Instead of opening the box to find out whether the cat is alive or dead, let’s analyze the single radioactive atom whose half-life is one hour. Let |U> and |D> be the states of the atom if it’s undecayed or decayed after one hour, respectively.
Since, the undecayed and decayed states are mutually exclusive for a single atom, one has = 0.
Therefore, it’s sufficient to check after one hour whether the atom is remaining undecayed or decayed in order to infer the actual state of the cat, whether it’s alive or dead, without opening the box. Hence, there is no paradox at a single-quantum’s single event.
Suppose that there are a large number of similar experimental setups. Then, surely, half of the cats will be alive and the other half, dead after one hour. The statistical average yields a probability ½ for both live and dead cats. If one uses this statistical average/probability to a single experimental situation, then we will encounter the cat paradox, i.e., the cat is both alive and dead at the same time until the box is opened. Also, the same statistical average implies that the single atom is in both undecayed and decayed states at the same time.
The final conclusion is that the cat states so far observed in laboratories are due to the statistical nature of doing the experiment. Moreover, as one can note from the above, there is no need to adopt any particular interpretation of quantum mechanics to resolve the cat paradox at a single-quantum’s single event.
I welcome your valuable insights and comments.
Thanks and best regards … N.G.
(PS: What's the meaning of half-life for a single radioactive atom?)
The reason behind asking the above question:
The actual doubt one may express in this question is whether it's allowed to check the radioactive atom or not after one hour.
But, it’s necessary to separate the radioactive atom from the rest of the Schrodinger’s Cat experimental setup after one hour; otherwise, it will anyhow decay at some later time, if it didn’t before one hour, and the cat will be surely dead.
Now the question is, whether the separated atom can be subjected to observation or not.
Case (i): If the atom has decayed, then decayed products and the emitted particle will be in an entangled state. However, the moment the emitted particle interacts with the Geiger counter, the entanglement is lost, according to the quantum formalism. However, a new entanglement forms between the particle and the Geiger counter.
Case (ii): If it didn’t decay, then nothing happened between the atom and the rest of the experimental setup.
In both the above cases, observation on the radioactive atom after one hour has no effect on the rest of the experimental set up and it becomes trivial to infer whether the cat is dead or alive.
However, if the same experiment is done on a large number of similar systems, then, half of the cats will be in dead state and the other half, in live state. The statistical average yields a probability ½ for dead and live cat. And the same statistical average also tells that the single-atom is in a superposition of both decayed and undecayed states. If this statistical average is used to describe a single experiment involving a single quantum event, then the cat paradox pops up.
It will appear like, the observation is collapsing the state of the atom randomly into either decayed or undecayed state, throwing the cat into corresponding dead or live state.
Hence, the observation seems to be responsible for the decay or undecay of the radioactive atom, which is absurd to say.
Dear Prof. Srecko Amrit Sorli ,
I completely agree with your statement, "The fact is, the cat is alive or dead. It cannot be both" and that's my whole point as well. I am just trying to deduce the same fact using single quantum event.
Moreover, the act of opening the box was said to be the cause for collapsing the superposition state of dead and live cat to either dead or live one. This also implies that, the same is the cause for collapsing the superposition of the radioactive atom into either decayed or undecayed state which is clearly absurd because the radioactive decay is due to weak interactions and have nothing to do with our opening the box to find out whether the cat is dead or alive.
Thanking you and best regards ...N.G.
PS: If I don't remember whether I left my hat at my office or at home does not mean that the hat is in a state of superposition of being both at office and at home. My ignorance can't be the reason for the superposition.....
All concepts and analyzes come from the statistical perspective of the problem, while it may conflict with the reality of the immediate situation.
@ T. H. Ray
Yes, of course dear Sir,
For example, the individual clicks of a single photon detector ....
Freedmann-Clauser, followed by Allan Aspect et al. , were the first ones to achieve single photon source in the context of Bell inequality experiments. Later, Young's double slit experiment was done with individual quanta like photons, electrons, neutrons, atoms, molecules and even with some viruses.
If I am not wrong, Prof. Feynmann was the first one to theoretically propose Young"s double slit experiment with individual electrons. See Feynmann Lectures, Vol. III. Also the link below:
https://youtu.be/b0EChbwSuuQ
Thanking you and best regards,
N. G
@ T H Ray,
I forgot to include a recent double alt experiment done with individual particle of antimatter ...
N. Gurappa
Isn't every experiment prepared in the higher energy state? = 0 therefore cannot hold, unless a dead cat is put into the box at the initial condition.
Forgive me, please. I had completely forgotten about this forum. One of the great disadvantages of being 75 years old.
Tom
N. Gurappa
I had another thought. If the cat were replaced by a 2-state particle, it seems to me that it has to occupy the same state as the pair, for the reason that the experiment is compelled to be prepared in the higher energy state.
So has to be non zero. Important implications for research into the quantum vacuum state.
I also forgotten, some of the concepts in the question. When looking at the Popular answer of the 'Deleted profile'; it's not a paradox, until you add for example that it could be 1/2 , bcz it agrees with the figures 0 and 1. (Then, the paradox is that it was not a state of the cat). ..to become quantum mechanics; there is need to for example add the atoms assumption, bcz the actual cat and box was observed , 'to begin with'.?
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