Forum in astronomy or astrophysics research

On Thu, 7 Aug 2003, Serenus Zeitblom wrote:
> I think it is pretty well-known by now that DeSitter space can be
> sliced in lots of different ways, eg by flat slices or by
> spherical ones.

Indeed, families of hyperslices with the geometry of S^3, E^3, and H^3
respectively are all present and valuable for various purposes.

> What I don’t understand is this: why does anyone take the flat slicing
> seriously? I mean, it is obviously going to lead to a geodesically
> incomplete spacetime—you can have timelike worldlines coming in from
> "beyond the universe"! That is pretty ridiculous

It would indeed be absurd to say that by changing to a different
coordinate chart on M, you can alter an intrinsic property (geodesic
completeness).  Of course the answer is that you -can’t- do this; you must
be somehow confusing the notion of a coordinate chart on M (which need not
cover all of M) with M itself.

In this case, M is the de Sitter manifold H^(1,3).  Examples of intrinsic
properties include its topology (M is homeomorphic to the topological
manifold RxS^3), the geodesic completeness property, and its conformal
structure, which can be diagrammed
         ______
        |\    /|
        | \  / |
        |  \/  |
        |  /\  |
        | /  \ |
        |/____\|

(This crude ASCII sketch is a stand-in for a similar diagram in which the
diagonals have slope +/-1.)

For details concerning what I just said, see

author = {S. W. Hawking and G. F. R. Ellis},
title = {The Large Scale Structure of Space-Time},
publisher = {Cambridge University Press},
year = 1973}

In this book you will also find details of several charts; as an exercise
you can find transformations from any of those to any in the following
list which are not discussed in HE.

1. Comoving with an irrotational timelike geodesic congruence (integral
curves of a vector field X) everywhere orthogonal to a (contracting then
re-expanding) family of hyperslices with S^3 geometry:

  ds^2 = -dt^2 + a^2 cosh(t/a)^2 [cos(r)^2 dz^2 + dr^2 + sin(r)^2 du^2 ],

  -infty < t < infty, 0 < r < pi/2, -pi < z,u < pi

This chart covers almost all of M.  Note that the coordinate lines z = z0,
r = r0, u = u0 correspond to the world lines of a certain family of
inertial observers, i.e. a certain family of timelike geodesics on M.
Because the geodesics "fill up an open set without intersection"– or
better yet, because they are the integral curves of a vector field X on
M– we call it a "congruence".  Because this congruence of timelike
geodesics is irrotational (i.e. the vector field X has vanishing vorticity
tensor), it defines an orthogonal family of spatial hyperslices t = t0.
(See Hawking & Ellis for congruences and vorticity.)  From the form of the
line element it is obvious that these hyperslices are three-spheres of
"radius" rho = a cosh(t/a), i.e. on -infty < t < 0 they contract to a
minimal size reached at t = t0, and then expand again.

It is very important to understand that this chart actually corresponds to
a whole family of different congruences.  To understand this, consider the
usual embedding as a hyperboloid of one sheet of the two dimensional de
Sitter space H^(1,1).  Here the "latitude circles" correspond to the
slices t = t0, with the "equatorial circle" corresponding to the "minimal
size" circle t = 0.  Note that as t increases, the latitude circles shrink
to radius a and then re-expand.  (This is obviously very closely analogous
to what we saw for our irrotational congruence of inertial observers
orthogonal to S^3 hyperslices above.)  But now imagine applying a boost in
the embedding space E^(1,3) to our H^(1,1), moving the original latitude
circles to a new family of "tilted" circles on H^(1,1).  The same boost
moves all but two of the world lines of our observers to new hyperbolas,
so we have a new irrotational congruence of timelike geodesics with a new
family of orthogonal slices (circles).  Similarly on H^(1,3).

If this seems puzzling, it might help to note that one can define on E^3
not just one "cylindrical coordinate chart"

  ds^2 = dz^2 + dr^2 + r^2 du^2,

  -infty < z < infty, 0 < r < infty, -pi < u < pi

but a whole -family- of similar charts.  To obtain the others: rotate the
omitted half plane u = pi, or less trivially, translate/rotate the axis of
symmetry r = 0 to a new line.

Similarly, by choosing various pairs of antipodal points on S^2 (embedded
in E^3 in the usual way) we obtain different families of "latitude
circles", so we have a whole family of "polar spherical charts" on S^2.
Given any one we can obtain the others by rotating the semicircle
("International Date Line" u = 0) or, less trivially, by choosing a new
pair of antipodal points ("North Pole" and "South Pole").

