How does the expanding universe affect matter/energy

[TheScienceOrca]

Rephrase from another thread I posted a while back;

If you believe as masses increase in distance gravitational potential increases relative to the distance (the greater the distance the greater the gravitational potential).


So as matter increases in distance from each other due to expansion is gravitational potential created?

 

[Simon Bridge]

Insofar as the gravitational potential energy between two masses is related to their separation ... yes: as masses move apart for any reason then the gravitational potential energy between them increases.
Careful though - this is a Newtonian picture.

 

[TheScienceOrca]

Insofar as the gravitational potential energy between two masses is related to their separation ... yes: as masses move apart for any reason then the gravitational potential energy between them increases.
Careful though - this is a Newtonian picture.

Correct but on any scale this is profound...

"scientists were able to calculate the expansion rate to 42 miles (68 kilometers) per second per 1 million light-years with greater precision, while looking farther back in time" (http://www.space.com/26279-universe-expansion-measurement-quasars-boss.html).



Lets say the distance between the two objects is 890,700,000 miles or 0.000151518249 light years which is a very small distance (the distance between Saturn and the sun).

If you follow that law, then every year due to expansion (no forces), the distance between the sun and saturn increase by 200820.7417384602 miles.

That is a WHOLE lot of gravitational potential energy if you follow the Newtonian equation mgh.


So even on the Newtonian scale, how is it possible to create energy? ( This isn't philosophy keep in mind I am citing evidence from reputable sources and made a few calculations anyone at home can do, I guess no one just ever thought to http://www.space.com/26279-universe-expansion-measurement-quasars-boss.html ).

So what is wrong Newtonian mechanics as we know it? Or space.com?


Please help me get a better understanding

 

[Simon Bridge]

The scale of the solar system is not quite Newtonian. The Newtonian scale is only a few to a few thousand kilometers depending on what sort of measurments are being made and the circumstances. Newtonian mechanics is only an approximation, a good approximation ... it has been replaced by the theory of relativity.

The law of conservation of energy you are used to does not work in general relativity. Cosmological expansion is from general relativity.

 

[TheScienceOrca]

The scale of the solar system is not Newtonian. The Newtonian scale is only a few to a few thousand kilometers depending on what sort of measurments are being made. Newtonian mechanics is only an approximation, a good approximation ... it has been replaced by the theory of relativity.

The law of conservation of energy you are used to does not work in general relativity. Cosmological expansion is from general relativity.

Ok where is the definition for distance that defines an event as Newtonian or GR or SR?

Also, with your statement that you agree that energy is created, is it possible this will be the counter to a deep freeze model?

 

[Simon Bridge]

Ok where is the definition for distance that defines an event as Newtonian or GR or SR?

There is no such definition.
An "event" in this context (cosmological expansion) is a point in space-time. Events are not Newtonian.

We use Newtonian physics in circumstances where it is useful.
i.e. where the difference between the prediction from Newtonian models and reality is smaller than the uncertainty in our measurements.

Also, with your statement that you agree that energy is created, is it possible this will be the counter to a deep freeze model?

No - I did not agree that energy is created - I said that the conservation of energy that you are used to does not hold for GR. This is why you have to be careful about mixing ideas from different models.

There are other conservation laws related to the stress-energy tensor. Bottom-line: you need to learn more about general relativity before continuing this line of speculation.

Note: what counts as "big" depends on the scales used.
Your own calculation has the cosmological drift of Saturn being about 200,000 miles each year.
This is about 0.2% of the normal variation in Saturn's orbit due to it's eccentricity.
So - not all that large. Probably too small to notice - though over the 50 or so years of accurate observations this shift would probably have been noticed if there was one.

Basically the solar system does not expand with the Universe,
http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS (the rest of that FAQ should be useful to you as well.)
... however, the expansion could have some local effects.
http://arxiv.org/abs/gr-qc/0602098

Basically the cosmological expansion is actually an effect that appears on average over very large distances and is not uniform on all scales.

 

[TheScienceOrca]

There is no such definition.
An "event" in this context (cosmological expansion) is a point in space-time. Events are not Newtonian.

We use Newtonian physics in circumstances where it is useful.
i.e. where the difference between the prediction from Newtonian models and reality is smaller than the uncertainty in our measurements.


No - I did not agree that energy is created - I said that the conservation of energy that you are used to does not hold for GR. This is why you have to be careful about mixing ideas from different models.

