The question becomes: before you open the box, is the cat alive or dead? Or is it somehow...both?
Your gut instinct is to say, "That's stupid. Of course it's either alive or dead. How the fuck could it be both?"
But the thing is, there are certain, non-cat-related experiments that we've done that REQUIRE the answer to be BOTH. Perhaps the simplest (and certainly the one we physicists learn about first) is the double-slit experiment. The basic idea is, you shoot a beam of something (light, gold atoms, DNA, doesn't really matter) at a slit, and it forms a pattern on a wall. It'll form this pattern even if you shoot your particles one at a time. Then, you close that slit and open another one, and fire your beam again. It forms a different pattern.
The problem is, the double-slit experiment doesn't tell you a thing about the cat.
Any single run of the cat experiment will have the cat either alive, or dead, before you open the box. 50% will be one, and 50% will be another.
Firing electrons at slits -- 1 or 2 -- does not change the fact that the electrons do have a location. We may not be able to measure it -- measuring requires an interaction, and the interaction will change what happens. There's a number that represents that ultimate limit -- plank's constant.
Toss electrons, one at a time, through a slit, see one pattern. Fine.
Toss electrons, one at a time, through another slit, see a different pattern. Fine.
In each case, you have electrons with a location. Different electrons have different locations. You don't get spots, you get slits. But slits made of one spot, then another spot, then another spot, etc. Each electron hits the screen at one point. Each electron has one location. Each cat is either alive or dead.
Toss electrons through a pair of slits, with detectors measuring the electrons: See a pair of slits (no interference) on the screen.
Remove the detectors: see the interference.
But in each case, you see spot, spot, spot. The final outcome location is different. The electron's path may not be linear, it may be doing quantum tunneling from point A to B as it "moves". In the process, it may move near the second slit, before coming back. Hence, the ability to "Detect the non local slit" and change the path.
But it has a single spot when you measure it.
The cat has a single state.
We may have no tools to describe it other than "We don't know, but a 40% chance of here, a 10% chance of here, a 10% chance of there, etc.". We may have no tools to describe it other than "We don't know, but a 50% chance of being alive".
It is not both.
It is "we don't know".
It is "we can not possibly know -- the universe does not let us know without changing the outcome".
But "Cannot know" is not the same as "Does not exist".
What is the "width" of an electron?
Since the location of an electron has uncertainty, there is a concept of "width" -- the area in which an electron might be found if you measured it.
If you have a single slit, then you are filtering out the "wide" electrons, that are too far off.
If you have a double slit?
If the two slits are close enough, that the "width" of the electrons includes both slits, what does the result look like? If the slits are far enough apart, that the width does not include both, what does the result look like?
My understanding is that if the two slits are far enough apart, you do NOT get any interference patterns.
The basic idea is, you shoot a beam of something (light, gold atoms, DNA, doesn't really matter) at a slit, and it forms a pattern on a wall.
But tossing bigger things at the slits means that the slits have to be closer to see the interference, and the slits have to be bigger to let the things through. Eventually, the "closeness" of the slits and the "wideness" of the slits means that you have one slit, not two.
Toss an electron at a single slit, it behaves one way.
Toss it at two slits, far enough apart that they are not within its "width", it behaves the same way.
Toss it at two slits within its width, and it "Sees" both, and behaves differently.
None of this is odd. How that behavior changes when the second slit is there is odd.
None of this has anything to do with the cat.
Each cat is alive or dead.
We can't tell ahead of time, only by opening and measuring.
Each electron goes to a location.
We can't tell ahead of time, only by putting a screen there and measure.