The potential energy is a property of the system composed of the rock and the earth – the result of gravitational attraction. You can also look at it as a property of the system composed of you and the rock – if you ran the “tricorder scan” on yourself, you’d see a pattern of energy expenditure, which would stop when you let go of the rock.
Potential energy is sort of formal, but it is there.
I’m not sure this is a question with a clear-cut factual answer. My view would be that all energy is hypothetical until it is used to do something that a sentient being “wants” to do.
For example, it you are a hunter shooting an animal (to feed your starving children for you anti-hunting types), the kinetic energy of the bullet is strictly of theoretical interest until the bullet hits the animal.
The chemical energy stored in something is only hypothetical until a bacterium ingests it to maintain its existence.
And so on. It seems to me that it’s the conversion of energy from one form to another that is important.
Potential energy due to a change in gravitational potential is kind of a bookkeeping artifact, although it works mathematically. You are right about the rock–you cannot tell by examining it what its potential energy is. It’s all about its context.
Even something already sitting on the ground has potential energy–if you move it laterally over a hole you can drop it and it will get kinetic energy. The same rock also has potential with respect to the sun, etc.
Similar to potential difference in electricity, it makes more sense to talk about potential energy changes, or potential with regard to a reference point.
You are expending energy while standing there holding the rock motionless, but that does not affect the potential energy of the rock. You would even expend energy to put it back down. What counts is only the mass of the rock, distance moved, and gravitational force, not the actual energy you’re expending.
I won’t get into the sentient being part, but the concept of potential energy is an accurate model of how energy works. So it’s more than just hypothetical. Remember that physics in general is a model–you have to get philosophical about what is the relationship between the model and reality.
Call it real or imaginary, whichever way you want to use the words. You’re really asking a language question, not a physics question.
You could in fact easily tell that there is some potential gravitational energy in the rock (even without a fancy tricorder scan) if you were holding it, by the fact that you can feel its weight.
Now there’s no way to know how much of this potential energy will be released if you let it go, because that all depends on the details of where it falls – if you let it go hanging over the edge of the Empire State building it will turn quite a bit of gravitational potential into kinetic energy (OK, let’s all pretend for a moment that the building doesn’t have any stepbacks. Call it the Hancock building in Boston, instead). However, if you bring it back onto the platform and release it, if only gets a meter or so of gravitational acceleration.
But I think you do understand the physics, so as I said, this is all a question about what you want ‘imaginary’ to mean. Me, I don’t think calling graviational potential ‘imaginary’ is very useful (as opposed to centrifugal force, which is a situation where using the word ‘imaginary’ is useful for reminding each other of the real physics of the situation). But, as in almost all language questions, YMMV.
Actually, if you had the UltraScan 3000[sup]TM[/sup] with the GR option I think you could see something.
I would think that in addition to readings of mass and composition, you could also see that the rock is at a point on a slope of a gravitational well with a particular gravitation gradient. Inside the rock I would expect to see some (slight) structual stresses caused by the earth or your hand preventing the rock from moving along its least action geodesic.
No question about the “accurate model” bit. I think saying “you have to get philosophical” is close to what I was trying to get at. I think, as ** Quercus** said, this isn’t so much a physics question as it is a language or philosophy question.
An Earth/satellite system with the satellite in orbit has a higher mass than when the satellite is sitting on the surface of the Earth. This is theoretically measurable and it’s also the mechanism of fission and fusion reactions.
Eyer8, if it has a higher potential energy, it would invariably have a higher mass too, as all energy has mass.
There is one idea, I seem to remember, that GPE is infact the ‘negative’ version of the orginal kinetic energy which caused the universe to expand from the big bang. This would mean that all the matter at the point of the big bang singularity would have no mass.
OK, E=mc[sup]2[/sup] and all that… But work with me on this. The potential energy of two particles attracted by a force can be defined as the the energy required to separate them (13.6 eV for a Hydrogen atom IIRC). For a satallite sitting on the earth, lets define the potential energy as zero. Once you lift the satellite into orbit, now you will have more energy in the system (equal to the energy you used in lifting), both potential and kinetic. So now lets take the satellite and accelerate it to the end of the universe (move the satellite to infiinity). So now we have an infinite amount of potential energy in the system, which makes sense since we used an infinite amount of energy to send it away, but an infinite amount of mass?
Eyer8, for one thing it does not take infinite energy to take an object outside of the gravitational field of another object, the energy required to take an object outside of the gravitational field of another object is the energy required to reach the escape velocity.
The convential point (of course, disreguarding my previous post, the point is arbitary) for an object to have zero GPE is when it is outside of any other gravitational fields (except obviously it’s own), finding out the amount of GPE is just a case of subracting the effect the strength of the graviational field the object is in has on it’s GPE from zero.
Photons do not have rest mass, but they have relativistic mass, which is a simple function of their energy. All Energy has mass, if mass had energy but energy didn’t have mass and you could (as you can) convert mass into energy, it would be a violation of **the principle of conservation of mass[/b.]
You are right of course, I posted in haste and repented at my leisure…
Typically, the potential energy is defined as zero at infinity and then the potential energy has the form (working hard to remember that freshman physics of ten years ago…):
U[sub]g[/sub]=-G M[sub]1[/sub] M[sub]2[/sub]/R
where R is the distance between them.
Thus it is easy to solve for the escape velocity as
So no potential energy or kinetic energy when the mass escapes…
1/2 m v[sup]2[/sup][sub]esc[/sub]-G M[sub]1[/sub] M[sub]2[/sub]/R = 0
But with this definition we have the problem that the gravitational potential energy is always negative and grows in magnitude as the two masses get closer together. With this definition, would there be more or less “energy mass” with the particles at infinity or when almost touching? Would the mass be defined as negative in the same way the energy is negative?
What is the equation that defines the relativistic mass of the photon? This is the first time I have heard of a photon having any kind of mass, rest, relativistic, or otherwise… In a word, cite?