Schrodinger's Cat radioactive source

[bhobba]

Do you believe in this experiment the state of the atom whichever you call it alive or dead or both at same time or however do you believe it is directly relative to the state of the cat?

We know 100% for sure the cat is not in any kind of superposition that is detectable. In fact decoherence shows it decays to way way below our ability to detect very very quickly.

Thanks
Bill

 

[PeterDonis]

Do you believe in this experiment the state of the atom whichever you call it alive or dead or both at same time or however do you believe it is directly relative to the state of the cat?

The state of the system atom + cat looks like this:

a|atom intact>|cat alive> + b|atom decayed>|cat dead>

where the coefficients a and b are time-dependent (as I said before, a^2 decreases and b^2 increases as time passes), and a^2 + b^2 = 1.

This is a perfectly definite quantum state, but it does not have a classical description. It is *not* a state in which "we do not know" whether the atom is decayed or not decayed, or whether the cat is alive or dead.

 

[PeterDonis]

That is exactly what I am saying

Is it? It seems to me that you are saying that a theory of the kind you've been describing, where the only reason we can't predict exactly when a radioactive atom will decay is that we can't measure its properties accurately enough, can explain everything, and therefore it can explain the Schrodinger's cat experiment. But this amounts to saying that a local hidden variable theory can explain everything. It can't.

What atyy was saying is that a theory of the kind you've been describing *can't* explain everything; but it might turn out that a theory that *can* explain everything (which would *not* be a theory of the kind you've been describing), would have a theory of the kind you've been describing as a useful approximation for a case like the Schrodinger's cat experiment. (For what it's worth, I don't think that's very likely, but I can't say it isn't possible.)

 

[PeterDonis]

Sure. But it VERY quickly decays below our ability to detect.

But this is a limitation on our detection technology, not a limitation imposed by the laws of physics, correct? I.e., in principle there's nothing preventing us from eventually building a detection technology that *could* detect the superposition in this kind of scenario.

 

[nikkkom]

http://arxiv.org/abs/1007.4184 section 4.3.2, postulates 3 & 4
http://www.theory.caltech.edu/people/preskill/ph229/#lecture section 2.1, postulates 2 & 3

From the postulate of projective measurements, one can derive more general classes of measurements called POVMs. So some people prefer to use different axioms, making the POVMs fundamental rather than derived, eg.
http://arxiv.org/abs/1110.6815
http://arxiv.org/abs/0706.3526
http://arxiv.org/abs/0810.3536

Thanks, really helpful!

 

[bhobba]

But this is a limitation on our detection technology, not a limitation imposed by the laws of physics, correct?

Correct. But its used to explain the existence of the classical world that we generally interact with day to day unaided by technology. It happens so fast and goes to such a low level it's way below what can be detected even with the aid of our current most advanced technology, and certainly not unaided by it in everyday life.

In Schroedinger cat the thought experiment is not about someone who has some future technology (it may not even ever exist) that will allow them to detect not only the very quick decoherence of the cat but the decoherence that is going on around us all the time.

Thanks
Bill

 

[durant35]

Isn't it the case that the macroscopic object cannot be in a state of superposition in any instant if it isn't isolated? So decoherence happens at the particle detector and from that point on everything is classical, the cat evolves causally.

 

[bhobba]

Isn't it the case that the macroscopic object cannot be in a state of superposition in any instant if it isn't isolated? So decoherence happens at the particle detector and from that point on everything is classical, the cat evolves causally.

Yes - but the caveat is superposition of position.

This thread is so old I can't recall what I and others said - but I doubt I said anything to contradict that.

Thanks
Bill

 

[durant35]

But according to the MWI, it *is* a superposition (the mixed state is just an approximation). According to the MWI, unitary evolution is the only kind of evolution there is, and a unitary transformation can't turn a pure state into a mixed state.

(Bear in mind that I'm not necessarily agreeing with the MWI; I'm just trying to be clear about what it says.)

This is what PeterDonis said, that the mixed state is only an approximation. Is that only according to mwi? What does it mean for decoherence itself and the cat state?

 

[bhobba]

This is what PeterDonis said, that the mixed state is only an approximation. Is that only according to mwi? What does it mean for decoherence itself and the cat state?

Theoretically decoherence does not create an exact mixed state - but very very quickly is way way below detectability using current or any envisaged future technology. Some take this point to an extreme IMHO and claim its a big problem. IMHO it isn't, but there is no point in arguing it and I won't be drawn into it. IMHO it's how you approach applied areas where things are often like that. - they don't like things along the lines of for all practical purposes.

Thanks
Bill