Schrodinger's cat, the multiverse and isolated systems

[quantumfunction]

I know the debate about Schrodinger's cat is usually about things like consciousness but I want to talk about what it might say about isolated systems.

Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets?

Say you have the radioactive material isolated from the cat in the box and the box the cat is isolated from the outside environment, wouldn't a live/dead cat be two observable states of an isolated system until the box is open and the wave function collapses locally?

This collapse isn't just because of the Scientist opening the box, but the state of the cat interacts with his lab, the car on the highway and the entire observable universe.

So if an isolated system remains isolated do all probable states of that isolated system occur?

If you extrapolate that out to the universe and the universe is an isolated system doesn't that mean that every probable universe exist because there's nothing external to the universe to collapse it's wave function.

I was reading a paper where Max Tegmark said this was a postulate of Everett.

All isolated systems evolve according to the Schrodinger's equation.

So our universe could be an observable state of an isolated system and if this observable state is isolated then you can have probable states within probable states. This would occur maybe for trillions of years until two observable states of the isolated system interacted and maybe you get something like a big bang and everything reboots.

I saw where Penrose talks of Objective Reduction where isolated systems self collapse after they reach a certain threshold due to quantum gravity but I haven't seen much evidence for that. I think Tegmark may have a point if the universe is an isolated system.

 

[rootone]

...
If you extrapolate that out to the universe and the universe is an isolated system...

If you use the definition of 'Universe' as meaning 'everything that exists', then an isolated system is what it is.

Incidentally there is no underlying assumption in QM that the results of experiments have something to do with consciousness.

 

[bhobba]

Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets?.

Unless interacted with - of course.

All an observation is is an interaction.

As far as the universe is concerned by definition it can't interact with anything so you can't observe it.

Thanks
Bill

 

[Derek Potter]

Unless interacted with - of course.
All an observation is is an interaction.
As far as the universe is concerned by definition it can't interact with anything so you can't observe it.
Thanks
Bill

So the universe's state cannot collapse even in Copenhagen.
Nevertheless, the state space can be factorized an almost infinite number of ways making it possible for an observer (one subsystem) to interact with another. Collapse is then not objective but is how a subsystem's state appears to behave when there is an observation.
I believe the OP was talking about these improper collapses, to coin a phrase, :) under a factorization of the universe's state space, not about literally observing the universe as a whole.

Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets?

Nobody knows. But there is nothing in the standard formulations of QM to suggest anything otherwise.

So if an isolated system remains isolated do all probable states of that isolated system occur?

Every *possible* state. Yes.

If you extrapolate that out to the universe and the universe is an isolated system doesn't that mean that every probable universe exist because there's nothing external to the universe to collapse it's wave function.

Not every interpretation even has wavefunction collapse, observer or no observer. But one should not think of this humungous superposition as being every *possible* universe existing alongside each other. Instead, each possible "world of observations" exists in the one superposition. Just as Schrodinger's Cat isn't two cats but one cat in two states. Which, for the purists, are of course entangled with those of the observer and the environment.

I was reading a paper where Max Tegmark said this was a postulate of Everett.
All isolated systems evolve according to the Schrodinger's equation.
So our universe could be an observable state of an isolated system and if this observable state is isolated then you can have probable states within probable states. This would occur maybe for trillions of years until two observable states of the isolated system interacted and maybe you get something like a big bang and everything reboots.
I saw where Penrose talks of Objective Reduction where isolated systems self collapse after they reach a certain threshold due to quantum gravity but I haven't seen much evidence for that. I think Tegmark may have a point if the universe is an isolated system.

I haven't read much Tegmark but I understand that he says there is no reason to assume that "our" universe has a monopoly on existence. The maths of physics, QM in this context, allows a vast space of possible universes and it it is perfectly possible that they all exist or don't exist to the same extent.

I can't comment on the cosmological implications of Tegmark or of OR. The only time I heard of the universe rebooting was in Doctor Who :)

 

[bhobba]

So the universe's state cannot collapse even in Copenhagen.

No - and obviously so.

Thanks
Bill

 

[alexepascual]

I know the debate about Schrodinger's cat is usually about things like consciousness but I want to talk about what it might say about isolated systems.

