How Does Environmentally Induced Decoherence Affect Quantum State Reduction?

[Demystifier]

OK, here I give two of my early artistic works from a dark phase. In one of them you can see an influence of Dali.

 

[Feeble Wonk]

Definite artistic prowess. But.. How old were you? These seem awfully dark for an early life creation.

 

[Demystifier]

Definite artistic prowess. But.. How old were you? These seem awfully dark for an early life creation.

Well, in those works I was not really a child. At that time I was already in high school, meaning old enough to be dark.

I also have some works from a real childhood. They are technically good too, but do not have such an artistic feature. That's why I didn't show them.

Or maybe I should have shown the high-school works from the erotic phase?

 

[Feeble Wonk]

Interesting. Is the second drawing a reflection of "Nature being subjugated by mankind", "Mankind being a slave to its animal instincts"... Or "just a cool drawing"? [emoji848]

 

[Demystifier]

Interesting. Is the second drawing a reflection of "Nature being subjugated by mankind", "Mankind being a slave to its animal instincts"... Or "just a cool drawing"? [emoji848]

The last one.

 

[Feeble Wonk]

The last one.

[emoji106]

 

[Feeble Wonk]

...maybe I should have shown the high-school works from the erotic phase?

"Phase"? Is that supposed to be a phase? [emoji33]

 

[Demystifier]

"Phase"? Is that supposed to be a phase? [emoji33]

I meant in the artistic sense only.

 

[Demystifier]

Anyway, if one forgot what it has to do with the topic, here is a reminder. Decoherence -> MWI -> two very different simultaneous topics of discussion in the same thread. I hope the moderators will accept that argument.

 

[Feeble Wonk]

Anyway, if one forgot what it has to do with the topic, here is a reminder. Decoherence -> MWI -> two very different simultaneous topics of discussion in the same thread. I hope the moderators will accept that argument.

[emoji39] OK. Back to the decoherence discussion...
So, if I've followed you correctly, the three primary "non-collapse" QT interpretation models (ensemble, MW and dBB) view the "cat in the box" as fully decohered into a mixed state (dead OR alive), even from the external perspective. Right?

If so, before considering collapse models, are there any other interpretations (other than your SHV - which I'd like to address later) that might view the isolated system box contents as still being in a "pure" state of superposition (with the cat dead AND alive)?

 

[vanhees71]

Well, one of the topics is totally irrelevant for physics, but that's also something it has in common with the MWI ;-)). SCNR.

 

[Demystifier]

So, if I've followed you correctly, the three primary "non-collapse" QT interpretation models (ensemble, MW and dBB) view the "cat in the box" as fully decohered into a mixed state (dead OR alive), even from the external perspective. Right?

Sort of, but one has to be careful in wording. In MWI there are TWO cats; dead AND alive. But any ONE of them is dead OR alive.

 

[Demystifier]

Well, one of the topics is totally irrelevant for physics, but that's also something it has in common with the MWI ;-)). SCNR.

If physics is really fundamental as physicists like to think that it is, then everything has to do physics.

 

[Demystifier]

If so, before considering collapse models, are there any other interpretations (other than your SHV - which I'd like to address later) that might view the isolated system box contents as still being in a "pure" state of superposition (with the cat dead AND alive)?

Perhaps something like that is valid in quantum logic. Roughly speaking, in quantum logic it is true that
(Cat is dead) AND (cat is alive).
but it is not true that
Cat is (dead and alive).

 

[Feeble Wonk]

Sort of, but one has to be careful in wording. In MWI there are TWO cats; dead AND alive. But any ONE of them is dead OR alive.

Got it. In fact, I presume, there are innumerable cats... all with minuscule quantum differences... but all of them are dead OR alive.

 

[Feeble Wonk]

Perhaps something like that is valid in quantum logic. Roughly speaking, in quantum logic it is true that
(Cat is dead) AND (cat is alive).
but it is not true that
Cat is (dead and alive).

OK. So, I guess this gets us to the general category of collapse interpretations. Conceptually, do you think the various forms of this interpretational genre should be further subdivided to accurately discuss how they view the state of the cat within the isolated system? If so, how and why?

 

[Demystifier]

OK. So, I guess this gets us to the general category of collapse interpretations. Conceptually, do you think the various forms of this interpretational genre should be further subdivided to accurately discuss how they view the state of the cat within the isolated system? If so, how and why?

They can be subdivided according to the cause of collapse (consciousness, stochastic law for all matter, ...), according to the ontology (abstract state $|\psi\rangle$, wave function $\langle x|\psi\rangle$, flashes, ...), etc.

 

[ddd123]

Isn't the "consciousness causes collapse" camp dead today? I only find old speculations by Wigner, but the consensus on the role of consciousness seems shifted towards some aspects of MWI.

