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However, velocity is a frame dependent quantity. One reference frame may measure the velocity of a particle to be 1 m/s, while another frame might measure the velocity of the same particle to be 10 m/s. Furthermore, if we assume the mass of the particle is 2 kg, then the first frame will measure a kinetic energy (scalar quantity) of 1 joule and the second frame will measure 100 joules.

Clearly, these tensor quantities are not invariant with respect to the two frames. Am I confusing coordinate systems with reference frames?