Potential energy

Hi!
I'm a real noob in physics, so to say in modern international language. I just got interested in it by starting to read Feynman's lectures on physics. So after reading a several dozen pages, collecting back much of the basic knowledge I threw out of my mind after school, spiced up with Feynman's insightful comprehensive way of explaining and putting it all together, it got me really intrigued and fascinated. But together with this forgotten knowledge and interest came back also some old questions that are bugging me. My English may be a bit buggy, too. I hope you will understand me anyway :)
First question: What is potential energy? Is potential energy always defined in terms of an arbitrarily chosen reference point? For example: The potential energy in the earth's gravitational field is _defined_ to be zero for a mass that is placed on the earth's surface and more than zero for a mass placed somewhere above in the sky, but it could be defined in another way, the difference from the other definition being a constant? Or is it the case that in fact there is a _canonic_ reference point (the earth's mass center that would be probably)?
If the first was the case it would bug me for the following reason: According to the theory of relativity mass is equivalent to energy, and energy, just as mass, causes gravitation. So what about potential energy? If we can define it this or that way things are spoiled. And, second, _where_ is the potential energy? A source of gravitation should be located somewhere. So, is the center of gravitation caused by the potential energy at the potential's zero point?
If, on the other side, the potential's zero is located at the mass center of the earth any other position would have a potential energy of infinity because it would take an infinite amount of energy (E=GMm(1/r_0-1/r) with 1/r_0 being infinity) to move a mass from the center of the gravitational field to somewhere else, wouldn't it?
As you may critizize I talked about the theory of relativity and am still using a classical formula for the potential energy of the gravitational field. That's because I don't know the relativistic formulae, and I hope that my question is not totally led ad absurdum by that.

The second question: I forgot. :(

So, I hope someone can answer this question that already got me suspicious towards physics back when I was at school among other things that I forgot. I'm really curious.

Sincerely
Unkraut

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That's an awesome train of thought! I've often tumbled over the very same question throughout my pysics education, however the only acceptable conclusion I can compose is this:
Potential energy is not, in fact energy at all, despite it's name. It is merely an ability for one property of something to add kinetic energy to another object. The reason graviational potential energy is oft' zero at the earths surface is because it is the most practical refrerence height for everyday use. The reason we can set the reference point arbitrarily is because one is looking for a change in energy from one point in time and space to another, not an actual amount of energy that exists before the object falls or is launched by a spring.
As for objects falling to the center of gravity of a planet, you must realize that as the object moves inside the planet there eventually is as much planet on one side of the object as there is on the other, making no real center point of gravitational attraction at which it is possible to arrive. The only acception to this would be the singularity of a black hole.
You may want to take this with a grain of salt because I have had only a slight education in classical physics.

Potential energy is not, in fact energy at all, despite it's name. It is merely an ability for one property of something to add kinetic energy to another object. The reason graviational potential energy is oft' zero at the earths surface is because it is the most practical refrerence height for everyday use. The reason we can set the reference point arbitrarily is because one is looking for a change in energy from one point in time and space to another, not an actual amount of energy that exists before the object falls or is launched by a spring.
That's not a satisfactory answer. Suppose a "black box" - whose interiors are not observable from the outside and nothing can come out. Probably a black hole would do the job. And this object has a mass, say M. Now suppose, something is going on inside the black box. Maybe for example there is big mass M' in its center and a small mass m some distance away but still inside the black box. At the time t_0 the two masses are at rest relative to one another. But there is a gravitational force acting between them. Considering the mass M' to be much bigger than the mass of m we say for simplicity that M' is standing still and m is picking up kinetic energy, losing its potential energy. So if, as you say, the potential energy is not real energy where does the kinetic energy come from? Is kinetic energy real? If so, the mass of the whole black box M' should increase for no apparent reason as observed from the outside while m is accelerating because there is kinetic energy coming from out of nowhere.

As for objects falling to the center of gravity of a planet, you must realize that as the object moves inside the planet there eventually is as much planet on one side of the object as there is on the other, making no real center point of gravitational attraction at which it is possible to arrive. The only acception to this would be the singularity of a black hole.
No. Suppose the planet to have the shape of a ball with a certain radius r and suppose its mass to be distributed uniformly throughout the ball's volume. Then the center of gravitation is the center of the ball and as long as you are not at the center there is more planet on the side towards the center than on the other side.

Andy Resnick
I have come to understand 'potential energy' better when I call it 'configuration energy'. Let's take something simple- a ball in an empty room with gravity present.