Note that the freedom to define a whole family of charts such that the
metric tensor takes the same form in terms of the various coordinates is
closely connected to the existence of symmetries (Killing vector fields)
for these familiar Riemannian manifolds.

Pedantic aside: I said above that the domain of the chart above covers
-almost- all of H^(1,3).  Only "almost" because we need to delete certain
"world sheets" corresponding on t = t0 to a pair of linked great circles
(the degenerate Hopf tori at r = 0 and r = pi/2)  as well as "cuts" on
each Hopf torus t = t0, r = r0 along u = 0 and along z = 0.  IOW, the
failure of this chart to cover all of M is due only to the failure of the
Hopf chart to cover all of S^3, which is closely analogous to the failure
of an ordinary polar spherical chart to cover all of S^2 (which omits the
two poles), or of a cylindrical chart to cover all of E^3 (which omits a
half plane with boundary the axis of cylindrical symmetry).  So this
failure to cover all of M is as harmless as the failure of a cylindrical
coordinate chart to cover all of E^3.  Another way to understand this is
to observe that our vector field X is defined on all of H^(1,3), and by
moving around the omitted surfaces on each S^3 hyperslice we obtain
"trivially different" charts which taken together cover M, and are each
associated with one and the same vector field X on M.

2. Comoving with irrotational timelike geodesic congruence (integral curves
of vector field Y) everywhere orthogonal to an expanding family of spatial
hyperslices with E^3 geometry:

  ds^2 = -dt^2 + exp(-2t/a) [ dx^2 + dy^2 + dz^2 ],

  -infty < t,x,y,z < infty

(Not the same t coordinate an in (1)!) The domain of this chart covers the
region

         ______
        |\*****|
        | \****|
        |  \***|
        |   \**|
        |    \*|
        |_____\|

Note well: even though the coordinates range over all of R^4, the chart
only covers half of M!  This doesn’t mean that the other half has
vanished, only that it is not represented in this chart.  In particular,
even though our new irrotational timelike geodesic congruence (integral
curves of vector field Y) is defined only on half of M, our original
vector field X is of course still defined, and as the diagram suggests
half of each integral curve of X appears in our new chart.

To understand the nature of Y, look again at H^(1,1), embedded in E^(1,2)
in the usual way.  This is a ruled surface with rulings comprising two
families of null geodesics in E^(1,2) (straight lines in the embedding
space), which are precisely the null geodesics on H^(1,1).  On "the"
equatorial circle of H^(1,1) choose two antipodal points, and choose a
pair of "parallel" rulings.  These define the boundary of the analogous
chart on H^(1,1).  Note that H^(1,1) can be covered "piecewise" using
different examples of such charts (change the defining circle and
antipodal point pair).

Exercise: does each Y define a unique chart of the above form?  Compare
with X vs. the S^3 slices above.

(See the discussion in Hawking and Ellis for a nice picture of the
analogous slices in H^(1,1).)

Readers familiar with hyperbolic geometry should note that these vanishing
(three-dimensional) intrinsic curvature slices of H^(1,3) are analogous to
"horospheres" in H^3 and "horocycles" in H^2, which also have vanishing
intrinsic curvature.

Exercise: Use the method of geodesic Lagrangians to find the geodesic
equations for our chart.  Use the method of effective potentials to find
the following first integrals (asterisk = d/ds, s the parameter of the
geodesic to be found, e = -1,0,1 for timelike, null and spacelike
geodesics respectively):

  x* = A exp(-2t/a)  y* = B exp(-2t/a)   z* = C exp(-2t/a)

  t*^2 = e – (A^2 + B^2 + C^2) exp(-2t/a)

Explain why this shows at once that the coordinate lines mentioned above
are indeed timelike geodesics.  Can you write down the complete solution
of the geodesic equations?

Exercise: Read off the obvious coframe o^1 , o^2, o^3, o^4 from the line
element (dual respectively to one timelike and three spacelike vector
fields).  Take the exterior derivatives of these one-forms and guess the
connection one-forms

  o^1_2 = exp(t/a) dx/a

  o^1_3 = exp(t/a) dy/a

  o^1_4 = exp(t/a) dz/a

Compute the covariant derivative D_X X and verify again that the
coordinate lines above are geodesics.

Exercise: Use the connection one-forms above to compute the curvature
two-forms and read off the components of the Riemann tensor wrt the given
coframe.  (You should get R^1_(212) = 1/a^2 etc.; this corresponds to
geodesic divergence of our congruence, i.e. uniform negative curvature, as
expected.  Note that again a appears as a "size" parameter analogous to
the "radius" of a sphere.)

