Why is gravitational potential energy relative to the height you set?

[baouba]

Why is gravitational potential energy relative to the height you set?

When I say relative, I don't mean anything having to do with relativity. Obviously as you go further from the earth, you have more potential energy but in the equation Ug=mgh if you set the height to 0 there is no potential energy. If you set h to 5 say, for example, you get potential energy even if you're talking about the same point in space.

This makes no sense that you can assign any height to a point on Earth and change an object's energy. I just don't get how it can have "this" much potential energy when I can easily change the reference height and also change the energy.

Please help!

 

[Nabeshin]

The fact you note is precisely because only DIFFERENCES in potential energy ever matter. Think about every time you've ever used a potential energy to calculate something. Want to know the velocity of a ball you dropped? Well, the difference between the potential energy at the top and bottom is mg(h)-mg(0)=mgh. Doesn't matter if you alter your vertical scale: mg(h+h')-mg(h')=mgh, and all of our answers come out the same. Implicitly, whenever we say an object has X potential energy, we always mean "relative to some reference point Y", it's just cumbersome to say, and the point Y is usually something taken to be convention (the surface of the Earth, a point at infinity, etc.).