Exploring Schrodinger's Cat and Quantum Theory: A Gedankenexperiment

[Vacrin]

I'm not going to pretend i know everything about quantum theory nor even part of it. All I have is a incomplete basis of how things work. Please try to bare with me as I describe my gedankenexperiment.

Suppose we have the usual set up of schrodinger's cat, A cat in a box that might be either dead or alive based on a decaying atom that we can't know the state of until we look in the box. Suppose before we actually set this experiment up, we entangled radioactive particle with a non-radioactive particle. Then we separated the two of them, putting one in the box, and moving the other to another location to be measured at a later time. Assuming the the cat doesn't some how measure the radio active atom so entanglement is still viable. What happens if we wait long enough for the atom to be equally in the state of decayed and not decayed. And then measure the outside atom? Would we cause the atom inside to pick a state, and would that state be the same as if we were to open the box and look? Also how does the entanglement deal with the fact that there are 3 outcomes and it can only choose 2? ( either the atom is not decayed (so the outside atom can be up or down) or the atom is decayed and ='s neither up nor down? or does it still have to pick?) Not sure what state the atom would be in, or how we could tell weather the atom had decayed.

the point of this is to see if we can know whether or not the atom is in two states at once ( the cat is both alive and dead) or it is just probability that the cat is either alive or dead.


Thank you everyone who reads this. Please feel free to add anything to my description if it is lacking or flawed.

 

[PeterDonis]

A cat in a box that might be either dead or alive based on a decaying atom that we can't know the state of until we look in the box.

More precisely, the cat, at least according to standard QM, is in a superposition of being dead and being alive until a measurement is made that distinguishes the two.

What happens if we wait long enough for the atom to be equally in the state of decayed and not decayed. And then measure the outside atom? Would we cause the atom inside to pick a state, and would that state be the same as if we were to open the box and look?

Yes. More precisely, when you open the box and look, you will see the atom (and the cat) in the state that you would predict it to be in based on your measurement of the outside atom.

If, OTOH, you open the box and look *before* you measure the outside atom, then when you measured the outside atom, it would be in the state that you would predict it to be in, based on what you saw when you opened the box.

Also how does the entanglement deal with the fact that there are 3 outcomes and it can only choose 2?

There aren't 3 outcomes; there are only 2.

( either the atom is not decayed (so the outside atom can be up or down) or the atom is decayed and ='s neither up nor down? or does it still have to pick?)

It still has to pick. More precisely, when you measure the outside atom, you will measure it to be either up or down; and when you look at the atom inside the box, you will see it to be either decayed or not decayed. And these two measurement results will have to be consistent with the entanglement relation between the two atoms.

the point of this is to see if we can know whether or not the atom is in two states at once ( the cat is both alive and dead) or it is just probability that the cat is either alive or dead.

"The atom is in two states at once" is not a good way of describing the state it is in before measurement. A better way is that the atom is in a superposition of decayed and not decayed. (And the outside atom, before it is measured, is in a superposition of up and down.) A superposition is not the same as "being in both states at once". It is simply a different state, which is not either of the two being superposed.

Another way of putting this is as follows: consider the outside atom before it is measured. We say it is in a superposition of spin up and spin down. But suppose we change the orientation of our spin measuring device, so that it is oriented left-right instead of up-down. It could well be that, if we ran our experiment a thousand times and measured each outside atom, *all* of those atoms would be measured as spin-left. In other words, the "spin-left" state is a superposition of the "spin-up" and "spin-down" states. And similarly, the "spin-up" state is a superposition of the "spin-left" and "spin-right" states. And so on.

In other words, whether or not a state is a superposition depends on what measurement you make on it. There will always be some measurement that, when made on that state, always gives the *same* result; so with respect to that measurement, the state is *not* a superposition. So being a superposition is not a property of the state alone; it's a property of the state and the measurement together. That's why it's not a good idea to think of superpositions as "being in two states at once".