Exercise: Verify that Y is irrotational and show that it has constant
expansion, to wit, in our coframe we have 1/a diag(1,1,1).  Compute

  E_(ab) = R_(abcd) Y^b Y^d

and verify that in our coframe this is -1/a^2 diag(1,1,1). Interpret these
results in terms of physical observations by the family of observers
corresponding to Y.  Does the scaling with parameter a make sense?
(Hint:  think "dilation"!)

Exercise: Look up past posts on finding the wave operator on a Lorentzian
manifold, starting with a coframe o^1, o^2, o^3, o^4.  Show that the wave
equation on H^(1,3) in our chart takes the simple form

  h_(tt) + 3/a h_t = exp(-2t/a) [ h_(xx) + h_(yy) + h_(zz) ]

Separate the variables, finding h(t,x,y,z) = P(t) F(x) G(y) H(z) where

   F(x) = a1 exp(-A x) + a2 exp(A x)

   G(y) = b1 exp(-B y) + b2 exp(B y)

   H(z) = c1 sin(q z) + c2 exp(q y), q^2 = (A^2 + B^2) – E^2/a

   P(t) = e1 [ exp((-t+a^(3/2) E exp(-t/a))/a) a E
        - a^(1/2) exp(a^(1/2) E exp(-t/a)) ]
        + e2 [ a^(1/2) exp(-a^(1/2) E exp(-t/a))
        + exp(-(t+a^(3/2) E exp(-t/a))/a) a E ]

Here, A,B,C,D,a1,a2,b1,b2,c1,c2,e1,e2 are constants. Are they redundant?
Can you write down the general solution of the wave equation on H^(1,3)?
Next, look up past posts on computing symmetry groups of PDEs; can you
find the symmetry group of the wave equation in the form above?  Choose
unidimensional subgroups and find the corresponding solutions.  Explain
how these results are related to what you found using separation of
variables.

Exercise: Verify that

   k = exp(-t/a) (e_1 + e_2)

defines a null geodesic congruence with expansion scalar exp(-t/a)/a and
vanishing shear and twist scalars.  Interpret physically.

Exercise: Find a transformation to another chart based on Y,

  ds^2 = a^2/w^2 [-dw^2 + 2 dw dx + dx^2 + dy^2 + dz^2 ],

  0 < w < infty, -infty < x,y,z < infty

Analyze this following the model of the preceding exercises.

Exercise: Find a transformation to a third chart based on Y,

  ds^2 = -dT^2 + (dr + r/a dT)^2 + r^2 (du^2 + sin(u)^2 dv^2),

  -infty < T < infty, 0 < r < infty, 0 < u < pi, -pi < v < pi

Sketch some null geodesics and integral curves of Y. What happens to Y at
the sphere r = a?  Is this a coordinate singularity?  Interpret
physically.  (Hint: this chart is the "zero mass" case of a Painleve chart
for the Schwarzschild-de Sitter spacetime.)

3. Comoving with irrotational timelike geodesic congruence (integral
curves of vector field Z) everywhere orthogonal to a family of spatial
hyperslices with H^3 geometry:

  ds^2 = -dt^2 + a sinh(t/a)^2 [ (dx^2 + dy^2 + dz^2)/z^2 ],

  0 < t, z < infty, -infty < x, y < infty

(Not the same t coordinate as in (1),(2)!) The domain of this chart covers
the region
         ______
        |\****/|
        | \**/ |
        |  \/  |
        |  /\  |
        | /  \ |
        |/____\|

Note that the hyperslices t = t0 are each -complete- hyperbolic spaces
H^3.  IOW, note that in our first slicing, the slices were compact but in
the second two they are noncompact.  The discussion above, especially if
read with reference to the pictures/discussion in Hawking and Ellis,
should make it clear why this is not at all a contradiction.

> We don’t normally do that kind of thing; geodesic incompleteness is
> tolerated only when the curvature diverges or something like that. So
> why should we tolerate it in the case of DeSitter space?

Geodesic completeness is an intrinsic property enjoyed by H^(1,3).  This
property holds irrespective of what coordinate charts we use to represent
this manifold.  If we choose a chart whose domain does not cover the
entire manifold, we will be able to find some geodesics which reach a
"boundary" of that chart (or have coordinates which diverge) after finite
parameter lapse, but this just means we can’t study the entire geodesic in
question using the given chart.  To follow it outside the domain of our
chart we must switch to another chart.