 

[Feeble Wonk]

They can be subdivided according to the cause of collapse (consciousness, stochastic law for all matter, ...), according to the ontology (abstract state $|\psi\rangle$, wave function $\langle x|\psi\rangle$, flashes, ...), etc.

And, these collapse theory subdivisions view the state of the cat in the box differently in terms of being pure or mixed (being in true superposition)? If so, could you please offer a brief (conceptual) explanation of why/how?

 

[Feeble Wonk]

Isn't the "consciousness causes collapse" camp dead today? I only find old speculations by Wigner, but the consensus on the role of consciousness seems shifted towards some aspects of MWI.

At this point, I'm not too interested in arguments for or against the interpretational positions, but I'm just looking for a conceptual description of "what" the position is regarding the state of the cat in the isolated system of the box.

 

[Demystifier]

Isn't the "consciousness causes collapse" camp dead today?

It's not very popular, but not disproved either.

 

[Demystifier]

And, these collapse theory subdivisions view the state of the cat in the box differently in terms of being pure or mixed (being in true superposition)? If so, could you please offer a brief (conceptual) explanation of why/how?

They pretty much agree that the cat is not in superposition, except for a very short time which is too short to be measured.

 

[Feeble Wonk]

They pretty much agree that the cat is not in superposition, except for a very short time which is too short to be measured.

OK. So, if I've followed you correctly, regardless of the interpretational perspective, the cat in the box (a completely isolated system) should be thought of as always decohering into a mixed state of dead OR alive, and never really in a pure state of dead AND alive. That makes sense to me.
I suppose the next step for me is to better understand the nature of the "post-decoherence" mixed state. The conceptual difference between a "proper" and an "improper" mixed state remains somewhat fuzzy to me. Is there a decent way of explaining that which doesn't require the use of density matrices?

 

[Demystifier]

The conceptual difference between a "proper" and an "improper" mixed state remains somewhat fuzzy to me. Is there a decent way of explaining that which doesn't require the use of density matrices?

It depends. Can I use pure entangled states such as $|\varphi_1\rangle |\psi_1\rangle + |\varphi_2\rangle |\psi_2\rangle$?

 

[Feeble Wonk]

Well, I'd definitely have a better chance of understanding that than the density matrix explanation... but words would be even better. [emoji849]
I know that's asking a lot, and is likely too limiting for you. Use the mathematical (bra-ket) symbols necessary, and I'll struggle through.

 

[Demystifier]

I cannot explain it with words only. So let me give an explanation in terms of pure states without density matrices.

Consider the Schrodinger cat together with the unstable atom. If the atom decays then the cat dies, in which case the full state is $|decay\rangle |dead\rangle$. Likewise, if the atom does not decay then the cat lives, in which case the full state is $|not\; decay\rangle |live\rangle$. But we don't know which of the two possibilities is realized, so the full state is the superposition
$$|decay\rangle |dead\rangle + |not\; decay\rangle |live\rangle$$
A state which is in a superposition is not in a mixture.

So we know the state of the full system (the superposition above), but what is the state of the cat alone? Someone's first guess might be the superposition $|dead\rangle + |live\rangle$. But why $+$? Why not $|dead\rangle - |live\rangle$? Or why not $|dead\rangle + i|live\rangle$? Since we cannot decide which of those superpositions would be the correct one, we must decide that neither is correct. We cannot write the state of the cat alone as a superposition. So the state of the cat is only a mixed state (dead OR alive).

Is it a proper or improper mixture? It is improper mixture. Why? Because mixture is an artefact of looking only at a subsystem (the cat) and not on the the full system (cat + atom). In the full system we still have the superposition above with a definite $+$ sign, so the full system is not mixed. Hence the mixture is improper.

On the other hand, the proper mixture would takes place if there was no bigger system that made the whole system not mixed. For instance, if the atom somehow disappeared from the universe (without giving its information to something else), then the cat would be in the proper mixture. But as far as we know such a thing does not happen, so the cat must be in the improper mixture.

Does it make sense to you?

 

[Feeble Wonk]

Why not $|dead\rangle - |live\rangle$? Or why not $|dead\rangle + i|live\rangle$? Since we cannot decide which of those superpositions would be the correct one, we must decide that neither is correct. We cannot write the state of the cat alone as a superposition. So the state of the cat is only a mixed state (dead OR alive).

This is the decoherence part... Right?

Does it make sense to you?

I think this is going to work for me. Let me roll it around in my head for a bit. Thank you.

 

[Demystifier]

This is the decoherence part... Right?

Right.

 

[Feeble Wonk]

It is improper mixture. Why? Because mixture is an artefact of looking only at a subsystem (the cat) and not on the the full system (cat + atom). In the full system we still have the superposition above with a definite $+$ sign, so the full system is not mixed. Hence the mixture is improper.
>>>
Does it make sense to you?

