I Do macro objects get entangled?

[stevendaryl]

I understand that the situation goes quickly to $(|observer_d\rangle |Dead\rangle) + (|observer_a\rangle |Alive\rangle)$ ¹, in which the cat is not in superposition for the observer. Also, nonwithstanding that the cat is isolated in the box, inside the box it is not in superposition but rather already decohered. However, when the observer has not looked in the box, his assessment of the situation is $|observer\rangle (|Dead\rangle + |Alive\rangle)$ ², right?

No, after decoherence, it's no longer appropriate to use kets to describe the cat. He can either go the route of Many-Worlds, and describe the state of the entire universe as a ket, or he can describe the state of the cat alone as a mixed-state. In a mixed state, the cat has a certain probability of being alive, and a certain probability of being dead. But that is not the same as the cat being in a superposition. Kets are only appropriate for pure states.

So I wonder, if the cat is almost never in superposition, why the observer nevertheless is in state ²?

That's the point---that description is never appropriate for more than a tiny fraction of a second.

Also, when does state ¹ occur? Already in the box, or only when the observer takes a look?

Almost immediately. Cats have influences on the rest of the universe even if nobody looks at them.

It seems to me that the formulations ¹ and ² depend on whether the observer actually observes the cat.

 

[entropy1]

Ok, so I'm wondering, are there two stages of decoherence the case here? First, the cat in the box on its own, and then again, when the box is opened and the observer takes a look? Which one are we talking about in this situation? I guess it matters if the box is open or closed?

 

[stevendaryl]

Ok, so I'm wondering, are there two stages of decoherence the case here? First, the cat in the box on its own, and then again, when the box is opened and the observer takes a look? Which one are we talking about in this situation? I guess it matters if the box is open or closed?

I don't think anything very mysterious happens when you open the box, other than the observer learns what state the cat is in. That's not quantum mechanical, it's just light from the cat reaching the observer's eyes and causing changes to the state of his brain.

 

[entropy1]

I don't think anything very mysterious happens when you open the box, other than the observer learns what state the cat is in. That's not quantum mechanical, it's just light from the cat reaching the observer's eyes and causing changes to the state of his brain.

Ok. So what is it about the box open or closed in Schrödingers Cat?

Then it would mean that the cat in MWI terms is, in the closed box, already in two different branches $|Dead\rangle + |Live\rangle$, right?

 

[stevendaryl]

Ok. So what is it about the box open or closed in Schrödingers Cat?

The original discussion of Schrodinger's cat was from the point of view of the idea that observation "collapses the wave function", and so it was important that the cat was actually observed to be alive or dead. But that ignored decoherence. Decoherence can be thought of (according to one view) as the environment constantly observing macroscopic things, so that they are always in a "collapsed" state. The more sophisticated view is that decoherence is constantly coupling macroscopic objects' states to the rest of the universe, so that no macroscopic object exists for long in a superposition (except possibly the entire universe). But in either interpretation, there is no longer anything special about opening the box and looking inside it, except that afterwards, you know what happened to the cat.

 

[Derek P]

Ok. So what is it about the box open or closed in Schrödingers Cat?

Schroedinger mentioned it, saying that the situation is resolved when the experimenter opens the box and looks in. He did not say that opening the box causes anything to happen, he was referring to the fact that the observer finds out whether the cat is alive or dead. Don't forget, Schroedinger invented the scenario to highlight a problem in the then-current understanding of quantum mechanics. He was quite specific - Heisenberg's (?) "fuzzy reality" idea would mean the cat would be in a fuzzy state. [Pause for fuzzy cat jokes.] But since then we have moved on and Schroedinger's Cat is now a familiar scenario to test various interpretations. There is no significance to opening the box other than the fact that the observer can then look inside.

 

[StevieTNZ]

Remember to keep in mind that decoherence is "FAPP". The probabilities of a mixed state do not represent something that is there in a classical sense (i.e. a cat dead). They are still probabilities of what the outcome will be. See 'Quantum Enigma' by Bruce Rosenblum and Fred Kuttner.