There are other conservation laws related to the stress-energy tensor. Bottom-line: you need to learn more about general relativity before continuing this line of speculation.

Note: what counts as "big" depends on the scales used.
Your own calculation has the cosmological drift of Saturn being about 200,000 miles each year.
This is about 0.2% of the normal variation in Saturn's orbit due to it's eccentricity.
So - not all that large. Probably too small to notice - though over the 50 or so years of accurate observations this shift would probably have been noticed if there was one.

Basically the solar system does not expand with the Universe,
http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS (the rest of that FAQ should be useful to you as well.)
... however, the expansion could have some local effects.
http://arxiv.org/abs/gr-qc/0602098

Basically the cosmological expansion is actually an effect that appears on average over very large distances and is not uniform on all scales.

Why do you think that is? Also you can't just negate it's value because of the relatively small amount of distance gain, ANY increase is an increase.

 

[PeterDonis]

as matter increases in distance from each other due to expansion is gravitational potential created?

No, because the concept of "gravitational potential" doesn't apply to a non-stationary spacetime. The expanding universe is a non-stationary spacetime.

 

[PeterDonis]

This is about 0.2% of the normal variation in Saturn's orbit due to it's eccentricity.

But it's secular, not periodic, so in 50 years it would have built up to 10% of the variation due to eccentricity, which is quite large enough to have been noticed if it had actually happened.

 

[Simon Bridge]

But it's secular, not periodic, so in 50 years it would have built up to 10% of the variation due to eccentricity, which is quite large enough to have been noticed if it had actually happened.

... which is what I said ;)

 

[Simon Bridge]

Why do you think that is?

Why do I think what is what?
The cosmological expansion is an average over large distances because that is the meaning of the words. That is how "cosmological expansion" is measured.

On smaller scales the energy densities are too lumpy and the distribution of dark matter etc is not uniform. It's like dirt can be treated as a homogeneous substance when you have lots of it but on the small scale it is grainy, it's got stones in it etc. Averages that work for a whole truckload don't work for a thimbleful. Thus we don't normally think of cosmological expansion being all that important at a sub-galactic scale.

Also you can't just negate it's value because of the relatively small amount of distance gain, ANY increase is an increase.

I didn't "just negate it" though - please review the links about why the cosmological expansion does not count so much for the solar system.

I was trying to make a point about what counts as "big"... Astrophysics throws large numbers at you all the time, it's easy to think they are big just because they have a lot of zeros in them so the trick is to find a useful comparison.

 

[PeterDonis]

you can't just negate it's value because of the relatively small amount of distance gain, ANY increase is an increase.

But there is *not* any increase in the solar system, for example in the distance of Saturn from the Sun; if there were, as Simon Bridge said, we would have seen it by now, and we haven't. That was his point.

 

[Simon Bridge]

But there is *not* any increase in the solar system, for example in the distance of Saturn from the Sun; if there were, as Simon Bridge said, we would have seen it by now, and we haven't. That was his point.

... well it was part of the point - and an important consideration.
This is what I get for trying to be clever :(

 

[PeterDonis]

well it was part of the point

Yes, I know, but it was the only part that TheScienceOrca appeared to respond to. (Well, that and "why do you think that is", but as you noted, it's not clear what that was referring to.)

 

[Orodruin]

If you follow that law, then every year due to expansion (no forces), the distance between the sun and saturn increase by 200820.7417384602 miles.

Even if the solar system expanded like this, your numbers are way off. Wolfram Alpha is your friend when it comes to unit conversions and getting numbers:
http://www.wolframalpha.com/input/?i=(Sun+to+Saturn+distance)*(Hubble+parameter)

The correct incorrect number would be 0.07 miles/year.

 

[TheScienceOrca]

No, because the concept of "gravitational potential" doesn't apply to a non-stationary spacetime. The expanding universe is a non-stationary spacetime.

But the gravitational force still exists so regardless of whatever you like to call "that forces potential energy" it still exists.

That increase can now be converted to kinetic energy.

 

[pervect]

But the gravitational force still exists so regardless of whatever you like to call "that forces potential energy" it still exists.

That increase can now be converted to kinetic energy.

Not really. GR's results for energy are not at all intuitive. For a somewhat historical reference see for instance http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html.

