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Natural Science Forum / Physics / Relativity / April 2005



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Article: 13 things that do not make sense

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Robert Karl Stonjek - 21 Mar 2005 06:01 GMT
13 things that do not make sense
19 March 2005
Michael Brooks
2 The horizon problem
OUR universe appears to be unfathomably uniform. Look across space from one edge of the visible universe to the other, and you'll see that the microwave background radiation filling the cosmos is at the same temperature everywhere. That may not seem surprising until you consider that the two edges are nearly 28 billion light years apart and our universe is only 14 billion years old.

Nothing can travel faster than the speed of light, so there is no way heat radiation could have travelled between the two horizons to even out the hot and cold spots created in the big bang and leave the thermal equilibrium we see now.

This "horizon problem" is a big headache for cosmologists, so big that they have come up with some pretty wild solutions. "Inflation", for example.

You can solve the horizon problem by having the universe expand ultra-fast for a time, just after the big bang, blowing up by a factor of 1050 in 10-33 seconds. But is that just wishful thinking? "Inflation would be an explanation if it occurred," says University of Cambridge astronomer Martin Rees. The trouble is that no one knows what could have made that happen.

So, in effect, inflation solves one mystery only to invoke another. A variation in the speed of light could also solve the horizon problem - but this too is impotent in the face of the question "why?" In scientific terms, the uniform temperature of the background radiation remains an anomaly.

3 Ultra-energetic cosmic rays
FOR more than a decade, physicists in Japan have been seeing cosmic rays that should not exist. Cosmic rays are particles - mostly protons but sometimes heavy atomic nuclei - that travel through the universe at close to the speed of light. Some cosmic rays detected on Earth are produced in violent events such as supernovae, but we still don't know the origins of the highest-energy particles, which are the most energetic particles ever seen in nature. But that's not the real mystery.

As cosmic-ray particles travel through space, they lose energy in collisions with the low-energy photons that pervade the universe, such as those of the cosmic microwave background radiation. Einstein's special theory of relativity dictates that any cosmic rays reaching Earth from a source outside our galaxy will have suffered so many energy-shedding collisions that their maximum possible energy is 5 × 1019 electronvolts. This is known as the Greisen-Zatsepin-Kuzmin limit.

Over the past decade, however, the University of Tokyo's Akeno Giant Air Shower Array - 111 particle detectors spread out over 100 square kilometres - has detected several cosmic rays above the GZK limit. In theory, they can only have come from within our galaxy, avoiding an energy-sapping journey across the cosmos. However, astronomers can find no source for these cosmic rays in our galaxy. So what is going on?

One possibility is that there is something wrong with the Akeno results. Another is that Einstein was wrong. His special theory of relativity says that space is the same in all directions, but what if particles found it easier to move in certain directions? Then the cosmic rays could retain more of their energy, allowing them to beat the GZK limit.

Physicists at the Pierre Auger experiment in Mendoza, Argentina, are now working on this problem. Using 1600 detectors spread over 3000 square kilometres, Auger should be able to determine the energies of incoming cosmic rays and shed more light on the Akeno results.

Alan Watson, an astronomer at the University of Leeds, UK, and spokesman for the Pierre Auger project, is already convinced there is something worth following up here. "I have no doubts that events above 1020 electronvolts exist. There are sufficient examples to convince me," he says. The question now is, what are they? How many of these particles are coming in, and what direction are they coming from? Until we get that information, there's no telling how exotic the true explanation could be.

5 Dark matter
TAKE our best understanding of gravity, apply it to the way galaxies spin, and you'll quickly see the problem: the galaxies should be falling apart. Galactic matter orbits around a central point because its mutual gravitational attraction creates centripetal forces. But there is not enough mass in the galaxies to produce the observed spin.

Vera Rubin, an astronomer working at the Carnegie Institution's department of terrestrial magnetism in Washington DC, spotted this anomaly in the late 1970s. The best response from physicists was to suggest there is more stuff out there than we can see. The trouble was, nobody could explain what this "dark matter" was.

And they still can't. Although researchers have made many suggestions about what kind of particles might make up dark matter, there is no consensus. It's an embarrassing hole in our understanding. Astronomical observations suggest that dark matter must make up about 90 per cent of the mass in the universe, yet we are astonishingly ignorant what that 90 per cent is.

Maybe we can't work out what dark matter is because it doesn't actually exist. That's certainly the way Rubin would like it to turn out. "If I could have my pick, I would like to learn that Newton's laws must be modified in order to correctly describe gravitational interactions at large distances," she says. "That's more appealing than a universe filled with a new kind of sub-nuclear particle."

Read all 13 at NewScientist
http://www.newscientist.com/channel/fundamentals/mg18524911.600

Message me if you can't get a copy and I'll send a copy.

Signature

Posted by
Robert Karl Stonjek

Morituri-|-Max - 21 Mar 2005 08:12 GMT
13 things that do not make sense
19 March 2005
Michael Brooks
2 The horizon problem
OUR universe appears to be unfathomably uniform. Look across space from one
edge of the visible universe to the other, and you'll see that the microwave
background radiation filling the cosmos is at the same temperature
everywhere. That may not seem surprising until you consider that the two
edges are nearly 28 billion light years apart and our universe is only 14
billion years old.

-- -- -- --

Duh,. wake up... the universe is expanding in ALL directions, not one.
N:dlzc D:aol T:com (dlzc) - 21 Mar 2005 17:17 GMT
Dear Robert Karl Stonjek:

> 13 things that do not make sense
> 19 March 2005
> Michael Brooks

> 2 The horizon problem
> OUR universe appears to be unfathomably uniform.

The Universe is closed.  What appears "28 billion light years
total distance" could easily be only 1 billion light years apart,
or even be "wrapped around", and be the same structures on both
sides of us.

The Universe was some tens of million light years across at the
time of the CMBR.  No one currently believes the Universe started
from a point.

> 3 Ultra-energetic cosmic rays
> FOR more than a decade, physicists in Japan...
...
> As cosmic-ray particles travel through space,
> they lose energy in collisions with the low-energy
> photons that pervade the universe, such as those
> of the cosmic microwave background radiation.

Why?  Are all cosmic rays charged?  Light only interacts with
charged particles, and then only in certain "energy bands".

> Einstein's special theory of relativity dictates that
> any cosmic rays reaching Earth from a source
> outside our galaxy will have suffered so many
> energy-shedding collisions that their maximum
> possible energy is 5 × 10^19 electronvolts.

The theory of special relativity says no such thing.
Probability, and "laws of physics" accepted as postulates might.

Note that in your haste to post this, you did not pay any
attention to the fact that your stated energies detected are much
less than the upper threshold you provided.  Big Mystery!

...
> Read all 13 at NewScientist
> URL:http://www.newscientist.com/channel/fundamentals/mg18524911.600

Based on these samples, if I had a subscription, I'd cancel it.

David A. Smith
Morituri-|-Max - 21 Mar 2005 19:19 GMT
> Dear Robert Karl Stonjek:
>
[quoted text clipped - 11 lines]
> The Universe was some tens of million light years across at the time of
> the CMBR.  No one currently believes the Universe started from a point.

No one?  Hmmmmmm... that certainly doesn't seem to jibe considering all the
people in the scientific community who said otherwise..
N:dlzc D:aol T:com (dlzc) - 21 Mar 2005 19:46 GMT
Dear Morituri-|-Max:

>> Dear Robert Karl Stonjek:
>>
[quoted text clipped - 17 lines]
> considering all the people in the scientific community who said
> otherwise..

Note the fully formed and *aged* galaxies that are found close to
the age of the CMBR.  Certainly NOT a singularity as an origin...
something along the lines of a finite size.

David A. Smith
Bjoern Feuerbacher - 22 Mar 2005 10:57 GMT
> Dear Morituri-|-Max:
>
[quoted text clipped - 23 lines]
> the age of the CMBR.  Certainly NOT a singularity as an origin...
> something along the lines of a finite size.

Err, "singularity" does not mean the same as "point". Even in an
infinite universe, there was a singularity at time zero. (using
the improbable assumption that GR is valid back to time zero,
and no quantum effects destroy this conclusion...)

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 22 Mar 2005 18:24 GMT
Dear Bjoern Feuerbacher:

...
>>>No one?  Hmmmmmm... that certainly doesn't seem to jibe
>>>considering all the people in the scientific community who
[quoted text clipped - 9 lines]
> the improbable assumption that GR is valid back to time zero,
> and no quantum effects destroy this conclusion...)

I suggest that those people that point to a singularity also have
to resort to an infinite c (for a short time) to allow the
singularity to "evaporate".  I'll stick with a finite size,
finite c, and distributed mass.  "Before" that is not part of
*this* Universe, IMHO.

David A. Smith
Bjoern Feuerbacher - 24 Mar 2005 16:41 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 17 lines]
> to resort to an infinite c (for a short time) to allow the
> singularity to "evaporate".

Err, how does that follow?

> I'll stick with a finite size, finite c, and distributed mass.

Due to philosophical reasons? The observations so far support
an infinite universe equally well as a finite universe.

> "Before" that is not part of *this* Universe, IMHO.

Well, I did not talk about "before". Only about t=0.

Bye,
Bjoern
tadchem - 24 Mar 2005 17:02 GMT
<snip>

> Due to philosophical reasons? The observations so far support
> an infinite universe equally well as a finite universe.

