# Gravitational potential energy storage location

1. Dec 18, 2011

### jpo

Hello,

I thought of asking would someone know what is the correct thinking here...
A body is thrown upwards, its kinetic energy gradually transforms into gravitational potential energy until it is entirely absorbed.

At this moment, where is the potential energy? According to wikipedia (N. Umov)
"Umov considered potential energy as kinetic energy of some environments "imperceptible for us". From this hypothesis, he made a conclusion: it is always possible to specify a place where the energy is in."

2. Dec 18, 2011

### Staff: Mentor

3. Dec 19, 2011

### jpo

How should one think of the gravitational potential energy location then...

With a moving body it seems easier, because wherever the body is, at this same locale is the capability of collision and consequently doing work. With waves, the Poynting vector shows the direction of energy flow, which still gives an idea of "energy location"

Potential energy seems very confusing; the body at height h does not have energy yet; it has the "potential" to have it. Where , in what locale did the energy go?

Another confusing issue with the thrown up body is the loss of kinetic energy. Can we say its kinetic energy has been absorbed by the gravitational field?

Last edited: Dec 19, 2011
4. Dec 19, 2011

### Staff: Mentor

One shouldn't think of the location of the potential energy. Just think of it as a property of the system as a whole. Don't try to attribute it to one part of the system.

5. Dec 19, 2011

### jpo

What about the energy storage? If a body has been lifted up and put on a shelf indefinitely, this should mean that the gravitational field has stored its kinetic energy (needed to have it lifted), correct?

Last edited: Dec 19, 2011
6. Dec 19, 2011

### Staff: Mentor

Yes, the energy is stored, but that doesnt mean that there is a need to localize.

7. Dec 19, 2011

### jpo

DaleSpam, thank you for your replies. Is there a text one can read about how gravitational field stores energy? Esp. a text for those without GR knowledge :)

I'd like to read more on the storing mechanism... Or perhaps you can share more on this subject?

8. Dec 19, 2011

### zonde

It goes into mass of the body.

It can be easily seen for reverse scenario. When body falls down on other mass there is mass deficit after energy equivalent of kinetic energy is radiated out.

9. Dec 19, 2011

### pervect

Staff Emeritus
If you can get a hold of MTW's gravitation, https://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440

you'll find one whole chapter (a short one) that explains why you can't localize the energy in a gravitational field, which is what people have been telling you here and where your question started out.

Offhand I'd say that this fact about gravity is incompatible with your idea of a "mechanism", because I would think any concept of a "mechanism" as being basically some mechanical analogue, would localize the gravitational energy.

Perhaps I'm wrong, as it's not totally clear what sort of "mechanism" you're asking for.

Unfortunately, localizing the energy of the gravitational field is not possible, at least not within the context of GR. There are some other theories of gravity that might allow such a localization, most of these theories predict and require extra fields that nobody has been able to observe to date.

Classical GR, however, does NOT allow such a localization of gravitational energy.

10. Dec 19, 2011

### jpo

I am trying to understand what people have posted above (for which posts I am thankful)...

The problem is that the conversion of kinetic energy of a thrown up body into gravitational potential energy leaves the said body at height h. It has lost its kinetic energy and has gained nothing, except the potential to produce back the lost kinetic energy. In the meantime, if put on a shelf at height h, its temperature has not risen; its internal pressure has not risen etc; there are no methods to prove it has energy, unless it is dropped back down.

zonde, do I understand you correctly? You wrote that the gained gravitational potential energy actually adds mass to the body and it becomes m + dm, where dm is a result of the binding energy, e.g. when the body is dropped down, its mass will be reduced back to m and dm will be lost through heat etc which is the binding energy

Do I understand this correctly?

Many thanks.

Last edited: Dec 19, 2011
11. Dec 19, 2011

### zonde

Yes, that's correct.

12. Dec 20, 2011

### my_wan

The whole notion of the localization of energy ill conceived to me. This is not unique to either kinetic or potential energy. Starting with kinetic energy, if two asteroids have kinetic energy $E_k$ with respect to each other then asteroid at asteroid A it is said that asteroid B possesses $E_k$. At asteroid B it is said asteroid A possesses $E_k$. Neither A nor B, which may be separated by millions of km, alone possesses $E_k$. So where is $E_k$ really at? The question itself is meaningless.

In the potential energy $E_p$ case the $E_p$ is not defined by a property of the mass, but rather by the fact that there happens to be another lower energy state available nearby. Hence it's relational in a similar way to the relational character of $E_k$. Remove this nearby lower energy state and the $E_p$ of that mass disappears without making any changes to the state of that mass alone. Asking where $E_k$ or $E_p$ is at is like an American asking a Chinese why they call up down.

This same issue comes up over and over again which even the basics of relativity illustrate how pointless it is. Yet relativity tends to be falsely thrown out only in the context of disavowing realism while the location of purely relational properties we associate with such objects is debated as if even the basics of relativity do not so obviously disavow the meaning of the question. We have even formalized this reality of objects = reality of relational properties locally inhere to said object in many of our no-go theorems. You can instantly increase $E_k$ of an object many light years away simply by walking toward it.

13. Dec 20, 2011

### jpo

the gravitational potential energy adding a mass dm to the lifted body...
I am assuming this has been verified experimentally, (specifically for gravity)?

14. Dec 20, 2011

### PAllen

So far as I know, the only thing measured is lower mass in a bound state. However, the relation between this and purported higher mass from simply moving something 'up' a potential well is tricky.

Consider gravity and collapsing dust: as the dust collapses, the dust gains KE, thus heats up. The excess heat is radiated away (in the typical case where it started in thermal equilibrium with its surroundings). Before radiating away heat, mass has not changed - both rest mass and KE contribute to inertial and gravitational mass (per relativity). As thermal equilibrium is re-gained, the mass of the collapsed dust is lower, but only by virtue of radiating away random KE = heat as EM radiation.