A homely example: consider an ordinary polar coordinate chart

  ds^2 = du^2 + sin(u)^2 dv^2,

  0 < u < pi, -pi < v < pi

Note that the domain omits the North pole (u = 0), the South pole (u =
pi), and the International Date Line (the semicircular arc v = 0, aka v =
pi).  Now, every latitude circle (including the equator u = pi/2, which is
a geodesic) will encounter the Date Line.  This doesn’t mean that S^2 is
geodesically incomplete, only that to follow latitudes across the Date
Line, we need to change to another chart, e.g. by setting v’ = v + pi/2,
which gives a new polar chart in which the Date Line is just the
semicircular arc v’ = pi/2, which lies in the domain of validity of the
new chart.  Similarly, to follow longitudes through the North Pole, we
need to change to a new polar chart defined by a different pair of
antipodal points; e.g. choose such a pair lying on the equator of our
original chart.

Compare this example with a polar chart for H^2, and then with H^(1,1) as
above.  It should be clear that whether our chart omits a "set of volume
zero" or "half the manifold", in each case we can follow geodesics or
other curves outside a given chart simply by changing to another chart
partially overlapping the first, but covering at least some of the region
omitted by it.

> The only special thing there is that, being empty of matter, DeSitter is
> extremely symmetric, so you can hide the incompleteness with a nice
> choice of coordinates.

Both H^(1,3) and S^2 are geodesically complete.  This is an intrinsic
property which is not affected by the failings of particular charts.

> This is just like the Milne Universe, a so-called cosmology which is
> really just a chunk of Minkowski space.

The Milne chart is analogous to chart with H^3 hyperslices above.  The
fact that these charts don’t cover all of E^(1,3) or H^(1,3) respectively
do not contradict the geodesic completeness of these manifolds.

> The fact is, however, that the full DeSitter has spheres as slices; the
> flat slicing is just a mathematical trick of no real importance,

                                                       ^^^^^^^^^^

How about -utility-?

Exercise: use the method of geodesic Lagrangians to find the geodesic
equations in a chart you may be more familiar with:

  ds^2 = -dt^2

  + a^2 cosh(t/a)^2 [dR^2 + sin(R)^2 (dU^2 + sin(U)^2 dV^2) ],

  -infty < t < infty, 0 < R < pi, 0 < U < pi, -pi < V < pi

Compare with the equations found in the exercises above.  Which would you
rather try to solve?

> In short, DeSitter is REALLY a cosmology with finite spherical space.
> Right?

I hope it is now abundantly clear that H^(1,3) has multiple slicings with
any of S^3, E^3 or H^3 geometry.  REALLY! :-/ Each of these slicings gives
different geometrical insight into the nature of the geometry of H^(1,3),
but in various circumstances one may be more convenient or natural than
the others.

Just a note to all s.a.r readers and potential posters — due to our
primary moderator being away this week, and our backup moderator (me)
having some rather buggy moderation software, you should expect some
longer-than-usual delays in processing crossposts between s.a.r and
other moderated newsgroups (notably sci.physics.research).

We hope to have the software problems sorted out within the next few
weeks; in the meantime please be patient if you’ve submitted such
crossposts and they haven’t appeared yet.  Articles posted solely to
s.a.r, or crossposted only to unmoderated newsgroups, shouldn’t have
any problems.

–
— "Jonathan Thornburg (remove -animal to reply)" <jth…@aei.mpg-zebra.de>
   Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
   Golm, Germany, "Old Europe"     http://www.aei.mpg.de/~jthorn/home.html
   Advice for yard maintenance:

[[Mod. note -- over-long lines rewrapped to c.72 columns -- jt]]

Suppose that I know that my telescope is not properly polar aligned and
that I know how much in alt and az it is off. Now I take my telescope
and point it at some well known star in the sky, say Spica, and use some
package like TheSky to synch on Spica. If I send the scope off to some
arbitrary point in the sky, say, Vega or a specified RA/Dec, would like
to know the position error of the object. There’s a very good chance
that the scope won’t be pointing directly at Vega. It’s been a long time
since I’ve used spherical trig. Maybe there’s a software package that
will do this for me, or maybe it’s ridiculously simple.

–
      Wayne T. Watson (121.015 Deg. W, 39.262 Deg. N, 2,701 feet, Nevada
      City, CA) — GMT-8 hr std. time, RJ Rcvr 39° 8′ 0" N,  121° 1′ 0" W

                  Gleaned from Bill Bryson’s A Brief History of Nearly
                  Everything: Yellowstone National Park is the largest
                  active volcano in the world.  Massive erruptions have
                  occured on an average every 600,000 years. They dwarf
                  the one at Mt. St. Helens. It’s been 630,000 years
                  since the last major erruption. Good luck to us all
                  in the West.

