Re: Question on gravitational energy

On Jun 19, 12:14 am, Phil <toob-head...@xxxxxxxxxxxxx> wrote:
Sue... wrote:
On Jun 18, 3:26 pm, Phil <toob-head...@xxxxxxxxxxxxx> wrote:

Sue... wrote:

[snip]

Sue, MTW flatly states that the mass of the Earth is less than it would
be if the particles were all far apart.

The mass of my MTW keeps my door from blowing shut in
the stiffest of winds. That much it can claim empirically.

Good point. Actually, I think I quoted the entire contents in MTW that
even vaguely dealt the situation at hand (we're talking a very high pain
to gain ratio).

Rees flatly states that part of
the mass of objects spiraling into a black hole is converted into
kinetic energy and radiates away into space.

I won't ask why Rees doesn't express radiation as angular
momentum.

Good, since I haven't a clue as to the answer.

Simply stating that "you
are confused about mass" is ridiculous. So is the claim that everyone
has "seen this misinterpretation" -- unstated in any detail by you --
hundreds of times, when the entire subject of the quantity of
gravitational energy acquired by objects, not to mention the loss of
mass from kinetic energy turning into photons and radiating away into
space, almost NEVER comes up. Name a post where these are discussed!
There are very, very few.

By mixing graviational effects with photons I'll assume you are
publishing a quantum theory of gravity as an appendix to your
work.

Nothing so fancy; I'm just using the energy in the photons to measure
the kinetic energy.

See if the section about the Compton effect suggests that
approach might not be fancy enough.
http://nobelprize.org/physics/articles/ekspong/index.html

[snip]

You need to understand where relativistic mass does NOT
apply. It is a heuristic bridge that ties the energy density
of space time to gravitaional/inertial mass. It is not carte'
blanche to convert between mass and energy as the
spirit moves us.

Okay, I see your point, and it's a good one. However, let me take a tip
from Ben's post and BRIEFLY rephrase this just to make sure that your
point is not only valid, but also relevant to the question I have in
mind. Let's start with a spherical shell of iron dust with the mass of
the Earth, but with a radius equal to Pluto's orbit. Not a solid sphere,
just an outer shell of dust particles. The dust then collapses from
gravity into an object a little smaller than the Earth, radiating a
great deal of radiation in the process.

That sounds like gravity we can modulate by telekinesis.
The other effects might be whatever the telekinetic master
thinks they should be. :-)

If I understand correctly, (1)
the mass of this iron-Earth is now LESS than the mass of the spherical
shell, by an amount that is exactly equal to the energy radiated away. A
distant observer (although the radiation has moved beyond him) will
measure LESS gravity than he measured prior to collapse. Also, (2) the
iron-Earth contains a quantity of gravitational binding energy which,
again, is exactly equal to the total radiation, although this includes
both the radiation that has radiated away, and the radiation which is
still trapped within the iron-Earth.

If you let thermal agtitation keep the cloud from collapsing
in the first place, then laser cool it to make it collapse
you might find the missing energy. Then again ya might not
because cold helium does strange things.

In Clifford Will's "Was Einstein
Right?", he has a chapter showing that tests have confirmed that the
Earth and the moon "fall the same," even though the Earth has far more
gravitational energy per kg than the moon, which tells me that
physicists regard gravitational energy as being quite real, something
that turned out to fall under the equivalence principle, along with all
other forms of energy.

Prof Will is pretty optimistic about relativly moving neutrally
charged bodies causing *radiation*. I don't share his optimism
nor am I convinced there aren't better better explanation for
Hulse-Taylor.

The other six days of the week we have to set *charged*
bodies in relative motion to produce radiation. So how does
Hulse-Tayor get special privileges on Sunday afternoon?
<rhetorical>

Now, given an iron-Earth where ALL of the energy released by the
collapse has radiated away, my question is whether there is something
INHERENT about the equations of GR that would FORCE the quantity of
energy radiated away, and the quantity of gravitational binding energy,
to always be the same, even if we envision scenarios where the amount of
energy radiated away is, if we INCLUDE the energy lost by the photons as
they rise up out of the gravitational field, 9 times greater than mass
of the particles in the spherical shell. Obviously, if this is the case,
then the iron-Earth would end up with MORE mass after it collapsed, even
after the energy radiates away, with 9 parts gravitational energy, and
1 part "original" mass, meaning it would end up with 10 times the total
mass that it started with. I realize that this appears to violate
conservation laws, but that is the scenario I have been working with. I
just need to know if the radiated energy and the gravitational energy
would ALWAYS be the same, although I realize it might be a question that
no one can answer.

It might be a question that GR can't answer because it strikes
to the heart of an issue rasied by Hilbert:

<< In the concluding section of her paper, she
[Noether] refers to Hilbert's having said that 'the failure of the
energy theorem' is a characteristic feature of the general theory.
The last section is entitled "A HILBERTIAN ASSERTION",
and says in part [16]: "From the foregoing ... [we] obtain
the proof of an assertion of Hilbert concerning the connection
between the failure of proper energy conservation laws and
general relativity, and indeed in a general group- theoretic
setting." It seems to me this remark is a notable understatement.
Her powerful results are deep and general; far more than
simply a verification of Hilbert's assertion. >>
http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

Perhaps there is a modern resoluton the authors you mention
are using. Search the Google archives of sci.physics.research
(moderated) for something about "Hilbert's Assertion".

If you don't find some enlightenment, post a question.
There are several posters to that group, well versed in GR.

Sue...

Phil

Well, you're going over my head, although I must say the discussion on
"improper" energy conservation when gravitational fields are involved is
interesting, even if I can only understand a small part of it. Based on
everything I've come across, I would certainly agree that having local
energy conservation when G-fields are involved is NOT going to happen!
Now if you include the energy contained in the entire universal medium
of space, that's different, but that's not exactly local anymore.

Thanks,
Phil-

I just wondered if you have discovered the wondrous concept that it
is.

I'm not sure why you favored a small and large mass. Its just as
simple two consider two neutron stars of equal mass. If they are just
light enough to have surfaces outside their schwartchild radius they
would each seem to collide with almost twice the kinetic energy than
their original masses. The key here is at least one of the object has
to have intense gravity.

Can it happen? I think so, because of the concept previously
mentioned. Their is only one way this kind of thing can happen. The
stress-energy of each object's gravity field must exceed the rest mass
of the objects themselves.

.

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