# Questions on potential gravitational energy

• Xilor

#### Xilor

Hello, the concept of potential gravitational energy seems very confusing to me, and it leads me to several questions, and I was wondering if some of you could explain this energy conceptually to me perhaps based with these questions as guidelines.

Potential gravitational energy increases mass right? So if I lifted an object up from the earth, it should get heavier.

Potential energy keeps increasing as you lift something up more and more if I'm not mistaken, but the amount it increases at would start decreasing after certain heights right? Does this energy ever start decreasing? Would voyager1 still be a bit heavier because it left the earth?

When lifting an object, the potential gravitational energy of the particles inside the Earth would also increase a bit as they are also attracted to whatever is lifted slightly. So lifting an object should increase the mass of the Earth right?

If both the mass of the object and the Earth get higher, shouldn't that also increase the amount of gravity between them as gravity depends on mass? Leading to some sort of endless loop. Mass increases, meaning more potential gravity, meaning more mass,and so on.

If you lift object A from the north side of the earth, and you then lift object B from the south side, what happens to the potential gravitational energy in the Earth's particles? Does it increase during A and then decrease during B as it's canceled out, or do these add to each other?

If you lift a particle to a certain height, and if you could create a new particle right next to it somehow, would this new particle have the same potential gravitational energy as the old one, increasing its mass instantaneously?

Hello, the concept of potential gravitational energy seems very confusing to me, and it leads me to several questions, and I was wondering if some of you could explain this energy conceptually to me perhaps based with these questions as guidelines.

Potential gravitational energy increases mass right?
Wrong.
So if I lifted an object up from the earth, it should get heavier.
Nope - it loses weight, mass stays the same.

Potential energy keeps increasing as you lift something up more and more if I'm not mistaken, but the amount it increases at would start decreasing after certain heights right?
Yep - at all heights.
Does this energy ever start decreasing? Would voyager1 still be a bit heavier because it left the earth?
Voyager1 has the same mass, apart from spent fuel, that it started out with.

Gravitational potential energy decreases as you leave the ground, and as you decent benieth it. It's continuous. However the Earth is so big that we don't notice the decrease over the kinds of distances we normally move about in.

I've deleted some questions because they refer to mass depending on potential energy.

If you lift object A from the north side of the earth, and you then lift object B from the south side, what happens to the potential gravitational energy in the Earth's particles? Does it increase during A and then decrease during B as it's canceled out, or do these add to each other?
This is the same problem as finding the potential energy of a mass exactly half-way between two other masses. It would be zero because there is no gravitational force.

Thing what "potential" means... potential to do what? To fall, in this case. If it won't fall (if unsupported), the potential energy will be zero.

If you lift a particle to a certain height, and if you could create a new particle right next to it somehow, would this new particle have the same potential gravitational energy as the old one, increasing its mass instantaneously?
Gravity does not affect mass.

The new particle has the same gravitational potential energy as the old one.

Of course, I'm working in the classical regime here ... you are having a hard enough time without worrying about the mass-energy relation.

This hangs on how you actually define the potential. Classically, the gravitational potential at a point is defined as the work done in bringing a unit mass from infinity to that point. For an attractive field, this always gives you a negative value ('potential well') because you would actually get energy out when going that way.

At a position between the Earth and Moon, where the forces 'balance out', there is still a finite value for the gravitational potential. Moreover, it requires different amounts of energy to get to that point from the Moon's surface and the Earth's surface. Which is why it is more convenient to use the normal definition of GP, referring to Infinity.
Also, at the centre of a spherical mass, the force is zero but the potential is not - it is more negative than at the surface.

When you are talking of GPE on or near the Earth's surface, you normally mean the energy needed to raise a unit mass to that height. The approximate answer is mgh, which is what you get when you use the accurate definition of the absolute potential at each distance from the centre (-GMm/r) for each point and then subtract them:
-GMm(1/r1-1/r2)
then put
r2 = r1+h
The algebra gives you the more common expression for small values of h but would also give you the answer for any point in space, such as half way to the Moon (natch). (I may have got the signs the wrong way round but the point is still there)

This is the same problem as finding the potential energy of a mass exactly half-way between two other masses. It would be zero because there is no gravitational force.

