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What is an inertial frame of reference? Suppose in our location we do a variety of experiments and verify fundamental laws of physics. Then we are in an inertial frame of reference! What is more, ANY other frame of reference moving at constant velocity relative to us is ALSO an inertial frame of reference.
What we mainly need from our discussion of relativity is the correct, general expressions for things like momentum, kinetic energy, total energy, etc. A reminder that the energy of a system is a very abstract idea! By definition, the value of an energy is always arbitrary up to an additive constant, and the same object observed from different inertial frames obviously has a totally different kinetic energy in each frame. This is vitally important in particle physics, where the largest possible energy needs to be brought into the system of two colliding particles, in order to find new things. As a result of the way energy transforms relativistically, high energy experiments MUST be done in the center-of-momentum frame, which requires two colliding beams instead of a beam incident on a fixed target. Otherwise, almost all the beam energy provided by a particle accelerator is lost in the recoil of the target particle. [See pages 124 - 5 in our text.] Do you know what an eV (electron volt) is? Then what is a GeV? In physics we measure masses in energy units. A proton mass is roughly 1 GeV or 1000 MeV.
