Gravitaional field can store mass?

magnetar

If i separate two rocks,the total weight of them will increase? If so,the extra mass stored in the gravitational field between them?

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Jonathan Scott

If you separate two rocks, the total energy (and effective rest mass) of the system increases. However, the location of the additional energy is not clear in General Relativity.

In a semi-Newtonian equivalent, one apparently mathematically self-consistent solution is that each of the rocks increases in energy by the potential energy gained relative to the other rock, and the field loses the same amount of energy as either rock, so the total energy gained is the change in Newtonian potential energy of the system as a whole. In this model, for a field [itex]g[/itex] the energy density is [itex]g^2/(8 \pi G)[/itex] which is analogous to the Maxwell energy density [itex]\epsilon_0 E^2/2[/itex] in electromagnetism, where [itex]\epsilon_0[/itex] is matched with [itex]1/(4 \pi G)[/itex]. The field energy is maximized when mass is concentrated together, and decreases to zero as the masses are separated to infinity.

bcrowell

Jonathan Scott's answer is correct. Just to amplify on it a little, here's the reason why you can't localize the gravitational field energy in GR as you would have been able to in Newtonian mechanics. In GR, the equivalence principle says that the gravitational field can be anything you want it to be, depending on your frame of reference. In particular, give any point in space, you can always choose a frame of reference defined by an observer free-falling through that point, so the gravitational field is zero there.

When you're dealing with gravitational waves, you can get around this by averaging over multiple wavelengths.

Jonathan Scott

On rereading my own post, I see I've been a bit inaccurate; if you separate two rocks to infinity, the field energy of their interaction decreases to zero, but of course the separate rocks still have field energy due to their own individual fields as concentrations of mass. That field energy would decrease if you break each of them into smaller rocks and separate those, and so on.

Naty1

...because you have done work....that is, put energy into the system, done work to overcome the attractive gravitational force. But it's clearer to say the energy rather than the mass has increased....and that seems to be a modern preference/convention as discussed here in other threads.

A similar situation exists when a relaxed spring is compressed and held...the jack in the box example.....there is more energy in the coiled than the uncoiled spring....

and a hot blob of metal contains more energy than the same blob when cold....heat added is a form of energy....

You'll also observe more energy in a faster moving mass than when it is slowed....

Thanks to Einstein!!!

Naty1

Jonathan posts:

Which field energy...seems like both would increase???...according to your earlier post:

The second quote is, I believe, the correct one....

Mentz114

I think what Jonathan means is that when a rock is broken, some binding energy is lost from the effective mass ?

( I'm confined at home because of a bad foot tonight - I'm glad the forum isn't deserted )

Jonathan Scott

Sorry, the actual "breaking" of the rock is not relevant - just assume it can be dismantled. I'm only talking about the gravitational energy. If you separate it into thinly spread dust, that minimizes the gravitational interactions and the external field of the whole system.

As I seem to remember mentioning recently in some other thread, there are two ways of extending Newtonian gravity to include energy in the field.

If you just assume in a non-relativistic way that the masses are not affected by gravity, then the potential energy has to be assumed to be in the field, which then has a negative field density, [itex]-g^2/8 \pi G[/itex], because the total energy of the system decreases as masses are brought together, giving a more intense outward field overall (although the field between the masses cancels, of course).

If however you include the known relativistic effect of gravity on time and hence on energy, then each mass is effectively modified by the potential due other masses. Since this occurs both ways, this means that the effective total mass is modified by TWICE the potential energy, but mathematically this cancels out nicely if you assume that there is also a positive energy density in the field of [itex]g^2/8 \pi G[/itex], the same as in the original Newtonian model except that it has the opposite sign.

Note also that this is only a model in a particular frame of reference. General Relativity tells us that this model is probably incomplete because it only works for certain frames of reference.

Regardless of these details, the total effective mass of a system of objects is decreased slightly when they are brought together (in a static configuration) and increased again if they are moved apart. The increase tends to a limit as the separation goes to infinity. If all of the components are separated as far apart as possible, the external field of the system as a whole is minimized.

edpell

Yes the gravitational field has energy just as a fast moving ball has kinetic energy. We do not say the ball stores energy though I suppose that is correct. Likewise for fields.

If the masses are increasing then energy is being drawn out of somewhere else. Maybe the person or object that is doing the work to move the masses apart is supplying the energy?

Frame Dragger

If you ever want a practical and dangerous demonstration of the "storage" of energy, buy a flywheel. Spin that sucker up, then break it FAST, and as the shards pass through your body, you'll realize that the explosive 'breakup' of the wheel is a result of the 'stored' potential kinetic energy becoming not-so-potential anymore.

Given that nothing else in the room explodes, I have to assume the potential energy is a property of the dynamic system that is the flywheel, and if there is "storage" it's in the medium which is in motion relative to a rest frame.

Mentz114

One of the issues raised in this thread is whether a field can store energy. It seems to me that as soon as one 'stores' energy in a field then (1) either the field must be non-local, or (2) one must accept non-conservation of energy, or (3) accept the existence of an infinite resevoir of energy.Take your pick. ( But please don't hit me with it ! ).

Jonathan Scott

I don't think any of those are needed. There are energy-momentum pseudotensors which say where the energy is from any one point of view, but in GR it gets mixed up with the shape of space-time, in that what appears to be a free fall geodesic from one point of view involves a change of momentum (and possibly energy) from another more global point of view. The non-linearity of GR seems to make this worse, in that if gravitational energy is also a source of gravity then it's tricky to understand how it can appear to be in different places for different observers.

Personally, I think GR isn't working very well except in the case of a single dominant central object with a fairly weak field, where it is obviously extremely successful. Despite the neatness of the idea, I think that it will probably turn out eventually that the concept is only accurate to first (Newtonian) order and the second-order fit in the solar system (with the PPN beta parameter) is a result of two or more equal and opposite second-order errors (for example relating to Machian variation with location and non-zero energy density in the field). I think it's likely that a future improved theory of gravity will eliminate the concepts of dark matter, dark energy and black holes, will fix the incompatibility with QM, and will clearly include some form of Mach's principle. I just wish someone would come up with it quickly; my own attempts have so far been unsuccessful.

sweet springs

Hi,magnetar

No, "gravitational energy" does not hold energy that appear in Einstein's gravitation equation.
Total mass is considered to be reserved in spite of the separation, however the summation of rest mass in different location is physically meaningless.
Regards.

edpell

I am not following please explain more. In the case of gravity the field goes as 1/r so it is not local? What exactly do you mean by local? Why non-conservation of energy? I like conservation of energy.

Frame Dragger

By non-local he is talking about "big N/L" Local/Non-Locality". As in, Entanglement, EPR, etc. He doesn't mean local in the Astronomical sense. As for conservation of energy, it's already only conserved in certain instances, and questions like "where does all energy come from" is analogous to, "what IS space-time?" or "Why is the universe the way it is?"

Naty1

Jonathan: good post in #8....

says it all......

lightarrow

It's not clear to me if this assumption (the one I coloured in blue) is arbitrary or if there are strong physical reasons to make it.