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[LeoLeonardoIII]

The physics explanation for "potential energy" of, say, water held behind a dam, and how gravity works, always felt like a placeholder kludge to me. I wouldn't be surprised to hear that they've figured it out better and were kinda wrong the whole time. Not like new spaceship drives and stuff, I just mean explaining it differently. All the formulae will probably still work out.

[i2amroy]

Hypothetical antimass is equivalent to negative energy, due to the relationship with general relativity.  Negative energy is just as hypothetical as antimass.

Specifically, if E=MC^2, then to have a negative E, you must have a negative mass term, or you must assert that there is such a thing as negative C. One of the terms must be negative for E to be negative.

Isn't C^2 always positive anyway?

Interestingly enough Einstein's equations work with a negative answer, you just end up with light that goes backwards in time. This of course doesn't really make sense, so we ignore it generally, but it is a valid solution.

[LeoLeonardoIII]

I understand the explanation. I just think it's a lame placeholder to make the equations work.

Take a liter of water and spend energy to work against gravity to raise it a meter. Assume air pressure is the same. Will the water have gained observable energy or mass compared to a liter of water one meter lower? AFAIK, no. Where did the energy go that was used to move it away from the gravitational center? When the water is released, and falls, it expends kinetic energy which it got from somewhere. That kinetic energy can be captured by a machine.

Basically what I'm getting at is, if you have a device that can detect the greater amount of energy in the liter of water that's farther from the gravitational center, then there's nothing like "potential energy", it would just be kinetic or thermal or whatever.

It seems like the water doesn't store the energy, it's just that the work done to raise it involves the gravity field somehow.

[wierd]

Actually, yes. You expend energy to lift the water higher up. That energy is conveyed to the water in the form of kinetic motion. It is then held in that state by electromagnetic repulsion of the vessel containing it, and of the counter the vessel is sitting on.

This is basically the same thing as twisting up a rubber band.

[Il Palazzo]

Will the water have gained observable energy or mass compared to a liter of water one meter lower?

...

Basically what I'm getting at is, if you have a device that can detect the greater amount of energy in the liter of water that's farther from the gravitational center, then there's nothing like "potential energy", it would just be kinetic or thermal or whatever.

The difference in the total energy of the system due to potential energy can be seen in principle by measuring the combined gravitational effect of two bodies of mass m each, at infinity and when brought together. At infinity each has m mass, when together the system will have M<2m mass and produce correspondingly lower gravitational field than 2m masses would. You can extract energy from a system like that, and the extracted energy lowers its mass.

It's the same with charged particles. Two like charges brought together have more energy(need work to overcome the Coulomb force) and so, are heavier(more mass), than the same charges far away from each other.

There's no other energy involved here. No thermal or kinetic energy. It's just the position in the field that matters and causes changes in mass.

edit: I should note before somebody gets confused: these are not isolated systems! work is done on/extracted from them.

[LeoLeonardoIII]

Actually, yes. You expend energy to lift the water higher up. That energy is conveyed to the water in the form of kinetic motion. It is then held in that state by electromagnetic repulsion of the vessel containing it, and of the counter the vessel is sitting on.

This is basically the same thing as twisting up a rubber band.

Shouldn't the EM repulsion at the atomic level be working when gravity is pulling on the object, forcing the two into contact, rather than specifically in relation to how far the object and the "counter" are from the center of gravity?

By that I mean, the atoms of the vessel and counter repel each other regardless of energy input from someone doing work to lift the vessel.

Or are you talking about something else?

@Il Palazzo: isn't mass the same regardless of gravity, but weight is the result of gravitational effect on the mass?

[Il Palazzo]

@Il Palazzo: isn't mass the same regardless of gravity, but weight is the result of gravitational effect on the mass?

Yes, but here, the mass is lower/greater due to the difference in potential energy caused by work being performed by/on the system. As a result, in a given gravitational field, the system will weigh less/more.

[wierd]

Leo-

The state of the atoms inside the vessel and table changes as a result of restraining that energy. They get slightly pushed together. The energy configuration of the system changes as a result of the added energy.

a spring that is all coiled up and ready to snap, but held in place with a cotter pin is NOT in a rest state.

Yes, a pebble sitting on the beach has an accellerating force trying to pull it toward the center of the earth's mass, relational to the distances between the center of mass of the pebble, and of the earth.  That force is arrested by the forces exerted by the atoms comprising both bodies, because the EM force is radically stronger than the gravitational one. It doesn't mean the pebble does not contain energy, or that the energy state of the pebble is unchanged when it is moved closer or farther from the earth.

There comes a point where gravitational forces can exceed the EM force. Then you get electron degenerate matter. Even stronger than that, and the strong nuclear force breaks down in the face of the onslaught, and it becomes a black hole.

The energy contained in the water being held above the surface of the planet by the EM forces of the atoms of the container, table, and crust of the earth makes only a slight change in the rest states of those systems, but the rest state does change as a result of adding the energy.

[Il Palazzo]

Weird, what you're saying is, eh, weird.

