Law of conservation energy according to NOETHER'S THEOREM.

Conservation of energy is, perhaps, the most solidly established law of physics.  It is not violated by any known process.

The question of "what is energy" was answered in a definitive way by Emmy Noether, a woman who Einstein called one of the greatest mathematicians of all time.  She showed that if you knew the equations of physics (they could by Maxwell's equations, or relativity, or anything else) then you could find a combination of your parameters (typically velocity, position, mass, etc.) that would not change with time. This method gave the quantity that she recognized was "energy" in all previous theories.  Her work is called "Noether's Theorem"  and you can look it up on Wikipedia.  When physicists come up with a new theory, they calculated the energy by using Noether's theorem.

In quantum physics, energy is conserved.  However, when you look at the equations you derive, it often appears that energy is not conserved in the details of the process.  For example, in "tunneling" the particle appears to be inside the potential barrier.  But that is only a way of looking at the equations; for the actual observables, the energy is indeed conserved. You don't actually observe the particle when it is inside the barrier, presumably violating energy conservation.

The uncertainty principle says that when you are about to measure a state, you will not know exactly what energy you will observe.  Yet the conservation of energy is still absolute.  If you put in a precisely known amount of energy, then what you will observe will be that energy, made uncertain by the process of measurement which could disturb that value.

The photo of  EMMY NOETEHR is in below link.

https://qph.is.quoracdn.net/main-qimg-2a1743c09d7e6b4af500fa2fe4890b5b?convert_to_webp=true