What Happens to a Cat in a Box Without Factorization?

[cube137]

In interpretations without natural factorizations, the cat won't just be dead or alive. It won't even be a cat. So let's say the cat is isolated in a box totally shielded from any decoherence from any environment.. and the any factorization between system and environment inside the box is suppressed.. what would become of the cat? just a blob or without any form? Would it's brain still work even if it's not a classical brain but totally composed of wave function without any factorization? How can you imagine, visualize or think of dynamics of wave functions without factorization and without any collapse?

 

[A. Neumaier]

let's say the cat is isolated in a box totally shielded from any decoherence from any environment

It will die very quickly due to suffocation.

 

[bhobba]

In interpretations without natural factorizations, the cat won't just be dead or alive.

That's incorrect.

Any interpretation contains the QM formalism. And from that formalism alone deoherence occurs and the cat is dead or alive.

Don't be confused by the factorisation issue - it's not what some make it out to be. Its not that a quantum system can't be factored into cats etc, its that decoherence MAY depend on that factorisation. As yet theorems are lacking to decide the issue one way or another. It's a very fringe issue - and for good reason - similar assumptions are made in many areas of physics and it would be silly to think that are all 'wrong'. I remember one discussion on it where it was shown even classical mechanics has the problem - but few would doubt that branch of science in its domain of applicability.

Thanks
Bill

 

[bhobba]

It will die very quickly due to suffocation.

Just to elaborate a bit further things like cats etc gain their classicality from interaction with the environment. Remove that environment and they would not even be alive - the biochemical processes simply can't exist.

Thanks
Bill

 

[jfizzix]

what would become of the cat? just a blob or without any form? Would it's brain still work?

If the environment inside the box is completely decoupled from the environment outside the box, then that only means that the cat in the box is totally independent of the environment outside. Before its air runs out, it wouldn't know anything weird is going on, other than that it's stuck in a box.

Our (on the outside) best estimate of what's going on inside the box is our knowledge of the quantum state of everything inside the box, and our knowledge of the equation of time evolution for the environment inside the box given by the total energy and interactions of all particles inside. Putting all that together, we can get some unusual estimations, like that there's a state that containes both live-cat and dead-cat possibilities, but just as we will only ever see one of these possibilities when we look inside the box. we can imagine the cat only experiences one of these possibilities as well.

This too, is a matter of interpretation.

 

[cube137]

That's incorrect.

Any interpretation contains the QM formalism. And from that formalism alone deoherence occurs and the cat is dead or alive.

Don't be confused by the factorisation issue - it's not what some make it out to be. Its not that a quantum system can't be factored into cats etc, its that decoherence MAY depend on that factorisation. As yet theorems are lacking to decide the issue one way or another. It's is a very fringe issue - and for good reason - similar assumptions are made in many areas of physics and it would be silly to think that are all 'wrong'. I remember one discussion on it where it was shown even classical mechanics has the problem - but few would doubt that branch of science in its domain of applicability.

Thanks
Bill

For sake of discussions. Supposed there were no factorizations of any kind and the cat has no classical correlates and composed of pure wave function. How would the cat behave? Or let's take the case of simple particles. What would happen if the electrons had no factorizations of any kind.. how do you characterize the electrons? Or are wave functions and factorizations always go together. I was then asking what if you separate them.

 

[bhobba]

For sake of discussions. Supposed there were no factorizations of any kind

How do you know you have a cat in there if the system hasn't been factored into cat and rest of the set-up? In Schroedinger's Cat you have precluded no factorisation by the very set-up of the experiment.

With electrons you have precluded they can't be factored into electrons and the rest by discussing electrons in the first place. They are excitations of the electron field and that field is everywhere.

It like the immovable object meets the irresistible force - its a non-sense statement because the universe can't contain both by the definition of the terms used.

Thanks
Bill

 

[cube137]

How do you know you have a cat in there if the system hasn't been factored into cat and rest of the setup?

