# Momentum Basis Dynamics

#### jlcd

Can you describe or how does one visualize a decoherence branch where the position basis is not preferred (copenhangen, bohmian) but momentum basis (as say one of the Everett).

Or if a world has position basis disallowed (suppressed for sake of discussion) and it's all momentum basis.. would there be physical objects, would there be form or would we have blobs of momentum only (and how does one visualize this).

I have spent 3 days reading about decoherence in dozens of papers suggested by Hobba and company and this is what I need to know at this point. Thank you.

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#### bhobba

Mentor
Can you describe or how does one visualize a decoherence branch where the position basis is not preferred
The position basis is nearly always singled out - there is a general argument based on radial interactions ie interactions without a preferred direction. It is independent of interpretation. In cases (usually experimentally contrived) where you measure energy or momentum the setup singles out a different basis. There is nothing else to it - no visualisation etc etc. Its simply the 'observational' setup.

Thanks
Bill

#### jlcd

You are saying that in Many worlds, there will be no branches without position basis?

Remember there are branches where the cat is dead and alive plus 1/2 dead and alive plus 1/4 dead and 1/8 alive as the superposition can be decomposed in any combination. So I was wondering if there was combination where there is no position basis selection but only momentum basis.

#### bhobba

Mentor
You are saying that in Many worlds, there will be no branches without position basis?
Of course not. Why you would think that has me beat.

Remember there are branches where the cat is dead and alive plus 1/2 dead and alive plus 1/4 dead and 1/8 alive as the superposition can be decomposed in any combination. So I was wondering if there was combination where there is no position basis selection but only momentum basis.
That's false. The cat is never in superposition - end of story. Its in a mixed state which is different to a superposition:
http://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf

Here is what's happening in Schroedinger's cat. Decoherence occurs at the particle detector so you get a mixed state of particle detected or particle not detected. Everything is common-sense classical from that point on. You can go the whole hog and think of the cat and the other paraphernalia as entangled with the detector and hence also in a mixed state of dead or alive. But there is no need for that - simply say the observation occurred at the particle detector and everything is sweet.

Thanks
Bill

#### jlcd

That's false. The cat is never in superposition - end of story. Its in a mixed state which is different to a superposition:
http://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf

Here is what's happening in Schroedinger's cat. Decoherence occurs at the particle detector so you get a mixed state of particle detected or particle not detected. Everything is common-sense classical from that point on. You can go the whole hog and think of the cat and the other paraphernalia as entangled with the detector and hence also in a mixed state of dead or alive. But there is no need for that - simply say the observation occurred at the particle detector and everything is sweet.

Thanks
Bill
I'm aware of what you were describing. I was inquiring whether any of the mixed state of many worlds can occur without any position basis. Remember in the beginning it's all Hilbert space.. all decompositions or combinations occur.. resulting in many kinds of mixed state.. there should be one where there is no position basis..

#### bhobba

Mentor
I'm aware of what you were describing. I was inquiring whether any of the mixed state of many worlds can occur without any position basis.
Of course it can. All that's happening in MW is you interpret the parts of the mixed state after decoherene as different worlds. If you have a momentum observation then the mixed state is in the momentum basis.

One of the things that decoherence solves is the preferred basis problem - it singles out the basis of the resultant mixed state.

The measurement problem has three parts:
1. Why we generally don't see interference effects. Decoherence solves that easily.
2. The preferred basis problem ie why is say a position basis singled out. Decoherence solves that - but with more work. It turns out that most of the time a position basis is singled out - but most of the time is not all of the time - sometimes its momentum, or energy, or something else.
3. Why we get any outcomes at all. Technically how does an improper mixed state become a proper one. Most interpretations stand powerless before that - but MW doesn't have that issue - its trivial. Each part of the mixed state is a separate world.

Thanks
Bill

#### jlcd

The law of physics (like constants of nature) is the same in all branches of the many worlds? I thought they could differ. What is the principle or theorem that disallow or allow it?

#### Nugatory

Mentor
The law of physics (like constants of nature) is the same in all branches of the many worlds? I thought they could differ. What is the principle or theorem that disallow or allow it?
MWI says that if I start with a wave function that is a superposition of A and B, I'll end up with two worlds. In one of the them the Copenhagen crowd will be saying that the superposed wave function collapsed to A; in the other they'll be saying that it collapsed to B. If the laws of physics could be different between the branches, then in at least one of the branches we'd be seeing them changing across the observation that led to the collapse or split - and that's contrary to our experience.