      Web Page: <home.earthlink.net/~mtnviews>
      Imaginarium Museum:
           <home.earthlink.net/~mtnviews/imaginarium.html>

The s.a.r primary moderator is away this week, and I (the backup moderator)
will be away tomorrow.  So… any articles submitted between now and
sometime friday morning (European time) 15.Aug.2003, will be queued
and won’t be moderated until then.  My apologies for the disruption —
hopefully we won’t miss the next nearby supernova or some other such
time-sensitive event…

–
— Jonathan Thornburg, sci.astro.research backup moderator

So far we’ve been subjected to gamma ray Burst ( that would probably be
fatal to civilizations living near by one), Magnetstars, Eta Carina ,
an exploding star whom astro-physist think might be acting has a huge
ultraviolet laser, Black holes, Neutron stars, Novas  and Supernovas.

I’m wondering …how close can some stellar phenomena has to be before it
can represent a threat to life on this planet,and what’s a safe distance
that would provide the people on this planet a spectacular light show
but wouldn’t represent a danger to life here.  Are there any particular
candidates that we should look out for?

Second question, I used to look at pictures of galaxies and marvel
that all that white hot gaseous looking stuff you see in a picture of a
galaxy were stars. Now I’m wondering if alot of that white hot "stuff"
you see when looking at a galaxy is just what it is ..white hot gas. Can
the stars in a picture of a galaxy be spotted individually, or are they
truly too numerous too count.

"When I die, I would like to go peacefully in my sleep, like my
grandfather did.  Not screaming and yelling like the passenger in
his car."  Jack Handey

[[Mod. note -- Michael Richmond has written an informative web page
on this for supernovas,
   http://www.tass-survey.org/richmond/answers/snrisks.txt
-- jt]]

I was wondering, I have heard that space is a vaccuum, but is it totally
empty in the voids between the planets? The sun jettison matter during
solar flares, and there is such a thing as a solar wind. Does that
mean that matter like hydrogen or helium gas might be distributed in
interplanetary space? Or does the gavitational forces of the planets soak
all the gas up? It might be interesting to know if gas gas/dust clouds
form withing the solar system or if the stuff is even in distribution.

[[Mod. note -- The interstellar medium is quite nonuniform, but
a rough order-of-magnitude estimate for its density is a few atoms
per cubic centimeter (most hydrogen and helium).  There is also a
significant amount of matter in dust grains, but I don't have
specific numbers handy.  -- jt]]

Just curious,
RustyS

Several elliptical galaxies (eg: M105) have apparently little or no dark
matter content.  Some theorists have conjectured that some dark matter
is associated with stellar mass black holes, though this does not seem
to be the case with our Milky Way spiral galaxy (viz: microlensing and
x-ray surveys).  However, if these ellipticals do have a unusually low
total black hole mass content, that might be a check on the conjectured
bh/dark matter link.

Stellar mass black holes are notoriously difficult to detect at the distances
of the ellipticals in question, so I have a backdoor ‘theoretical’ question:

Has there been any *theoretical* work suggesting that some ellipticals
should have an unusually low stellar mass black hole content…eg: because
conditions exist which have suppressed formation of sufficiently high mass
stars whose end states include the creation of bhs? If so, this would be
circumstantial evidence for a bh/dark matter link of some sort.

I’ve just read in the popular press another astronomical result that seems
to be consistent with the radical hypothesis I mentioned in another thread.
An easy to read description of that hypothesis is available at
http://physics.rssternberg.org/. Please comment and correct any
misperceptions I have of the newly reported findings:

Apparently, Professor Niel Brandt, of Penn State, who is leading the x-ray
side of the GOODS survey, has noted that, when looking in the x-ray band,
one sees a immense number of black holes, estimated at 300 million active
black holes plus other non-feeding black holes, evenly distributed across
space. Of significance here, in the early Universe, black holes are much
much less common.

One hypothesis from Professor Brandt to explain this phenomenon is that
"early generations of massive stars exploded as supernovas and blew away the
black-hole food supply." (Washington Post, June 23, 2003, page A9). Since
the galaxies were smaller, it is suggested that they might not have been
able to hold their gasses from the fierce supernova forces. It is
hypothesized that the black holes, which are invisible in optical light but
appear only in x-ray bands, must therefore be the most distant black holes
ever found or be covered by the thickest coat of dust known.