If we think about the box isolating the cat from the rest of the environment and any "observer", then environmental decoherence would be prevented. Then we could think about the cat as being in both states at the same time but as far as I know, the only way that is being used to confirm superposition nowadays is by observing interference. In this case, I think as the cat and whatever else inside the box is macroscopic, you would not be able to see interference when some time in the future we make a measurement. Let's say that we don't see interference because the wavelength becomes too short and/or the phases disrupted by the interaction of the original microscopic quantum system with the immediate (inside the box) macroscopic surroundings. We could still think about a kind of superposition different form the typical quantum superposition in which we can observe interference. I think this could be described according to what some call an "improper mixture" and would correspond to a reduced density matrix where all the diagonal elements are still there.
Of course it can be said that in practice it is impossible to make the box to prevent any leakage of information to the outside. But if we ignore that practical difficulty and imagine an ideal experiment in which the walls of the box achieve such insulating power, then it would be interesting to know what people adhering to different interpretations think about it. What do you think guys? (if there is a girl on this thread please forgive me for my sexist expression).

 

[bhobba]

If we think about the box isolating the cat from the rest of the environment and any "observer", then environmental decoherence would be prevented. Then we could think about the cat as being in both states at the same time

That's incorrect. The cat can't be isolated from the environment and remain a cat eg it must breathe air.

And it is entangled with the atomic source which means it is not in a superposition by the definition of entanglement - in fact its in a mixed state of dead and alive meaning it is either dead or alive - not in some weird combination of the two.

Thanks
Bill

 

[Derek Potter]

That's incorrect. The cat can't be isolated from the environment and remain a cat eg it must breathe air.

And it is entangled with the atomic source which means it is not in a superposition by the definition of entanglement - in fact its in a mixed state of dead and alive meaning it is either dead or alive - not in some weird combination of the two.

Thanks
Bill

Even without Alexepascual's isolating box, if one considers the system of [particle plus cat plus observer plus environment] then, under the assumed unitary evolution, the state of this system does evolve to a superposition of
|everything that follows from the particle being emitted> or "|dead>" for short
and
|everything that follows from the particle not being emitted> or "|alive>" for short
which is just as weird a combination as the cat itself being in a pure superposition.

Would you not agree?

 

[bhobba]

Even without Alexepascual's isolating box, if one considers the system of [particle plus cat plus observer plus environment] then, under the assumed unitary evolution, the state of this system does evolve to a superposition of

This has been discussed many many times. I have even posted the math. For the umpteenth time, but from past experience it won't be the last, if you observe inside the system things do not remain in superposition - its a mixed state.

You can do a google search and find where I went through the math.

The solution to the whole thing in the ignorance ensemble interpretation is that the observation occurs just after decoherene. In Schroedinger's Cat the earliest point decoherence occurs is at the particle detector. The superposition of particle detected, not detected is converted into a mixed state and that mixed state is interpreted as a proper one so it no longer a superposition - but it is an actual state - not detected or detected.

Now to someone observing it outside - everything continues on just the same - what they observe is also in a mixed state. The issue comes if they were to observe everything including the particle source - but that would be a totally different set-up.

Thanks
Bill

 

[alexepascual]

That's incorrect. The cat can't be isolated from the environment and remain a cat eg it must breathe air.

Well, it depends on what we mean by environment. I was using the word environment to refer to everything outside the box as once a signal leaks out of the box it is supposedly "uncontrollable" and we can't "erase" the information that has leaked out. According to Environmentally Induced Decoherence (at least as presented by Zurek) it is this uncontrollable leakage of information that produces decoherence. Now let's go back to the practical issue. I got a solution. We can put an oxygen tube inside the box and a small CO2 absorber. We can also put some toy for the cat to play so that he/she doesn't get bored. We would have to select a cat that is not claustrophobic. So Bhobba your statement is incorrect, the cat can continue alive for some time within the box.

 

[alexepascual]

This has been discussed many many times. I have even posted the math. For the umpteenth time, but from past experience it won't be the last, if you observe inside the system things do not remain in superposition - its a mixed state.

