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I was reading books where I realized an interesting thing:

In quantum, the evoluation of states/wave funciton is governed by hamiltonina operator $H$, which is bascially the energy operator.

In special and general relativity, the most important quantity, the four vector, is also bascially the energy of the similiar form.

In newtonian physics, one of the most fundmental things is also, well, energy.

But as we know, there are lots of more symmetry relation and conservative quantiities, i.e. spin, linear and anglular momentum. But non of them played the same role as that of the enery.

My question is that:

  1. What made it so unique for the "energy", more specifically, the energy in motion, played such an important role, that is almost fundmental across all theories and at the "first order", in physics.

  2. Is there theory in physics that "ditched" the center role of energy, rather paied a much more attention towards other conservative quantities? i.e. conservative of linear momentum in description of object's motion. (I'm thinking more like a field theory that depend heavily on some quantities other than "energy". )

J C
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  • Whether energy plays an important role or not depends on the problem at hand. In any case, the Hamiltonian $H$ is important because it generates time translations of the physical system. If we want to study the non-trivial, time-dependent evolution of a system, $H$ is what we need. – Avantgarde Nov 03 '18 at 05:53

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