1. Sep 1, 2014

### TheScienceOrca

http://en.wikipedia.org/wiki/Schrödinger's_cat

I don't understand, if the radioactive source is put in there then of course the Geiger counter will detect radioactivity so we know the cat must be dead?

2. Sep 1, 2014

### phinds

What did you not understand about the article's statement:

3. Sep 1, 2014

### TheScienceOrca

Thanks now I understand, I thought it would always be radioactive.

Doesn't this simply mean that we just don't know whether it's dead or alive?

Not that it's both dead and alive?

Thanks for the help

4. Sep 1, 2014

### phinds

It IS always radioactive, just at a low level.

Schrodinger came up with the cat thing to show how absurd the Copenhagen interpretation of QM can be sometimes. Yes, the cat is always either alive or dead, we just don't know which until we open the box and if it's dead, we don't know when it died (unless we put a timer on the counter).

Also, the moon really IS there whether it's being observed or not.

5. Sep 1, 2014

### TheScienceOrca

I see, so it could be alive or it could be dead.

When they said the statement it could be dead or alive at the same time I thought they meant both states at the same time. The cat can only be in one state at a time, but since we don't know it's state; it COULD be alive or it COULD be dead.

That is how they should state it so there is no confusion.

Correct me if I made any mistakes in my understanding.

6. Sep 1, 2014

### StevieTNZ

How do you come to that conclusion?

7. Sep 1, 2014

### Staff: Mentor

No, it's more counterintuitive than that. The cat can only be in one state at a time, yes. But the states |ALIVE> and |DEAD> are *not* the only possible states the cat can be in, according to quantum theory. It can also be in a more general state that, mathematically, we would write as

where a and b are complex numbers whose squared moduli add up to 1. (In general, a and b are time dependent; in the setup as Schrodinger originally gave it, a^2 decreases as time goes on, while b^2 increases). The point is that this general state |C> is a state which is a perfectly valid quantum state, according to the theory, but in which the cat is neither alive nor dead, nor is it correct to say that the cat "could" be alive or "could" be dead in this state. This state |C> that the cat is in during the experiment is simply a state that has no classical analogue, and no classical description like "cat alive" or "cat dead" or even "cat could be alive or could be dead".

We observe small objects like electrons in states like this all the time; but Schrodinger's point with the cat thought experiment was to raise the question of whether things like cats can really be in such states. (IIRC he thought they couldn't, and intended his thought experiment as a reductio ad absurdum of the claim that quantum mechanics was a complete theory.)

8. Sep 2, 2014

### Staff: Mentor

I think he is referring to the many threads we have had on this forum where many interpretations, via decoherence, lead to that.

All he forgot to mention is its interpretation dependant.

Thanks
Bill

9. Sep 2, 2014

### TheScienceOrca

But the thing is regardless of whatever state you would like to call the cat it's either dead or alive in actuality.

If it's not then what is the arrangement of atoms (the cat) that is inside the box while no one is observing the cat.

If you are saying that is not there, then when you observer the now alive or dead cat where did this atoms come from that the observer now sees.

10. Sep 2, 2014

### Staff: Mentor

Absolutely.

The purpose of Schroedinger's Cat is to highlight an issue with Copenhagen.

In Copenhagen observations occur in an assumed classical world. For Schroedinger's Cat it's trivial - it happens at the particle detector - everything is classical from that point on - the cat is not in some kind of superposition - its alive or dead - period.

The issue is how does a theory that assumes the existence of a classical world explain that world. What is needed is a fully quantum theory of measurement, and Schroedinger's Cat shows the difficulty with trying to do that.

Since then a lot of work has been done on decoherence and much progress made - but a few issues remain.

Thanks
Bill

11. Sep 2, 2014

### nikkkom

That's the point: QM math is saying that the cat *can be* in a state of a mix (linear superposition, mathematically speaking) of a dead cat and a living cat. It's not that we don't know whether the cat is dead. QM says that he is neither. That's what equations are saying.

And yet, we see either a dead cat, or living cat. QM is fine with it: it says that observable states must be eigenstates. *Observed* cat can't be a linear superposition of eigenstates. *Observed* cat will be seen in one eigenstate. Dead. Or Living.

Which made people realize that the phrase "in actuality" is not as unambiguous as we thought. What is "actuality"? What word "exists" means? Or word "real"? What happens when we "observe"?