#### bhobba

Mentor
The law of physics (like constants of nature) is the same in all branches of the many worlds? I thought they could differ. What is the principle or theorem that disallow or allow it?
Just think about what's going on.

Instead of one part of the mixed state being the one that occurs they all occur but in separate worlds. Since any outcome keeps the same laws of physics obviously each world has the same laws.

Thanks
Bill

#### jlcd

Ok. Thank you. I think my level of question is in this context. In Bohmian mechanics, position is the preferred basis. What if there was a Bohmian Mechanics where momentum (instead of the position) is the preferred basis or hidden variable. Then what will happen to position of objects? Or what would a world with BM that has position vs momentum preferred (as hidden variable) differ? I think this is my question.

#### bhobba

Mentor
Ok. Thank you. I think my level of question is in this context. In Bohmian mechanics, position is the preferred basis
Since BM has been cooked up to be equivalent to standard QM its exactly the same. You can get position basis, momentum basis etc etc - there is none preferred.

However it also resolves the outcomes issue trivially since the particle has position, momentum energy etc at all times.

Thanks
Bill

#### jlcd

Since BM has been cooked up to be equivalent to standard QM its exactly the same. You can get position basis, momentum basis etc etc - there is none preferred.

However it also resolves the outcomes issue trivially since the particle has position, momentum energy etc at all times.

Thanks
Bill
I guess my confusion can be traced to this odd thing called Factorization. You always said whenever this is mentioned. there is hot debate.. but note you only have debate about this with Ruth Kastner in the archives.. not with others. So since she doesn't participate anymore, there will be no debates.. especially with newbies or even experts who may not be familiar with it. For us newbies.. we just want a clear treatise on it. Do you have other references of the basic about Factorization besides the ones already shared in this room? Because it seems that Many worlds alone can't create any outcome. You have to add hidden variable to it to get the Factorization. This means Many worlds must have Bohmian Mechanics in combination for it to work to produce any outcome. Or Quantum Darwinism to produce it.. but then Quantum Darwinism still need a classical hidden variable to produce any Factorization since Quantum Darwinism is purely Hilbert Space. You can't argue that the quantum fluctuations being random can give quantum Darwinism factorization.. it seems a separate problem. I think Scientific American or other sci magazines must present this clearly to the public.

#### bhobba

Mentor
I guess my confusion can be traced to this odd thing called Factorization. You always said whenever this is mentioned. there is hot debate.. but note you only have debate about this with Ruth Kastner in the archives.. not with others.
I seem to remember it with others eg Quantumental.

Forget about it. Its a fringe issue and seems to worry philosophy types more than mathematicians like myself. Do you really think how you divide a system for analysis is a critical thing? I dont, and it seems rather obvious to me. But everyone's different.

Thanks
Bill

#### jlcd

I seem to remember it with others eg Quantumental.

Forget about it. Its a fringe issue and seems to worry philosophy types more than mathematicians like myself. Do you really think how you divide a system for analysis is a critical thing? I dont, and it seems rather obvious to me. But everyone's different.

Thanks
Bill
In a few words that summarize the main idea. What is the connection of Factorization to Preferred Basis. Is it right the choice of Factorization can affect the Preferred basis?

#### bhobba

Mentor
In a few words that summarize the main idea. What is the connection of Factorization to Preferred Basis. Is it right the choice of Factorization can affect the Preferred basis?
None. Factorisation is simply the idea how you decompose a system gives different results. Its always decomposed in the obvious way - what does the observing, what is being observed, and maybe the environment. Those that harp on about factorisation think if you decompose it differently you get a different result.

Thanks
Bill

#### jlcd

I have been reading one of Tegmark paper mentioned in your past conversations with others and I came across this line "Finally, out of all the possible factorizations of Hilbert space, why is the particular factorization corresponding to classical space so special? Why do we observers perceive ourselves are fairly local in real space as opposed to Fourier space, say, which according to the formalism of quantum field theory corresponds to an equally valid Hilbert space factorization?"

I'd like to know about Fourier space, is it a legal mixed state? Tegmark asked why we were in classical space and not in Fourier space, was he talking about after decoherence? This means Fourier space is not a superposition but a legal mixed state, is this about right? Thank you.