Though the general theory of relativity was completed in 1915, there remained unresolved problems. In particular, the principle of local energy conservation was a vexing issue. In the general theory, energy is not conserved locally as it is in classical field theories - Newtonian gravity, electromagnetism, hydrodynamics, etc.. Energy conservation in the general theory has been perplexing many people for decades.

I don't care for their use of "local", but the point is the problem exists, and has been around for a long time.

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html is a good summary written at the lay level.

The FAQ's description of the situation is as follows.

In flat spacetime (the backdrop for special relativity) you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below). The two formulations are mathematically equivalent. But when you try to generalize this to curved spacetimes (the arena for general relativity) this equivalence breaks down. The differential form extends with nary a hiccup; not so the integral form.

The differential form says, loosely speaking, that no energy is created in any infinitesimal piece of spacetime. The integral form says the same for a finite-sized piece.

The point I hope to get across is that this is not a simple problem, it's been around for a long, long time, and that it really requires an actually working knowledge of GR (as distinct from misleading popularized notions of GR based on a Newtonian framework) to appreciate the subtle details.

 

[PeterDonis]

But the gravitational force still exists

No, it doesn't. Gravity isn't a force in GR. It's spacetime curvature.

There are still phenomena in the expanding universe that bear a resemblance to masses "attracting each other by gravity" (for example, the presence of ordinary matter and energy in the universe tends to slow its expansion), but calling that a "gravitational force" is a serious misnomer, because it does not work the same way as Newtonian "gravitational force" does. For example:

so regardless of whatever you like to call "that forces potential energy" it still exists.

No, it doesn't, because "potential energy" is just a label for a particular concept, and if that concept doesn't apply (which it doesn't in an expanding universe), the label simply doesn't label anything.

That increase can now be converted to kinetic energy.

How? Please be specific.

 

[michael879]

I think Orodruin answered your question better than anyone else. Your math is off by a factor of 1 million (Im guessing you used /lightyear instead of /1 million light years). Using the numbers you give in your post, the expansion of saturn relative to the sun would only end up being 0.2 miles/year. If the universe were expanding a million times faster, we probably WOULD notice effects on the solar scale. But as it is there is no measurable effect until you get to very large scales

 

[TheScienceOrca]

First of all expansion occurs on all scales to our knowledge, please link me to one post stating otherwise for those who made that claim within this thread you know who you are I don't have time to quote.

I haven't double checked the math but I am willing to take your word for my mistake as it doesn't change the outcome of the question.

"No, it doesn't, because "potential energy" is just a label for a particular concept, and if that concept doesn't apply (which it doesn't in an expanding universe), the label simply doesn't label anything."

Great so let's use the proper terminology for the same concept;

Let me help explain this to you, it doesn't matter what you call the term or the idea at the end of the day energy is being created but since you would like to be vocab let me explain this concept to you in an easier manner; If you are still having troubles understanding let me know and I would love to clarify and correct my vocabulary if it is indeed wrong.

Imagine a universe with 2 masses separated by 1 million light years.
Imagine the objects are also not moving relative to each from both frames of reference.

The distance between them is increasing due to expansion even though they are not traveling or accelerating.

This is an important fundamental point to the question.

Lets imagine this scenario again, but now with no forces on the masses.

Due to space curvature these masses will now fall towards each other increasing in kinetic energy exponentially.

Upon contact this kinetic energy would likely be turned into much heat and other usable forms of energy, although that is irrelevant to the concept. So regardless of what you like to call it a force, or space time curvature, and the end of the day energy is still created and that can't be avoided by trying to say the whole concept is wrong due to a misuse of vocabulary that is just absurd.

 

[TheScienceOrca]

Also since gravity is something most scientists agree exists, when any number of masses greater than 1 are separated the space time curvature have potential to accelerate towards each other thus gaining energy.

So I think it would be fair to say this is POTENTIAL ENERGY without referring to the term potential energy which is commonly used in Newtonian mechanics.

I am using potential energy in a literal sense which is exactly what it means.i.e;

Those two masses have gravitational potential energy.

You could think of it as this; Those two masses have the potential to create kinetic energy due to the space time curvature.Both statements are true.

Hopefully this explanation helps you.

 

[TheScienceOrca]

No, it doesn't. Gravity isn't a force in GR. It's spacetime curvature.

