![]() ![]() That's why Noether's theorem didn't apply. The conservation law for the mass defined in this way didn't lead to any symmetries because the definition only depends on parameters - masses of all point masses are parameters - and not on dynamical, time-dependence quantities such as the positions or velocities. In their understanding of the world, the total mass of the Universe was the sum of the rest masses of the electrons, protons, and other massive particles. ![]() So they believed that mass was conserved even if the energy is not included. In the old world "before Marie Curie", people didn't know any relativity or any other indications of relativistic physics such as radioactivity. Its conservation is linked to the time-translational symmetry of the laws of physics. So up to the conventional factor $c^2$, the total energy - including the latent one - and the total mass is the same thing. For example, uranium power plants convert about 0.1% of the uranium mass to a huge energy, according to the $E=mc^2$ formula. ![]() In the real world, mass may be converted to energy. Noether's relationship implies that for every conserved quantity, there is a symmetry, and vice versa. ![]()
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