem. He doesn't - but does mention other unresolved issues eg see page 206. My recollection is that is not the only one either but I would have to go through the book to find them.

But the factorization problem has a number of papers about it eg:
https://arxiv.org/abs/1210.8447

However the link I gave above makes some conjectures on how structure can emerge.

Right now that's where it stands - we don't know.

But you have not wasted your money on that book - ts very good and at what I would call the B level.

Thanks
Bill

 

[cube137]

In MWI, the preferred basis problem is much more serious than in other interpretations
https://www.physicsforums.com/threads/many-worlds-proved-inconsistent.767809/

For instance, in BM one can pick the position as a preferred observable simply because it leads to results which agree with observations. In principle one can do that even in MWI, but this breaks the spirit of MWI.

Dear Demystifier. Having mastered the subject.. is it possible MWI uses Spacetime itself as the Preferred Basis? Without Spacetime, you don't have position basis... But can the wave function in Hilbert space itself with vector rays not in any basis also occur inside Spacetime?

 

[stevendaryl]

Its caused by the radial nature of most interactions.

The reason is technical but is explained in detail here:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

For those who don't have that book, can you summarize what, exactly, is the nature of the preference for position?

The way I understand decoherence mathematically is this:

• You start with some complex system with many components (I guess infinitely many in QFT).
• You form the density matrix for the composite system.
• You trace out the unobservable "environmental" degrees of freedom (typically, the electromagnetic field).
• What's left is a density matrix for the system(s) of interest, and voila, you have a mixed state.

So is the claim that this process naturally results in a mixed state in which massive objects have more-or-less well-defined positions?

 

[stevendaryl]

Its the legit Factorization problem I mentioned before.

Its worse in MW because it does not explicitly assume the existence of structure like other interpretations do.

I have never however seen exactly why the same issue doesn't occur in Decoherent Histories which as far as I can see doesn't either.

My understanding of Decoherent Histories (like my understanding of most advanced topics) is pretty superficial. But here's the way I think about it:

It starts off sort of like MWI, where you just have pure evolution of the wave function. But then to get "histories" out of this evolution, you pick a time-slicing of history, and pick a set of projection operators (satisfying the consistency constraint). Then you can interpret the deterministic evolution of the wave function as a way of getting probabilities for histories.

That's sort-of nice, but I'm a little confused about the role of the choice of projection operators. For a given choice, we get a stochastic model for the evolution of the universe. But we could have chosen a different set of projection operators, and we would have gotten a different stochastic model. So is there supposed to be an objective set of the actual projection operators (and if so, how are they determined?), or is the history of the universe subjective, relative to the set of projection operators you prefer?

 

[bhobba]

For those who don't have that book, can you summarize what, exactly, is the nature of the preference for position?

I dug up my copy and went through it. Of course it took me some time to locate the exact page. Its page 83 under the heading of Selection Of Quasi-Classical Properties.

Its because, typically for radial type interactions ie those depending on some power of distance eg proportional to 1/r2, the position operator commutes with the Hamiltonian. Now on page 77 he proved what is commonly called the commutativeity criteria that says if the associated observable commutes with the Hamiltonian, then the resultant eigenstates (also called pointer states) must be stable ie is the only possible basis it can be diagonal in after decoherence. It's pretty obvious anyway because its well known that if an observable commutes with the Hamiltonian its conserved. But of course the exact implication for pointer states needs to be detailed - which is what's done on page 77. It is also detailed on page 4 of the following:
http://faculty.up.edu/schlosshauer/publications/decoherence_book.pdf

For issues related to the factorization problem (there its called the closed universe objection) see section 4 page 5)

But I have to say at the beginner level this will largely be gibberish. It really requires at least an I level thread and someone with sufficient time to post the relevant details. It would be even better to get the book and go through it yourself like with Omnes book.

Thanks
Bill

 

[bhobba]

or is the history of the universe subjective, relative to the set of projection operators you prefer?

Decoherent Histories is a nice interpretation and I like it. In it QM is the stochastic theory of histories. It is also exactly the same as the modern version of MW as detailed in Wallace's book except instead of one history being singled out as actually occurring they all do - except in separate worlds.

I personally don't hold to it because its looks too much to me like defining your way out of problems - but that's just my personal reaction, so means the prize sum of zilch.

All interpretations are equally as good or equally as bad - one chooses one based on personal preferences which mean absolutely nothing - scientifically of course. Now as fodder for the endless machinations of philosophers - well that's another matter. That of course, despite my well known penchant for tweaking philosophy types a bit, in no way demeans philosophy, it just approaches things differently.

Thanks
Bill

 

[Demystifier]

is it possible MWI uses Spacetime itself as the Preferred Basis?

It's possible.

 

[cube137]

It's possible.

Do you have any references that described it?

 

[Demystifier]

Do you have any references that described it?

No. MWI people don't like it.

 

[cube137]

No. MWI people don't like it.

Why?

 

[Demystifier]

Why?

MWI people like MWI because it is mathematically elegant. With a priori preferred basis it ceases to be mathematically elegant.

 

[Demystifier]

For those who don't have that book, can you summarize what, exactly, is the nature of the preference for position?

The way I understand decoherence mathematically is this:

• You start with some complex system with many components (I guess infinitely many in QFT).
• You form the density matrix for the composite system.
• You trace out the unobservable "environmental" degrees of freedom (typically, the electromagnetic field).
• What's left is a density matrix for the system(s) of interest, and voila, you have a mixed state.

You only described kinematics. Decoherence involves also the dynamics i.e. depends on the Hamiltonian.

So is the claim that this process naturally results in a mixed state in which massive objects have more-or-less well-defined positions?

Yes, but that's related to the fact that Hamiltonian is local in the position basis.

 

[martinbn]

.. is it possible MWI uses Spacetime itself as the Preferred Basis?

It's possible.

And what does this even mean!? To use spacetime as a basis!

 

[Demystifier]

And what does this even mean!? To use spacetime as a basis!

See
https://arxiv.org/abs/0904.2287
Sec. 3.2.

 

[martinbn]

See
https://arxiv.org/abs/0904.2287
Sec. 3.2.

Not sure how this clarifies the problem. The statement was that the space-time is used as a basis. That's complete nonsense. The statement wasn't to use the space-time, or some property of it, to produce in some canonical way a basis of the Hilbert space. It was that space-time can be a basis!

 

[Demystifier]

Not sure how this clarifies the problem. The statement was that the space-time is used as a basis. That's complete nonsense. The statement wasn't to use the space-time, or some property of it, to produce in some canonical way a basis of the Hilbert space. It was that space-time can be a basis!

Precise statements are always welcome, but in their absence it is equally welcome to distinguish what one said from what one meant.