Isn't Schrodinger's cat doomed anyways?

[Bharath Siva]

I am not a physicist, just a mere electrical engineer (who has off late developed an interest in quantum mechanics). I have a few questions about the Schrödinger cat thought experiment and about whether quantum entangled states can be preserved indefinitely forever, at least theoretically.Please excuse my questions if they sound ridiculous.

My questions are as follows:
1. With regard to Schrödinger's original thought experiment with the cat, isn't true that as time goes to infinity, the cat HAS to be dead, whether the box is opened or not? There is a probabilistic reason for this, as time goes to infinity, the unstable radioactive source has to have emitted the particle with probability 1 and so the cat HAS to have died. So if we do not open the box at all for an infinite time, the cat HAS to be dead with probability 1 and so this leads me to believe that with time, the quantum state (i.e. the wave function) of the cat evolves to the dead state and so the cat somehow gets into an untangled state of DEAD. Is this reasoning correct? Or am I missing something?
2. The previous question leads me to believe that in general, quantum entanglement cannot be preserved for an indefinitely long time, even theoretically. At some point, the wave function of entangled particles HAS to collapse to 1 steady state with time. Is this reasoning also correct or am I again missing something?

 

[StevieTNZ]

1. With regard to Schrödinger's original thought experiment with the cat, isn't true that as time goes to infinity, the cat HAS to be dead, whether the box is opened or not? There is a probabilistic reason for this, as time goes to infinity, the unstable radioactive source has to have emitted the particle with probability 1 and so the cat HAS to have died. So if we do not open the box at all for an infinite time, the cat HAS to be dead with probability 1 and so this leads me to believe that with time, the quantum state (i.e. the wave function) of the cat evolves to the dead state and so the cat somehow gets into an untangled state of DEAD. Is this reasoning correct? Or am I missing something?

Welcome to PF!

"whether the box is opened or not?"
There is 0.5 probability, if we 'assume' macroscopic objects and the environment they interact with are in a superposition, of the cat being alive at least at some point before infinity, if a measurement is made.

 

[Bharath Siva]

Welcome to PF!

"whether the box is opened or not?"
There is 0.5 probability, if we 'assume' macroscopic objects and the environment they interact with are in a superposition, of the cat being alive at least at some point before infinity, if a measurement is made.

I don't disagree with what you say. However, with time, isn't it true that the probability that the cat is in state DEAD seems to increase? What I am trying to say is that, even if I don't open the box, I know that the probability that the cat is in the DEAD state keeps increasing with time, because the probability that the radioactive source will emit a particle keeps increasing with time? Since the cat's fate is ultimately tied to that of the source, isn't there an intrinsic evolution of the cat's state towards the dead state even if we don't make a measurement?

 

[StevieTNZ]

I don't disagree with what you say. However, with time, isn't it true that the probability that the cat is in state DEAD seems to increase? What I am trying to say is that, even if I don't open the box, I know that the probability that the cat is in the DEAD state keeps increasing with time, because the probability that the radioactive source will emit a particle keeps increasing with time? Since the cat's fate is ultimately tied to that of the source, isn't there an intrinsic evolution of the cat's state towards the dead state even if we don't make a measurement?

I am unsure whether over time there would be more likelihood of the radioactive source to emit a particle, but this may be correct - https://en.wikipedia.org/wiki/Radioactive_decay

The chance that a given atom will decay never changes, that is, it does not matter how long the atom has existed.

 

[Nugatory]

1. With regard to Schrödinger's original thought experiment with the cat, isn't true that as time goes to infinity, the cat HAS to be dead, whether the box is opened or not? There is a probabilistic reason for this, as time goes to infinity, the unstable radioactive source has to have emitted the particle with probability 1 and so the cat HAS to have died. So if we do not open the box at all for an infinite time, the cat HAS to be dead with probability 1 and so this leads me to believe that with time, the quantum state (i.e. the wave function) of the cat evolves to the dead state and so the cat somehow gets into an untangled state of DEAD. Is this reasoning correct? Or am I missing something?

You're doing fine, that's pretty much how it works. The longer the cat is in the box the more likely it is that the decay will occur and the more likely it is that the cat will die. That's true whether we open the box and look or not. There's nothing especially surprising about this, and you don't need quantum mechanics to explain it.
(That's actually the point of Schrödinger's thought experiment. He wasn't seriously suggesting that the cat might be in a dead/alive superposition until someone looked, he was identifying a problem in the 1920s-vintage understanding of QM, namely that the theory as it was then understood said the we'd have to open the box to eliminate that superposition).

2. The previous question leads me to believe that in general, quantum entanglement cannot be preserved for an indefinitely long time, even theoretically. At some point, the wave function of entangled particles HAS to collapse to 1 steady state with time. Is this reasoning also correct or am I again missing something?

Not "in general", as it depends on the system. The two electrons in the ground state of a helium atom can maintain their entangled state pretty much for the lifetime of the universe. On the order hand, a macroscopic object like a cat composed of maybe 10²⁶ particles will evolve into either a live state or a dead state in an infinitesimal fraction of a second.

If you get a chance, try David Lindley's book "Where does the weirdness go?". It's a layman-friendly summary of the advances since Schrödinger posed his thought experiment 85 years ago.

 

[Bharath Siva]

You're doing fine, that's pretty much how it works. The longer the cat is in the box the more likely it is that the decay will occur and the more likely it is that the cat will die. That's true whether we open the box and look or not. There's nothing especially surprising about this, and you don't need quantum mechanics to explain it.
(That's actually the point of Schrödinger's thought experiment. He wasn't seriously suggesting that the cat might be in a dead/alive superposition until someone looked, he was identifying a problem in the 1920s-vintage understanding of QM, namely that the theory as it was then understood said the we'd have to open the box to eliminate that superposition).

Not "in general", as it depends on the system. The two electrons in the ground state of a helium atom can maintain their entangled state pretty much for the lifetime of the universe. On the order hand, a macroscopic object like a cat composed of maybe 10²⁶ particles will evolve into either a live state or a dead state in an infinitesimal fraction of a second.

If you get a chance, try David Lindley's book "Where does the weirdness go?". It's a layman-friendly summary of the advances since Schrödinger posed his thought experiment 85 years ago.

Thanks for this information. It has clarified my doubt.