Why we can't prove the law of conservation of energy?

A conservation law is a hypothesis, based on observations and experiments. It is important to remember that a conservation law cannot be proved. It can be verified, or disproved, by

experiments. An experiment whose result is in conformity with the law verifies or substantiates the law; it does not prove the law. On the other

hand, a single experiment whose result goes against the law is enough to disprove it.

It would be wrong to ask somebody to prove the law of conservation of energy. This law is an

outcome of our experience over several centuries,

and it has been found to be valid in all

experiments, in mechanics, thermodynamics, electromagnetism, optics, atomic and nuclear

physics, or any other area.

Here's the most important thing to read:

Some students feel that they can prove the

conservation of mechanical energy from a body falling under gravity, by adding the kinetic and potential energies at a point and showing that it turns out to be constant. As pointed out above,

this is only a verification of the law, not its proof.

So, that's your answer! 

Hope you got it. 

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