You make it sound as if you are getting tired of talking about the same things. But I suspect that on the other hand in some way you enjoy it.
So let me see if I understand your position or interpretation. You are saying that as soon as the microscopic quantum system interacts with the macroscopic detector, the system-instrument-cat (and whatever else inside the box) are in a proper mixed state where the only reason we keep all values on the diagonal of the density matrix is because we don't "know" the actual value but one of those values has already been selected. In other words there is already definiteness, but on the other hand ignorance.

 

[Feeble Wonk]

...it is entangled with the atomic source which means it is not in a superposition by the definition of entanglement - in fact its in a mixed state of dead and alive meaning it is either dead or alive - not in some weird combination of the two.

Sorry to side track the discussion, but I'm hoping that this point helps me get a better handle on the general concept... which is the logical differentiation between "pure", "mixed" and "proper" quantum states. Please correct me where I'm wrong...

In superposition, which is a "pure" state, the cat is dead AND alive (and I am simply accepting for the sake of discussion that the cat IS in superposition here).

If we accept Bhobba's assertion that decoherence, even in the "isolated" system, prevents the cat from being in superposition (and I'm assuming that this does in fact cause "collapse" of the cat's quantum state), then the cat would be in a "proper", "mixed" state... meaning that the critter is dead OR alive, but we just don't know which.

Is that correct?

 

[alexepascual]

Even without Alexepascual's isolating box, if one considers the system of [particle plus cat plus observer plus environment] then, under the assumed unitary evolution, the state of this system does evolve to a superposition of everything that follows from the particle being |emitted> or "|dead>" for short and everything that follows from the particle not being emitted> or "|alive>" for short which is just as weird a combination as the cat itself being in a pure superposition. Would you not agree?

Let's see Derek what Bhobba thinks. I think that according to a more "many worlds" like interpretation, when the outside environment gets entangled with the cat, then a human observer also gets entangled with it. So you can say that the observer is in a state of superposition, but to each "version" of the observer, there is only one outcome and as Bohbba said the cat assumes a definite macroscopic state. The picture I proposed, was as the original poster did, to think of the box as isolating the inside of the box from the outside to prevent entanglement with the outside environment and with the observer. I was under the impression that in those circumstances, even other interpretations besides "many worlds" might see the cat as in a state of superposition. But this would be a superposition different from the one we are used to in quantum mechanics as it would not show any interference effects when measured. If we don't want to call it a superposition, we could always call it "indefiniteness". But for Bhbba, if I interpret him correctly, that's not the case and even if the inside of the box is isolated from the outside, as soon as the quantum system makes contact with the macroscopic instrument and we wait a little for the poison vial to break, the quantum system, the instrument and the cat assume a definite state. Well, I understand, the cat according to this view is always in a definite state because it is a macroscopic object. My view is different as you can see.

 

[alexepascual]

Sorry to side track the discussion, but I'm hoping that this point helps me get a better handle on the general concept... which is the logical differentiation between "pure", "mixed" and "proper" quantum states. Please correct me where I'm wrong...
In superposition, which is a "pure" state, the cat is dead AND alive (and I am simply accepting for the sake of discussion that the cat IS in superposition here).
If we accept Bhobba's assertion that decoherence, even in the "isolated" system, prevents the cat from being in superposition (and I'm assuming that this does in fact cause "collapse" of the cat's quantum state), then the cat would be in a "proper", "mixed" state... meaning that the critter is dead OR alive, but we just don't know which.
Is that correct?

Feeble, In my opinion your conclusion is correct if (as you said) we accept Bhobbas' assertion.

 

[bhobba]

In other words there is already definiteness, but on the other hand ignorance.

I am saying the ignorance is in how an improper mixed state becomes a proper one. Here is the detail:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Look up the ignorance interpretation in the above.

The observation occurs at the particle detector. Everything is common-sense classical from that point on. Opening or closing the lid makes no difference to anything. Decoherence breaks the von-neumann chain by placing the cut at the earliest point decoherence occurs which in Schroedinger's cat is at the particle detector.