To raise an object in a gravitational field you must perform work. You're adding energy to the system to lift it higher.
Let's say it's a spring scale with a rock on it.
The higher it's lifted, the less compression the spring experiences due to the lower gravitational field. So more gravitational PE means LESS PE stored in the spring - opposite to what you said.

[wierd]

I was approaching more from the PoV like this:

You have a ball of matter, that weighs 100kg. If you apply energy to it in the form of pressure, the ball's diameter will become reduced, but the forces inside the ball will eventually counter this.

If you push on the ball hard enough, it will stop being normal matter, and will become neutronium. If you KEEP pushing, all resistence to the pushing will break down, and instead it will shrink smaller than the schwatzchild limit, and no force in the universe will stop the implosion. (Though it may experience hawking radiation decay.)

The force exerted by the water is proportional to the distance between the masses, and the distances between their centers of mass. If this distance is very large, the force will be very small.

Moving the water jug off the floor, and onto the table, reduces the G exerted, but only slightly, considering the energy used to raise the jug off the floor. That energy wants to be released, by the jug returning to the floor.  The atoms in the jug and table arrest that energy, but in doing so, they get slightly compressed, and the system changes.

[LeoLeonardoIII]

Thanks weird.

A: So let's say you have an increasing output of energy in lifting the object farther and farther from the gravitational center. You have not yet received any output from the object. Eventually the object gets far enough from the gravitational center that the gravitational forces operating upon it are extremely weak. That means the vessel is no longer pushing against the table with much weight at all. You have put a lot of energy into lifting the vessel and table, but where is that energy now? If you stuck some kind of measuring device in an atom of the vessel, would any part of that atom be different from when the vessel is much closer to the planet?

B: Similarly, let us say an object very far from a planet has a tiny amount of kinetic energy. As it drifts slowly closer to the planet, it begins to move faster. Gravity had an effect on the object and caused an increase in kinetic energy in the object. Where did that energy come from? Does the object lose mass to account for the increased kinetic energy? Does it lose another kind of energy, for example becoming colder? Does the planet somehow lose energy or mass?

[Il Palazzo]

@weird: forget all that stuff about compressed atoms. Yes, the minutiae of the system change, but it's irrelevant to the PE problem and only confuses Leo.

@Leo: Take a sealed box and put inside the Earth and your water jug. Put the box on a scale in some other gravitational field, or use some other device that measures the mass of the box.
If you close the box and let the gravity do its magic as it sees fit(PE converted to KE, then KE into heat during collisions etc.), the box will always weigh the same.
But if you open the box for a moment and do work on the system by lifting the jug higher up, then close the box again and weigh it, it WILL be more massive.
The energy is not stored in any other way, no KE, no atoms pushing on each other. Just the change in the position of the jug w/r to the gravitational field of Earth matters. The distance in the field is in itself the expression of energy, just as the velocity is the expression of KE.

[wierd]

A: the momentum of the planet will have changed in accordance with the energy inputted. This is functionally the same as shooting the jug out into space. The force needed to push the jug out of the gravity well will alter the planet's motion. The jug is much less massive than the planet, so the change to the planet won't be easily noticed, but it will still happen. Likewise, the energy to overcome the gravity well will result in changes in the momentum of the jug. It's own mass will change as a result of this. (If you move the jug fast enough, it actually gains mass! This is why the near lightspeed collisions of the LHC can produce many many particles who's combined masses are far greater than the masses of the 2 protons smashed together.)

B) here, the jug never escapes the gravity well, it just moves to the tiny edge of it. The rate it starts to accellerate back toward the earth starts slow, but increases as it gets closer to the the energy of the jug as it falls back to the earth is equivalent to the energy used to move it out to the edge of orbit. That energy is dispersed in a number of forms as it re-enters the atmosphere and subsequently smashes into the planet.

[Il Palazzo]

You're mixing forces, motion, energy and momentum.

If you raise the jug in a gravitational field, it will have gained PE. As long as you make sure that by the end of the work done both the jug is stationary in the reference frame of the Earth, it will not have gained any KE(or momentum for that matter). Later on the jug may fall down and exchange the newly aquired PE for KE. But at the instant both bodies are motionless, the total energy of the system is already increased and the system will have more mass.

The whole point of this overly long discussion is to show Leo that PE is as tangible an energy as KE or heat, and that its only measure is the position in the gravitational field. Not any extra hidden energies that pretend to be PE, which is what you appear to be vaguelly suggesting.

[wierd]

No-- Not really.

PE is just energy that is not currently "doing" anything. It does have manifestations of being present though. It is the same as any other energy otherwise. It doesn't appear or vanish, simply because it isn't actively doing any work, and after work is done, the energy still doesn't "vanish"-- that would be an energy law violation. After the work is done, the energy is released in other ways, usually as either disperse kinetic energy (heat), or as radiated energy (Infrared), but it can take intermediates before getting there. (kinetic energy in sound waves, what have you.)

Leo might consider the schoolbook potential energy lab with the rubber band-- Pulling on the rubber band with it pressed against his upper lip, so he can feel the change in the thermal energy released when he relaxes the band and draws it tight again. A stretched band is also PE, just not in a gravitational context.