Some amount of energy the ball has depends on where the ball is (other parts of the total energy include how fast the ball is moving, what temperature the ball is, how much charge there is, etc. but never mind that for now). If the ball is on the floor, we say it has less potential energy than if the ball is up near the ceiling.

Why is this? Well, if gravity were not present it would not be true. But, the point is the *configuration* of the system- the location of the ball within the room- can be assigned a number (in this case, it's how far off the floor the ball is).

For this simple system, that seems like a pointless excersise. But, the same concept can be applied to any system- for example, a protein which has several quasi-stable *configurations* (foldings). And some protein configurations have less energy than others.

One great lesson from thermodynamics and quantum mechanics is that one does not need to have a detailed descriotion of a system in order to describe and predict the dynamical behavior. Thinking of "potential energy" as some quantitative description of the internal configuration of a system has been helpful for me.

I still don't get it really.
Let me put it another way by asking some other questions:
1. If we have a system consisting only of a single mass point with mass M in vacuum and with no other influences what is the energy of that system in its rest coordinate system? E=mc²?
2. If we put another smaller mass m into our system rotating around M in a gravitational orbit, what is the total energy of our system in M's rest coordinate system? E=(M+m)c²+E_kin+E_pot (E_kin and E_pot being the kinetic and potential energy of the mass m orbiting M)?
3. If we now lower the radius of m's orbit around M but we want the total energy to stay the same, decreasing its potential energy we must increase its kinetic energy by the same amount. m is rotating faster and faster as we push it closer and closer to M. But by pushing it closer and closer we can get m rotating arbitrarily fast. So now where is the zero of potential energy? If we can increase E_kin up to infinity we must therfore be able to decrease E_pot down to -infinity. So there can't be a canonical choice of an orbit where E_pot is zero. And consequently we cannot talk about the total energy of the system in a senseful manner since our choice of E_pot is arbitrary, or can we?
But if there is not an absolute energy for our system, independent of arbitrary choice, which energy is it the total energy of the system that causes gravitation according to the theory of relativity?
My humble understanding of it is: Mass is equivalent to energy. Through E=mc² one can assign a mass to an amount of energy and vice versa. And a system with mass m and an amount of Energy E stored in different forms (kinetic, heat, ...) could be assigned a total Energy E'=E+mc² or a total mass m'=m+E/c² which causes a gravitational field. A problem of intuitive understanding that arises to me is: _Where_ is the energy that is not stored in mass but in different forms? How can it be localized so we can assign a mass center to the absolute mass m'?
Is here nobody who sees my problems in understanding? Maybe it is due to my mixing up theory of relativity with classical newtonian mechanics without having decent knowledge of either of them. I'm quite sure I'm talking rubbish. But I don't know what part of my thoughts is rubbish. Please help me.

The problem is that with an object consisting of only one point with any sort of mass will result in some crazy stuff like a super tiny hole in spacetime, because the mass>0 and the area=0 the force of gravity is infinite at that point. This would cause anything falling into its center to accelerate to at least the speed of light, causing it's mass to also become infinite as well as it's speed. So if there were a point mass in space with another object orbiting it, the total energy (KE+PE) of the system would indeed be infinity.
As far as object's centers of gravity, I am not trying to refute their existance, I am simply trying to say that they are impossible to reach in all objects save the point mass described above. Say you fell into the center of the earth (and the earth was cool and you were immortal), upon reacing the 'center of gravity' you would feel no force on you at all save the super tiny tidal forces on your head and feet (which wouldn't be noticeable).
I have also found myself thinking of gravity as a property of the universe, rather than a force acting between two objects. I'm not sure if the existance of any sort of graviton has been confirmed, so I am more comfortable imagining it as a space-time warpage, rather than energy in itself. This, of course, could be debated to no end until conclusive evidence is produced on either side.

Think of potential energy as a measurring tape. It can show us how many inches are between point A and point B, however it doesn't make much sense for us to ask "how many inches are there?".

to a object who has a force acting on it PE is how much more of any energy can the object accumulate using that force
so it all depends to the setting and since most of the time is used in gravity type system (when the force acting on the object is gravity), PE is depended on the height or the possible distance that the force g can move the object o

if the setting was such that object earth's core which is let's say just the size of a peny exerts the force g on the person P and this person who stands on a cliff that goes all the way down to earth's core on a distance r = radius of the earth from earth's core
then the PE if person P were to fall would be g*r

this doesnt happen though because such a hole in the ground does not exist that's why we pick the surface of the earth as height=0 because if height=100 m then the gravitational force g can only move the object 100 m this is just a point of reference to determine the distance that the force moved the object