Conservation of Relativistic mass and thus energy is easily proven by considering an inelastic collision of two bodies while invoking the conservation of momentum. As such the momentum law appears more primitive. Is this somehow an artefact of momentum - space and energy- time as conjugate variables and the implicit necessity to assume causality in constructing such a scenario?
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Emmy Noether discovered a fundamental connection between symmetries and conservation laws, embodied in her famous theorem. In simple terms, Noether's theorem is that
For every symmetry in a physical system, there must be a conserved quantity.
The proof requires neither Lorentz invariance nor causality.
By applying Noether's theorem, we find that energy conservation is connected to the symmetry of time translations, $t \to t + \delta t$, and that momentum conservation is connected to the symmetry of space translations, $x \to x + \delta x$.
Within a relativistic theory, we can write space and time translations collectively as translations of a position four-vector, $x_\mu \to x_\mu + \delta x_\mu$. By applying Noether's theorem, we find that energy-momentum, $p_\mu = (E,\vec p$), is conserved.
The conservation of energy and momentum appear on an equal-footing from Noether's theorem; neither one is more "primitive" than the other.
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