There are still phenomena in the expanding universe that bear a resemblance to masses "attracting each other by gravity" (for example, the presence of ordinary matter and energy in the universe tends to slow its expansion), but calling that a "gravitational force" is a serious misnomer, because it does not work the same way as Newtonian "gravitational force" does. For example:
No, it doesn't, because "potential energy" is just a label for a particular concept, and if that concept doesn't apply (which it doesn't in an expanding universe), the label simply doesn't label anything.
How? Please be specific.

How?

Drop an apple on your head and you can feel it yourself.

 

[TheScienceOrca]

"which it doesn't in an expanding universe), the label simply doesn't label anything."Again it is a literal explanation not a label.

 

[PeterDonis]

If the universe were expanding a million times faster, we probably WOULD notice effects on the solar scale.

I'm not sure we would, because the solar system would still be gravitationally bound, and that effect would still be much stronger than any inertia involved with the expansion.

This does assume, though, that the solar system (and gravitationally bound systems in general) would still exist if our universe were expanding a million times faster. That might not actually be the case: if the universe were expanding a million times faster, and had been doing so right back to the Big Bang, gravitational clumping might not have been able to take place at all. But then we wouldn't be here.

 

[PeterDonis]

Imagine a universe with 2 masses separated by 1 million light years.
Imagine the objects are also not moving relative to each from both frames of reference.

The distance between them is increasing due to expansion even though they are not traveling or accelerating.

Um, what? Either they're moving relative to each other or they're not.

Lets imagine this scenario again, but now with no forces on the masses.

Huh? There weren't any forces on them before. They were both moving inertially.

You do understand that in our expanding universe, all the galaxies, which are moving apart because of the expansion, are moving inertially, feeling zero force, right? The expansion is not a force pushing on the galaxies to move them apart. It just is the galaxies moving apart.

when any number of masses greater than 1 are separated the space time curvature have potential to accelerate towards each other thus gaining energy

That depends on the spacetime. See below.

Drop an apple on your head and you can feel it yourself.

According to GR, I am not dropping an apple on my head; I am releasing it and letting it float freely, while the Earth pushes me upward into it. I am the one feeling a force, not the apple, and the force I feel is not "gravity", it's the Earth pushing up on me.

it is a literal explanation not a label

When I say the concept of "potential energy" doesn't apply to the expanding universe, I'm not talking about terminology or labels; I'm talking about physics. I'm saying that the physics that's going on in an expanding universe is not the same as the physics going on when an apple falls. I'm saying that the physics you are trying to apply the the expanding universe is the wrong physics; you are trying to apply the physics that works in a stationary spacetime, where the concept of "potential energy" is meaningful, to a non-stationary spacetime (the expanding universe), where it isn't. The same underlying theory (GR) can be used to describe both, but the specific models used--the specific solutions to the Einstein Field Equation--are different, and have different properties. The solution that applies to the apple falling has "potential energy" as one of its properties; the solution that applies to the expanding universe does not.

 

[michael879]

I'm not sure we would, because the solar system would still be gravitationally bound, and that effect would still be much stronger than any inertia involved with the expansion.

This does assume, though, that the solar system (and gravitationally bound systems in general) would still exist if our universe were expanding a million times faster. That might not actually be the case: if the universe were expanding a million times faster, and had been doing so right back to the Big Bang, gravitational clumping might not have been able to take place at all. But then we wouldn't be here.

Yea that's a valid point, but as Orca has clarified his question I don't think it matters to this thread. I was more thinking if the expansion was suddenly "turned up" by a factor of 1 million, its hard to imagine not noticing an effect that strong. It is conceivable that the solar system is still too small to be affected, but as you pointed out earlier the cumulative effect over 50 years would be quite large!

As for the OP, "energy" is not really conserved globally in GR, only locally. The conservation law is:
$$\nabla_\mu T^{\mu\nu} = 0$$
where the derivative is a covariant derivative, so it dependent on the metric and therefore the cosmological constant. This is only equivalent to the classical law
$$\partial _\mu T^{\mu\nu} = 0$$
locally, where you can make the metric vanish. Cosmological expansion is by definition a global phenomenon, as locally the effect dissapears.

I'm not 100% sure about this statement, but I'm pretty sure the total energy of the universe IS increasing due to the expansion. According to current theory, the energy-density of dark energy is a constant (specifically the cosmological constant) so that as the universe expands the total energy increases. The matter/radiation content of the universe is cooling down during this expansion, so it there IS some energy loss too. However, that energy can only approach 0, while the dark energy content can increase indefinitely as long as the universe continues to expand

 

[pervect]

So regardless of what you like to call it a force, or space time curvature, and the end of the day energy is still created and that can't be avoided by trying to say the whole concept is wrong due to a misuse of vocabulary that is just absurd.