Thing what "potential" means... potential to do what? To fall, in this case. If it won't fall (if unsupported), the potential energy will be zero.
Not correct! Brush up on your potential, Simon. The potential energy of a mass exactly halfway between two (equal) masses is not zero (relative to zero potential at infinity). Potential energy is subject to the superposition principle. The potential energy due to either object is negative at this halfway point. Add two negative numbers together and you get a negative number. What happens is that the potential is flat at this halfway point. Taking the gradient yields a null force.

Wrong.

Hmm, well I know that wikipedia and other online sources aren't considered accurate, but comments like these do seem to suggest that.
From http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence: [Broken]

Mass–energy equivalence states that any object has a certain energy, even when it is stationary. In Newtonian mechanics, a motionless body has no kinetic energy, and it may or may not have other amounts of internal stored energy, like chemical energy or thermal energy, in addition to any potential energy it may have from its position in a field of force. In Newtonian mechanics, all of these energies are much smaller than the mass of the object times the speed of light squared.
In relativity, all of the energy that moves along with an object (that is, all the energy which is present in the object's rest frame) contributes to the total mass of the body, which measures how much it resists acceleration. Each potential and kinetic energy makes a proportional contribution to the mass. As noted above, even if a box of ideal mirrors "contains" light, then the individually massless photons still contribute to the total mass of the box, by the amount of their energy divided by c2.[6]

Nope - it loses weight, mass stays the same.

Had been confusing up terms here, did not mean "heavier" but meant more mass instead.

Of course, I'm working in the classical regime here ... you are having a hard enough time without worrying about the mass-energy relation.

Well, that was mainly the part which I was wondering about. How gravitational potentials energy translates to mass and how that affects things.

This hangs on how you actually define the potential. Classically, the gravitational potential at a point is defined as the work done in bringing a unit mass from infinity to that point. For an attractive field, this always gives you a negative value ('potential well') because you would actually get energy out when going that way.

Ah I see. Well therein may lie my confusion as I assumed potential to be the total amount of energy a particle could rack up from being gravitated from its position to another particles position. And I had troubles combining that with massive bodies far away, which would then cause every particle near Earth to actually have way more gravitational potential energy towards those faraway places than potential towards particles near earth. Which would cause all sorts of strange things which would be seemingly impossible and are unobserved, especially if mass were affected by this potential.

Not correct! Brush up on your potential, Simon. The potential energy of a mass exactly halfway between two (equal) masses is not zero (relative to zero potential at infinity). Potential energy is subject to the superposition principle. The potential energy due to either object is negative at this halfway point. Add two negative numbers together and you get a negative number. What happens is that the potential is flat at this halfway point. Taking the gradient yields a null force.

So the forces cancel each other out, but the potentials don't, although they won't cause anything to happen?

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Hmm, well I know that wikipedia and other online sources aren't considered accurate, but comments like these do seem to suggest that.
From http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence: [Broken]
You need to take care here. You are referencing an article about special relativity. Think of the qualifier "special" in special relativity to mean "situations without gravity". That article cannot answer your question because your question is inherently about general relativity.

This question is a bit tough to answer because the concept of mass in general relativity is a bit complex. In general relativity, it is energy that gravitates, not mass. This energy comes from intrinsic mass, electromagnetic radiation, thermal energy, but not from gravitational potential energy. One way to look at it: Real energy gravitates; the apparent potential energy that arises from a fictitious force does not gravitate. Gravitation is a fictitious force in general relativity.

One way to arrive at an answer of "yes" to your question is to release a sticky blob of mass from at rest with respect to some massive object at some distance away from the massive object. The blob and object will fall toward one another. Assume the resultant collision between the sticky blob and the massive object is purely inelastic. The combined object+blob will convert the kinetic energy of the collision into heat, and voila! more energy, and thus in a sense more mass. However, that extra thermal energy will eventually be lost to space, making the combined object+blob have gravitate less and in a sense have a reduced mass. So is the answer "yes" or "no" here?