Thanks
Bill

Say you put a cat in the totally isolated box (with oxygen). And you suppress the bohmian natural factorization of position. What would happen to the cat. Would it just vanish physically?". If you can weaponize this. Then aim the factorization suppressor gun at any object and it can vanish. Wouldn't it.

 

[bhobba]

And you suppress the bohmian natural factorization of position

You can't do that in the BM interpretation - objects have well defined positions and momenta at all times.

But outside that interpretation say in the Ignorance Ensemble Interpretation - a cat is put in the box - you have factored it into the cat and the rest of the box by its very set-up. It always remains a cat as classical objects do. It simply dies of suffocation when the oxygen runs out or from being entangled with the radioactive source - whichever comes first. Everything in the box still remains classical.

The very set-up of Schroedinger's Cat precludes your issue. You can't have a system factored into cat and other things then assume it can't be factored - its a logical absurdity. Now if you want to discuss if the cat being dead or alive happens if you factor it differently in your analysis - that is the factorisation problem and as yet we do not know the answer.

Now if you were to truly isolate the box from the environment, and I mean actual isolation - even deep space has CBMR photons floating about - then you would likely have some very very strange effects like what happened with a tuning fork:
http://www.scientificamerican.com/article/quantum-microphone/

But observing such a situation to determine what's happening has me beat - since that will require interacting with it which you can't do if its isolated. I suspect that's where what Jfizzix said comes into play.

Thanks
Bill

 

[cube137]

You can't do that in the BM interpretation - objects have well defined positions and momenta at all times.

But outside that interpretation say in the Ignorance Ensemble Interpretation - a cat is put in the box - you have factored it into the cat and the rest of the box by its very set-up. It always remains a cat as classical objects do. It simply dies of suffocation when the oxygen runs out or from being entangled with the radioactive source - whichever comes first. Everything in the box still remains classical.

The very set-up of Schroedinger's Cat precludes your issue. You can't have a system factored into cat and other things then assume it can't be factored - its a logical absurdity. Now if you want to discuss if the cat being dead or alive happens if you factor it differently in your analysis - that is the factorisation problem and as yet we do not know the answer.

Now if you were to truly isolate the box from the environment, and I mean actual isolation - even deep space has CBMR photons floating about - then you would likely have some very very strange effects like what happened with a tuning fork:
http://www.scientificamerican.com/article/quantum-microphone/

But observing such a situation to determine what's happening has me beat - since that will require interacting with it which you can't do if its isolated. I suspect that's where what Jfizzix said comes into play.

Thanks
Bill

Factoring it is what chooses the position basis in the case of location of the cat. Won't it be possible for the cat to exist as pure wave function without collapsing into any position eigenstates? I guess collapse and factorization occur at the same time, so without them, you have pure wave function. And I'd like to imagine how a cat would behave if it is pure wave function. How can it tell its paws from its stomach for instance?

 

[bhobba]

Factoring it is what chooses the position basis in the case of location of the cat.

Incorrect.

Decoherence does that.

Thanks
Bill

 

[cube137]

Incorrect.

Decoherence does that.

Thanks
Bill

Ok. In interpretations where the wave function has ontological existence. Is it possible for the cat to be composed of wave function without any collapse? This is in contrast to ensemble where it has classical permanence. The former has extra prediction not possible in the latter, the extra prediction that you can uncollapse objects and make it exist as wave function only. If so, how does it feel to be wave function only.

 

[bhobba]

Ok. In interpretations where the wave function has ontological existence. Is it possible for the cat to be composed of wave function without any collapse?

No. Because of decoherence the position basis is singled out and its in a mixed state of position. The technical reason is because most interactions have radial symmetry - the detail can be found in:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

If so, how does it feel to be wave function only.

Entangled objects can't be in a pure state by the definition of a pure state. The whole system can be - but the entangled subsystems cant. Observationally they are in a mixed state.

Now a cat must breathe air - its entangled with the air molecules so can't be in a pure state.

