I am confused about Relative Motion.Lets suppose we have one train and two observer.One of them inside the train and the other one is outside.Lets think the outside observer see the train moves a constant velocity v.The observer in the train will be think it is not moving cause of Galileo Principle.The outside observer will think kinetic energy will be $mv^2/2$ but the inside observer cant say anything (or will say zero cause he will think its not moving). Now lets think a special situation which two observer can agree the speed.(I know its not possible but lets think that's possible). In this case Can two observers agree on kinetic energy of train(In this case again its violates Galileo principle cause the observer in the train know its moving but he cant proof)here I am started to confused.What can be solution Can they agree on kinetic energy cause of no proof of movement ?
First of all Galilean Transformation laws are not valid in most cases. For the moving reference frames the special theory of relativity is more suitable. In fact it is the most suitable one given the experimental data. In special relativity one defines a so-called energy-momentum four vector, whose magnitude every observer in an inertial reference frame agrees upon.