 

[Derek P]

Ok, so I'm wondering, are there two stages of decoherence the case here? First, the cat in the box on its own, and then again, when the box is opened and the observer takes a look? Which one are we talking about in this situation? I guess it matters if the box is open or closed?

Decoherence is inevitable with most systems, especially ones that have charged particles. Even the original particle, which was thought of as being in a superposition of emitted and not emitted, would be decohered because of the recoil etc that it left on the emitting atom. But even if we constructed apparatus that created a clean superposition, the moment the particle interacts with the detector, decoherence begins. And is complete before the electrical signal even leaves the detector!

But yes, if you want to describe exactly what happens, step by step, you can consider a whole cascade of interactions, each one subject to decoherence. Though, as several "A" level threads have done recently, you can actually lump them all together. But saying that the detector, its circuity, the killing mechanism, the cat, the box, the observer, the laboratory and everything else out to Mars (Schroedinger said "after an hour") is in a "dead" state is confusing. and it also obscures the fact that some of the global system (generally referred to as the environment) must be decohering the rest (the detector or observer)..

 

[entropy1]

Remember to keep in mind that decoherence is "FAPP". The probabilities of a mixed state do not represent something that is there in a classical sense (i.e. a cat dead). They are still probabilities of what the outcome will be. See 'Quantum Enigma' by Bruce Rosenblum and Fred Kuttner.

Does that mean the cat being dead or alive could depend on future events (measurements)?

 

[Derek P]

Remember to keep in mind that decoherence is "FAPP". The probabilities of a mixed state do not represent something that is there in a classical sense (i.e. a cat dead). They are still probabilities of what the outcome will be. See 'Quantum Enigma' by Bruce Rosenblum and Fred Kuttner.

Not sure who you're answering, but yes, decoherence is FAPP. But even it it were total, the mixture arising from decoherence would still be improper. There need be no randomness choosing which "possible" state to actualize. The randomness then comes from the fact that the observer doesn't know which state she is in. But I'd say that such a set of states is just as much "there in a classical sense" as a single state that has been selected at random out of it.

 

[Derek P]

Does that mean the cat being dead or alive could depend on future events (measurements)?

FAPP means FAPP. For ALL practical purposes. So when decoherence turns a superposition into a probability distribution FAPP, that means that whatever outcome you have at that point you will get it for ever more. FAPP.

 

[entropy1]

FAPP means FAPP. For ALL practical purposes. So when decoherence turns a superposition into a probability distribution FAPP, that means that whatever outcome you have at that point you will get it for ever more. FAPP.

I am not sure if I understand that, but if a situation is not determined factually at some point (which I understand from @StevieTNZ), it can become determined eventually. When we can find ourselves in a specific branch, the situation will match with the measurement. But that leaves the possibility open that the measurement has a part in determining which branch.

For instance:

• Cat = $|Dead \rangle + |Alive \rangle$
• Wigner's friend = $|friend \rangle(|Dead \rangle + |Alive \rangle)$ -> $|friend_{dead} \rangle|Dead \rangle + |friend_{alive} \rangle|Alive \rangle$
• Wigner = $Wigner(|friend_{dead} \rangle|Dead \rangle + |friend_{alive} \rangle|Alive \rangle)$ -> $|Wigner_{dead} \rangle|friend_{dead} \rangle|Dead \rangle + |Wigner_{alive} \rangle|friend_{alive} \rangle|Alive \rangle$

After his friend, Wigner still has a choice which branch he will take. This would be retrocausal, since Wigner comes after the poisoned jar.

But I think I make a mistake because there never was (except for a very short time) anything in superposition, right? Except for the single particle that was, right?

It seems to me the flow of things is as follows:

• Detector = $|0 \rangle + |1 \rangle$
• Cat = $|Cat \rangle(|0 \rangle + |1 \rangle)$ -> $|1 \rangle|Dead \rangle + |0 \rangle|Alive \rangle$ (a)

So now the cat decoheres. So then (a) is a superposition, but since the cat 'observed' itself, it agrees with itself that it is either dead or alive? So then we are left with:

Cat = $|0 \rangle|Alive \rangle$ (of course )?