Sometimes what one does NOT observe is even more important than what
one *does* observe.

Google "Olber's Paradox"...

Tom Davidson
Richmond, VA
Bjoern Feuerbacher - 24 Mar 2005 17:24 GMT
> <snip>
>
[quoted text clipped - 5 lines]
>
> Google "Olber's Paradox"...

The BBT has no problem explaining Olber's paradox, even if the
universe is infinitely large.

And even for a universe which existed forever, this is not a problem.
Try this:
<http://wwwphy.princeton.edu/~steinh/npr/>

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 25 Mar 2005 04:58 GMT
Dear Bjoern Feuerbacher:

>> <snip>
>>
[quoted text clipped - 13 lines]
> is not a problem.  Try this:
> <http://wwwphy.princeton.edu/~steinh/npr/>

What we have seen in this Universe is always something bigger,
and something brighter.  In an infinite Universe, with infinite
time, why can we not see beyond the CMBR?  It wasn't that
bright... only pervasive.

David A. Smith
Bjoern Feuerbacher - 26 Mar 2005 11:32 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 20 lines]
> time, why can we not see beyond the CMBR?  It wasn't that
> bright... only pervasive.

It was optically thick, i.e. opaque. Photons could not travel
freely through it.

Ever heard the term "surface of last scattering"?

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 26 Mar 2005 17:23 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>>
[quoted text clipped - 26 lines]
>
> Ever heard the term "surface of last scattering"?

It was thick but not opaque, to provide the spectrum that it has
achieved.  In fact, it had to be pretty non-dense, and "just so
thick" in order to achieve a pure black body spectrum (which I
still don't understand).  Remember, we can't see granularity with
the methods used, but we can see structure, so variations in
density (if not energy) are present.

David A. Smith
Bjoern Feuerbacher - 29 Mar 2005 10:17 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 31 lines]
> It was thick but not opaque, to provide the spectrum that it has
> achieved.

Err, why do you think so?

> In fact, it had to be pretty non-dense, and "just so
> thick" in order to achieve a pure black body spectrum

Err, why do you think so?

> (which I still don't understand).  Remember, we can't see granularity with
> the methods used, but we can see structure, so variations in
> density (if not energy) are present.

Indeed. Your point?

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 25 Mar 2005 04:48 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>>
[quoted text clipped - 21 lines]
>
> Err, how does that follow?

This is what I have seen discussed.  The term singularity (and
not Black Hole) places limits on what can leave and how.  We have
*structures* exceedingly close to the CMBR...

>> I'll stick with a finite size, finite c, and distributed mass.
>
> Due to philosophical reasons? The observations so far
> support an infinite universe equally well as a finite universe.

The anwser Olber's paradox takes care of "infinite universe" to
my satisfaction, but perhaps not yours.  As to my conclusion, I
take the position of Heinlein's Fair Witness ("Stranger In a
Strange Land").  "I" can see as far as the CMBR, but no further.
"My" science makes reasonable sense to that point (if you swallow
objections about DM and DE).  I stop guessing at that point.

>> "Before" that is not part of *this* Universe, IMHO.
>
> Well, I did not talk about "before". Only about t=0.

And I stop at t=270,000 years, and toy with solutions to GR that
have this Universe as a black hole in the Universe that contains
us, with our "t" equal to its "r" at what the container Universe
describes as an event horizon.  And that "t" is not constrained
to be "0", there.

David A. Smith
Bjoern Feuerbacher - 26 Mar 2005 11:34 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 26 lines]
> This is what I have seen discussed.  The term singularity (and
> not Black Hole) places limits on what can leave and how.

Please tell me where you have seen discussed that.

>  We have  *structures* exceedingly close to the CMBR...

For example?

>>>I'll stick with a finite size, finite c, and distributed mass.
>>
[quoted text clipped - 5 lines]
> take the position of Heinlein's Fair Witness ("Stranger In a
> Strange Land").  "I" can see as far as the CMBR, but no further.

By looking at elemental abundances, we can "see" much further back.

> "My" science makes reasonable sense to that point (if you swallow
> objections about DM and DE).  I stop guessing at that point.

So in your opinion, we shouldn't try to find out what happened
before the CMBR was generated?

[snip]

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 26 Mar 2005 17:49 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>>
[quoted text clipped - 28 lines]
>
> Please tell me where you have seen discussed that.

I don't recall, however...
URL:http://origins.colorado.edu/~ajsh/hawk.html#hawking
If all the mass of a black hole is in a "finite-sized"
singularity << than the event horizon, how can it evaporate with
Hawking radiation?  It can't get TO the horizon, since it is in
the anti-gravity (anti-time) direction.

>>  We have  *structures* exceedingly close to the CMBR...
>
> For example?

z = 5.8 I think I have seen as "recent".  I can't seem to find a
"z" value for the CMBR...

>>>>I'll stick with a finite size, finite c, and distributed
>>>>mass.
[quoted text clipped - 11 lines]
> By looking at elemental abundances, we can "see"
> much further back.

Looking at our own Milky Way galaxy (and its "products"), we have
globular clusters that show essentially pure hydrogen lines
still, yet are as aged as our own Sun.  I don't think we know
enough to "see much further back".

>> "My" science makes reasonable sense to that point (if
>> you swallow objections about DM and DE).  I stop
>> guessing at that point.
>
> So in your opinion, we shouldn't try to find out what
> happened before the CMBR was generated?

"Finding out" is exactly what I'd like to do.  Currently we are
"guessing", which is what you have to do without achievable space
travel.  This is pretty far removed from "finding out".

David A. Smith
Bjoern Feuerbacher - 29 Mar 2005 10:23 GMT
> Dear Bjoern Feuerbacher:

[snip]

>>>>>I suggest that those people that point to a
>>>>>singularity also have to resort to an infinite c
[quoted text clipped - 10 lines]
>
> I don't recall,

I suspect you simply misremember or misunderstood.

> however...
> URL:http://origins.colorado.edu/~ajsh/hawk.html#hawking
> If all the mass of a black hole is in a "finite-sized"
> singularity << than the event horizon, how can it evaporate with
> Hawking radiation?  It can't get TO the horizon, since it is in
> the anti-gravity (anti-time) direction.

You have no clue how Hawking radiation actually works, right? Hint:
it does not require anything from the BH singularity getting to the
horizon.

Try this:
<http://en.wikipedia.org/wiki/Hawking_radiation>

>>> We have  *structures* exceedingly close to the CMBR...
>>
>>For example?
>
> z = 5.8 I think I have seen as "recent".

That is not "exceedingly close" to the CMBR". That's actually a
good time after the CMBR was emitted (I think about 2 billion years, I
don't have the exact numbers right now).

>  I can't seem to find a "z" value for the CMBR.

z = 1089, according to WMAP.

>>>>>I'll stick with a finite size, finite c, and distributed
>>>>>mass.
[quoted text clipped - 15 lines]
> globular clusters that show essentially pure hydrogen lines
> still, yet are as aged as our own Sun.

Reference, please.

AFAIK, globular clusters are in general much older than our own Sun!

> I don't think we know enough to "see much further back".

Then why does the BBT predict so nicely that there should be about
75% hydrogen and 25% helium in the universe?

>>>"My" science makes reasonable sense to that point (if
>>>you swallow objections about DM and DE).  I stop
[quoted text clipped - 5 lines]
> "Finding out" is exactly what I'd like to do.  Currently we are
> "guessing",

Making predictions and testing them is not guessing.

I see that you also conveniently ignore that inflation predicts
certain structures in the CMBR, which have been observed.

[snip]

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 29 Mar 2005 15:02 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 16 lines]
>
> I suspect you simply misremember or misunderstood.

I suspect you don't realize (yet) that Hawking radiation is the
mass of the BH leaving the hole.  And not half of all nearby
*new* particles leaving the hole.

>> however...
>> URL:http://origins.colorado.edu/~ajsh/hawk.html#hawking
[quoted text clipped - 10 lines]
> Try this:
> <http://en.wikipedia.org/wiki/Hawking_radiation>

<QUOTE>
One can gain physical insight on the process by imagining that
(particle-antiparticle) radiation is emitted from just beyond the
event horizon
<END QUOTE>

The mass of the black hole evaporates, as described.  If you can
be sure the mass has formed a singularity, the characteristic
radiation would be hotter.  As it is the characterisitc radiation
is constrained to be some function of the event horizon geometry.

We cannot say that mass/energy inside the hole forms a
singularity.  At the horizon, we would agree the mass/energy is
relatively diffuse.  If our Universe is the inside of a BH, then
the mass/energy inside the black hole creates its own space, and
expands until cool.  Until no particle has any other particle in
its future.

>>>> We have  *structures* exceedingly close to the CMBR...
>>>
[quoted text clipped - 6 lines]
> (I think about 2 billion years, I don't have the exact
> numbers right now).

Close enough.  And as our observational tools get sharper, do you
think we might find some closer?  With some older stars?  Perhaps
they will reach some asymptote.  The question remains as to
whether the "origin" of structure lay earlier than the formation
of the CMBR.  I think it does.  You appear to be satisfied that
it doesn't.  I don't have a good argument either way.

>>  I can't seem to find a "z" value for the CMBR.
>
> z = 1089, according to WMAP.

