I have fundamental question about what is called the “law of conservation of energy”.
We all hear about the tidal power stations which using the tidal power. The source of the tidal power came from the changes in the gravity field between the moon and the earth. Allegedly, because of the law of conservation of energy this influence must cause to some energy lose in the moon or the earth. And indeed we know that the moon orbit get longer and slower over time. My question is, are we really must say that the energy of the tide and the loss of the kinetic energy of the moon are equal?
According to the general relativity theory the gravitation is the time space curve effect of a big object. This curve is not “energy consuming”, which means basically - two objects can spin around each other in space forever even that such a spin is a change in momentum that should consume energy according to the classic theory. The question is did the tidal effects caused by that “miracle” eternity momentum changes are indeed “energy consuming”?
Let's imagine that instead of the moon, there is black hole and the earth is spinning around it. This can cause to tidal power effects exactly like happen by the moon. This energy coming from the black hole which means that the black hole mass must be reduce according to the equation of $E=mc^2$. This is against what we know about black holes which are never losing any mass.
But if the answer is “no” that mean in other words that the tidal power stations are kind of “Perpetuum Mobile” - creating energy from nothing. This is of course a weirder conclusion.