#### bhobba

Mentor
I'd like to know about Fourier space, is it a legal mixed state?
Who knows what Tegmark means - I find him particularly opaque and to be blunt, sometimes downright silly (eg his writings on quantum suicide)

His fellow MIT professor is more my style:
http://www.scottaaronson.com/democritus/lec9.html

But my reaction to the above is if you do a Fourier transform on a wave-function you go from position space to momentum space. The reason position space is more useful is the position basis is usually singled out rather than momentum.

Thanks
Bill

#### jlcd

Who knows what Tegmark means - I find him particularly opaque and to be blunt, sometimes downright silly (eg his writings on quantum suicide)

His fellow MIT professor is more my style:
http://www.scottaaronson.com/democritus/lec9.html

But my reaction to the above is if you do a Fourier transform on a wave-function you go from position space to momentum space. The reason position space is more useful is the position basis is usually singled out rather than momentum.

Thanks
Bill
The paper is in message 163 in this thread you also participated https://www.physicsforums.com/threads/why-does-nothing-happen-in-mwi.822848/page-2

We won't discuss Tegmark stuff but just the meaning of Fourier Space or the general meaning of classically being singled out by decoherence.. Specifically I'd like to know example of mixed state that is not classical.. can you cite any?

#### bhobba

Mentor
TSpecifically I'd like to know example of mixed state that is not classical.. can you cite any?
First explain what you mean by a mixed state that is not classical. Classical in the sense of mixed states I would take to mean the absence of interference terms so classical probability applies.

Thanks
Bill

#### jlcd

Based on Mentor Peterdonis own words in message #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."

So by mixed state that is not classical. Maybe cat-dog combination factorization? So instead of a cat or dog.. we have half cat and half dog as legal mixed state (that is unclassical).. why don't we have them after decoherence is the question. So do you agree that half cat and half dog is unclassical mixed state?

#### bhobba

Mentor
Maybe cat-dog combination factorization?
I said before:
Factorisation is simply the idea how you decompose a system gives different results. Its always decomposed in the obvious way - what does the observing, what is being observed, and maybe the environment. Those that harp on about factorisation think if you decompose it differently you get a different result.
What Peter wrote doesn't change the above. All he is adding is you need to be able to determine what is each of parts in the first place. There is no quantum rules to determine that.

Thanks
Bill

#### jlcd

Reading that thread over again. I think you are having a mixed state or classical bias. In that you think the world is simply after decoherence or mixed state.. and you have the familiar classical objects and hence think purely classical with only probability math to contemplate. I think what Tegmark, Peterdonis and even Demystifier are up to is contemplating on what occurs before decoherence.. and Tegmark context means one can navigate the Hilbert Space prior to decoherence. Here you can see cat and dog in one body etc. Is my observation correct? The application of this is that if you can control the additional structure that gives the classical factorization in Hilbert Space, and say aim it at the cat.. you can make it change to a dog. Is at least my understanding of the concepts and differences correct?

#### bhobba

Mentor
structure that gives the classical factorization in Hilbert Space,
I have zero idea what you mean by that.

I think you are getting confused by terms and not using them in a way I can follow.

I will have to leave it to others to help.

Thanks
Bill

#### jlcd

I have zero idea what you mean by that.

I think you are getting confused by terms and not using them in a way I can follow.

I will have to leave it to others to help.

Thanks
Bill
It's very simple. Tegmark, Peterdonis, Demystifier focus on what caused the collapse or more technically what happens before decoherence. In your case. You totally focus on what happens after decoherence. You almost reject any effort of investigation of what occurs before decoherence or what caused collapse. You got tired thinking of them and hence become an Emsembler or playing with statistics as this is what the density matrix and mixed state result is all about and you just want to narrow your interest specifically to them. I'm correct, am I not.

#### jlcd

I'm tracing Mr. Hobba confusion of my confusion.

The conventional meaning of Many World is there are classical branches in each world like the electron passing via left and right as 2 worlds or branches.
But what Tegmark, Peterdonis, Demystifier are saying is that in Many worlds without special structure to produce classicality, the many world is nothing but the Hilbert Space where everything is in ghostly superposition. So what produce the decoherence is the additional structure. What is this additional structure? The consequence of this is that if you suppress this additional structure in the cat.. it can turn into a dog where there is changing of the basis (say of position) from reordering the additional structure. Can anyone see any flawed understanding of mine in understanding their arguments?

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