I keep forgetting that isn't a really good indicator of distance.
Thanks!

>>>>>>I'll stick with a finite size, finite c, and distributed
>>>>>>mass.
[quoted text clipped - 21 lines]
> AFAIK, globular clusters are in general much older
> than our own Sun!

Older in some cases, yes.  With the heavier elements like our
Sun, not always.

All I am saying is that "elemental abundances" isn't the clear
indicator you think it is, IMHO.  Our perspective is skewed,
because we are still strapped to the surface of this rock.
URL:http://verdi.as.utexas.edu/globulars.html
URL:http://www.aas.org/publications/baas/v36n5/aas205/1197.htm
URL:http://www.kernchemie.uni-mainz.de/~pfeiffer/ages.html
... but we do have eyes to see.

>> I don't think we know enough to "see much
>> further back".
>
> Then why does the BBT predict so nicely that
> there should be about 75% hydrogen and 25%
> helium in the universe?

What that a *derivation*, or simply
not-in-disagreement-with-observation?  I haven't seen fundamental
"engineering like" formulae come out of BBT.  Do you have a
reference?

This one looks pretty juicy...
URL:http://www.library.uu.nl/digiarchief/dip/diss/2002-1004-084000/c1.pdf

>>>>"My" science makes reasonable sense to that point (if
>>>>you swallow objections about DM and DE).  I stop
[quoted text clipped - 11 lines]
> predicts certain structures in the CMBR, which have
> been observed.

Reference for "inflation predicts"?  Yes, I know the CMBR is
"lumpy".  That was my point, that there was structure, even at
the "poor" resolution we have available.  Even though the CMBR is
at the "center of the lens", we don't/can't resolve it well.

{adding back in the other branch of this thread... didn't mean to
start two]
"Bjoern Feuerbacher" <feuerbac@thphys.uni-heidelberg.de> wrote in
message news:d2b6f0$gsm$2@news.urz.uni-heidelberg.de...
>> Dear Bjoern Feuerbacher:
...
>>>>>The BBT has no problem explaining Olber's paradox,
>>>>>even if the universe is infinitely large.
[quoted text clipped - 19 lines]
>
> Err, why do you think so?

That is a nasty little mannerism... "Err".  Just say "no".  ;>)

A half-remembered discussion George Dishman had on this topic.
I'll try and search back about two years ago, he was responding
to someone (not me).  I'll see if I can locate the reference.

>> In fact, it had to be pretty non-dense, and "just so thick" in
>> order to achieve a pure black body spectrum
>
> Err, why do you think so?

I'll look it up.  Maybe tonight I can find it.

>> (which I still don't understand).  Remember, we
>> can't see granularity with the methods used,
>> but we can see structure, so variations in density (if not
>> energy) are present.
>
> Indeed. Your point?

The "Home Alone Two" model of creation of a Universe.  In one
scene, one of the bad guys opens a door, which through clever
rigging unzips a toolbag (the CMBR or its mental equivalent) and
all the tools spill out (expansion, Big Rip).

If a BH is large enough, structures are not damaged in crossing
the horizon...

David A. Smith
N:dlzc D:aol T:com (dlzc) - 30 Mar 2005 03:44 GMT
Adding a bit near the end, relating to the reference to "George
Dishman"

Dear Bjoern Feuerbacher:

"Bjoern Feuerbacher" <feuerbac@thphys.uni-heidelberg.de> wrote
in
message news:d2b6qc$h0o$1@news.urz.uni-heidelberg.de...
> N:dlzc D:aol T:com (dlzc) wrote:
>> Dear Bjoern Feuerbacher:
[quoted text clipped - 22 lines]
>
> I suspect you simply misremember or misunderstood.

I suspect you don't realize (yet) that Hawking radiation is the
mass of the BH leaving the hole.  And not half of all nearby
*new* particles leaving the hole.

>> however...
>> URL:http://origins.colorado.edu/~ajsh/hawk.html#hawking
[quoted text clipped - 10 lines]
> Try this:
> <http://en.wikipedia.org/wiki/Hawking_radiation>

<QUOTE>
One can gain physical insight on the process by imagining that
(particle-antiparticle) radiation is emitted from just beyond
the
event horizon
<END QUOTE>

The mass of the black hole evaporates, as described.  If you can
be sure the mass has formed a singularity, the characteristic
radiation would be hotter.  As it is the characterisitc
radiation
is constrained to be some function of the event horizon
geometry.

We cannot say that mass/energy inside the hole forms a
singularity.  At the horizon, we would agree the mass/energy is
relatively diffuse.  If our Universe is the inside of a BH, then
the mass/energy inside the black hole creates its own space, and
expands until cool.  Until no particle has any other particle in
its future.

>>>> We have  *structures* exceedingly close to the CMBR...
>>>
[quoted text clipped - 6 lines]
> (I think about 2 billion years, I don't have the exact
> numbers right now).

Close enough.  And as our observational tools get sharper, do
you
think we might find some closer?  With some older stars?
Perhaps
they will reach some asymptote.  The question remains as to
whether the "origin" of structure lay earlier than the formation
of the CMBR.  I think it does.  You appear to be satisfied that
it doesn't.  I don't have a good argument either way.

>>  I can't seem to find a "z" value for the CMBR.
>
> z = 1089, according to WMAP.

I keep forgetting that isn't a really good indicator of
distance.
Thanks!

>>>>>>I'll stick with a finite size, finite c, and distributed
>>>>>>mass.
[quoted text clipped - 21 lines]
> AFAIK, globular clusters are in general much older
> than our own Sun!

Older in some cases, yes.  With the heavier elements like our
Sun, not always.

All I am saying is that "elemental abundances" isn't the clear
indicator you think it is, IMHO.  Our perspective is skewed,
because we are still strapped to the surface of this rock.
URL:http://verdi.as.utexas.edu/globulars.html
URL:http://www.aas.org/publications/baas/v36n5/aas205/1197.htm
URL:http://www.kernchemie.uni-mainz.de/~pfeiffer/ages.html
... but we do have eyes to see.

>> I don't think we know enough to "see much
>> further back".
>
> Then why does the BBT predict so nicely that
> there should be about 75% hydrogen and 25%
> helium in the universe?

What that a *derivation*, or simply
not-in-disagreement-with-observation?  I haven't seen
fundamental
"engineering like" formulae come out of BBT.  Do you have a
reference?

This one looks pretty juicy...
URL:http://www.library.uu.nl/digiarchief/dip/diss/2002-1004-084000/c1.pdf>>>>"My" science makes reasonable sense to that point (if>>>>you swallow objections about DM and DE).  I stop>>>>guessing at that point.>>>>>>So in your opinion, we shouldn't try to find out what>>>happened before the CMBR was generated?>>>> "Finding out" is exactly what I'd like to do.  Currently>> we are "guessing",>> Making predictions and testing them is not guessing.>> I see that you also conveniently ignore that inflation> predicts certain structures in the CMBR, which have> been observed. Reference for "inflation predicts"?  Yes, I know the CMBR is "lumpy".  That was my point, that there was structure, even at the "poor" resolution we have available.  Even though the CMBRis at the "center of the lens", we don't/can't resolve it well. {adding back in the other branch of this thread... didn't meanto start two] "Bjoern Feuerbacher" <feuerbac@thphys.uni-heidelberg.de> wrotein message news:d2b6f0$gsm$2@news.urz.uni-heidelberg.de...> N:dlzc D:aol T:com (dlzc) wrote:>> Dear Bjoern Feuerbacher: ...>>>>>The BBT has no problem explaining Olber's paradox,>>>>>even if the universe is infinitely large.>>>>>>>>>>And even for a universe which existed forever, this>>>>>is not a problem.  Try this:>>>>><http://wwwphy.princeton.edu/~steinh/npr/>>>>>>>>>>>>>What we have seen in this Universe is always>>>>something bigger, and something brighter.  In>>>>an infinite Universe, with infinite time, why can>>>>we not see beyond the CMBR?  It wasn't that>>>>bright... only pervasive.>>>>>>It was optically thick, i.e. opaque. Photons>>>could not travel freely through it.>>>>>>Ever heard the term "surface of last>>>scattering"?>>>> It was thick but not opaque, to provide the>> spectrum that it has achieved.>> Err, why do you think so? That is a nasty little mannerism... "Err".  Just say "no".  ;>) A half-remembered discussion George Dishman had on this topic. I'll try and search back about two years ago, he was responding to someone (not me).  I'll see if I can locate the reference.[[[ADDED IN]]]Just so you don't have to respond to two threads:George Dishman; 2003jan05; "Olber's Paradox"; responding to PaulStowe...<QUOTE>The CMB spectrum follows the blackbody curve to withinabout 1 part in 10^5 which means the source must be athin shell.<END QUOTE>(PS: It was a fluke that it was exactly two years ago, by theway!  ;>)  )[[[END ADDED IN]]]>> In fact, it had to be pretty non-dense, and "just so thick" inorder to achieve a pure black body spectrum>> Err, why do you think so? I'll look it up.  Maybe tonight I can find it.>> (which I still don't understand).  Remember, we>> can't see granularity with the methods used,>> but we can see structure, so variations in density (if notenergy) are present.>> Indeed. Your point? The "Home Alone Two" model of creation of a Universe.  In one scene, one of the bad guys opens a door, which through clever rigging unzips a toolbag (the CMBR or its mental equivalent) and all the tools spill out (expansion, Big Rip). If a BH is large enough, structures are not damaged in crossing the horizon... David A. Smith
Bjoern Feuerbacher - 30 Mar 2005 10:37 GMT
> Adding a bit near the end, relating to the reference to "George
> Dishman"

[snip a lot]

>>> It was thick but not opaque, to provide the
>>> spectrum that it has achieved.
[quoted text clipped - 8 lines]
> means the source must be a thin shell.<END QUOTE>
> (PS: It was a fluke that it was exactly two years ago, by theway!  ;>)  )[[[END ADDED IN]]]

That the source of the CMBR we can see right at the moment here on
earth was a "thin shell" does not in the least disprove that the
universe was optically thick before the CMBR was emitted.