If instead of dropping the blob from a distance we had gently placed the blob on the object (drop it via a sky hook, fly it in on a space craft, ...), then that gain in energy would never have existed. So now the answer is clearly "no".

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Perhaps we should have some sort of convention. If the OP contains the word 'relativity' then we can assume that the question is not just a classical mechanics one. If someone suspects that relativity is involved then they should challenge the questioner before launching out on another level of complexity. I think there are far too many relativistic replies to straightforward classical-based questions and I'm not sure it is always helpful.

It's not limited to relativity, either. Even the most straightforward question, which deals with a 'top level' situation, can so easily be subjected to a bewildering level of extra analysis before the original poster has had a chance to get back. Perhaps people should realize that many posts mean exactly what they say and are not fancy trick questions - the sort that a tutor might hit a smartarse student with.

I know some posts are put there to stimulate a good argument about a dodgy area but that's a different kettle of fish and excellent potential sport. But we are trying to help, aren't we?

To sophiecentaur: Xilor opened that door all by him or herself by asking about relativity. The answer to the Xilor's question in Newtonian mechanics is simple: Mass doesn't change.

To Xilor: Don't try to learn to run before you know how to walk. It is best to learn Newtonian mechanics first and get that down solid before jumping into relativity or quantum mechanics.

Not correct! Brush up on your potential, Simon. The potential energy of a mass exactly halfway between two (equal) masses is not zero (relative to zero potential at infinity). Potential energy is subject to the superposition principle. The potential energy due to either object is negative at this halfway point. Add two negative numbers together and you get a negative number. What happens is that the potential is flat at this halfway point. Taking the gradient yields a null force.

Argh 2am effect!
I am corrected.

Yep - OP reply to my own referred to the mass-energy relation.
The concept of "mass" is one of those things that gets weird in General Relativity.

There's another question around here that asks about something that looks like the "mass increase" in special relativity except that the gravitational potential is in the place of speed in gamma.

also throws in higgs bosons and the expansion of the universe...

You need to take care here. You are referencing an article about special relativity. Think of the qualifier "special" in special relativity to mean "situations with gravity". That article cannot answer your question because your question is inherently about general relativity.

I'm unable to comprehend this statement somehow, I must be missing something somewhere. Aren't most generally accepted theories models to describe reality as accurate as possible? Why would a statement within special relativity not apply because my question has more to do with general relativity? I was hoping to get some sort of conceptual understanding of this that is as close to generally accepted understanding as possible, not to see a question within just one theory.

This question is a bit tough to answer because the concept of mass in general relativity is a bit complex. In general relativity, it is energy that gravitates, not mass. This energy comes from intrinsic mass, electromagnetic radiation, thermal energy, but not from gravitational potential energy. One way to look at it: Real energy gravitates; the apparent potential energy that arises from a fictitious force does not gravitate. Gravitation is a fictitious force in general relativity.

Ok, so potential energy is then not really stored anywhere? But rather is something abstract which strangely enough can be converted into from kinetic energy? What happens if a particle enters the radius which affects the particle gravitationally? Does this change the total amount of energy (both real and potential) in the universe?

One way to arrive at an answer of "yes" to your question is to release a sticky blob of mass from at rest with respect to some massive object at some distance away from the massive object. The blob and object will fall toward one another. Assume the resultant collision between the sticky blob and the massive object is purely inelastic. The combined object+blob will convert the kinetic energy of the collision into heat, and voila! more energy, and thus in a sense more mass. However, that extra thermal energy will eventually be lost to space, making the combined object+blob have gravitate less and in a sense have a reduced mass. So is the answer "yes" or "no" here?

Well if you mean the question if potential energy has mass, then it would be a no as this action would transform potential energy into kinetic energy before anything happens.

