Changes

*If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained. After a measurement is made, the wave function is permanently changed in such a way that any successive measurement will certainly return the same value. This is called the collapse of the wave function.

*If we measure such an observable, generally the wave function does not predict exactly which value we will obtain. Instead, the wave function gives us the probability that a certain value will be obtained. After a measurement is made, the wave function is permanently changed in such a way that any successive measurement will certainly return the same value. This is called the collapse of the wave function.

===Random collapse of wave function===

===Collapse of The Wave Function===

[[File:norm.png|right|150x250px|thumb|An example of a wave that could be a position function.  (Actual position functions are normally much more concentrated.)]]

[[File:norm.png|right|150x250px|thumb|An example of a wave that could be a position function.  (Actual position functions are normally much more concentrated.)]]

A particle is traditionally considered to be fixed at one definite point. However, each particle's position function is a wave, that stretches over space, giving the probability of finding the particle at each point. While there might be a 99% chance of finding a particle within 2 angstroms of a specific location, the function always has nonzero "tails" everywhere else in the universe. This means that there is always an infinitesimal chance of the particle suddenly "jumping" a foot or even a light-year away from its original location.

When speaking in the quantum sense, it becomes impossible to make definite statements such as "the particle is here". This is a consequence of the Heisenberg Uncertainty which (simply) states that particles do move. Thus the only useful way one can talk about the position of a particle is the likelihood that it exists at any given spot. The wave function is just this, it tells us the probability of finding the particle in one place or another. This wave function can be "collapsed" if the particle is observed. What this means is that if the particle is measured to be in one spot, then is quickly measured again the probability of finding the particle around that position is drastically increased. Graphically the wave function will peak at the location where the particle was measured. If the particle is not measured again it will take on its original wave function.

 

Scientists have tried but failed to find a way to predict where the wave function will "collapse"; that is, where the particle will actually appear.

===The uncertainty principle===

===The uncertainty principle===