Now imagine trying to reverse the process. Energy must be expended pulling the dust apart again. Assuming KE of dust particles is unchanged (in, e.g. COM frame of the system), the mass of the dust farther apart is unchanged. What has decreased in mass is whatever provided the energy separating the dust back to greater distance from COM.

I think my_wan's post is thus particularly apt - the whole issue of localizing energy misguided or at least frame dependent and convention dependent.

15. Dec 20, 2011

### Staff: Mentor

That isn't correct/the same problem exists for KE as PE. Consider a car on a road. You can't attribute a single KE to it: it has a different KE to different observers. For example, it could collide with a wall or a moving car and have two different energies. As said, the energy is a property of the system, not the car.

16. Dec 20, 2011

### my_wan

Yes it has been verified directly through momentum, i.e., relativistic mass, gains in photons traveling up and down the side of a tall building using interferometers. The frame and convention dependence of these descriptions can be quantitatively justified by the fact that given any set of these frame dependent descriptions can be be converted to any other via affine transforms. So any one is a valid description of all other valid frames. It is only when you start with questions about which affine space of the system is the "real" affine space that you get into trouble with trying to localize observables that do not have locations.

17. Dec 20, 2011

### PAllen

Can you indicate what experiments you're referring to? Things like Pound-Rebka do not, in any way, demonstrate a kg at the top of building is more massive that a kg at the bottom. They measure the anolog for photons of the following: drop a mass from tall building, and at bottom it has more total energy (mass + KE) than it does locally at the top. If it bounces inelastically back to the top, it again has the original total energy (same mass, no KE). What Zonde seemed to be proposing is some sense in which (in principle) a stationary kg at the top of a building is more massive than a stationary kg at the bottom. This runs up against the fact that there is really no way to measure 'mass at a distance'. The closest I can come to a coordinate framework in which you can claim to measure this effect is as follows:

At the top of the building, have a measuring instrument that is moving upwards at a speed such that its clock is in synch with the ground, and light it emits would not be blueshifted (upward motion red shift balancing gravitational blue shift). Then, that instrument, as it approaches the top of the building, would see light emitted from the top of the building blueshifted the same as a ground observer would; further, a stationary kg will have more total energy than one moving with the instrument - a truism because it is moving relative to the instrument. So setting up coordinates in just this special way, you could claim to demonstrate the high kg having more energy but it would look like extra KE not extra rest mass.

Can you suggest a more direct way to measure, in principle, a higher mass for the higher kg block?

[Edit: removed edit. Just confused matters. ]

Last edited: Dec 20, 2011
18. Dec 20, 2011

### PAllen

Re #17, I thought of another example of how you try to measure mass change of an 'identical' object at different altitudes. It shows just how difficult it is to physically justify the claim of that a higher kg is has more mass.

Consider an ideal spring oscillator running horizontally (so gravity not directly involved) on a frictionless surface. Spring fixed at one end, attached to frictionless 1kg block on the other. Set up e.g. 10 cm oscillation. Its period depends on the mass, for a given ideal spring (longer period, greater mass). Then transport your apparatus to the top of a tall building. Ask someone remaining at the top to repeat the experiment while you go back down and watch. Compared to your original timing, it runs fast. So you conclude, measured this way, the 1kg at the top must be less massive. Of course, if you then say that's stupid, let me adjust for time dilation, you find the mass is the same.

Last edited: Dec 20, 2011
19. Dec 21, 2011

### my_wan

I tried looking it up but it was before the internet though after Pound-Rebka. At least the 70s. From the best of my recollection lasers pointed down a building and reflected back up compared to a reference reflected parallel to the ground was employed, with the results I think obtained by a phase shift in the interference. Though I don't have a clue at this point how they got a reference. Given the time period it was likely either Discover or Scientific America, more likely the later, where I read the description.

Even the setup I read had to calculate the effective mass. The effective mass variance of Mercury also plays a role in the procession.

The most relevant scheme I have previously thought about was not explicitly to measure mass variances at different heights, or even mass itself as such, but rather a scheme to measure more directly the variance in the spacetime metric as the result of a gravitational field. Like a GR based version of a gravimeter. This consisted of a large wheel, or magnets on the end of a spinning wheel or spokes, passing a magneto. The output of the magnetos would be input such that the voltages cancelled. In this way it would only read the voltage difference, which could be arbitrarily amplified within noise constraints. To obtain a reference where cancellation of voltages occur you turn the magneto pairs so they're parallel to the gravitational and adjust out the voltage differences. To insure this cancellation is not biased do the same with the magneto positions swapped. Now when the magnetos are set top to bottom there should be a voltage difference as a result of the different spacetime metrics at the two magnetos. This difference should also vary depending on the height of the difference meter relative to the two magnetos, due to the relativistic character of the difference. At least within the min/max heights defined by the difference in magneto distances. Noise would be a particularly troublesome issue but it may at least be possible to verify the effect with enough noise control and shielding on magnetic bearings. This explicitly depends on the spacetime metrics covariant effects on all physical phenomena, not just mass.

I'll look some more and/or try to come up with other schemes. My memory of the experiment I mentioned is likely faulty in significant ways.

20. Dec 21, 2011

### PAllen

That should be possible, but that has nothing to do with Zonde's claim that there is physically meaningful sense in which an object maintaining constant temperature, density, etc. gains mass by moving up a gravity well. That is, that there is a well defined way to localize potential energy to an object and measure it as mass increase. I dispute this. I would be really interested in a measurement that claimed to do this (even in principle; esp as I've proposed two thought experiments that suggest it is not so).