Thanks
Bill

 

[cube137]

No. Because of decoherence the position basis is singled out and its in a mixed state of position. The technical reason is because most interactions have radial symmetry - the detail can be found in:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Thanks
Bill

In intepretations where the wave functions are ontological (Not Ensemble but maybe Quantum Darwinism). Can you think of any experimental setup where you can totally isolate an object like a marble and suppress the position basis by turning it into momentum eigenstates. I'd like to see the object vanishing from physical world. Theoretically is there a way to do even if our present technology is not yet sufficient for this experiment, but possible in say 100,000 A.D.?

 

[bhobba]

isolate an object like a marble and suppress the position basis by turning it into momentum eigenstates

No. We technologically can't totally isolate an actual object from everything - eg we would have to suppress all stray vibrations somehow.

Maybe sometime in the future but not now.

When you do that what will happen will depend on the total set-up like with the tuning fork.

But as technology progresses and we get closer and closer to that expect some strange things to emerge - but without the exact set-up knowing exactly what that is is not possible.

And some vague general set-up is not good enough - you must be exact. And being exact with future technology is impossible otherwise we would have the technology now.

Thanks
Bill

 

[cube137]

[

Entangled objects can't be in a pure state by the definition of a pure state. The whole system can be - but the entangled subsystems cant. Observationally they are in a mixed state.

Now a cat must breathe air - its entangled with the air molecules so can't be in a pure state.

Thanks
Bill

Supposed you were inside a hypothetical box that can isolate against any CMR or even gravity, etc.. your whole body can be said to be the whole system itself and hence you are in pure state. But your head as subsystem is in mixed state. Yet your whole body is purely wave function only (pure state). Is this an accurate description? Supposed there were no collapse. Would your head as subsystem be in mixed state? Or without collapse, would the entangled subsystems still be in pure state? I plan to write a book of cartoon guide to decoherence and other matters that doesn't use any math but verbal summaries for laymen and need to understand some basic to avoid mistakes. Thank you.

 

[bhobba]

And some vague general set-up is not good enough - you must be exact. And being exact with future technology is impossible otherwise we would have the technology now.

[Supposed you were inside a hypothetical box.

Thanks
Bill

 

[cube137]

Thanks
Bill

Or let's not use any actual example. I just want to be acquainted with the basic. I read some books already and need a few clarifications of some points. For a pure state.. would it turn into mixed state if there was no collapse of any kind? Would entangled subsystems be in mixed states if there were no collapse?

 

[bhobba]

For a pure state.. would it turn into mixed state if there was no collapse of any kind? Would entangled subsystems be in mixed states if there were no collapse?

Collapse is not part of the formalism of QM.

But basically decoherence leads to apparent collapse which is collapse for all practical purposes. I can't explain the difference at the lay level. If its entangled then, roughly, it has collapsed.

Thanks
Bill

 

[cube137]

That's incorrect.

Any interpretation contains the QM formalism. And from that formalism alone deoherence occurs and the cat is dead or alive.

Don't be confused by the factorisation issue - it's not what some make it out to be. Its not that a quantum system can't be factored into cats etc, its that decoherence MAY depend on that factorisation. As yet theorems are lacking to decide the issue one way or another. It's is a very fringe issue - and for good reason - similar assumptions are made in many areas of physics and it would be silly to think that are all 'wrong'. I remember one discussion on it where it was shown even classical mechanics has the problem - but few would doubt that branch of science in its domain of applicability.

Thanks
Bill

Let me go back to the core of this thread. You said any interpretation contains the QM formalism and from that formalism alone decoherence occurs and the cat is dead or alive. But according to the famous classic paper http://arxiv.org/pdf/1210.8447v1.pdf

"If the state vector is considered as the only fundamental entity, the world is
completely structureless. The illusion of interacting subsystems is due to a “bad” choice
of factorization (i.e. decomposition into subsystems) of the Hilbert space. There is
always a more appropriate factorization available in which subsystems don’t inter-
act and nothing happens at all. This factorization absorbs the time evolution of the
state vector in a trivial way. The Many Worlds Interpretation is therefore rather a
No World Interpretation. A state vector gets the property of “representing a structure” only with respect to
an external observer who measures the state according to a specific factorization
and basis."