[snip]

Bye,
Bjoern
Bjoern Feuerbacher - 30 Mar 2005 10:30 GMT
> Dear Bjoern Feuerbacher:

[snip]

>>>>>This is what I have seen discussed.  The term
>>>>>singularity (and not Black Hole) places limits
[quoted text clipped - 8 lines]
> I suspect you don't realize (yet) that Hawking radiation is the
> mass of the BH leaving the hole.

I realize that. But I also realize that that does not require
that anything from the BH singularity gets to the horizon.

> And not half of all nearby *new* particles leaving the hole.

That's clear.

>>>however...
>>>URL:http://origins.colorado.edu/~ajsh/hawk.html#hawking
[quoted text clipped - 18 lines]
>
> The mass of the black hole evaporates, as described.

Yes. And the quote you just gave shows that that does not require
anything from the BH singularity getting to the horizon.

> If you can
> be sure the mass has formed a singularity, the characteristic
> radiation would be hotter.

Huh? How does that follow?

> As it is the characterisitc radiation
>  is constrained to be some function of the event horizon geometry.
>
> We cannot say that mass/energy inside the hole forms a
> singularity.

Why not?

> At the horizon, we would agree the mass/energy is
> relatively diffuse.

Huh?

> If our Universe is the inside of a BH,  then
> the mass/energy inside the black hole creates its own space,  and
> expands until cool.  Until no particle has any other particle in
> its future.

But our universe isn't the inside of a BH. Read up on the difference
between a Schwarzschild and a Robertson-Walker metric.

>>>>>We have  *structures* exceedingly close to the CMBR...
>>>>
[quoted text clipped - 8 lines]
>
> Close enough.

For what? Galaxies existing 2 billion years after the BB is
not such a big surprise, you know.

> And as our observational tools get sharper, do you
> think we might find some closer?

This has not so much to do with "sharper". What is needed is
more efficient light collecting, because these sources are
very dim, and especially observations in the infrared, due
to the high redshift of these objects.

And yes, I think we will find something closer: galaxies in
their very process of forming, and the very first stars.
According to the WMAP results, these should have formed about
200 million years after the BB.

> With some older stars?

I don't think so.

> Perhaps they will reach some asymptote.

Huh?

> The question remains as to
> whether the "origin" of structure lay earlier than the formation
> of the CMBR.  I think it does.

All cosmologists think it does. The quantum fluctuations which grew
to the structure observable in the CMBR, and on to the large-scale
structure we observe today, happened a *long* time before the CMBR
was emitted.

Inflation makes predictions about the properties of these structures
(fluctuations); predictions which have already been partly confirmed.

> You appear to be satisfied that it doesn't.

No. Where did you get that idea from?

[snip]

>>>Looking at our own Milky Way galaxy (and its
>>>"products"), we have globular clusters that show
[quoted text clipped - 8 lines]
> Older in some cases, yes.  With the heavier elements like our
> Sun, not always.

Since globular clusters consist mainly of population II stars,
it is expected that they contain mainly hydrogen and only very
few heavy elements.

> All I am saying is that "elemental abundances" isn't the clear
> indicator you think it is, IMHO.

I never said it is "clear". Lots of work is required to figure
that out.

> Our perspective is skewed,
> because we are still strapped to the surface of this rock.
> URL:http://verdi.as.utexas.edu/globulars.html

That link does not say that we see "essentially pure hydrogen
lines". In fact, it says actually the opposite.

> URL:http://www.aas.org/publications/baas/v36n5/aas205/1197.htm

That link does not say that we see "essentially pure hydrogen
lines". In fact, it says actually the opposite.

> URL:http://www.kernchemie.uni-mainz.de/~pfeiffer/ages.html

That link does not say that we see "essentially pure hydrogen
lines". It only points out that there are very few *heavy*
elements there.

So, where are the references for your claim?

> ... but we do have eyes to see.
>
[quoted text clipped - 7 lines]
> What that a *derivation*, or simply
> not-in-disagreement-with-observation?

Sorry, I don't understand the question.

> I haven't seen fundamental
> "engineering like" formulae come out of BBT.

I didn't claim that these is such a formula.

> Do you have a reference?

Kolb&Turner, The Early Universe.

> This one looks pretty juicy...
> URL:http://www.library.uu.nl/digiarchief/dip/diss/2002-1004-084000/c1.pdf

This doesn't seem to say much about elemental abundances. And it
doesn't give a single formula, just a lot of rhetoric.

>>>>>"My" science makes reasonable sense to that point (if
>>>>>you swallow objections about DM and DE).  I stop
[quoted text clipped - 13 lines]
>
> Reference for "inflation predicts"?

See e.g.
<http://www.sciam.com/article.cfm?chanID=sa006&articleID=00042F0D-1A0E-1085-94F48
3414B7F0000&pageNumber=7&catID=2
>,
especially page 7, or sections 5.2 and 6.4 here:
<http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/parameters/wmap_par
ameters.pdf
>

> Yes, I know the CMBR is
> "lumpy".  That was my point, that there was structure, even at
> the "poor" resolution we have available.  Even though the CMBR is
> at the "center of the lens", we don't/can't resolve it well.

I don't understand what you mean with "at the center of the lens" here.

[snip]

>>>>>What we have seen in this Universe is always
>>>>>something bigger, and something brighter.  In
[quoted text clipped - 14 lines]
>
> That is a nasty little mannerism... "Err".  Just say "no".  ;>)

Sorry. ;-)

> A half-remembered discussion George Dishman had on this topic.
> I'll try and search back about two years ago, he was responding
> to someone (not me).  I'll see if I can locate the reference.

Thanks. I am by no means an expert on cosmology, but everything
I read so far said "optically thick", IIRC. I'll also see if
I can dig up some references.

[snip]

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 31 Mar 2005 05:00 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>>
[quoted text clipped - 13 lines]
> I realize that. But I also realize that that does not require
> that anything from the BH singularity gets to the horizon.

The entire BH evaporates.  So if something cannot get from the
"singularity", then perhaps there isn't one.

>> And not half of all nearby *new* particles leaving the
>> hole.
[quoted text clipped - 27 lines]
> does not require anything from the BH singularity
> getting to the horizon.

The entire hole evaporates, given sufficient time.

>> If you can be sure the mass has formed a singularity,
>> the characteristic radiation would be hotter.
>
> Huh? How does that follow?

Wavelength emitted is a function of the geometry the radiation is
emitted from.  A singularity is smaller than the event horizon,
no?

>> As it is the characterisitc radiation is constrained to be
>> some function of the
[quoted text clipped - 4 lines]
>
> Why not?

There are solutions to GR that have the contents of a BH become
infinitely diffuse.  Quite different than a singularity.

>> At the horizon, we would agree the mass/energy is relatively
>> diffuse.
>
> Huh?

You are pulling my chain, right?  Matter infalls, but you expect
it to hang around "just inside" the event horizon?

>> If our Universe is the inside of a BH,  then
>> the mass/energy inside the black hole creates its
[quoted text clipped - 4 lines]
> up on the difference between a Schwarzschild
> and a Robertson-Walker metric.

Let each man his dead according to his own fashion.  I'm not
talking about a Schwarzchild metric.

>>>>>>We have  *structures* exceedingly close to the CMBR...
>>>>>
[quoted text clipped - 11 lines]
> For what? Galaxies existing 2 billion years after the BB is
> not such a big surprise, you know.

"2 billion years or so is close enough.  Additional precision is
not required, since I have not my self been very precise."  Is
that more clear?

>> And as our observational tools get sharper, do you think we
>> might find some closer?
[quoted text clipped - 4 lines]
> observations in the infrared, due to the high
> redshift of these objects.

My intent was not "sharper focus", but "sharper tools".  You
correctly identify what it will take to make the tools sharper.
Idiom,  I apologize.

> And yes, I think we will find something closer:
> galaxies in their very process of forming, and
> the very first stars.  According to the WMAP
> results, these should have formed about
> 200 million years after the BB.

And I think we will find stars and galaxies as old as the CMBR,
eventually.  I am likely a party of one.

>> With some older stars?
>
> I don't think so.

We have millions of years (if we are lucky) to gather enough data
to find out.

>> Perhaps they will reach some asymptote.
>
> Huh?

Apparent age of "stellar objects" vs. distance.  You expect the
apparent age to always be less than the age of the CMBR.  I
don't.

>> The question remains as to whether the "origin" of structure
>> lay earlier
[quoted text clipped - 9 lines]
> of these structures (fluctuations); predictions
> which have already been partly confirmed.

