To start, in quantum mechanics everything is viewed as a probability wave. For instance, the postion of an electron obiting an atom is given by a probability function (a wave function). This wave function can have many observable states but they all exist until you make an observation of teh electron. Once you make an observation, you force the wave function to one state – it’s called the collapse of the wave function. That state is randomly determined. A simple example (and this is really over-simplified but it gets the point across) is you flip a coin into the air. Now let’s suppose that we do this in the Space Shuttle in orbit so the coin just spins and doesn’t fall. As long as the coin is spinning there is a 50% probability that you will see heads and a 50% probability that you will see tails if you stop the spin. Until you do stop the spin, quantum theory would say that the coin is in both the heads and tails state. Stopping the spin is equivalent to making a measurement or observation, and the coin selects one of teh two states – heads or tails – to be in. But you don’t know which state will be selected when you stiop the spin – that state is determined by the wave function collapse. In this case the wave function is simple – it is 50% probability of heads and 50% probability of tails.
Now the poor Schrodinger’s cat is a thought experiment about wave functions. It goes like this. You place a cat inside a sealed opaque box. Inside the box is a radioactive source that decays with some half life. You set up a radiation counter inside teh box along with a poison gas container. When the radioactive substance has produced some number of counts that you have chosen randomly, the gas is released ending the cat’s life.
Now radioactive decay is governed by quantum mechanics. Thus there is a probability at any given time that the counter has not reached the fatal value and the cat is alive. But there is also 1 minus that probability that the poor cat had bad luck and the counter has reached the value causing the gas to fill the box and end the feline’s life. Since you can’t tell which has happend without opening the box, the cat is both alive and dead according to quantum theory. This thought experiment was used to show that there are fundamental flaws in quantum theory – namely the simultaneous occupation of many states by a system until a measurement is made. We would all argue that the cat is either dead or alive – not both at once – and all we need do is open the box to find out which it is. But from a quantum view point, the cat is both dead and alive and will remain that way until we open teh box.