Perhaps we should have some sort of convention. If the OP contains the word 'relativity' then we can assume that the question is not just a classical mechanics one. If someone suspects that relativity is involved then they should challenge the questioner before launching out on another level of complexity. I think there are far too many relativistic replies to straightforward classical-based questions and I'm not sure it is always helpful.

Well I was wondering mainly about the relativistic part. If I happen to be wrong about my classical interpretation of things than it's nice to be corrected in that as well, but I'm mainly wondering about what the current understanding about this is, and not so much what is predicted by theory's that don't paint the entire picture.

It's not limited to relativity, either. Even the most straightforward question, which deals with a 'top level' situation, can so easily be subjected to a bewildering level of extra analysis before the original poster has had a chance to get back. Perhaps people should realize that many posts mean exactly what they say and are not fancy trick questions - the sort that a tutor might hit a smartarse student with.

Ha, yes I'm just curious, and if I'm saying things that are complete nonsense then that is because I don't understand things, not because I'm trying to trick anyone.

To sophiecentaur: Xilor opened that door all by him or herself by asking about relativity. The answer to the Xilor's question in Newtonian mechanics is simple: Mass doesn't change.

To Xilor: Don't try to learn to run before you know how to walk. It is best to learn Newtonian mechanics first and get that down solid before jumping into relativity or quantum mechanics.

Wise words perhaps, but I've got far more interest in learning how things actually work than in learning how they work according to Newtonian mechanics. I knew Newtonian mechanics didn't say anything about masses changing when energy gets added, but I thought that that was part of the mass energy equivalence. But I guess that this equivalence works a bit differently than I expected.

I'm unable to comprehend this statement somehow, I must be missing something somewhere. Aren't most generally accepted theories models to describe reality as accurate as possible?
No.

The development of relativity and quantum mechanics did not, as pop-sci literature suggests, throw out Newtonian mechanics. Newtonian mechanics is still used, validly, in the domain in which Newtonian mechanics is a valid approximation.

A better way to look at the world of physics today is that general relativity simplifies to special relativity in the case of negligible masses, general relativity simplifies to Newtonian gravity in the case of smallish masses and smallish velocities, and special relativity simplifies to Galilean relativity in the case of smallish velocities. That leaves out quantum mechanics, which simplifies to Newtonian mechanics in the case of largish distances and time scales. There are plenty of occasions where those simplified forms of physics let's us answer complex questions. There is no way that physicists could describe the physics of a hurricane from the perspective of general relativity or quantum mechanics.

Why would a statement within special relativity not apply because my question has more to do with general relativity?
You are not going to get an accurate picture of what goes on inside an atom by using Newtonian mechanics. That domain is outside of the domain in which Newtonian mechanics is a valid approximation. Similarly, you are not going to get an accurate picture of what goes on near massive bodies using special relativity. You are once again outside the domain in which special relativity is a valid approximation.

Wise words perhaps, but I've got far more interest in learning how things actually work than in learning how they work according to Newtonian mechanics. I knew Newtonian mechanics didn't say anything about masses changing when energy gets added, but I thought that that was part of the mass energy equivalence. But I guess that this equivalence works a bit differently than I expected.
There's a very good reason to learn Newtonian mechanics first: Those more advanced concepts build upon Newtonian mechanics. The descriptions and mathematics of those more advanced concepts assume (require!) that the practitioner of those concepts be fully versed with the techniques of Newtonian mechanics.

@ Xilor & DH:

It might be that Xilor is somewhat confused about DH's typo in the following sentence:
You need to take care here. You are referencing an article about special relativity. Think of the qualifier "special" in special relativity to mean "situations with gravity". That article cannot answer your question because your question is inherently about general relativity.
DH meant to say "without gravity"! Hence the refrence to general relativity, which is "with gravity". Hopefully this clarifies...

@ Xilor & DH:

It might be that Xilor is somewhat confused about DH's typo in the following sentence:

DH meant to say "without gravity"! Hence the refrence to general relativity, which is "with gravity". Hopefully this clarifies...

