What is a paradox?
A paradox is like a snake eating its own tail. You don't know how or where the thing starts or ends. Consider this,
You are 20 years old. You met with an old man today. After few days,you realised that man is the older form of you(from 2080). So how do you define this? Is it you meeting with your older form today or is it you living 80 years then meeting your younger form? Where did it start?
Confused? It's normal.I would recommend watching the movie predestination. Its worth the time!
Schrödinger's cat
It came as a thought of Erwin Schrödinger while discussing with Albert Einstein about Quantum mechanics.
Consider a setup where you put a cat, a flask containing hydrocyanic acid(poisonous), a hammer and a radioactive sample in a sealed box for one hour.
The amount of radioactive substance is so less that within an hour, there is equal probability that only one atom decays or none of the atoms decays.
If that one atom decays, it releases the hammer that breaks the flask of poison. The cat inhales the poison and dies.If no atom decays, the cat is still alive.
Now, Quantum physics states that both the situations are happening simultaneously, that is, the cat is both dead and alive, in multiple realities.
In one reality, the cat is lying dead and in the other, the cat is alive.This is called Quantum superposition just like wave superposition.
The system stops being a superposition of realities only when an observation is made. That is, only when the box is opened after an hour, the two realities collapse into one of the reality and we see either a dead cat or an alive cat.This establishes the so called parallel universe. That is, when the box is not yet opened,if in one universe the cat is alive, in the parallel universe the cat is dead and vice versa.
However, Classical mechanics says whether or not the observation is made, there is only one possibility. Either the cat is dead or its alive.
Take a moment and realise the beauty of this! :)