Thanks
Bill

 

[bhobba]

I was using the word environment to refer to everything outside the box as once a signal leaks out of the box it is supposedly "uncontrollable" and we can't "erase" the information that has leaked out.

You are talking about Zurecks Quantum Darwinism. I am talking about the ignorance ensemble interpretation which is much simpler. The mystery occurs at the earliest point decoerence happens - which is at the particle detector. Everything is classical from that point on.

Thanks
Bill

 

[bhobba]

Is that correct?

No.

The trouble is the answer is technical and can't be explained in lay terms. You simply have to accept that this weird thing known as a superposition gets converted into this less weird thing called a mixed state by decoherence.

Thanks
Bill

 

[Feeble Wonk]

Is my mistake in the "proper" designation after decoherence?

 

[bhobba]

Is my mistake in the "proper" designation after decoherence?

Yes - its interpreted as a proper mixed state - its really a improper one.

Thanks
Bill

 

[Feeble Wonk]

That's what I thought... and that's where my cognitive wheels grind to a halt. >_<

I have a rough idea that it has something to do with diagonalizing through density matrices of potential quantum states... none of which I understand.

But, my primary question is this... Does the "improper" mixed state imply that it's not arrived at by an ACTUAL quantum state "collapse" (assuming that such a thing really occurs)?

 

[bhobba]

But, my primary question is this... Does the "improper" mixed state imply that it's not arrived at by an ACTUAL quantum state "collapse" (assuming that such a thing really occurs)?

That's correct - an improper mixed state observationally is exactly the same as collapse - but it really isn't. Interpreting it as a proper one is exactly the same as collapse. In fact how an improper mixed state becomes a proper one is the modern version of collapse ie the measurement problem. It colloquially is called why do we get any outcomes at all. Some say it resolved nothing - but being part of decoherence has REASONABLY solved the following issues:

1. The preferred basis problem.
2. Why its so hard to observe interference effects

Note the use of the word REASONABLE - there are a few issues around it like the so called factorisation issue and some key theorems are lacking.

What it hasn't solved is - why do we get outcomes at all.

Thanks
Bill

 

[Feeble Wonk]

...being part of decoherence has REASONABLY solved the following issues:

1. The preferred basis problem.
2. Why its so hard to observe interference effects

Note the use of the word REASONABLE - there are a few issues around it like the so called factorisation issue and some key theorems are lacking.

What it hasn't solved is - why do we get outcomes at all.

I think I'm hanging on so far. But, I'd like to make sure I have the general idea right for your point #1...

The preferred basis issue refers to the variable "observable" by which the quantum state is reduced. Is that correct?

 

[bhobba]

The preferred basis issue refers to the variable "observable" by which the quantum state is reduced. Is that correct?

Yes. For example in a position measurement why does it measure position and not say momentum.

Thanks
Bill

 

[Feeble Wonk]

Yes. For example in a position measurement why does it measure position and not say momentum.

OK. I'm afraid that this is where my mathematical ineptitude is going to bite my gluteal tissue, but...

My understanding is that there are "observables" that can not, even in principle, be observed simultaneously (such as your examples of position and momentum). And, it seems to me that "which" of these observables is selected as the preferred basis might well have a significant effect on the unitary evolution of a system's wave function. Is there any way in the world you can try to explain to me (remembering my mathematical limitations) HOW decoherence selects the preferred basis?

 

[bhobba]

HOW decoherence selects the preferred basis?

Sorry - that is some deep math.

What I can say is it turns out most of the time position is singled out because interactions are usually radially symmetric - but the reason is in the math.

Thanks
Bill

 

[Feeble Wonk]

Sorry - that is some deep math.

What I can say is it turns out most of the time position is singled out because interactions are usually radially symmetric - but the reason is in the math.

>_< I was afraid you were going to say something like that.

 

[Feeble Wonk]

That's correct - an improper mixed state observationally is exactly the same as collapse - but it really isn't. Interpreting it as a proper one is exactly the same as collapse. In fact how an improper mixed state becomes a proper one is the modern version of collapse ie the measurement problem.

This part is still confusing me. If I've understood you correctly, the mixed state is "improper" because it has not yet actually collapsed.

Is that correct?

