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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 ?

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  • $\begingroup$ The kinetic energy is not unique. That is, not all observer will measure it to have the same value. This is not a problem for the conservation of energy, because the conservation rule presupposes that the before and after measurements are made in the same frame of reference. $\endgroup$ – dmckee --- ex-moderator kitten May 4 '15 at 18:43
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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.

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  • $\begingroup$ Meh. This is strictly true but not helpful unless the OP is more advanced that the question suggests. For the purposes of day-to-day understanding the the Galilean transformation is fine and a lot less confusing than the Lorentz transformation. $\endgroup$ – dmckee --- ex-moderator kitten May 4 '15 at 18:45
  • $\begingroup$ So they can agree ? Is there any importance that you can proof you can move or not move $\endgroup$ – Arman Çam May 4 '15 at 18:47
  • $\begingroup$ @dmckee Though it is true and I also know that OP doesn't have the knowledge of SR, I didn't know how else to answer since Galilean transformations can lead to paradoxes like that. I could also say that you set the kinetic energy to be zero for an object that is not moving in your reference frame, which I find to be really vague. eg. I am now going around the sun and the milky way but I don't say that my car has a kinetic energy of such and such joules, as far as the effects of these motions is not present. $\endgroup$ – Gonenc May 4 '15 at 18:48
  • $\begingroup$ @ArmanÇam Yes of course it is important that you can prove (actually it is somewhat postulated) you cannot tell if you are moving or not as long as you don't look out the window. The very principles of SR are based on this fact. $\endgroup$ – Gonenc May 4 '15 at 18:50
  • $\begingroup$ There is no "paradox" here. Not in the Galilean transformations nor in the Lorentz transformations. Kinetic energy is not a invariant quantity in either case, and observers in different frames will get different values for both theories. $\endgroup$ – dmckee --- ex-moderator kitten May 4 '15 at 18:51

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