My question is how would the cat appear or behave if the cat is just state vector which is the only fundamental entity and the world is completely structureless. Is the latent structures of the cat encoded in the structureless state vector? How. I just can't imagine it. You mentioned earlier that
"The very set-up of Schroedinger's Cat precludes your issue. You can't have a system factored into cat and other things then assume it can't be factored - its a logical absurdity. Now if you want to discuss if the cat being dead or alive happens if you factor it differently in your analysis - that is the factorisation problem and as yet we do not know the answer."

Again I just want to imagine how the cat would behave as pure state vector without any classical position or collapse state. Just theoretically.

 

[bhobba]

But according to the famous classic paper

It not a famous classic paper. IMHO its a load of BS. There has been thread after thread about it on this forum - much more than it deserves in my view - all that can be said has been said. My view is as I said at the beginning. In Schroedinger's Cat you have defined a factorisation by the set-up of the experiment. Does the decoherence analysis depend on it - I doubt it, most doubt it, but key theorems are missing.

The large amount of discussion about that paper means I really need to clarify what I mean by its BS. Its not that its issue is not legit - it is. Its just blown way out of proportion by some.

Thanks
Bill

 

[bhobba]

Again I just want to imagine how the cat would behave as pure state vector without any classical position or collapse state. Just theoretically.

You can't do that. Its impossible by what a cat is. It must breathe air so is entangled with the air. I explained that to you before. If you keep repeating things that have been asked and answered the thread will be, correctly, shut down.

Thanks
Bill

 

[cube137]

Collapse is not part of the formalism of QM.

But basically decoherence leads to apparent collapse which is collapse for all practical purposes. I can't explain the difference at the lay level. If its entangled then, roughly, it has collapsed.

Thanks
Bill

I'm quite familiar with the improper mixed state vs proper mixed state. And how the system is entangled with the environment. And how measurement is the apparatus entangling with the system. But just to clarify.. when you mentioned "If its entangled then, roughly, it has collapsed.". Were you referring to the entangling of apparatus and system or system and environment? Because the system and environment as a whole is in pure state and not collapsed. Perhaps you were referring to the apparatus entangling with the system causing apparent collapse?

 

[bhobba]

Because the system and environment as a whole is in pure state and not collapsed. Perhaps you were referring to the apparatus entangling with the system causing apparent collapse?

It doesn't have to be an apparatus. The cat is entangled with the air it breathes (and other things as well) and via decoherence gives the cat its classical properties like definite position.

And yes for theoretical purposes is modeled as the system and environment being in a pure state - but in actuality it isn't. For example electrons interact with the EM field that pervades all space and leads to things like spontaneous emission.

Thanks
Bill

 

[A. Neumaier]

a cat in the totally isolated box (with oxygen).

Its not just oxygen. The cat sits on the bottom of the box, which in turn stands on the floor of the lab. This contact already generates enough decoherence to make things look classical. There is no way to remove the decoherence for a macroscopic object. You can do it (approximately) only for very tiny objects such as electrons or buckyballs - and the cost for doing it grows drastically with the size of the object.

 

[cube137]

It not a famous classic paper. IMHO its a load of BS. There has been thread after thread about it on this forum - much more than it deserves in my view - all that can be said has been said. My view is as I said at the beginning. In Schroedinger's Cat you have defined a factorisation by the set-up of the experiment. Does the decoherence analysis depend on it - I doubt it, most doubt it, but key theorems are missing.

The large amount of discussion about that paper means I really need to clarify what I mean by its BS. Its not that its issue is not legit - it is. Its just blown way out of proportion by some.

Thanks
Bill

I'm trying to understand why some are interested in the factorization while some brush it off or tend to ignore it. I guess those who tend to ignore it or not so interested are those who see quantum mechanics as simply probability in a classical world? While those who view it with importance are those who see the state vector as more primary like Many Worlders? This is Demystifer summary of it:

"To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves."