I was not referring to atomic or subatomic structure.

>> You appear to be satisfied that it doesn't.
>
> No. Where did you get that idea from?

I think it is clearer now, that I was not talking about "three
forces structures", but gravitationally bound structures.

>>>>Looking at our own Milky Way galaxy (and its
>>>>"products"), we have globular clusters that show
[quoted text clipped - 12 lines]
> stars, it is expected that they contain mainly hydrogen
> and only very few heavy elements.

Agreed (adding helium), but you bust my chops about the "spectral
contaminants" that are identified in my links below.

>> All I am saying is that "elemental abundances"
>> isn't the clear indicator you think it is, IMHO.
[quoted text clipped - 21 lines]
>
> So, where are the references for your claim?

You, for one.  You accept it, based on "common knowledge", but
you argue over key contaminant levels.

>>>>I don't think we know enough to "see much
>>>>further back".
[quoted text clipped - 7 lines]
>
> Sorry, I don't understand the question.

It helps if the context is clear:
Was 75-25 a result of derivation, or was the expected range
simply broad enough to include the observation?

>> I haven't seen fundamental "engineering like" formulae come
>> out of BBT.
>
> I didn't claim that these is such a formula.

And not danged likely *I* could understand and operate such
formulae anyway.  ;>)

>> Do you have a reference?
>
> Kolb&Turner, The Early Universe.

Thanks.  I've got to find Principles of Optics first...
extinction length, Wigner delay.

>> This one looks pretty juicy...
>> URL:http://www.library.uu.nl/digiarchief/dip/diss/2002-1004-084000/c1.pdf
>
> This doesn't seem to say much about elemental
> abundances. And it doesn't give a single formula,
> just a lot of rhetoric.

Leave it to me to find hand waving.  I apologize.

>>>>>>"My" science makes reasonable sense to
>>>>>>that point (if you swallow objections about
[quoted text clipped - 19 lines]
> especially page 7, or sections 5.2 and 6.4 here:
> <http://lambda.gsfc.nasa.gov/product/map/pub_papers/firstyear/parameters/wmap_par
ameters.pdf
>

I'll check them out.  Thanks!

>> Yes, I know the CMBR is "lumpy".  That was my point, that
>> there was
[quoted text clipped - 4 lines]
> I don't understand what you mean with "at the
> center of the lens" here.

URL:http://www.astro.ucla.edu/~wright/cosmo_02.htm
... down to the space-time diagram.  The CMBR is located down
where all the lines converge... the center of the lens.  I am
sorry that I am not more clear.

>>>>>>What we have seen in this Universe is always
>>>>>>something bigger, and something brighter.  In
[quoted text clipped - 17 lines]
>
> Sorry. ;-)

Its OK.  I could start "speaking" good English, and you'd have a
much easier time of it.

>> A half-remembered discussion George Dishman
>> had on this topic.  I'll try and search back about
[quoted text clipped - 4 lines]
> but everything I read so far said "optically thick", IIRC.
> I'll also see if I can dig up some references.

Don't worry too much.  This is all I've seen "advertised" too.
But then we cannot duplicate this "perfect blackbody radiation
curve" with real matter, no matter how optically thick it is.

"Bjoern Feuerbacher" <feuerbac@thphys.uni-heidelberg.de> wrote in
message news:d2ds11$itr$1@news.urz.uni-heidelberg.de...
>> Adding a bit near the end, relating to the reference
>> to "George Dishman"
[quoted text clipped - 28 lines]
> thick before the CMBR
> was emitted.

Agreed, it doesn't speak to this at all.  Well, it was good
exercise!

We can end this thread, if you don't want to talk about BHs more.

David A. Smith
Bjoern Feuerbacher - 31 Mar 2005 18:19 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 17 lines]
>
> The entire BH evaporates.

Yes.

> So if something cannot get from the
> "singularity", then perhaps there isn't one.

I did not say that "something cannot get from the singularity".
I only said that nothing has to get to the horizon.

[snip more of that]

>>>If you can be sure the mass has formed a singularity,
>>>the characteristic radiation would be hotter.
[quoted text clipped - 4 lines]
> emitted from.  A singularity is smaller than the event horizon,
> no?

Yes. But the radiation comes from the event horizon (AFAIK).

And "hotter" is also quite ambiguous above. Did you mean "has smaller
wavelength"?

>>>As it is the characterisitc radiation is constrained to be
>>>some function of the
[quoted text clipped - 7 lines]
> There are solutions to GR that have the contents of a BH become
> infinitely diffuse.  Quite different than a singularity.

Interesting. Do you have a reference?

>>>At the horizon, we would agree the mass/energy is relatively
>>>diffuse.
[quoted text clipped - 3 lines]
> You are pulling my chain, right?  Matter infalls, but you expect
> it to hang around "just inside" the event horizon?

No. I expect it to go to the center, to the singularity. Not
being diffusely distributed.

>>>If our Universe is the inside of a BH,  then
>>>the mass/energy inside the black hole creates its
[quoted text clipped - 7 lines]
> Let each man his dead according to his own fashion.  I'm not
> talking about a Schwarzchild metric.

Then about what metric are you talking?

[snip]

>>And yes, I think we will find something closer:
>>galaxies in their very process of forming, and
[quoted text clipped - 4 lines]
> And I think we will find stars and galaxies as old as the CMBR,
> eventually.

Well, probably we will know a lot more in a few years already.
I think the James Webb telescope will give a lot of new data on
this problem.

> I am likely a party of one.

At least among cosmologists. Among crackpots, there are a lot
people who would agree with you. ;-)

[snip]

>>>The question remains as to whether the "origin" of structure
>>>lay earlier
[quoted text clipped - 11 lines]
>
> I was not referring to atomic or subatomic structure.

I weren't, too.

>>>You appear to be satisfied that it doesn't.
>>
>>No. Where did you get that idea from?
>
> I think it is clearer now, that I was not talking about "three
> forces structures", but gravitationally bound structures.

At the time of the CMBR, there were density fluctuations on the
order of 10^(-5) (IIRC). I don't think it makes much sense to
talk about "gravitationally bound structures" at that point yet.

Do you think the density fluctuations were much greater at that time?
If yes, how do you explain that there are only such small
*temperature* fluctuations in the CMBR?

[snip]

>>>Our perspective is skewed,
>>>because we are still strapped to the surface of this rock.
[quoted text clipped - 18 lines]
> You, for one.  You accept it, based on "common knowledge", but
> you argue over key contaminant levels.

About 25% helium is *not* "essentially pure hydrogen", and
neither simply a "contaminant".

And that there are only little heavier elements is entirely expected.
So what's your point?

>>>>>I don't think we know enough to "see much
>>>>>further back".
[quoted text clipped - 11 lines]
> Was 75-25 a result of derivation, or was the expected range
> simply broad enough to include the observation?

I don't know how big the errors bars are exactly, but
I think they are around 2 percent (25 +-2 % or something like that).

[snip]

> We can end this thread, if you don't want to talk about BHs more.

If you give me a reference for this "matter inside a BH can be
diffuse" stuff, fine. That really sounds interesting, and IIRC
I never heard that before.

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 01 Apr 2005 04:19 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
...
>> So if something cannot get from the "singularity", then
>> perhaps there isn't one.
>
> I did not say that "something cannot get from the singularity".
> I only said that nothing has to get to the horizon.

OK.  You offer that once mass enters the BH, it is going to enter
a singularity, right?  How can the BH then evaporate?

>>>>If you can be sure the mass has formed
>>>>a singularity, the characteristic radiation
[quoted text clipped - 12 lines]
> And "hotter" is also quite ambiguous above.
> Did you mean "has smaller wavelength"?

Yes.  If the radiation comes from some structure smaller than the
event horizon, it should be characteristic of that structure.  If
you are sure that such a structure exists, it has implications if
it does.  If the BH radiates ONLY as a gestalt, then there can be
NO assurance there is a singularity.

>>>>As it is the characterisitc radiation is
>>>>constrained to be some function of the
[quoted text clipped - 10 lines]
>
> Interesting. Do you have a reference?

Skip to the bottom.  We can address it once.

>>>>At the horizon, we would agree the
>>>>mass/energy is relatively diffuse.
[quoted text clipped - 7 lines]
> No. I expect it to go to the center, to the
> singularity. Not being diffusely distributed.

OK.  So the "positions" just inside the event horizon are
unpopulated.  The matter/energy that entered before have "moved
on", right?  The "density" just inside the horizon is therefore
relatively low.  Correct me if I am wrong here...

>>>>If our Universe is the inside of a BH,  then
>>>>the mass/energy inside the black hole creates its
[quoted text clipped - 9 lines]
>
> Then about what metric are you talking?

Probably the some one you speak of.  Skip to the bottom.

>>>And yes, I think we will find something closer:
>>>galaxies in their very process of forming, and
[quoted text clipped - 9 lines]
> telescope will give a lot of new data on
> this problem.

OK.  I will miss the Hubble though...

> > I am likely a party of one.
>
> At least among cosmologists. Among crackpots,
> there are a lot people who would agree with you. ;-)

OK.  I don't need to be right, I just strive to be consistent.