 

[bhobba]

This part is still confusing me. If I've understood you correctly, the mixed state is "improper" because it has not yet actually collapsed.

No. Its improper because its prepared differently to a proper one where collapse would have occurred. There is no way to tell the difference. It may be collapsed or not - its unknown. I assume however it is. Also if it is collapsed there is no mechanism for that - that's the ignorance bit.

Thanks
Bill

 

[Feeble Wonk]

No. Its improper because its prepared differently to a proper one where collapse would have occurred. There is no way to tell the difference. It may be collapsed or not - its unknown. I assume however it is. Also if it is collapsed there is no mechanism for that - that's the ignorance bit.

Thanks
Bill

I'm not sure I'm following you here. I think I need to better understand your definition of the term "prepared" in this context.

 

[bhobba]

I'm not sure I'm following you here. I think I need to better understand your definition of the term "prepared" in this context.

Here is one way to create a mixed state. Randomly select a pure state. There is a pure state there - but its unknown what it is. Such are called proper mixed states. Another way to create a mixed state is from decoherence. Such are called improper. Now there is no way to tell the difference between the two. It may be like a proper one and a pure state is there - but we don't know which one - or not. We simply don't know. We are ignorant - hence the name ignorance interpretation. If it was a proper mixed state collapse would have occurred - the state that's observed is there before observation - everything is sweet. So the interpretation simply assumes it is.

Thanks
Bill

 

[Feeble Wonk]

Here is one way to create a mixed state. Randomly select a pure state. There is a pure state there - but its unknown what it is. Such are called proper mixed states.

Ugh... I'm getting MORE confused rather than less.

My previous understanding was that the "pure" state was in actual superposition... still in the "and" state, so to speak. In contrast, I thought the "proper mixture" was in an "either/or" state. It's admittedly a subtle difference, but logically significant.

 

[Feeble Wonk]

Or... are you saying that the "proper" mixed state actually contains a "pure" state in addition to a null (nonexistent) state? Nonexistent, in the sense that it MIGHT have been, but it's not.

 

[bhobba]

Or... are you saying that the "proper" mixed state actually contains a "pure" state in addition to a null (nonexistent) state? Nonexistent, in the sense that it MIGHT have been, but it's not.

Its what I said. Imagine you have a heap of pure states that are the possible outcomes of an observation. You randomly select one. There is a pure state there - but because it was randomly selected you don't know which one - only the probability of what it is. That is a proper mixed state.

Thanks
Bill

 

[quantumfunction]

I think the real question is about decoherence and isolated systems.

If the box is an isolated system doesn't the cat and everything in the box become observable states of that isolated system (the box)? If I understand Tegmark and Everett's postulate about isolated systems, it's saying that decoherence doesn't occur if there's nothing external to the isolated system. In this case all observable states of the isolated system would be realized.

So if the universe is an isolated system then our universe would be an observable state of that isolated system because there's nothing external to the universe to interact with so no decoherence.

The reason we can see the wave nature of particles is because they can remain isolated for long periods of time. So in a sense these particles have free will according to the Free Will Theorem.

The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.[1] They published a stronger version of the theorem in 2009.[2]

https://en.wikipedia.org/wiki/Free_will_theorem

A baseball can't remain isolated from it's environment so it's always in one observable state. This would mean classical objects don't have free will. There different states can't exist in the same environment so they're in different universes.

On a side note, this could mean if we have free will it's due to a quantum mind. So on a classical level you have no choice but to go to medical school instead of law school because you're in this observable state of an isolated system. Your quantum mind would be like the isolated particle and experiences a choice between law school and medical school.

I think Tegmark understood this dilemma and he recently proposed that consciousness was a state of matter. I think it makes more sense if consciousness is quantum because that would mean the mind could remain isolated from the environment and could make choices or appear to make choices because it would have a wave nature like an isolated particle.

 

[bhobba]

If the box is an isolated system doesn't the cat and everything in the box become observable states of that isolated system (the box)?.

If the box is an isolated system its the same story. The observation happens at the particle detector - everything is common-sense classical from that point on. The cat lives or dies regardless of if the box is opened, is isolated etc.

Thanks
Bill