I wonder if this isn’t more consistent with another model. If the Big Bang
was an actual explosion within a larger Universe and what we perceive as the
Universe is the interior region of an inverted black hole (a white hole),
then matter-energy outside the white hole would be almost completely
excluded from our observation. Thus, it might appear to us that the whole
Universe was the Big Bang. Our perceptions of time and space would be
defined by the expanding Big Bang event, and almost all of the matter and
energy we could perceive would have been produced in the Big Bang.

However, when our explosion began, some elements would be left behind
because of their mass or density as well as other routine physical factors
considered in fluid dynamics. As the explosion progressed, more matter would
be expected to fall out of the reaction as the Big Bang continued and the
more massive matter lost its kinetic energy in exchanges with other
matter-energy and from gravity. Anything that fell out of the reaction would
cease to exist in our perceived time-space, since we are limited to
perception in our four dimensions. Time would seem to stop and the resulting
laggard matter would appear as black holes. Black holes of all sizes would
be present from the beginning of the event, but would become more populace
over time.  

In addition, some matter-energy outside the white hole event — the
equivalent of Hawking radiation — might enter the event horizon of our
expanding Big Bang. As the Big Bang got older, perhaps the event horizon
would become more porous, just as in a relativity adjusted fluid explosion.
In another thread, we explored whether that matter overtaken by that
explosion might appear as GRBs, since we might expect them to be
blue-shifted and they might be everything from quite powerful to quite
small, depending only on the size of the matter-energy overtaken.

I wonder whether these newly discovered black holes might be careening at us
(relatively speaking: we are also careening at them) and are therefore
blue-shifted into the x-ray band. They are more numerous in the present
Universe than in the early Universe, which seems quite consistent with my
hypothesis and only vaguely consistent with the notion that early galaxies
were "shreddy little things" that could not keep their gasses from being
blown away in supernova winds.

One respected astrophysicist commented in a private email that my hypothesis
is not the standard Big Bang model, since I hypothesize a Universe larger
than the Big Bang in which the Big Bang is just a local explosion. I
appreciate that comment and I believe I understand it. Are the x-ray
findings of the GOODS survey consistent or inconsistent with this radical
hypothesis?

Thx!

– Richard

[[Mod. note -- I have taken the liberty of altering the Subject: line
to more accurately reflect the subject material.  -- jt]]

Craig Markwardt <craigm…@cow.physics.wisc.edu> wrote in message <news:mt2.0-25632-1056376051@sshserv.aei.mpg.de>…

> Note the illogic of these two sets of statements.  If the IPN system
> *can* work, then it is impossible for it also to *not* work.

I hoped over the length of my last post that the meaning of that
statement would be clear in that because I believe I can show that the
confirmation of OTs in optical radio etc was a lot lower than the 100
per cent error box location then I was suggesting that the error box
localization was flawed in the sense that they *used* the error boxes
to define the annuli. Please note my explanation in more detail at the
end of this post

- Hide quoted text — Show quoted text -

> Since you apparently admit that the IPN can work, your subsequent
> statistical analysis of GCN circulars from 2000, 2002 and 2003,
> basically addresses the question of multi-wavelength detection
> *efficiency*, as opposed to functionality.  You have then entered a
> realm of complex interplay between many observing constraints and
> sensitivities.

> In particular, you have not addressed:
>  * what fraction of GRB follow-ups were attempted in optical or radio;
>  * what fraction of the IPN confidence region was covered in those observations;
>  * what fraction of GRBs could not be realistically followed-up, either because they
>    were on the day-side of the earth, or because they were only annulus solutions;
>  * if there is any inherent difference between GRBs detected by the
>    IPN detectors and the imagers (for example the burst spectrum), and
>    if those burst spectral properties are correlated with optical
>    transient properties;
>  * what fraction of GRBs had *joint* IPN and non-IPN confidence
>    regions.  You only classified bursts as IPN or non-IPN, but in a
>    majority of cases, the joint region between both kinds of solutions
>    is much smaller (example, GRB 000301C)
>  * what fraction of GRBs – if any – had optical transients inside of a
>    non-IPN region, but outside of the IPN region.  The answer to this
>    question will address whether the IPN ever gets the "wrong" solution.

> Since you are dealing with small numbers of events, you also need to
> address whether your findings of differences between the IPN and
> non-IPN solutions – if any – are statistically significant.

> Without going into this kind of detail, your claims about the
> inefficiency of the IPN are fairly unsubstantial.
>I`ll Try to cover the above points. I didnt count the fractions

attempted for IPN nor HETE compared to those posted. At a guess it
seems that 1/2 to 3/4 for both  but I dont know for sure. Surely
though it is the success rate between attempted and successful that is
important. For instance if lets say only 10 per cent of IPN`s were
followed up and 90 per cent of HETE etc`s. What difference would that
make ?