>>>>The question remains as to whether the "origin"
>>>>of structure lay earlier than the formation of the
[quoted text clipped - 13 lines]
>
> I weren't, too.

I don't think of "lumps" as structure, but we can cease this
semantics game.

>>>>You appear to be satisfied that it doesn't.
>>>
[quoted text clipped - 8 lines]
> think it makes much sense to talk about
> "gravitationally bound structures" at that point yet.

Agreed.

> Do you think the density fluctuations were much
> greater at that time?  If yes, how do you explain
> that there are only such small *temperature*
> fluctuations in the CMBR?

Because they are averaging (IMO) over areas that are about the
size of the Virgo supercluser, or at least as big as it would
have been at the time of the CMBR.  What is the bulk temperature
of this volume, with the appropriate definition of temperature
(average velocity when viewed at 13 Gy)?  Pretty low, and
mathematically forced to be uniform.  I can wait for James
Webb... not that I expect a great deal of information to bolster
my near-crank position.

>>>>Our perspective is skewed,
>>>>because we are still strapped to the surface of
[quoted text clipped - 21 lines]
> About 25% helium is *not* "essentially pure hydrogen",
> and neither simply a "contaminant".

Helium is not mentioned *at all* on those sites.  I'll accept
your 25% number without reference.

> And that there are only little heavier elements
> is entirely expected.  So what's your point?

These stars have been around longer than our own Sun.  Yet our
Sun has more heavy elements.  We attribute that to "we started
with used material".  I think our perspective is a bit skewed
(provincial) when we go to estimate "atomic abundance" at the
time of the CMBR, when we cannot get local hydrogen+helium to
produce *that* kind of spectrum.

>>>>>>I don't think we know enough to "see much
>>>>>>further back".
[quoted text clipped - 16 lines]
> but I think they are around 2 percent (25 +-2 %
> or something like that).

OK.

>> We can end this thread, if you don't want to talk about BHs
>> more.
>
> If you give me a reference for this "matter inside a BH can be
> diffuse" stuff, fine. That really sounds interesting, and IIRC
> I never heard that before.

URL:http://cosmology.berkeley.edu/Education/BHfaq.html
<QUOTE>
That is, "r", the coordinate that describes how far away you are
from the center, is a timelike coordinate, and "t" is a spacelike
one. One consequence of this is that you can't stop yourself from
moving to smaller and smaller values of r, just as under ordinary
circumstances you can't avoid moving towards the future (that is,
towards larger and larger values of t). Eventually, you're bound
to hit the singularity at r = 0. You might try to avoid it by
firing your rockets, but it's futile: no matter which direction
you run, you can't avoid your future. Trying to avoid the center
of a black hole once you've crossed the horizon is just like
trying to avoid next Thursday.
<END QUOTE>
... anything that *ever* enters a BH, does so at the same
internal time "coordinate".  It's Big Bang.

Looking at our Universe as the inside of a BH, we see that we
move to a more diffuse colder state, in "accordance" with the 2nd
law of thermodynamics.  To quote Chris Hillman, In the far
distant future, no particle will have any other particle in its
future.

Now look from the ouside of the BH again.  Consider the speed of
light as a function of density (in general).  As something
approaches your singularity, the speed of light goes down.  This
means that, in general the "distance" between objects may be
staying the same, or even getting larger... *locally*.  It
depends on the relationship assumed.  Keep in mind that space
inside the BH is orthogonal to time, which means it has NO
relationship to space outside the BH, excepts to be orthogonal to
it also.

Sorry about the exposition.  Hope it suffices.  If not...
URL:http://math.ucr.edu/home/baez/PUB/generichole

David A. Smith
Bjoern Feuerbacher - 01 Apr 2005 09:58 GMT
> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 10 lines]
> OK.  You offer that once mass enters the BH, it is going to enter
> a singularity, right?  How can the BH then evaporate?

Don't know. I have never looked at the actual calculations. I am
only aware of the pop-science explanation, and that's lacking.

>>>>>If you can be sure the mass has formed
>>>>>a singularity, the characteristic radiation
[quoted text clipped - 18 lines]
> it does.  If the BH radiates ONLY as a gestalt, then there can be
> NO assurance there is a singularity.

Right. I never said that the radiation is "assurance" that there
is a singularity.

[snip]

>>>>>At the horizon, we would agree the
>>>>>mass/energy is relatively diffuse.
[quoted text clipped - 12 lines]
> on", right?  The "density" just inside the horizon is therefore
> relatively low.  Correct me if I am wrong here...

I would agree with that.

[snip]

>>Do you think the density fluctuations were much
>>greater at that time?  If yes, how do you explain
[quoted text clipped - 7 lines]
> (average velocity when viewed at 13 Gy)?  Pretty low, and
> mathematically forced to be uniform.

Even when averaging over such a large volume, shouldn't the
fluctuations be much greater than 10^(-5)?

> I can wait for James
> Webb... not that I expect a great deal of information to bolster
> my near-crank position.

How do you explain that when one takes the fluctuations seen
in the CMBR and studies how they grow with time (due to gravity),
one gets the large-scale structure we see today?

[snip]

>>And that there are only little heavier elements
>>is entirely expected.  So what's your point?
>
> These stars have been around longer than our own Sun.  Yet our
> Sun has more heavy elements. We attribute that to "we started
> with used material".

Indeed.

Bear in mind that the amount of heavy elements is determined from
the spectra of the stars, and that the spectra are produced in
the photospheres of the stars, i.e. in their outermost layers.
Using spectra, we can't see what's further inside the stars.

And the theories of stellar evolution say that heavy elements
are produced exactly there, in the cores of the stars. And usually
don't get outside to the photosphere easily (not enough convection).

Stars in globular clusters are mainly population II, i.e. they
formed when still not much heavy elements were around. So in their
outer layers, we don't see much heavy elements. But in their cores,
there are much more.

Our sun is a population I star. It formed essentially from the debris
of explosions of population II stars. That debris contained the heavy
elements produced in the cores of these stars. So our sun has more
heavy elements in its photosphere than the population II stars.

Conclusion: that we see more heavy elements in our sun than in
the globular cluster stars does in no way contradict that these
stars are older. In contrast, this is essentially an inevitable
conclusion!

> I think our perspective is a bit skewed
> (provincial) when we go to estimate "atomic abundance" at the
> time of the CMBR, when we cannot get local hydrogen+helium to
> produce *that* kind of spectrum.

Sorry, I don't understand your problem.

[snip]

>>>We can end this thread, if you don't want to talk about BHs
>>>more.
[quoted text clipped - 17 lines]
> trying to avoid next Thursday.
> <END QUOTE>

That quote says that everything that enters a BH, goes straight
to the singularity, so this actually goes counter to your "diffuse
distribution" claim above!

> ... anything that *ever* enters a BH, does so at the same
> internal time "coordinate".

What is this supposed to mean? That's not what the quote above says.

> It's Big Bang.

Huh? Sorry, how on earth does this follow?

> Looking at our Universe as the inside of a BH, we see that we
> move to a more diffuse colder state, in "accordance" with the 2nd
> law of thermodynamics.  To quote Chris Hillman, In the far
> distant future, no particle will have any other particle in its
> future.

Agreed, with the exception of the first half-sentence.

> Now look from the ouside of the BH again.  Consider the speed of
> light as a function of density (in general).

Why should I?

> As something
> approaches your singularity, the speed of light goes down.

The speed of light, as measured by a free-falling observer, is
always the same.

> This means that, in general the "distance" between objects may be
> staying the same, or even getting larger... *locally*.  It
> depends on the relationship assumed.  Keep in mind that space
> inside the BH is orthogonal to time,

Space outside a BH is also orthogonal to time.

> which means it has NO
> relationship to space outside the BH,

And how does *that* follow???

> excepts to be orthogonal to it also.

Why do you think so?

> Sorry about the exposition.  Hope it suffices.

No. The quote actually contradicts you, and I don't see how you get
all your strange conclusions above from it.

> If not...
> URL:http://math.ucr.edu/home/baez/PUB/generichole

I have no idea what this has to do with your claims of a "diffuse
distribution" of matter inside a BH.

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 01 Apr 2005 15:03 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>>
[quoted text clipped - 16 lines]
> calculations. I am only aware of the
> pop-science explanation, and that's lacking.

OK.  Awareness of this "necessary discontinuity" will direct you
to your own solution.

>>>>>>If you can be sure the mass has formed
>>>>>>a singularity, the characteristic radiation
[quoted text clipped - 23 lines]
> Right. I never said that the radiation is
> "assurance" that there is a singularity.

As I said before, if these two disjoint implications bothers you
enough, you will find your own solution.  "It must enter a
singularity" is disjoint with "a singularity cannot evaporate so
therefore a BH cannot evaporate".

>>>>>>At the horizon, we would agree the
>>>>>>mass/energy is relatively diffuse.
[quoted text clipped - 16 lines]
>
> I would agree with that.

OK.  Then how can the BH evaporate, if we can be sure there is
little mass/energy near the event horizon?  Isn't it really true
that we don't know where the mass/energy is?

>>>Do you think the density fluctuations were much
>>>greater at that time?  If yes, how do you explain
[quoted text clipped - 13 lines]
> shouldn't the fluctuations be much greater than
> 10^(-5)?

Given better resolution, it might be.  And keep in mind it was a
picture of the contents of this entire Universe, only some 10's
of million light years "across".