For example, a box with Schrodinger's cat can be put in a bigger box, with a scientist inside the bigger box. And we are on the outside. The scientist opens a smaller box. He will see either a living cat or a dead cat. But we, on the outside, don't know what he sees. For *us*, the scientist is *still* in a superposition of "I see dead cat" and "I see living cat" states.

Last edited: Sep 2, 2014
12. Sep 2, 2014

### Staff: Mentor

I think it made people realize we need a quantum theory of measurement rather than semantics.

Not so sure after decoherence that's the case.

Thanks
Bill

13. Sep 2, 2014

### phinds

Well said !

14. Sep 2, 2014

### Staff: Mentor

This may be true; but if it's true, then quantum mechanics is incomplete.

The arrangement corresponding to the quantum state |C> = a|ALIVE> + b|DEAD>.

I'm not. Of course the atoms are "there"; the stuff inside the box has a quantum state. It's just not a quantum state that has any classical description.

Basically, you are claiming that anything that is "real" has to have a classical description. That may be true, but once again, *if* it's true, then quantum mechanics is incomplete, because quantum mechanics, as it stands, allows "real" things to be in states that have no classical description, like the state |C> above.

15. Sep 2, 2014

### Staff: Mentor

Decoherence is what ensures that the only branches of the wave function that have nonzero amplitudes are the branches |ALIVE>|sees alive> and |DEAD>|sees dead>. In other words, decoherence is what ensures that there aren't any branches where the cat is alive but the observer sees a dead cat, or where the cat is dead but the observer sees a live cat.

But decoherence, by itself, can't explain why only one branch of the wave function "survives" the measurement: i.e., it can't explain why the final wave function of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, as opposed to a|ALIVE>|sees alive> + b|DEAD>|sees dead>. The latter wave function is what you get when you just apply unitary evolution, i.e., without any collapse of the wave function. Decoherence doesn't collapse the wave function; so *if* it really is true that the final state of the whole system is either |ALIVE>|sees alive> *or* |DEAD>|sees dead>, and not a superposition of the two, then we need something more than just decoherence; we need a collapse. (This may be more or less what you meant when you said we need a quantum theory of measurement.)

16. Sep 2, 2014

### Staff: Mentor

You left out a very important qualifier here: observable states must be eigenstates of the operator corresponding to the observable. So the reason we only observe cats that are alive or dead is that the physical process we use to observe cats realizes an operator that has |ALIVE> and |DEAD> as its eigenstates.

But it's perfectly possible in principle that there is some *other* physical process that we could use to interact with cats, which realizes an operator with different eigenstates, say (1/sqrt(2))(|ALIVE> + |DEAD>) and (1/sqrt(2))(|ALIVE> - |DEAD>). If we could construct a cat-observing device that realized this operator, then it would observe cats in what we ordinarily call superpositions of being alive and being dead. But with respect to this other operator, those states would *not* be superpositions; they would be eigenstates.

17. Sep 2, 2014

### nikkkom

At a risk of starting to build my own interpretation, I'd say that it's possible that the reality is a|ALIVE>|sees alive> + b|DEAD>|sees dead>.
QM has linear superpositions as a valid solutions exactly because parts of linear superposition do not "feel" each other.
The quantum system "you" which "sees a dead cat" can't know that there is also a quantum system "you" which "sees a living cat", and the full reality is a linear superposition of these.

A "Big box with (scientist and small box with cat)" situation seems to be easier to explain if we postulate that both versions of scientist are "real". We don't think that scientist sees a definite state of the cat *before* we ask the scientist what he sees, right?

18. Sep 2, 2014

### Staff: Mentor

You don't need to build your own interpretation; this is just the MWI.

If we are modeling the scientist and the cat as both being "in the box", and our asking the scientist what he sees is what "opens the box", then that just pushes the question up a level: how do we model *our* state on interacting with the scientist? Asking the scientist what he sees just puts *us* into a superposition of hearing the scientist respond "I see a live cat" and hearing the scientist respond "I see a dead cat". (At least, it does if you believe the MWI.)

19. Sep 2, 2014

### nikkkom

While we are at it, can someone tell me which part of QM math says that observables are always eigenstates? This is a part which is less clear to me than the part where QM says that linear superpositions of solutions are solutions too.

20. Sep 2, 2014