What fraction of the confidence region I assume you mean what fraction
of the refined final IPN error box and once again I have made no
statistical measure but I would imagine  that on average IPN had a
larger per cent of its error boxes covered than HETE etc simply
because the IPN box  is smaller ussually than the HETE etc boxes. And
if there was any importance to this statistic it would be that IPN was
even less successful.

Regarding what fraction were followed up due to other circumstances
and this I dont have even access to that sort of statistical
information. The only thing I can think is that both HETE and IPN
error boxes are subject to the same extenuating circumstances so the
statistic would  be identical for both.

Thats a difficult question to understand regarding inherent
differences. In my opinion all GRB`s are the same phenomena and it is
only length and flux that vary. And this  we know has some effect on
observing because shorter bursts are harder to `catch` as they
disapear faster (the OT ) proportionate to gamma burst length. And
lower flux bursts have fainter OT`s which then make them
proportionately more difficult to resolve and shorten the time frame
for such observations. But isnt it true that as all IPN boxes are
within HETE boxes that as they are in a sense in the same spot they
should therefore be subject to the same `restrictions ` that you
suggest should define them from each other?

These are hard questions to understand. What do you mean by `joint`
confidence regions? Do you mean that if the initial annuli ring is
lets say 1000 sq degrees, the error box 10 and the overlap between the
two only 2 sq degrees then therefore the joint region is 1/500 of IPN
annuli and 1/5 of the error box?
I dont see the importance of this statistic except maybe that one
could say that as the the joint region  for IPN is only 1/500 then it
has a lot less chance of success? But if thats the case  then it seems
pointless to even bother supplying IPN overlaps localizations if the
chances are equal that the OT could be found everywhere else on all
the annuli rings.

And finnaly what fraction of OT`s were located outside an IPN box but
within the HETE etc error box. And from my recollection no OT has been
located outside a supplied  IPN error box but then again no radio or
optical imaging has been made outside of any IPN localization where
supplied. I think Chandra has on a couple of occassions imaged  areas
outside IPN boxes and  they have found possible sources both inside
and outside the IPN box. But I think only optical follow ups at least
were done  inside the IPN boxes on those Chandra sources.

I have to say that to do all the above numbers properly I would need
a research grant for  about couple of months full time work and free
hi speed access to the web. Also some in depth access and
collaboration with NASA archives and staff itself would be neccesary
that arent available to me now. So I probably wont be able to answer
your above tests . However it is worth mentioning that if further
analysis did reveal that the low success rate of IPN of having OT`s
confirmed was due to other factors that you mention then yes  my claim
would be proven wrong. However the uncomfortable truth would remain
that you would have verified that the IPN method was at best  only 1/4
as successful as HETE etc and it would better for astronomers to use
only HETE etc error boxes and ignore IPN.Either way IPN fails. I would
hope of course that my claim isnt proven wrong

It may be that some weighting in favor or against IPN would occur but
I cant think how one of the above points would dramatically effect my
results. For example what sort of hypothetical finding that you
mention above would make a big difference?

I have to also mention that in my previuos posts I didnt add the IPN
success numbers to the HETE etc as they should also count for HETE
successes.. This pushed up the HETE etc success rate higher and
interestingly the new HETE etc success rate is 78.7per cent  for both
2000 and 2002! Odd.
So you suggest my claims are insubstantial. I think a fairer critisism
would be that on the basis of the statistics I have gathered  my
claims are substantiated but that much further analysis is needed
before they can be wideley accepted. Dont forget that my statistics
that on there own show a very poor IPN performance come from NASA. I
havent made them up.

Incidentally this new paper proving the SN/grb link.How does that
square with the Nature paper a month earlier that suggests that with
maximum linear polarization possible observed for a grb at about 80
per cent all current theories will have to be scrapped? It seems  that
to get that sort of polarization the grb would have to be within our
solar system as distance ( to next star or galaxy)results in a decline
of the percentage of linear polarization . It would be impossible then
for any conceivable extra solar source to retain this polarization as
it would decay over distance? I say this as it seems that solar flares
 are the only known source of pure linear polarization. And if most
stars also have `flares` but only our suns can be observed then it
follows that distance reduces the total linear polarity of stellar
sources and irregardless of the mechanism for such polarization it
would never make it past interstellar distances. In a sense it proves
that GRB`s have to be local to our solar system
Do you know any more about this.

> Analyzing any real life data is complex.  If you are seeking to apply
> your "own methods," as you claimed in a previous posting, then you are
> surely aware of this.  You did not mention the data cited in either of
> the Laros et al papers; why were they not suitable?

