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Well, I'm not sure whether you are enquiring as to a definition of the concept of falsification or whether you want clarification onexactly how you would go about testing for falsification.
The key principle is that a good scientific theory prohibits particular occurences or events. The more it prohibits, the more testable it is.
If a theory prohibits a particular occurence and that occurence can be (repeatedly) reproduced, it is considered falsified.
For example, If I made the assertion that all foxes are red, it is equivillent to the assertion that: "you will not find a fox that is not red." Now, it doesn't matter how many red foxes I come accross, the theory is not considered verified. However, if I find a black fox, my theory has now been falsified (and must consequantially be revised or rejected).
Ok, lets go back to the example with relaticistic theory and newton mechanics.