I am confused about tensor invariance as it applies to velocity and energy. My understanding is a tensor is a mathematical quantity that has the same value for all coordinate systems. I also understand that a vector is a first order tensor and energy is a zero order tensor. Thus, they should have the same values for all coordinate systems.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# I Vector and Scalar Tensor Invariance

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