I tried out the paper above and they both seem to be about sn/grb
relationships and statistics regarding coincidences between the two.
Its not exactly what I need . What I would need to do is create a 3-d
model with x,y and z axis .  With  the galactic plane being on lets
say x, y with z being at right angles to the plane. I then need The
speeds and direction of orbit expressed as vectors in x, y and x,z and
y,z axis. I should end up with a 3-d model that can show me at any
time the relative speeds and directions of each satelitte in the x,y z
framework to our galaxy and with each other. That way I can see for
instance that at one point in time two satelittes are travelling in
opposite directions on the x axis at a speed difference of 100,000km/h
and in the y axis maybe they are moving at the same speed and in z
maybe there is a smaller speed difference. Having this I can make a
calculation of direction using the fact that the x,y,z axis also
refers to the  galactic plane and thus RA dec etc can be derived.
Although I still struggle with some aspects of RA and dec.and how
these relate to the galactic plane.

> Your term "anti-relativistic" is unclear.  The IPN system does not
> rely heavily on the principles of either special or general
> relativity, except that the speed of light is constant.  If you are
> claiming that the speed of light is not constant, you will need to
> substantiate that, in the face of many experiments that show that it
> is constant.

Yes I meant that c is not constant. I was hoping that if I could show
in argument that the time of arrivals were not consistent with c then
that would be one way to `substantiate` my argument.
Anti- relativistic I thought was an obvious term but if not, then  its
meaning is : a phenomena observed that violates the `rules` of
relativity or in particular a phenomena which exhibits a variable
speed of light or where c is dependent on the observer.
> No.  X-ray and gamma-ray localizations by imaging satellites like
> INTEGRAL/IBIS/SPI or HETE, and soon Swift, do not rely on the IPN
> triangularization technique.  Also, consider GRB 021125, which has a
> smaller IPN localization than its associated IBIS position.

I think you misunderstand me here. I realize that the "X-ray and
gamma-ray localizations by imaging satellites like INTEGRAL/IBIS/SPI
or HETE, and soon Swift"  do not rely on IPN. What I was saying was
that these localizations you mention above are the error boxes which
IPN then uses to refine the annuli. Also the time of arrival of the
signals in x and gamma at each of these sattelites become the time of
arrivals that IPN uses to triangulate annuli. Is that not the case?
I then wondered how one could see these as being successful
localizations of OT`s from IPN when they were not only just error
boxes and thus covering a general area  but also made prior to the IPN
localization posting which in itself was derived from their (x and
gamma ray) time of arrivals.

Also regarding 021125 yes as with most IPN the refined overlap
position is smaller then the error boxes but there were no OT`s
observed there so we have no proof that that particular refined IPN
localization is correct. And I believe that it isnt. The OT was most
likely located within the larger error box but outside the later and
smaller IPN box.
> Which "stages" are you referring to?  It may be true that an IPN error
> circle is refined when more data comes in from another spacecraft, but
> this is a response to new independent data.  How can you argue with
> that?

AS I mentioned at the beginning of this post I believe that the annuli
were derived not by pure time of arrival but actually by changing the
time of arrival data to suit an annuli that does overlap the error
boxes. I believe that the data must come in to the network with  many
unexplained inconsistencies that IPN finds impossible to compute
without admitting c is not constant and therefore they actually make
or alter existing data until they can come up with an annuli that does
match the known error boxes. They then refine that annuli with the
error box. MY claim is contentious and I believe that the
inconsistency between the 100 per cent error box success and the
around 5- 20 per cent OT success is a symptom of this altering of
arrival time data even though it probably isnt deliberate or
conciously done on IPN`s part.
regards
Sean

Elveto <zo…@zipzap.ch> wrote in message <news:mt2.0-647-1056716301@sshserv.aei.mpg.de>…
> Rob Oldershaw wrote:
> > Some authors have used the term "metagalaxy" in place of the
> > expression "observable universe". [...]

> > I like the term because it leads one away from the anthropocentric
> > "what we see is all there is" viewpoint to the more likely possibility
> > that "what we see is a bubble in an ocean".

> But isn’t this implying some kind of anthropomorphic metaobserver
> capable of seeing the ocean ? fwiw, I percieve the term of "metagalaxy"
> as an allusion to the equation of the order of magnitude of the number
> of galaxies observable in the universe, with that of the number of stars
> in our own galaxy.

No.  That is not implied, far less required.  "Percieve"(sic) away,
but the concept of a metagalaxy is simply the idea that galaxies are
building blocks of a vastly larger system, of which we view only a