>> I can wait for James Webb... not that I expect a great deal of
>> information to bolster my near-crank position.
[quoted text clipped - 3 lines]
> how they grow with time (due to gravity),
> one gets the large-scale structure we see today?

You can resolve "traffic" into individual cars, as well.  That
doesn't mean there weren't cars at great distances.  In this
metaphor, stars would be cars.

>>>And that there are only little heavier elements
>>>is entirely expected.  So what's your point?
[quoted text clipped - 4 lines]
>
> Indeed.

But not "certainty".  We have less than 100 years of observation,
done entirely from our Solar System.

> Bear in mind that the amount of heavy elements
> is determined from the spectra of the stars, and
[quoted text clipped - 6 lines]
> cores of the stars. And usually don't get outside
> to the photosphere easily (not enough convection).

I know this is a problem in our atmosphere.  But I do not accept
that heavier elements cannot be driven out by light pressure and
their greater nuclear charge.  Diffusion is likely very strong,
but like dissolved air flotation, "sticky stuff" rises to the
top, even when it is more dense than water.  Air bubbles are
metaphor for photons in this case.

> Stars in globular clusters are mainly population II,
> i.e. they formed when still not much heavy elements
> were around. So in their outer layers, we don't see
> much heavy elements. But in their cores, there are
> much more.

I'm not so sure.  Let's split one open to find out.  ;>)

> Our sun is a population I star. It formed essentially
> from the debris of explosions of population II stars.
[quoted text clipped - 8 lines]
> contrast, this is essentially an inevitable
> conclusion!

Not inevitable.

>> I think our perspective is a bit skewed (provincial) when we
>> go to estimate "atomic
[quoted text clipped - 3 lines]
>
> Sorry, I don't understand your problem.

Not trained in psychiatry?  ;>)
I don't find our assumptions of atomic abundance compelling.  You
(and all of the scientific community) do.  I can live with that.

>>>>We can end this thread, if you don't want to talk
>>>>about BHs more.
[quoted text clipped - 23 lines]
> goes straight to the singularity, so this actually
> goes counter to your "diffuse distribution" claim above!

I tried to be circumspect, to not give a quote out of context.
You got lost in the detail of the balance of the paragraph.  The
first sentence says that outer r becomes inner t,  and later r =
0 maps to t = oo (the future).  I am building a case.  The
paragraph above is designed for those that are immersed in the
pool, and are not used to contemplating the boundary of the pool.

Think about the consequences of:
t_0 = 1 / r_S
t_0 inner time coordinate
r_S outer space coordinate
with r_S as the Schwarzchild radius (for lack of a definition I
can remember!), for a hole that is not still ingesting anything
except test masses.  Anything that it ever (outer time) ingests,
enters at the same inner time coordinate.

>> ... anything that *ever* enters a BH, does
>> so at the same internal time "coordinate".
>
> What is this supposed to mean? That's not
> what the quote above says.

What in the world do you think "timelike" means, Bjoern?

>> It's Big Bang.
>
> Huh? Sorry, how on earth does this follow?

Clearer now?

>> Looking at our Universe as the inside of a BH,
>> we see that we move to a more diffuse colder
[quoted text clipped - 4 lines]
>
> Agreed, with the exception of the first half-sentence.

Think again.

>> Now look from the ouside of the BH again.
>> Consider the speed of light as a function of
>> density (in general).
>
> Why should I?

I am trying to build a case.  If you aren't interested in hearing
it, we can stop.  The speed of light is roughly inversely
proportional to density

>> As something approaches your singularity, the speed of light
>> goes down.
>
> The speed of light, as measured by a free-falling
> observer, is always the same.

We are talking about someone *outside* the event horizon, looking
to a different "gradient level" in a curved spacetime.  Think
Shapiro Time Delay.  The *local* speed of light is now always c
to a free falling observer.

>> This means that, in general the "distance"
>> between objects may be staying the same,
[quoted text clipped - 3 lines]
>
> Space outside a BH is also orthogonal to time.

Yes, thank you.

>> which means it has NO relationship to space outside the BH,
>
> And how does *that* follow???

Does z have to be orthogonal to both y and x?  Can't you have a
coordinate space where x L y, y L z, but x < z?

Where "L" is perpendicular, and "<" is any angle...
It is only damned convenient to have x L z.  The internal space
inside a BH is not constrained by our space, but is constrained
by being "a product of the mass/energy that created it".

>> excepts to be orthogonal to it also.
>
> Why do you think so?

Because nothing of a BHs internal space is present in our
Universe.  Only its time axis is coincident to our space, at r =
r_S.

>> Sorry about the exposition.  Hope it suffices.
>
> No. The quote actually contradicts you, and I
> don't see how you get all your strange
> conclusions above from it.

Try again, or give up on me.  You choose.

>> If not...
>> URL:http://math.ucr.edu/home/baez/PUB/generichole
>
> I have no idea what this has to do with your claims
> of a "diffuse distribution" of matter inside a BH.

Maybe it will make more sense now.

David A. Smith
Bjoern Feuerbacher - 03 Apr 2005 14:10 GMT
> Dear Bjoern Feuerbacher:

[snip a lot]

>>>OK.  So the "positions" just inside the event
>>>horizon are unpopulated.  The matter/energy
[quoted text clipped - 7 lines]
> OK.  Then how can the BH evaporate, if we can be sure there is
> little mass/energy near the event horizon?  

Don't know. Some quantum effects...

> Isn't it really true that we don't know where the mass/energy is?

According to "classical" GR, we know where it is. I don't know
how that changes if one tries to do semi-classical GR, i.e.
tries to look for quantum effects in BHs.

[snip]

>>>I can wait for James Webb... not that I expect a great deal of
>>>information to bolster my near-crank position.
[quoted text clipped - 7 lines]
> doesn't mean there weren't cars at great distances.  In this
> metaphor, stars would be cars.

I don't see what your analogy has to do with my argument.
In the computer simulations, the fluctations became *bigger*
with time (i.e. the density contrast increased), and only
after a *long* time, the density contrasts were big enough
so that galaxies could form.

>>>>And that there are only little heavier elements
>>>>is entirely expected.  So what's your point?
[quoted text clipped - 7 lines]
> But not "certainty".  We have less than 100 years of observation,
> done entirely from our Solar System.

You won't find "certainty" in most of astronomy.

>>Bear in mind that the amount of heavy elements
>>is determined from the spectra of the stars, and
[quoted text clipped - 9 lines]
> I know this is a problem in our atmosphere.  But I do not accept
> that heavier elements cannot be driven out by light pressure

Gravity is much stronger than light pressure in stars. Do you
think our models of stellar evolution are totally wrong?

> and their greater nuclear charge.

Do you mean electrostatic repulsion, or what?

[snip]

>>Our sun is a population I star. It formed essentially
>>from the debris of explosions of population II stars.
[quoted text clipped - 10 lines]
>
> Not inevitable.

If you accept our models of stellar evolution, this *is*
essentially inevitable.

[snip]

>>>>>We can end this thread, if you don't want to talk
>>>>>about BHs more.
[quoted text clipped - 27 lines]
> You got lost in the detail of the balance of the paragraph.  The
> first sentence says that outer r becomes inner t,

Right.

> and later r =  0 maps to t = oo (the future).

No, "the future" does *not* mean "t = oo" (you meant infinity, I
suppose?).

> I am building a case.  The
> paragraph above is designed for those that are immersed in the
[quoted text clipped - 4 lines]
> t_0 inner time coordinate
> r_S outer space coordinate

But that formula is wrong. Where did you get it from?

> with r_S as the Schwarzchild radius (for lack of a definition I
> can remember!),

Make up your mind. Is r_s the outer space coordinate or the
Schwarzschild radius?

> for a hole that is not still ingesting anything
> except test masses.  Anything that it ever (outer time) ingests,
> enters at the same inner time coordinate.

Why do you think so?

>>>... anything that *ever* enters a BH, does
>>>so at the same internal time "coordinate".
[quoted text clipped - 3 lines]
>
> What in the world do you think "timelike" means, Bjoern?

That the metric coefficient is the same as that for the
time coordinate in a Minkowski metric.

>>>It's Big Bang.
>>
>>Huh? Sorry, how on earth does this follow?
>
> Clearer now?

No.

[snip]

>>>Now look from the ouside of the BH again.
>>>Consider the speed of light as a function of
[quoted text clipped - 3 lines]
>
> I am trying to build a case.

Why do you try to build it on statements which are simply wrong?

> If you aren't interested in hearing
> it, we can stop.  The speed of light is roughly inversely
> proportional to density

Why on earth do you think so?

>>>As something approaches your singularity, the speed of light
>>>goes down.
[quoted text clipped - 4 lines]
> We are talking about someone *outside* the event horizon, looking
> to a different "gradient level" in a curved spacetime.

We are? You didn't state that before, IIRC.

[snip]

>>>This means that, in general the "distance"
>>>between objects may be staying the same,
[quoted text clipped - 11 lines]
>
> Does z have to be orthogonal to both y and x?

Depends on what is meant. If you mean a usual cartesian coordinate
system, z *has* to be orthogonal to x and y.

> Can't you have a coordinate space where x L y, y L z, but x < z?
> Where "L" is perpendicular, and "<" is any angle...
> It is only damned convenient to have x L z.

