Undergrad Quantum Superposition While Observing Phenomena?

[DQuantum14]

I decided to perform a little thought experiment -- without the mathematics.
Assume we have two Schrodingers' Cats. After a while, they will be in a superposition of being alive and dead at the same time. Now assume that they are entangled, and we open the boxes at the exact same time.
Cases:
Cat 1 and 2 are alive
Cat 1 and 2 are dead
Cat 1 is alive, 2 is dead
Cat 1 is dead, 2 is alive

However, as they are entangled, the opposite must happen to the other cat, so the two cats cannot be both alive and dead at the same time -- or can they? Since you are opening the two boxes, or measuring the states of the cats at the exact same time, aren't all of these cases possible? If they are both dead, let's say, they also both must be alive at the same time, due to their entanglement. Therefore, even after measuring the states of the cats, there is a superposition happening.

Now assume there are two entangled particles, with a clockwise and counterclockwise spin at the same time. If both particles' states are measured at the same time, will the particles be in a superposition even after measurement due to entanglement?

I have heard that entanglement is an instantaneous process, but assuming both boxes are opened/both particles are measured at the same time, will a second superposition occur?

 

[Simon Bridge]

I decided to perform a little thought experiment -- without the mathematics.
Assume we have two Schrodingers' Cats. After a while, they will be in a superposition of being alive and dead at the same time. Now assume that they are entangled, and we open the boxes at the exact same time.
Cases:
Cat 1 and 2 are alive
Cat 1 and 2 are dead
Cat 1 is alive, 2 is dead
Cat 1 is dead, 2 is alive

... these last options describe 4 states that are only available if the overall state is not an entangled state, so you have written a contradiction.
The entangled state you are thinking of is a superposition of the third and fourth ones.
Think of the word "entangled" is a technical term that describes a class of total state ... sometimes used loosely to say that the individual states are not independent.

It does not matter which order the cat states are measured or if the measurement is simultaneous...
(note: it is always possible to find a reference frame where the measurements are simultaneous... the probabilities must still hold.)

Nice clear lecture on the basics of entangled states
http://www.lecture-notes.co.uk/susskind/quantum-entanglements/lecture-5/example-states/
- the notation |x,y> is just a state so |u,d> is a 2-particle state where the 1st one is spin-up and the second one is spin-down. The 4 independent cat states would be |aa>, |ad>, |da>, |dd>... much of the maths can be skimmed: just assume he did it right.

The main point of the Schrödinger cat experiment is to link the fates of the cats to a quantum system ... where the cat's fate is tied to a measurement of the system.
Try this for an entangled particle system.

 

[DQuantum14]

I see.. thanks!

 

[bhobba]

After a while, they will be in a superposition of being alive and dead at the same time.

A cat can never, ever be in a superposition of alive and dead. Its utterly impossible as cats are classical objects with definite position. The positions of the constituent parts of alive and dead cats are totally different eg the lungs and heart of an alive cat moves, but a dead cat doesn't.

Thanks
Bill

 

[Simon Bridge]

... which is, of course, the point of the Schrodingers Cat paradox: linking a QM system with a classical, macroscopic, one, and asking questions about the nature of measurement etc. The proposed mod would be to put two cats in boxes with entangled QM systems.