 

[Derek P]

• Wigner = $Wigner(|friend_{dead} \rangle|Dead \rangle + |friend_{alive} \rangle|Alive \rangle)$ -> $|Wigner_{dead} \rangle|friend_{dead} \rangle|Dead \rangle + |Wigner_{alive} \rangle|friend_{alive} \rangle|Alive \rangle$

After his friend, Wigner still has a choice which branch he will take. This would be retrocausal, since Wigner comes after the poisoned jar.

You haven't included decoherence. Without decoherence both states persist in superposition so Wigner does not make a choice at all. Wigner simply interacts with |friend_dead⟩|Dead⟩ making |Wigner_dead>|friend_dead⟩|Dead⟩. So Wigner's state in that term is |Wigner_dead> and similarly for the alive state and term, just as you've written. No fancy retro-causal choices.

With decoherence and including the state of the environment you just add the |environment_dead> state to the "dead" term and |environment_alive> state to the "alive" term. So still no choice.

But with decoherence but then omitting or ignoring the state of the environment (perhaps on the grounds that we can't measure it) we have either |friend_dead⟩|Dead⟩ or |friend_alive⟩|Alive⟩ So Wigner interacts with which ever one we have. Again no retrocausality. Whatever the cat was, the friend saw. And whatever the friend saw, Wigner sees.

Note that the environment can be replaced by some of the many degrees of freedom that the cat has which don't have much to do with whether it is alive or dead. So yes, in that sense, the cat can decohere itself. But I wouldn't call it "observing itself" or "agreeing with itself" as that tends to obscure the fact that you're treating the cat as two systems.

 

[StevieTNZ]

Not sure who you're answering

I'm clarifying what decoherence is. It does not produce a definite outcome from, for example, two potentialities (e.g. cat being in a superposition of |alive> + |dead>).

 

[Derek P]

I'm clarifying what decoherence is. It does not produce a definite outcome from, for example, two potentialities (e.g. cat being in a superposition of |alive> + |dead>).

So am I :)

 

[entropy1]

@Derek P So my conjecture would be that Wigner somehow could choose which timeline to be in, if the by Wigner to be observed object ('friend and his lab') is still in isolation! Like he could have a "bias" to the outcome. Same holds for friend and the box of the cat.

The problem with that is, that Wigner's friend could have a bias towards $|Cat_{dead} \rangle$ while Wigner could have a bias towards $|Friend_{alivecat} \rangle$, so they wouldn't be in the same branch. So I think that is the problem with my interpretation.

I have another question: are there only two branches in this story? Is it only the particle that hits the detector in the cat's box that creates branches?

 

[Derek P]

@Derek P So my conjecture would be that Wigner somehow could choose which timeline to be in, if the by Wigner to be observed object ('friend and his lab') is still in isolation! Like he could have a "bias" to the outcome. Same holds for friend and the box of the cat.

The problem with that is, that Wigner's friend could have a bias towards $|Cat_{dead} \rangle$ while Wigner could have a bias towards $|Friend_{alivecat} \rangle$, so they wouldn't be in the same branch. So I think that is the problem with my interpretation.

I have another question: are there only two branches in this story? Is it only the particle that hits the detector in the cat's box that creates branches?

Arguably the emitting atom sets the process off. Where branching actually happens is a matter of semantics, you could define it as the original superposition or you can say decoherence separates them. Either way, there are just two "coarse-grained" branches. But because decoherence involves countless interactions there is a huge number of superposed micro-states to each branch.

I don't understand what you mean by having a bias, the observer can't choose to see a dead cat if it's actually alive in his branch..

 

[Derek P]

Cats have influences on the rest of the universe even if nobody looks at them.

Especially if nobody looks at them.

 

[entropy1]

I don't understand what you mean by having a bias, the observer can't choose to see a dead cat if it's actually alive in his branch..

