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Gravity and levity



 
 
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  #1  
Old October 12th 03, 02:19 PM
Hans Aberg
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Default Gravity and levity

In article , Ulf Torkelsson
wrote:

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological glob might become, as it should set a limit as GR forces grow
strong.


This is rather the length scale at which the curvature of space-time
becomes significant. If we use the critical density of the universe 1.88e-26
kg/m3, then this lenght scale becomes of order
r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly
which is about the size of the observable universe.


There is one interesting consequence of this observation:

Suppose, for a start that the universe is made up by a series of globs,
each limited in size by the GR estimate GM/(c^2 r). Then this formula
would also act on the globs attracting to each other. It means that no
matter what the glob density is, the universe cannot be homogenous.

So this perhaps suggest that in such a case there should be another force
"levity" that counteracts gravity. This might be a an Einstein
cosmological constant or something or some other force. But this force
should be so that in the very large of the universe, the estimate GM/(c^2
r) is properly counteracted.

The interesting thing is that one ends up on a similar picture if one want
to explain the expansion of lit matter, if one wants to settle for an
older universe that is not created merely by a Big Bang.

I find this reasoning interesting, because I felt formerly sceptical over
the idea that GR should be augmented with some cosmological constant or
"levity" force. But perhaps this should be so.

Hans Aberg
  #2  
Old October 13th 03, 09:56 AM
Ulf Torkelsson
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Posts: n/a
Default Gravity and levity

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:
This is rather the length scale at which the curvature of space-time
becomes significant. If we use the critical density of the universe 1.88e-26
kg/m3, then this lenght scale becomes of order
r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly
which is about the size of the observable universe.



There is one interesting consequence of this observation:

Suppose, for a start that the universe is made up by a series of globs,
each limited in size by the GR estimate GM/(c^2 r). Then this formula
would also act on the globs attracting to each other. It means that no
matter what the glob density is, the universe cannot be homogenous.

So this perhaps suggest that in such a case there should be another force
"levity" that counteracts gravity. This might be a an Einstein
cosmological constant or something or some other force. But this force
should be so that in the very large of the universe, the estimate GM/(c^2
r) is properly counteracted.


In the last paragraph here you reason the same way as Einstein did
when he introduced his cosmological constant. Gravity is always
attractive, so in order to get a static universe he was forced to
introduce the cosmological constant to counteract gravity on large
distance scales. If you do not assume that the universe is static
the cosmological constant is no longer necessary, and we can for
instance get an expanding universe in which the expansion is
gradually slowing down due to the effect of gravity. If we keep
the cosmological constant, but allow the universe to change
over time, it turns out that the static solution is unstable, and any
perturbation will either cause it to contract or expand. The
interesting thing here is that the expansion can eventually become
exponential if we do have a cosmological constant.

Ulf Torkelsson

[Mod. note: quoted text trimmed -- mjh]
  #3  
Old October 13th 03, 09:56 AM
Ulf Torkelsson
external usenet poster
 
Posts: n/a
Default Gravity and levity

Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:
This is rather the length scale at which the curvature of space-time
becomes significant. If we use the critical density of the universe 1.88e-26
kg/m3, then this lenght scale becomes of order
r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly
which is about the size of the observable universe.



There is one interesting consequence of this observation:

Suppose, for a start that the universe is made up by a series of globs,
each limited in size by the GR estimate GM/(c^2 r). Then this formula
would also act on the globs attracting to each other. It means that no
matter what the glob density is, the universe cannot be homogenous.

So this perhaps suggest that in such a case there should be another force
"levity" that counteracts gravity. This might be a an Einstein
cosmological constant or something or some other force. But this force
should be so that in the very large of the universe, the estimate GM/(c^2
r) is properly counteracted.


In the last paragraph here you reason the same way as Einstein did
when he introduced his cosmological constant. Gravity is always
attractive, so in order to get a static universe he was forced to
introduce the cosmological constant to counteract gravity on large
distance scales. If you do not assume that the universe is static
the cosmological constant is no longer necessary, and we can for
instance get an expanding universe in which the expansion is
gradually slowing down due to the effect of gravity. If we keep
the cosmological constant, but allow the universe to change
over time, it turns out that the static solution is unstable, and any
perturbation will either cause it to contract or expand. The
interesting thing here is that the expansion can eventually become
exponential if we do have a cosmological constant.

Ulf Torkelsson

[Mod. note: quoted text trimmed -- mjh]
  #6  
Old October 29th 03, 08:19 PM
Hans Aberg
external usenet poster
 
Posts: n/a
Default Gravity and levity

In article ,
(Phillip Helbig---remove CLOTHES to reply)
wrote:

Sadly, as others have already observed, a "cosmological constant" does
=NOT= lead to a "stable" universe, convecting or otherwise; it leads to
an UNSTABLE universe that undergoes either runaway expansion or collapse.
It is analogous to trying to balance a pencil on its point: The Universe
"wants" to fall over into either an implosion or explosion.


That's true. The same argument can be used against the Einstein-de
Sitter universe. Why it wasn't (until the discussion of the "flatness
problem" turned up a couple of decades ago) is an interesting historical
question. Of course, there are other arguments against the static
universe (such as the fact that the universe is expanding), but that
only strengthens the disbelief in this model, not the credibility of
other arguments against it.


