PS:

If you carry a mass to the top of a building, it is said "to have potential energy mgh relative to the ground." This does not mean it contains this energy locked up inside it, waiting to escape like a genii in a bottle.

What the phrase in quotes above means is that if that stone drops from the building it will hit the ground at a certain speed, hence a certain kinetic energy 1/2mv**2. That is real energy, capable of doing work, like putting a dent in the pavement.

The potential energy is only a number that tells you how much kinetic energy you'll get after the stone drops. It has no reality in itself.

You will note potential energy is measured relative to the ground, it is how much energy the stone will add by falling to the ground.

Let's assume you now dig a very deep hole on the spot where the stone will hit. Let's say that hole is as deep as the building is tall. So when the stone hits the bottom of the hole it will be moving much faster, in fact it will have twice the kinetic energy because the stone fell twice as far. You have added extra potential energy to the stone without even touching it, or doing anything to the stone; you just dug a hole in front of it (in other words, you changed the value of h). You have just redefined what the potential is relative to.

The potential energy is not a property of the stone, it is a property of how far the stone is from the spot where it strikes. That stone has a potential energy relative to the bottom of the hole, it has half that potential energy relative to the street, it has a different potential energy relative to every floor of the building. And it will have zero potential energy relative to the spot on the roof where it rests at the start of the experiment. Potential energy is not a thing, its a place.