A followup to my previous question

[Fiziqs]

Thank you all for your help on my previous question concerning MWI (Interaction across many-worlds). Your answers have been helpful, even if they haven't actually made the picture much clearer They have at least made the debate clearer. I don't really understand all the "wave function" mumbo jumbo, so I have been trying to visualize just what is going on, and what wave function, entanglement, and collapse, et al, are all about.

So I was considering Schrodinger's cat. If you and I set up the experiment as described, we create a condition of superposition for the cat, inside the box. Now if you open the box and look inside, and then close it again before I have a chance to see the outcome. What is the state of the cat?

I can see how, for you, the cat is definitely either alive or dead. The cat is no longer in a state of superposition. But I still have no way of knowing the cat's condition for sure. I could ask you, but perhaps I'm a member of PETA sent to oversee your experiment, in which case you might well be lying, due to the fact that you don't want me to know the real state of the cat. For me, isn't the cat still in a state of superposition? Isn't the "collapse" of the wave function dependent upon the availability, to me, of the information about the state of the cat. I fail to see how your knowledge concerning the state of the cat, changes my potential knowledge of the state of the cat, and isn't that the key to wave function collapse? I have no way of knowing the state of the cat. The information is completely unavailable to me. Therefore, isn't the cat still in a state of superposition? But you looked at the cat, which means its wave function must have collapsed. So which is it? Has the wave function collapsed, remained, or both?

But this raises another question, how can the cat be in a state of superposition for me, and not for you. We're standing right beside each other, how can the cat be in two different states at the same time? The obvious answer, it seems to me, is that it isn't, the cat is still in a state of superposition. But what does that mean concerning your condition then? It would seem that for me, you must be in a state of superposition too. Even though I'm looking right at you. You could be lying, or you could be telling the truth. Two opposite states. Under such conditions wouldn't you be in a state of superposition? After all, you could be lying, or you could be telling the truth. Two possibilities, existing at the same time. Is this possible?

Anyway I have more questions, but I'll wait to read your answers to these questions and then hopefully I'll be able to answer any further questions on my own. Of course I'm always going to have more questions.

 

[Bill_K]

how can the cat be in a state of superposition for me, and not for you.

Exactly, this is the whole point to the paradox, the reason for considering a cat, who must himself "know" whether he is alive or dead, and yet to me he is half and half.

So now we're extending it one more level, Person A considers a system with one component: the cat. Person B considers a system with two components: the cat and person A. At t = 0 only the cat knows his state. Person A says the cat is in a superposition. When A opens his box he discovers the cat's state. To him, the cat's state has now been measured and its wavefunction has been reduced.

But to B, what has happened is that person A and the cat are now entangled. There is a superposition between two states: (cat alive, A knows he's alive) and (cat dead, A knows he's dead). Step two: when B opens his box, the state of the combined system is measured and its wavefunction reduced. Just as before.

Of course it doesn't have to stop there. B could also be in a bigger box along with A and the cat, and some person C outside considering the combined system would still not know its state. And so on and so on.

Be careful when you say "the" wavefunction of the cat, for it depends on exactly which system you're considering.

 

[Fiziqs]

Exactly, this is the whole point to the paradox, the reason for considering a cat, who must himself "know" whether he is alive or dead, and yet to me he is half and half.

Thank you Bill K, I had considered this, but in so doing it brought up another question, having to do with MWI.

If I understand the thought experiment correctly, before either Person "A", or Person "B", looks in the box, the cat is in a state of superposition. It couldn't accurately be said that the cat was "either" alive or dead, but rather the cat is actually "both" alive and dead. Superposition is a state of existence all its own, it isn't merely a mathematical construct, it actually exists. So the cat in the box can exist in three possible states:

1. It could be alive.
2. It could be dead.
3. It could be in a state of superposition. (Both)

These are three distinct states. Now if Person "A" looks in the box, the cat will then exist in at least two of these states simultaneously. To Person "A" the cat is either in state 1 or 2, but definitely not 3. But for Person "B" the cat is definitely in state 3. To me this seems to support MWI. Because the cat still exists in at least two of its three possible states. The wave function of the cat hasn't "collapsed" into one or the other. As far as Person "B" is concerned the cat's state may have become entangled with Person "A"'s state, but the cat is still in state 3.

To me this seems to support the idea that the wave function does not collapse, but rather Person "A" and Person "B" must now exist in separate "worlds" as it were. The only way around this that I can see, is if the only "reality" is either Person "A"'s or Person "B"'s. Without "many worlds" both realities cannot exist. They are mutually exclusive.

Without MWI this would essentially mean that the only "reality" is mine. I hope that my thought process at least makes sense, even if it's inaccurate.

So what am I missing?

 

[Mark M]

This is similar to Everett's example in his dissertation, and in my opinion, is an extremely flawed one. The problem that arises is that you treat the wavefunction as an objectively existing entity, but that isn't what it is (at least not in standard quantum mechanics). Instead, it is a subjective phenomenon that represents the information you posses about the system, and the probabilities of getting different results. So, different observers - say, the ones in your example, a a detector, etc. Have different information available to them. Another issue is a probabilistic one - how could the Born Rule, which is absolutely integral to quantum mechanics, be correct in MWI?

 

[Fiziqs]

This is similar to Everett's example in his dissertation, and in my opinion, is an extremely flawed one. The problem that arises is that you treat the wavefunction as an objectively existing entity, but that isn't what it is (at least not in standard quantum mechanics). Instead, it is a subjective phenomenon that represents the information you posses about the system, and the probabilities of getting different results. So, different observers - say, the ones in your example, a a detector, etc. Have different information available to them. Another issue is a probabilistic one - how could the Born Rule, which is absolutely integral to quantum mechanics, be correct in MWI?

Thank you Mark, it's going to take me awhile to process your answer. I'm not even sure what the Born Rule is...but I'll go read up on it.

I'm glad to see that I was at least thinking along the same lines as someone like Everett who actually knew something about this stuff. I thought that I was just being an idiot again.

Anyway, I'll be back with more questions I'm sure.