# I Nonclassicality described mathematically

#### jlcd

Ruth Kastner used to say that without collapse, there was no decoherence. I'd like to know if Hilbert space can store information nonclassically.. that is.. without using any position basis.

For example. Can atoms exist without any position basis? How many atomic combinations or molecules can you combine that doesn't use the position basis?

Can you transfer the information of an object with position into other basis in Hilbert space and then reform the object back into classicality? (Theoretically *assuming* Ruth was right an object need to collapse first before there was even decoherence or classicality or the paper like "Nothing Happens in Many Worlds" or similar ideas?)

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#### DarMM

Gold Member
Are you referring to Kastner's paper here about einselection:

If not, can you post a link.

#### PeterDonis

Mentor
I'd like to know if Hilbert space can store information nonclassically.. that is.. without using any position basis.
The Hilbert space doesn't "use" any basis. A choice of basis is a convenience for us humans trying to do calculations. It has nothing to do with the physics.

The questions in the rest of your post are not answerable because they are all based on this erroneous premise.

#### jlcd

The Hilbert space doesn't "use" any basis. A choice of basis is a convenience for us humans trying to do calculations. It has nothing to do with the physics.

The questions in the rest of your post are not answerable because they are all based on this erroneous premise.
In classical objects. Position is preferred basis.

We use the positions of objects as a choice of basis and the positions and physics is more primary than Hilbert space?

And instead of asking how we can shift the basis in Hilbert space so objects would no longer have position. We should instead manipulate the physics such as doing experiments and removing the positions (changing to momentum instead for example)?

Or it it interpretation defendent? In Kastner, Tegmark, Schwindt (author of the paper "Nothing Happens in Many Worlds). The state vectors are the matter themselves. Not state vectors modelling the objects. I guess its interpretation defendent?

#### PeterDonis

Mentor
In classical objects. Position is preferred basis.
I don't know what you even mean by "position is preferred basis" if we are talking about classical physics, since classical physics doesn't even use Hilbert space.

We use the positions of objects as a choice of basis and the positions and physics is more primary than Hilbert space?
I don't understand what you're asking. I suspect you have some basic misunderstandings about how quantum mechanics works, and you are trying to tackle a very advanced topic in QM, which requires a firm understanding of the foundations. That doesn't seem like it's going to work out well.

how we can shift the basis in Hilbert space so objects would no longer have position
I have no idea what you're talking about. In the Hilbert space of a single free particle in one dimension (which is the simplest Hilbert space that has a "position" observable), position is a valid observable whether we use the position basis or the momentum basis. So changing basis from position to momentum in no way means "objects would no longer have position". Again, you seem to have some basic misunderstandings about how QM works.

We should instead manipulate the physics such as doing experiments and removing the positions
This is nonsense.

I guess its interpretation defendent?
I have no idea because I can't understand what you're talking about.

#### jlcd

I don't know what you even mean by "position is preferred basis" if we are talking about classical physics, since classical physics doesn't even use Hilbert space.

I don't understand what you're asking. I suspect you have some basic misunderstandings about how quantum mechanics works, and you are trying to tackle a very advanced topic in QM, which requires a firm understanding of the foundations. That doesn't seem like it's going to work out well.

I have no idea what you're talking about. In the Hilbert space of a single free particle in one dimension (which is the simplest Hilbert space that has a "position" observable), position is a valid observable whether we use the position basis or the momentum basis. So changing basis from position to momentum in no way means "objects would no longer have position". Again, you seem to have some basic misunderstandings about how QM works.

This is nonsense.

I have no idea because I can't understand what you're talking about.
In an important thread about the emergence of classical world.. "Why does nothing happen in MWI"

You have contributed in post 33:

"The problem, according to Schwindt, is that the MWI doesn't have any states other than "the pure state of the entire universe". For example, when you say "cats decohere", you are assuming that there are "cats" picked out somewhere as identifiable quantum states. But if all we have is the pure state of the universe, there are no "cats"--or humans, or anything else. So you don't even have the structure needed to talk about "decoherence" at all."

I'm familiar with the arguments. You emphasized in post 43:

"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? If your answer to that is "well, that's the basis in which we have cats that are either dead or alive, instead of a superposition of dead and alive", then you're arguing in a circle."

Demystifier points: "Essentially, Tegmark proposes that the preferred basis is determined by consciousness. It could be true, but he certainly does not derive consciousness from MWI. Instead, one has to postulate consciousness as an independent assumption. I am fine with it, but this only confirms what I already said that pure MWI (i.e. MWI without any additional assumptions) cannot solve the problem. One has to assume something additional, be it Copehangen observers, Tegmark cosciousness, Bohmian trajectories, or something else."

In December of 2015 that year I wrote the thread Momentum Basis Dynamics to ask something about it.

Now 4 years later I want to clarify something so I hope you can answer it thoroughly before closing this thread and not let me wait another 4 years to ask it.

What I simply want to know is if you can override the additional structure.. be it Copenhagen observers, Tegmark consciousness, Bohmian trajectories or something else. Can you still retain the information of say a piece of balloon?

First I'm so familiar with decoherence.

Collapse or something like it produced mixed state from pure state by entangling with environment degrees of freedom. So atoms exist in the pure MWI because of the additional structure.

I'd like to know (once and for all) whether if you can remove the additional structure, and it's back to pure MWI. Whether physical objects can retain the information. For example if you can remove the additional structure from the cat in pure MWI. Then the cat would cease to be a cat and all the organs and cells would disassemble? Fine. But if you reintroduce the additional structure. Can it reform into a cat? Somehow the information is not loss switching from pure MWI with additional structure back to pure MWi and back?

Can you please answer this as I don't want to spent another 4 years thinking about it. So close this thread only after I have understood it please and/or clarify some questions or I'd suffer 4 more years contemplating on it. Lol. Thank you!

#### PeterDonis

Mentor
In December of 2015 that year I wrote the thread Momentum Basis Dynamics to ask something about it.
And that thread was closed because you were unable to make clear what you were asking. This thread is going the same way.

What I simply want to know is if you can override the additional structure
I'm sorry, but this question still makes no sense. You just quoted a bunch of posts from a thread whose topic was a paper arguing that there is no "additional structure" according to the MWI. Are you trying to use the MWI? If so, what "additional structure" are you talking about, since the thread you quoted from is arguing that there is none? If you are not using the MWI, what was the point of all those quotes from a thread discussing the MWI?

Collapse or something like it produced mixed state from pure state by entangling with environment degrees of freedom. So atoms exist in the pure MWI because of the additional structure.
Again, what additional structure? Remember, again, that in the thread you quoted all those posts from, the argument was that there is no additional structure.

I'd like to know (once and for all) whether if you can remove the additional structure, and it's back to pure MWI. Whether physical objects can retain the information.
What information are you talking about?

For example if you can remove the additional structure from the cat in pure MWI. Then the cat would cease to be a cat and all the organs and cells would disassemble? Fine. But if you reintroduce the additional structure. Can it reform into a cat? Somehow the information is not loss switching from pure MWI with additional structure back to pure MWi and back?
None of this makes any sense. You do understand that the MWI is an interpretation of QM, right? All interpretations agree about all experimental predictions, so you can't change the actual physics by changing interpretations. But you're talking as if you can change the physics by changing interpretations--as if switching to the MWI from some other interpretation can make a cat disassemble, and then switching back to the other interpretation can make it reassemble again. That's nonsense.

I've done the best I can to answer given that your questions don't really make sense. I strongly suggest that you stop trying to delve into advanced topics in QM until you have mastered the very basics, which you don't seem to have a good grasp on.

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