An idea that comes to my mind, by considering the generalized GR
Einstein-Hilbert equation that I discussed in earlier postings of this
thread, is that the universe might achieve its stability by a balance
between visible and dark matter: Suppose (as a thought experiment, even
though it may sound strange) that the visible matter has a special levity
force, perhaps due to its QM activities, which then would generate a
pressure on the before mentioned Lagrangian in a direction opposite to
that of classical matter. Then this would put a pressure on visible matter
to move apart, which dark matter would instead contract, until it ignites.
If there is an instability, the universe would adjust by producing more of
dark/visible matter, whatever needed to achieve the stability again.

There are several problems with such a model: Why isn't there a pressure
making double stars falling apart (perhaps the levity force only acts on
longer distances). And why isn't the universe more homogenous with respect
to local age differences of galaxies, i.e., why aren't there say more
quasars local to us. In general, the more homogeneous the universe (or our
"glob") is with respect to such local age differences of galaxies, the
older it should be.

I should also have said that the original reason that I started to think
about "cosmic convection" is if it possible for black hole matter to
tunnel out of the black hole. This might be possible via a generalized GR
Einstein-Hilbert equation as above, because then particles near the black
hole classical event horizon will have a state simultaneously inside and
outside it: The GRQM event horizon will be "fuzzy", not sharp. One can
construct intrinsic particle spin by letting the Clifford bundle acting on
the differential forms algebra. Then the Levi-Civita connection, which
communicates gravity in GR, will act trivially on those differential
forms. This suggests that at least intrinsic particle spin will be
preserved when matter entering a black hole, and therefore also if
tunneling out of it, if that is possible.

If this process generalizes so that other fundamental particle invariants
are preserved when entering the black hole (which should be in the case of
the GRQM Fock space model I mentioned, as it is known, I think, that the
Levi-Civita connection will be trivial on the cotensor bundle part), then
the particles tunneling out of the black hole might be the stable
particles composed of those invariants. This matter might then be not so
energetic, explaining why it can't be observed as visible matter.

And then one gets, at least locally, also dark matter leaving the
galaxies, i.e., from the black hole at the hub. This should be in the form
of a weak particle stream sort of trickling out of it.

Hans Aberg
  #7  
Old October 29th 03, 08:19 PM
Hans Aberg
external usenet poster
 
Posts: n/a
Default Gravity and levity

In article ,
(Phillip Helbig---remove CLOTHES to reply)
wrote:

Sadly, as others have already observed, a "cosmological constant" does
=NOT= lead to a "stable" universe, convecting or otherwise; it leads to
an UNSTABLE universe that undergoes either runaway expansion or collapse.
It is analogous to trying to balance a pencil on its point: The Universe
"wants" to fall over into either an implosion or explosion.


That's true. The same argument can be used against the Einstein-de
Sitter universe. Why it wasn't (until the discussion of the "flatness
problem" turned up a couple of decades ago) is an interesting historical
question. Of course, there are other arguments against the static
universe (such as the fact that the universe is expanding), but that
only strengthens the disbelief in this model, not the credibility of
other arguments against it.


An idea that comes to my mind, by considering the generalized GR
Einstein-Hilbert equation that I discussed in earlier postings of this
thread, is that the universe might achieve its stability by a balance
between visible and dark matter: Suppose (as a thought experiment, even
though it may sound strange) that the visible matter has a special levity
force, perhaps due to its QM activities, which then would generate a
pressure on the before mentioned Lagrangian in a direction opposite to
that of classical matter. Then this would put a pressure on visible matter
to move apart, which dark matter would instead contract, until it ignites.
If there is an instability, the universe would adjust by producing more of
dark/visible matter, whatever needed to achieve the stability again.

There are several problems with such a model: Why isn't there a pressure
making double stars falling apart (perhaps the levity force only acts on
longer distances). And why isn't the universe more homogenous with respect
to local age differences of galaxies, i.e., why aren't there say more
quasars local to us. In general, the more homogeneous the universe (or our
"glob") is with respect to such local age differences of galaxies, the
older it should be.

I should also have said that the original reason that I started to think
about "cosmic convection" is if it possible for black hole matter to
tunnel out of the black hole. This might be possible via a generalized GR
Einstein-Hilbert equation as above, because then particles near the black
hole classical event horizon will have a state simultaneously inside and
outside it: The GRQM event horizon will be "fuzzy", not sharp. One can
construct intrinsic particle spin by letting the Clifford bundle acting on
the differential forms algebra. Then the Levi-Civita connection, which
communicates gravity in GR, will act trivially on those differential
forms. This suggests that at least intrinsic particle spin will be
preserved when matter entering a black hole, and therefore also if
tunneling out of it, if that is possible.

If this process generalizes so that other fundamental particle invariants
are preserved when entering the black hole (which should be in the case of
the GRQM Fock space model I mentioned, as it is known, I think, that the
Levi-Civita connection will be trivial on the cotensor bundle part), then
the particles tunneling out of the black hole might be the stable
particles composed of those invariants. This matter might then be not so
energetic, explaining why it can't be observed as visible matter.

And then one gets, at least locally, also dark matter leaving the
galaxies, i.e., from the black hole at the hub. This should be in the form
of a weak particle stream sort of trickling out of it.

Hans Aberg
 




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