If energy were to be conserved in GR, there would indeed have to be a contribution from "gravitational field energy", which is, I believe the point of your somewhat long example. Unfortunately. if you consult an actual GR textbook such as "General Relativity", Robert M Wald, 1984, (see section $11.2 pg 286)

[quote =Wald ]
...not surprising since $T_{ab}$ represents only the energy content of matter, whereas "gravitational field energy" should make a contribution to total energy and thus should appear in any conservation law. However, as already mentioned in chapter 4, there is no known meaningful notion of the energy density of the gravitational field in general relativity.
[/quote]

So most of your post is wishful thinking based on assuming your conclusion :(. I'd summarize your "argument" as follows. "Energy is conserved in Newtonian theory, so I want it to be conserved in GR too. In Newtonian theory we can break total energy into two components, kinetic energy and potential energy, whose sum is a conserved quantity, so we'll assume that we can do the same in GR. We will ignore the textbooks, papers, and FAQ's that tell us that we can't do this because we don't want to believe them or even take the time to check out contrary references.

 

[PeterDonis]

I was more thinking if the expansion was suddenly "turned up" by a factor of 1 million, its hard to imagine not noticing an effect that strong. It is conceivable that the solar system is still too small to be affected, but as you pointed out earlier the cumulative effect over 50 years would be quite large!

If it actually occurred, yes. But as I noted in my previous post, the solar system would still be gravitationally bound, and I think (though I haven't done an actual calculation to confirm) that this would still be much stronger than any effect of the expansion. Remember that the expansion is just inertia--there is no force "pushing" the galaxies apart, and no force "pushing" planets away from the Sun. (Dark energy does complicate this a bit, but I think a dark energy density a million times larger than what we currently have would still be so much less than the average matter density in the solar system that its effect would be negligible. Again, I haven't done an actual calculation to confirm that, though.)

I'm not 100% sure about this statement, but I'm pretty sure the total energy of the universe IS increasing due to the expansion. According to current theory, the energy-density of dark energy is a constant (specifically the cosmological constant) so that as the universe expands the total energy increases. The matter/radiation content of the universe is cooling down during this expansion, so it there IS some energy loss too. However, that energy can only approach 0, while the dark energy content can increase indefinitely as long as the universe continues to expand

You're assuming that "the total energy of the universe" is a meaningful concept. But the same issues that make energy only conserved locally in GR make it impossible to define a "total energy of the universe" in a frame-independent way, because the spacetime that describes the universe lacks the properties that make that possible. In order to meaningfully define a "total energy" for a spacetime, it either needs to be stationary--so the Komar energy can be defined--or asymptotically flat--so the ADM energy or Bondi energy can be defined. The spacetime that describes our universe is neither. Your implicit definition of total energy as "energy density times volume" is basically the Komar energy, which can only be defined in a stationary spacetime.

(Note, btw, that for a spatially infinite stationary spacetime that is not asymptotically flat, the Komar energy is infinite--so even if we could extend the definition to a non-stationary spacetime, if our universe is spatially infinite--which it is according to our best current estimate--its "total energy" would be infinite by this definition, since the universe is not asymptotically flat.)

 

[michael879]

If it actually occurred, yes. But as I noted in my previous post, the solar system would still be gravitationally bound, and I think (though I haven't done an actual calculation to confirm) that this would still be much stronger than any effect of the expansion. Remember that the expansion is just inertia--there is no force "pushing" the galaxies apart, and no force "pushing" planets away from the Sun. (Dark energy does complicate this a bit, but I think a dark energy density a million times larger than what we currently have would still be so much less than the average matter density in the solar system that its effect would be negligible. Again, I haven't done an actual calculation to confirm that, though.)

Yea I haven't done any calculations either, so we're just arguing intuition about scales here :P

You're assuming that "the total energy of the universe" is a meaningful concept. But the same issues that make energy only conserved locally in GR make it impossible to define a "total energy of the universe" in a frame-independent way, because the spacetime that describes the universe lacks the properties that make that possible. In order to meaningfully define a "total energy" for a spacetime, it either needs to be stationary--so the Komar energy can be defined--or asymptotically flat--so the ADM energy or Bondi energy can be defined. The spacetime that describes our universe is neither. Your implicit definition of total energy as "energy density times volume" is basically the Komar energy, which can only be defined in a stationary spacetime.