Yes, one could have such a coordinate system. But what's the point?

> The internal space
> inside a BH is not constrained by our space, but is constrained
> by being "a product of the mass/energy that created it".

And what is *that* supposed to mean?

>>>excepts to be orthogonal to it also.
>>
[quoted text clipped - 3 lines]
> Universe. Only its time axis is coincident to our space, at r =
> r_S.

Yes. So what? What does this have to do with "being orthogonal"?

[snip]

Bye,
Bjoern
N:dlzc D:aol T:com (dlzc) - 03 Apr 2005 18:49 GMT
Dear Bjoern Feuerbacher:

>> Dear Bjoern Feuerbacher:
>
[quoted text clipped - 22 lines]
> to do semi-classical GR, i.e. tries to look for
> quantum effects in BHs.

According to this definition of classical, we know that the
mass/energy of any given "proton" for example is "smeared out"
along its timeline from r = r_S to r = 0 (its t = t_0 to t = oo
when inside).  I picked a proton because they seem to have a long
individual lifetme.  So the proton *never* (outside time)
entirely leaves the inside of the event horizon.

Smoke coming out yet?

>>>>I can wait for James Webb... not that I
>>>>expect a great deal of information to
[quoted text clipped - 16 lines]
> after a *long* time, the density contrasts were
> big enough so that galaxies could form.

OK.  Sounds reasonable.

Now, if a BH is large enough, "three forces structures" can
survive crossing the event horizon.  The gravity gradient at any
given point isn't large enough to break the bonds.  It is
remotely possible (read this as almost impossible) that stars and
galaxies existed before the CMBR.

>>>>>And that there are only little heavier elements
>>>>>is entirely expected.  So what's your point?
[quoted text clipped - 9 lines]
>
> You won't find "certainty" in most of astronomy.

No certainty this side of the grave.  ;>)

>>>Bear in mind that the amount of heavy elements
>>>is determined from the spectra of the stars, and
[quoted text clipped - 18 lines]
>
> Do you mean electrostatic repulsion, or what?

I mean the same light pressure with which we are able to create a
magnetic moment in latex balls, and manipulate them with light
beams.  You clipped my dissolved air flotation reference.  This
type of "gathering heavy stuff together" and "making heavy stuff
float" is well known in engineering.  All I am saying is that it
is *conceivable* that heavy elements are disproportionately
represented in the outer layers (where light is finally released
to space) of stars.

>>>Our sun is a population I star. It formed essentially
>>>from the debris of explosions of population II stars.
[quoted text clipped - 13 lines]
> If you accept our models of stellar evolution,
> this *is* essentially inevitable.

I accept what I have seen.  I have seen the heavy, made light.
Or at least floated.

>>>>>>We can end this thread, if you don't want to talk
>>>>>>about BHs more.
[quoted text clipped - 35 lines]
> No, "the future" does *not* mean "t = oo"
> (you meant infinity, I suppose?).

Yes I did mean infinity.  How how did you miss (or misinterpret):
"you can't avoid moving towards the future (that is, towards
larger and larger values of t)"?  Do you think that t will stop
at some finite value?

>> I am building a case.  The paragraph above is designed for
>> those that are immersed in the pool, and are not used to
[quoted text clipped - 6 lines]
>
> But that formula is wrong. Where did you get it from?

It makes the inner and outer solutions to GR congruent at the
event horizon.  There are others, I just don't know what they
are.

>> with r_S as the Schwarzchild radius (for lack
>> of a definition I can remember!),
>
> Make up your mind. Is r_s the outer space
> coordinate or the Schwarzschild radius?

r is the outer space coordinate.  When it has the value of r_S,
it is coincident with the event horizon.  t is the inner time
coordinate.  Then it has the value of t_0, it is coincident with
the Big Bang (aka. the inside of the event horizon).

>> for a hole that is not still ingesting anything except test
>> masses.  Anything that it ever
>> (outer time) ingests, enters at the same
>> inner time coordinate.
>
> Why do you think so?

What does a fixed position on a timelike axis represent to you?
The insde of the BH *does not contain* our time axis.  Time for
us is orthogonal to space.  So time for us is orthogonal to time
inside the BH.

>>>>... anything that *ever* enters a BH, does
>>>>so at the same internal time "coordinate".
[quoted text clipped - 7 lines]
> that for the time coordinate in a Minkowski
> metric.

This is a BH.  Minkowski doesn't apply.  Minkowski has time
orthogonal to space.  The GR solution to a BH has outer r
"parallel and contiguous" with inner t, at the horizon.  This
means outer time is orthogonal to inner time.  Care to reconsider
what you think timelike means inside a BH?

>>>>It's Big Bang.
>>>
[quoted text clipped - 3 lines]
>
> No.

URL:http://math.ucr.edu/home/baez/gr/oz1.html
... 22 pages.  Read slowly and carefully.  Pay carefull attention
to the last page.

>>>>Now look from the ouside of the BH again.
>>>>Consider the speed of light as a function of
[quoted text clipped - 6 lines]
> Why do you try to build it on statements
> which are simply wrong?

They aren't wrong.  They don't happen to be statements you
accept.  I don't accept you as the keeper of "Rightness".  You
know far more than me in most everything, and have infinite
patience.  But "Right" is not in your purview.

>> If you aren't interested in hearing it, we can stop.  The
>> speed of light
>> is roughly inversely proportional to density
>
> Why on earth do you think so?

Forget it.  It is wrong to push outer geometry performance into
the BH.

>>>>As something approaches your singularity,
>>>>the speed of light goes down.
[quoted text clipped - 7 lines]
>
> We are? You didn't state that before, IIRC.

What in the world does "Now look from the ouside of the BH again"
mean to you?  You sliced and diced, and lost the context, I
guess.

As I said, forget it.  It is bad practice to make geometric
assumptions of the inside of the BH, from the outside.

>>>>This means that, in general the "distance"
>>>>between objects may be staying the same,
[quoted text clipped - 16 lines]
> usual cartesian coordinate system, z *has*
> to be orthogonal to x and y.

I mean that Fred is orthogonal to James.  James is orthogonal to
Harry.  What can be said of the relationship between Fred and
Harry?

>> Can't you have a coordinate space where x L y, y L z, but x <
>> z?
[quoted text clipped - 3 lines]
> Yes, one could have such a coordinate system. But
> what's the point?

Because time_outide is orthogonal to space_outside, and
time_inside is "contiguous and parallel" with space_outside,
means that time_outside has no relationship with space_inside and
time_inside has only one surface in common with space_outside...
at the event horizon.  Space_inside has no bound in the Universe
that contains the BH.  It is "compactified", if you will.

>> The internal space inside a BH is not constrained by our
>> space,
>> but is constrained by being "a product of the
>> mass/energy that created it".
>
> And what is *that* supposed to mean?

The spacetime inside the BH is the product of the mass/energy
that forms the BH.  Same as it means in the Universe around us.
Why should it be any different?

>>>>excepts to be orthogonal to it also.
>>>
[quoted text clipped - 6 lines]
> Yes. So what? What does this have to do
> with "being orthogonal"?

Inner_space is orthogonal to outer_space.  Do you get it now?  So
inner_space is unconstrained by the Universe that contains the
BH.

David A. Smith
Dale Trynor - 04 Apr 2005 00:54 GMT
> Dear Bjoern Feuerbacher:
>
>>>Dear Bjoern Feuerbacher:
>>
>>[snip a lot]

[snip]

>>>We are talking about someone *outside* the
>>>event horizon, looking to a different "gradient
[quoted text clipped - 8 lines]
> As I said, forget it.  It is bad practice to make geometric
> assumptions of the inside of the BH, from the outside.

Dale Trynor wrote:
Sorry if I seam like I'm pestering you but this last sentence caught my
eye and I felt I might have some thoughts to add.

I tried modeling how an orbiting satellite could measure the curvature
in a light beam by using a meter stick and some surprising possibilities
evolved from this.
We have a level around a black hole where light is bent sufficiently to
 at least potentially travel in a complete orbit the 3m level, so try
asking yourself what would happen if this light beam were to travel
through our space craft and then asking if it's possible for our
astronaut to detect the curve in the light beam especially if matter and
all his references also end up curving.
We have to be careful with our thought experiment because its important
to remember that for a satellite to face the earth continually then it
must also rotate to do so and this would result in ones measuring an
curved light path. This can be prevented by using gyroscopes as a
gyroscope should follow the light path. Model how a gyroscope whose axis
of travel is in the crafts direction of travel and note how its lower
part is in a slower rate of time that should cause the gyroscope to
rotate giving our astronaut the impression that his craft is also not
rotating. Yes we do have two disagreeing prospectives but for now its
the astronauts prospective that counts.

It appears that if matter dose not contract under the influence of a
slower relative time then the perfectly straight meter stick would
remain straight for both observers and our astronaut would be able to
detect the curve in the light beam, as the beam would be higher in its
middle than at the ends of the stick.
However if matter dose contract then the meter stick will become curved
not so differently from how a bi metal thermostat works. Its reasonable
to expect that the curvature will always be exactly equal to match the
light beam rendering the curve undetectable for our astronaut. This
level near a black hole becomes perfectly flat to him but its still of
course, round to us.

What I am leading up to is a hypothesis where cur