A question about infinite energy

Question

I know the conservation of energy doesn't allow that, and i saw a question on this forum about infinite energy: Why can't I do this to get infinite energy?, it says we can convert matter into energy and pump it up and convert back to matter and let it fall to generate energy. Comments were of full this is impossible because of this and this etc.

The reason was General Relativity was telling that gravity affects energy as well, photons would slow down. But if it does, doesn't this mean energy is permanently lost and not converted to anything else? Energy is conserved because sum of kinetic energy and potential energy is always same, as long as particle doesn't give its energy to another thing such as colliding with it.

Then light mustn't lose his energy, never unless he collides with another thing. Comments were saying gravity will slow it down and light will lose speed and kinetic energy, but where did the kinetic energy go? It can't be potential energy, because potential energy requires mass and distance, where photon has no mass and no potential energy. So kinetic energy must always be same. Also, how gravitation affects a thing that even has no mass? Mass is energy yes but is energy necessarily mass? Why should all things that affect mass also affect energy, if not why photons slow down.

Some comments said there is no way to matter to energy and energy to matter but antimatter + matter is gamma rays and gamma rays when condensed could be converted to antimatter and matter. Matter can't do this conversion on its own, but it doesn't matter that it couldn't.

Some comments said energy will be used to make light go upwards will be equal to harvested energy from matter potential energy but why would energy be used to make light go upwards?

Answer 1

To put a simple answer, light travels along spacetime, gravity curves spacetime, hence gravity affects light.

Travelling across this curved spacetime, the photons are red-shifted i.e. increased wavelength. As we know, $$ c=\nu \times \lambda \tag{1} $$ and $$ E=h\nu \tag{2} $$ Light doesn't slow down. But the path it now takes across spacetime might be longer (as its curved) than it would be if spacetime was flat. As it has an increased $\lambda$, $\nu$ is smaller so the photon's energy is now less.

Answer 2

General Relativity was telling that gravity affects energy as well, photons would slow down.

From the viewpoint of a distant observer, light slows down as the gravitational potential increases (e.g. near black holes) AND speeds up as the gravitational potential decreases (in areas of space without masses near and around them).

But if it does, doesn't this mean energy is permanently lost and not converted to anything else?

It does not, see the explanations above. In addition, it is important to understand that the change in velocity perceived by a distant observer is not acceleration from the point of view of the photon. The movement on the geodetic path (seen as a curve from the distant observer) always happens without any acceleration. Your geodetic path will be different and more curved, but you will never feel any acceleration.

Then light mustn't lose his energy, never unless he collides with another thing.

Exact.