Thanks!

@ Xilor & DH:

It might be that Xilor is somewhat confused about DH's typo in the following sentence:

DH meant to say "without gravity"! Hence the refrence to general relativity, which is "with gravity". Hopefully this clarifies...

Ah, thank you. That just became a lot clearer.

No.

The development of relativity and quantum mechanics did not, as pop-sci literature suggests, throw out Newtonian mechanics. Newtonian mechanics is still used, validly, .. (snip)..the practitioner of those concepts be fully versed with the techniques of Newtonian mechanics.

Right, I understand, Newtonian is interesting in larger scale situations because it is simpler and good enough of an approximation. I didn't really think the questions were about large scale systems though, so that's why I didn't really think it was necessary to completely grasp the entire Newtonian side of it.

But anyway, all of that aside, what I'm getting out of all of this is that:

Potential gravitational energy is somewhat abstract thing, that is stored in position in a gravitational field rather than in the particles themselves. Because it is not stored as real energy within a particle, it also doesn't add mass.
Potential energy keeps existing no matter if it's partially canceled out by potential energy from other sides, but because the forces of closer bodies are far stronger, this potential energy is never really converted into kinetic energy.
Potential energy isn't created by moving away from a gravitational well, but is something that is created just because of its position.
Kinetic energy can be transformed into potential energy because it doesn't change the amount of work that can be done. When this happens, the total stored energy and mass actually decrease a bit because the kinetic energy did provide stored mass. When the potential energy is transformed back, the stored energy and mass also return.

Now if I'm correct in those statements, then I'm still confused about what happens when new particles enter the system. Most notably when the speed of gravity bridges the distance between two particles, two particles that weren't influencing each other gravitationally before. When this happens, does the potential gravitational energy of both particles increase? And does that violate the law of conservation of energy or isn't that considered an isolated system then? If it isn't isolated, is anything isolated then? The energy of the total universe would change. Abstract energy or not, it's still energy which could theoretically be converted to kinetic, even if it would never happen.

To sophiecentaur: Xilor opened that door all by him or herself by asking about relativity. The answer to the Xilor's question in Newtonian mechanics is simple: Mass doesn't change.

To Xilor: Don't try to learn to run before you know how to walk. It is best to learn Newtonian mechanics first and get that down solid before jumping into relativity or quantum mechanics.

You are right. I was rather aiming in the direction of the second half of your post, in my comment. Licence to ask questions about relativity but not license to draw conclusions without demonstrating a firm grasp of the classical basics (007).

Potential energy keeps existing no matter if it's partially canceled out by potential energy from other sides, but because the forces of closer bodies are far stronger, this potential energy is never really converted into kinetic energy.

Potential Energy isn't "canceled out". Forces cancel but Energy doesn't in the same way; avoid drawing wrong conclusions..
You get a force when there is a Gradient in the Potential Energy. Re-read what has been written earlier.

Potential Energy isn't "canceled out". Forces cancel but Energy doesn't in the same way; avoid drawing wrong conclusions..
You get a force when there is a Gradient in the Potential Energy. Re-read what has been written earlier.

This is actually what I meant, I just worded it strangely. Written like this it might be closer to what I wanted to bring across:

"Potential energy keeps existing no matter how potentials from other sides act on it,"

Potentials don't "act". Forces "act" as a result of a gradient in potential. If you try to rewrite Physics you own way you will surely fall over. Better men (and women) than you and me have sorted it all out. You should take some time to go along with their way of thinking if you want to make any progress. When you get there, you may stand a chance of pushing some frontiers.

That is not being stick in the mud - it's being pragmatic.

Potentials don't "act". Forces "act" as a result of a gradient in potential. If you try to rewrite Physics you own way you will surely fall over. Better men (and women) than you and me have sorted it all out. You should take some time to go along with their way of thinking if you want to make any progress. When you get there, you may stand a chance of pushing some frontiers.

That is not being stick in the mud - it's being pragmatic.