This is where things still get fuzzy for me.
The "cat in the box" seems to be a great mental tool to consider the decoherence process because there is such a definitive prohibition of information exchange between the "external" system and the "internal" systems.
But this hard delineation still creates confusion for me when I try to consider the extended system to include an external observer and the unopened box? The external observer does not know the state of the unstable atom (and resultant state of the cat). So, from the external observer's perspective, you might think the |DECAY>|DEAD + |NOT DECAY>|LIVE system is still in superposition. However, now the state of the "atom+cat" is not the "full" system, but a subsystem of "atom+cat+observer", and therefore "atom+cat" becomes a mixture relative to the extended system including the external observer. Yet, is that actually the case BEFORE the observer opens the box (before information exchange occurs)?
I strongly suspect that this is where my mathematical incompetence and inability to deal with density matrices bites my backside again. It still seems logical to me that, regardless of the external observer's lack of knowledge with respect to the unstable atom, there is no possible "informational state" of the cat that can represent both dead AND alive at the same time, but I'm trying to understand it using the guidelines of your explanation.

 

[Demystifier]

This is where things still get fuzzy for me.
The "cat in the box" seems to be a great mental tool to consider the decoherence process because there is such a definitive limit in information exchanged between the "external" system and the "internal" system.
But this hard delineation still creates confusion for me when I try to consider the extended system to include external observer and the unopened box? The external observer does not know the state of the unstable atom (and resultant state of the cat). So, from the external observer's perspective, you might think the |DECAY>|DEAD + |NOT DECAY>|LIVE system is still in superposition. However, now the state of the "atom+cat" is not the "full" system, but a subsystem of "atom+cat+observer" and therefore a mixture. Yet, is that actually the case BEFORE the observer opens the box?
I strongly suspect that this is where my mathematical incompetence and inability to deal with density matrices bites my backside again. It still seems logical to me that, regardless of the external observers knowledge with respect to the unstable atom, there is no possible "informational state" of the cat that can represent both dead AND alive at the same time, but I'm trying to understand it using the guidelines of your explanation.

There should be no additional confusion when external observer is added. Let the possible states of the observer be
|not look>, |see dead cat> and |see alive cat>
Then before opening the box the full state is
|DECAY>|DEAD>|not look> + |NOT DECAY>|ALIVE>|not look>
After opening the box it is
|DECAY>|DEAD>|see dead cat>+|NOT DECAY>|ALIVE>|see alive cat>
No new mathematics is needed.

One philosophical comment is in order. Here the states of the observer are the states of his brain. How the brain creates a mind is an unresolved question, but QM is probably not essential for that.

 

[Feeble Wonk]

One philosophical comment is in order. Here the states of the observer are the states of his brain. How the brain creates a mind is an unresolved question, but QM is probably not essential for that.

Fair enough. We'll leave that aside for now. But it seems clear to me that there should be a logical correlation between the the "brain state" of the observer and the state of the opened box being observed, regardless of the potential philosophical issues.

 

[Demystifier]

But it seems clear to me that there should be a logical correlation between the the "brain state" of the observer and the state of the opened box being observed

Of course, and that correlation is encoded in the last state above that I have written. Rougly speaking, the quantum state
|DECAY>|DEAD>|see dead cat>+|NOT DECAY>|ALIVE>|see alive cat>
can be translated into a logical expression
(DECAY and DEAD and see dead cat) OR (NOT DECAY and ALIVE and see alive cat).

But one should be careful, because the translation is not reversible. In the reverse direction, an expression like
A OR B
gets translated into
a|A>+b|B>
where a and b are unknown coefficients.

 

[Feeble Wonk]

After opening the box it is
|DECAY>|DEAD>|see dead cat>+|NOT DECAY>|ALIVE>|see alive cat>

This seems to be somewhat of a slippery slope for me. When considering the observer+cat+atom in the "post-observation" status, would this be thought of as a "full" system... meaning a "pure" system in superposition... if we imagine that the universe consists of only these physical elements.

 

[Demystifier]

This seems to be somewhat of a slippery slope for me. When considering the observer+cat+atom in the "post-observation" status, would this be thought of as a "full" system... meaning a "pure" system in superposition... if we imagine that the universe consists of only these physical elements.

Yes. If you are now going to ask why do we not see a superposition, I will tell you that the answer depends on the interpretation.

 

[Feeble Wonk]

Yes. If you are now going to ask why do we not see a superposition, I will tell you that the answer depends on the interpretation.

[emoji39] You saw that coming a mile away. I've got some more thinking to do, and then I'd like to ask you more about how this relates to the SHV interpretation if that would be OK.