If there is a superposition of branches for all Wigner knows (when the object is isolated in the box), then my conjecture says it is still not decided which branch he will be in. Of course this requires retrocausality, because the fact in the box is that decoherence already happened. Anyway, we would still have the (huge) problem that Wigner and his friend could end up in different branches, like:

Wigner's friend = $|friend_{deadcat} \rangle|Cat_{dead} \rangle$ and
Wigner = $|Wigner_{alivecat} \rangle|friend_{alivecat} \rangle|Cat_{alive} \rangle$

simultaneously. The friend (and te cat) would still be in superpostion after Wigner looked, because the friend is in the "dead"-branch and Wigner is in the "live"-branch where his friend is also in the "live"-branch. However, if the cat ends up dead, everyone ends up in the "dead"-branch. I think this is the fault in my conjecture. I am just wondering where the choice gets made, I think it is during decoherence or that it is the measurement problem.

 

[Derek P]

If there is a superposition of branches for all Wigner knows (when the object is isolated in the box), then my conjecture says it is still not decided which branch he will be in. Of course this requires retrocausality, because the fact in the box is that decoherence already happened. Anyway, we still have the (huge) problem that Wigner and his friend could end up in different branches.

You don't mean decoherence. Decoherence doesn't remove the superposition. You mean collapse of the wavefunction. If the cat has collapsed and Wigner doesn't know how, his later discovery doesn't change the past. You simply can't mix an epistemological interpretation for Wigner with a real collapse interpretation for the cat. Knowledge of the past may change, events in the past do not.

 

[entropy1]

Knowledge of the past may change, events in the past do not.

That is not what I mean. Events in the past, as well as events in the future, have an origin somewhere. I am suggesting that the events in the past could have been influenced by events in the future. That doesn't mean they change, it just means that their cause is not only in their past.

I thought that choosing a branch was choosing the past. But Wigner could make a differend choice than his friend, which would be inconsistent. If both branches coexist, a choice would be possible, but Wigner's friend would be a zombie in his world if she chose a different past and timeline than him.

 

[Derek P]

I am just wondering where the choice gets made, I think it is during decoherence or that it is the measurement problem.

The BRANCH structure does not involve a CHOICE. If there is a choice it means most of the branches are pruned away. Losing branches is an entirely different matter from Wigner choosing which branch to be in.

 

[entropy1]

The BRANCH structure does not involve a CHOICE. If there is a choice it means most of the branches are pruned away. Losing branches is an entirely different matter from Wigner choosing which branch to be in.

The confusing part to me, then, is that both branches have to be real, but at the same time only one is real.

 

[Derek P]

I thought that choosing a branch was choosing the past. But Wigner could make a differend choice than his friend, which would be inconsistent. If both branches coexist, a choice would be possible, but Wigner's friend would be a zombie in his world if she chose a different past and timeline than him.

Then I have no idea what you are talking about. So I'm going to have to go throuigh your replies point by point until I hit a snag and then ask you to refine your question...

I thought that choosing a branch was choosing the past.

Why did you think that? Nature makes a choice in some interpretations and in those interpretations the branch structuree is pruned back to a single stem. That is the choice and it is only the future that is affected - in the sense that some future possibilities are eliminated.

 

[Derek P]

The confusing part to me, then, is that both branches have to be real, but at the same time only one is real.

I didn't say that. In Many Worlds, all branches are real, in Copenhagen only one is. In either case the branch structure starts the same but in Copenhagen most branches fall off.

 

[entropy1]

Why did you think that?

Because if you could choose a branch, you would choose the past of it along with it.

 

[entropy1]

In Many Worlds, all branches are real

That's what I am talking about.

 

[Derek P]

Because if you could choose a branch, you would choose the past of it along with it.

Well that's the nature of branching. Many futures (whether real or merely possible) but just one past. You wouldn't choose the branch's past, you would be the branch's past. No choice of pasts.

 

[entropy1]

You wouldn't choose the branch's past, you would be the branch's past.

That is where we differ, or should I say differed, for I already found the inconsistence in my view. So you are probably right!

 

[Derek P]

That is where we differ, or should I say differed, because I already found the inconsistence in my view. So you are probably right!

Yes
I think you have been assuming that Wigner can still choose to be in either branch. That's not so. The dead-cat version of Wigner can only stay in the dead-cat world. Under collapse interpretations it's the only world. Under Many Worlds there is a living-cat world as well. But the version of Wigner in the dead-cat world cannot hop across to the living-cat world.