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I read that the Lorentz invariance Minkowski norm of the four-momentum

$$E^2-c^2\cdot \mathbf{p}^2=m^2\cdot c^4$$

has no analogue in Newtonian physics. But what about

$$E-\frac{\mathbf{p}^2}{2m}=0\quad ?$$

It might look trivial by the definition of kinetic energy, but it's still a relation between energy and momentum that's invariant under Galilei transforms.

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# I Newtonian analogue for Lorentz invariant four-momentum norm

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