So for Many Worlders its not just what you said earlier that "Now if you want to discuss if the cat being dead or alive happens if you factor it differently in your analysis - that is the factorisation problem and as yet we do not know the answer.". In Many Worlds it's more than that. It need additional structure not present in the states of the Hilbert space for there to be even factorization. Are you in agreement? So for Many Worlders and quantum Darwinists.. it's more acute? I'm a Many Worlder and not an Ensembler like you so I'm interested in it.

 

[bhobba]

I'm trying to understand why some are interested in the factorization while some brush it off or tend to ignore it.

Since I am in the ignore it category I am not a good person to ask. One can formulate MW without explicit reference to decoherence and factoring into what's being observed, the environment, and what does the observing.. This is done via the concept of history. You will find the full detail in Wallace's book:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

In fact its also a good primer on decohoerent histories, which many have described as MW without the many worlds:
http://quantum.phys.cmu.edu/CHS/histories.html

The above is just an introduction - full understanding needs a fair bit of math that you will find in Wallace's book which is very theorem, proof, theorem, proof in style. After going though it you understand providing you accept its premises its pretty unassailable. It the premises that need attacking if you want to attack MW - that paper does not do that.

Thanks
Bill

 

[cube137]

Since I am in the ignore it category I am not a good person to ask. One can formulate MW without explicit reference to decoherence and factoring into what's being observed, the environment, and what does the observing.. This is done via the concept of history. You will find the full detail in Wallace's book:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

In fact its also a good primer on decohoerent histories, which many have described as MW without the many worlds:
http://quantum.phys.cmu.edu/CHS/histories.html

The above is just an introduction - full understanding need a fair bit of math that you will fin in Wallace's book which is very theorem, proof, theorem, proof in style. After going though it you understand providing you accept its premises its pretty unassailable. It the premises that need attacking if you want to attack MW - that paper does not do that.

Thanks
Bill

So it has to do with the particular interpretation one prefers to see whether factorization is an issue. You are a bonafide Ensemble and it has a natural factorization. Supposed you became a Quantum Darwinist or a Many Worlder. Then it becomes an issue? just want to make it clear of the differences and distinctions. Also you mentioned elsewhere "Whenever decoherence is discussed on this forum, and it has been discussed a lot, it always seems to get around to this factorisation issue. Yes its a legit issue - but a fringe one.. It really only seems gain traction around here - there doesn't seem to be that much interest in it. The above review article doesn't mention it. Schlosshauer does but it doesn't have a lot on it - in fact I can't even really recall where it is like most of the things discussed here where I can easily find reference to it. The only reason I know its there is someone pointed out to me it was." But in Zurek paper, http://arxiv.org/pdf/quant-ph/9805065v1.pdf It's mentioned:

"In particular, one issue which has been often taken for granted is looming big, as a foundation of the
whole decoherence program. It is the question of what are the “systems” which play such a crucial role in
all the discussions of the emergent classicality. This issue was raised earlier,2,28 but the progress to date has
been slow at best. Moreover, replacing “systems” with, say, “coarse grainings” does not seem to help at all
— we have at least tangible evidence of the objectivity of the existence of systems, while coarse-grainings

are completely “in the eye of the observer.”

So the reason you said there doesn't seem to be that much interest out there is because progress to date has been slow.. so it's a very legit field.

Are you in agreement with all of the above so far? I want to write an article of cartoon guide to decoherence and I just don't want to make any mistakes or wrong statements. Hence it is not wrong to write in say Scientific American an article saying "There is a very big problem in quantum mechanics now especially as it relates to Many Worlds version where there is only a State Vector, it's because no Classical World can out, you need additional structure. This problem is even greater than the Hierarchy Problems, Dark Energy and Unification of QM and QFT"

 

[bhobba]

So it has to do with the particular interpretation one prefers to see whether factorization is an issue.

One can formulate MW without explicit reference to decoherence and factoring into what's being observed, the environment, and what does the observing..

With that in mind why do you still think its an issue? In other words since it can be formulated in terms of histories why does it worry you if there is an issue in factoring it.? There isn't (aside from what I mentioned at the start) - but I can't grasp your concern about it since, as I explained, modern treatments don't even use it. That really should have been the end of it.

Thanks
Bill