Saturday, July 24, 2010

Is Paul the wave function ?

Wave function is known as the mathematical model that used to calculate the probabilities of an observable. As an example wave function of an electron, Ψ(x,y,z) provides us the probabilities of finding it at the position x,y,z (actually modulus of squared wave function gives the probability) after the observation.
The phrase "after the observation" is very important in quantum mechanics. As an instance lets take the Schrödinger's cat. There is a cat inside a covered box and a gun is pointed to the cat. Triggering the gun is depended on a random event. Mechanism is gun will be triggered if a particular radiation happens within the period of the test. Hence there is a non-zero probability for both emission and non-emission. According to quantum mechanics, system is under quantum superposition until the observation is made. That is triggering and not-triggering at the same time which leads to the conclusion that cat is both dead and alive until it is observed.
When the observation is made, we can only see only one state, dead or alive. This is known as 'wave function collapsing'. From the superposition, it comes to a single state at the observation.
Lets go to the Paul's case. Lets assume the Germany vs Spain match is isolated so that quantum decoherance (avoidance of quantum superposition due to interaction/entanglement with environment) is avoided and no one observes the match. So match is in the superposition state of both teams are qualified for finals. Then we call our friend Paul, and give him the flags. He selects Spain and becomes a traitor.
Now, what happens ? we don't know the results of the match. But with the record of the Paul, we decide, chance of poor Germans to be in finals is 10% and 90% for spain. Isn't this the wave function ?
Then we go to Durban and open the gates of the ground to collapse the wave function. What we see is the verification of Paul's wave function...