Let's just say that my physics language skills aren't good enough to convey precisely what I am trying to say, but I did seem to arrive at a conclusion that is the same as what you are saying, please substitute the word act with anything that would be technically correct. I think the frontier pushing and rewriting of physics should be left for those better people, but I don't know what these frontiers are and I am curious about way the current lines of thinking are, so forgive me if I'm accidentally asking questions beyond frontiers or something (luckily it doesn't seem like I am so far).

Langauge difficulties aside, I'm still curious about that new particles entering the system thing, did that arrive from a false conclusion of mine on something, or is there any other form of a good explanation for that?

"Most notably when the speed of gravity bridges the distance between two particles,"

This is where the appropriate language is important. I have no idea what you meant by this. I think you are trying to jump in way down the line without getting the basics sorted out first.
Look up the actual definitions of potential, force and all the other terms you have been using. There is a well defined structure in all this and you can't get anywhere without following it through from the beginning. Follow the elementary Classical Physics first. I'm sorry but I think most other PF members would agree with me.

Let's face it, would you try to play lead guitar before you know the three basic chords or give a lecture in French without learning the language first?

Ok, well what I mean by that is:

Gravity waves/gravitons/whatever causes gravity can't travel faster than the speed of light, and because of this there are areas of space that have not yet had any gravitational pull on any particle on earth, no matter how fast gravity actually propagates. However, as time progresses, more and more areas will come within range.
Whenever any mass comes within range of another mass, then I would expect there to be potential energy which wasn't there before. This seems strange in the light of conservation of energy. When I asked if a newly created particle would instantly gain potential energy, the reply which remained uncorrected stated that this was indeed the case. For all intents and purposes, a particle entering the radius that is affected by another particles gravity could be considered a new particle (or the particles would've had to communicate faster than light with each other).

Maybe I'm just thinking too much that potential is something that 'exists', but I can't really imagine the conservation of energy either if kinetic energy is transformed into something which doesn't 'exist' in an at least similar way.

And I do understand Classical physics mostly, or I thought I did, I know what force is, have a basic grasp of what energy and mass are, know how most potential energies work, but gravity seems strange compared to those other potential energies. But I'm not accustomed to using the exact terms which you associate with physics and I do tend to get some nuances wrong (classical mistakes such as using weight instead of mass). I don't think I can blame it on English being my second language, perhaps it would be easier to blame it on the fact that I'm not studying anything related to physics. But anyway, I'm just curious about things, and if my knowledge in other aspects isn't sufficient to have my curiosity satisfied then I would love to hear which areas so I can study on those, but a blanket statement that I don't know enough is unfortunately not very helpful. Meanwhile, advanced answers which I may or may not understand would be appreciated greatly.

You have my sympathy. But, on those higher matters, at one time everything was very close together (big bang time) so the mass of everything was 'known about' by everything else. In an expanding universe I should say the situation you describe would be the opposite in fact. More and more mass would be beyond our horizon.

Well that doesn't seem satisfying to me, mainly because potential gravitational energy depends not only on mass but also on position, if positions would change while outside the gravityradius then the potential gravitational energy would change (slightly) without any cost, as the force of gravity wouldn't actually be puling the particles together anymore. Again changing the total energy of the universe. Or could gravity be redshifted endlessly so that the gravitational pull from Earth's particles is still experienced trillions of lightyears away?

Also, no matter how the universe actually happened to expand, it's still an imaginable situation that gravity has once moved faster than the expansion at any point, shouldn't the laws oh physics work in such a way that it's not actually possible if it would cause a violation? Can't see how that would be true unless gravity or the cause for gravity is actually causing the expansion itself.

Gravity "redshift"??
What colour is gravity?

Make that a dopplereffect on gravity caused by the expansion of space.

What would the frequency of gravity due to a static mass be?