Yea, you are right. Except, what's wrong with using a frame-dependent definition of "total energy" for the purpose of answering this question? I probably should have made that clearer, but this question was pseudo-relativistic from the beginning :P

 

[PeterDonis]

what's wrong with using a frame-dependent definition of "total energy" for the purpose of answering this question?

The OP would have to answer this, but I would say the problem is that it's frame-dependent. Potential energy, in spacetimes that admit such a concept (stationary spacetimes) is not frame-dependent, and the OP's question was about potential energy.

 

[michael879]

The OP would have to answer this, but I would say the problem is that it's frame-dependent. Potential energy, in spacetimes that admit such a concept (stationary spacetimes) is not frame-dependent, and the OP's question was about potential energy.

Agreed, but potential energy in an expanding universe is kindof paradoxical to begin with

 

[PeterDonis]

potential energy in an expanding universe is kindof paradoxical to begin with

I've been trying to convince the OP of exactly that point...

 

[TheScienceOrca]

Um, what? Either they're moving relative to each other or they're not.
Huh? There weren't any forces on them before. They were both moving inertially.

You do understand that in our expanding universe, all the galaxies, which are moving apart because of the expansion, are moving inertially, feeling zero force, right? The expansion is not a force pushing on the galaxies to move them apart. It just is the galaxies moving apart.
That depends on the spacetime. See below.
According to GR, I am not dropping an apple on my head; I am releasing it and letting it float freely, while the Earth pushes me upward into it. I am the one feeling a force, not the apple, and the force I feel is not "gravity", it's the Earth pushing up on me.
When I say the concept of "potential energy" doesn't apply to the expanding universe, I'm not talking about terminology or labels; I'm talking about physics. I'm saying that the physics that's going on in an expanding universe is not the same as the physics going on when an apple falls. I'm saying that the physics you are trying to apply the the expanding universe is the wrong physics; you are trying to apply the physics that works in a stationary spacetime, where the concept of "potential energy" is meaningful, to a non-stationary spacetime (the expanding universe), where it isn't. The same underlying theory (GR) can be used to describe both, but the specific models used--the specific solutions to the Einstein Field Equation--are different, and have different properties. The solution that applies to the apple falling has "potential energy" as one of its properties; the solution that applies to the expanding universe does not.

Ahhh I know why you weren't getting the understanding now ok.

So this is a big point for the explanation.Two masses that are moving towards each other and the distance between them can increase if the expansion rate between the masses is great enough.

I would like to call this point or radius the gravitational expansion radius for a simple understandable term to be used in posts throughout this thread.Let me know if you have any questions about this, I think you will catch yourself once you put this point together.

 

[TheScienceOrca]

Anyone posting on this thread saying potential energy is not relevant to GR or gravity is not a force is completely ignorant and fails to read full posts.I have made it very clear what I am saying when I say potential energy and I have explained it doesn't matter if gravity is a force or not!

PLEASE read my earlier posts fully it will save you time from posting the same question over and over.

I am not accusing all members as some have acknowledged my corrections in earlier posts.

If you have a question or counter not already stated, please post!

Thank you

 

[TheScienceOrca]

If energy were to be conserved in GR, there would indeed have to be a contribution from "gravitational field energy", which is, I believe the point of your somewhat long example. Unfortunately. if you consult an actual GR textbook such as "General Relativity", Robert M Wald, 1984, (see section $11.2 pg 286)

[quote =Wald ]
...not surprising since $T_{ab}$ represents only the energy content of matter, whereas "gravitational field energy" should make a contribution to total energy and thus should appear in any conservation law. However, as already mentioned in chapter 4, there is no known meaningful notion of the energy density of the gravitational field in general relativity.

So most of your post is wishful thinking based on assuming your conclusion :(. I'd summarize your "argument" as follows. "Energy is conserved in Newtonian theory, so I want it to be conserved in GR too. In Newtonian theory we can break total energy into two components, kinetic energy and potential energy, whose sum is a conserved quantity, so we'll assume that we can do the same in GR. We will ignore the textbooks, papers, and FAQ's that tell us that we can't do this because we don't want to believe them or even take the time to check out contrary references.[/QUOTE]all energy has mass, and all mass acts gravitationally