[..] One way to arrive at an answer of "yes" to your question is to release a sticky blob of mass from at rest with respect to some massive object at some distance away from the massive object. The blob and object will fall toward one another. Assume the resultant collision between the sticky blob and the massive object is purely inelastic. The combined object+blob will convert the kinetic energy of the collision into heat, and voila! more energy, and thus in a sense more mass. However, that extra thermal energy will eventually be lost to space, making the combined object+blob have gravitate less and in a sense have a reduced mass. So is the answer "yes" or "no" here? [..]
I interpreted the OP's question in that way: assuming that the total system mass incl. radiation must be conserved, the same atoms must have reduced mass when at rest at reduced potential. Consequently the inverse should also be true: if we lifted an object up from the earth, that object should indeed have increased mass. Note: I think that that is an SR argument.

I don't know, I don't necessarily mean anything that changed wavelength although I could see why you would think that.
But am I wrong in thinking that whatever is used to put a force on particles due to gravity be it gravitons or waves or whatever else would be stretched out over space if space would expand? If gravity were quantized I could imagine that if it were stretched out enough, that you would have large periods of time without any gravitons hitting. If it isn't quantized then the force would have to be stretched out over large areas as well right?

I don't know, I don't necessarily mean anything that changed wavelength although I could see why you would think that.
But am I wrong in thinking that whatever is used to put a force on particles due to gravity be it gravitons or waves or whatever else would be stretched out over space if space would expand? If gravity were quantized I could imagine that if it were stretched out enough, that you would have large periods of time without any gravitons hitting. If it isn't quantized then the force would have to be stretched out over large areas as well right?

I think you are making far too many classical assumptions about a relativistic model to be able to draw any valid conclusions. How do you envisage gravitons actually interacting with a mass?
You can be pretty sure that it's not as simple as you are implying.

I think you are making far too many classical assumptions about a relativistic model to be able to draw any valid conclusions. How do you envisage gravitons actually interacting with a mass?
You can be pretty sure that it's not as simple as you are implying.

Fair enough. There isn't anything that tells how gravitons would interact right? Pushing mass back to where the graviton came from is as far as I got without any idea how this might occur.
Anyway am I completely imagining a problem here then, or is there still a small amount of validity to my questions?

I interpreted the OP's question in that way: assuming that the total system mass incl. radiation must be conserved, the same atoms must have reduced mass when at rest at reduced potential. Consequently the inverse should also be true: if we lifted an object up from the earth, that object should indeed have increased mass. Note: I think that that is an SR argument.

Yes that was sort of my line of thinking, well, I didn't really think of that myself I was confused for a bit when I read that potential gravitational energy increased mass but it made sense. Apparently it seems it was wrong.

I think the best that can be drawn is that classical gravity does not work under the kinds of conditions in which you need relativity. Which would be a bit of a no-brainer.

Perhaps the question that is wanted is:
"How does General Relativity handle the kinds of situations where we would normally use gravitational potentials?"

[..] Yes that was sort of my line of thinking, well, I didn't really think of that myself I was confused for a bit when I read that potential gravitational energy increased mass but it made sense. Apparently it seems it was wrong.
I don't know why what you read now seems wrong to you. It is not contained in classical mechanics while in the context of GR there is an issue with definitions. However, it appears to be correct in the context of SR, just as D_H illustrated.

I think the best that can be drawn is that classical gravity does not work under the kinds of conditions in which you need relativity. Which would be a bit of a no-brainer.

Perhaps the question that is wanted is:
"How does General Relativity handle the kinds of situations where we would normally use gravitational potentials?"

That sounds good, what is the answer?

I don't know why what you read now seems wrong to you. It is not contained in classical mechanics while in the context of GR there is an issue with definitions. However, it appears to be correct in the context of SR, just as D_H illustrated.

I see, so what exactly is gaining mass then within SR? The system or the particles themselves? And has any mass gain ever been measured?

afaic, SR is totally irrelevant to all of this. It just doesn't apply where there's acceleration or gravity so it would be better not to introduce it into the conversation.
Either stick to classical ideas or go the whole hog and that means GR and beyond - in which case, there can be no valid conclusions based on classical ideas.