As I type this I am seated, alone, on the rim of Hypatia.  Here I have
found undreamt-of treasures, the secret of the nature of Gravity, and
a complete understanding of the Quasars' life cycle and appearance.  

But it all happened by accident.  I wasn't looking for the answers to
Gravity and Quasars, just the secret of the Redshift in a static
universe which would correspond to observations better than the Big
Bang theory, without any "new physics".  And I followed a clue which
no-one before had followed, the inverse correlation of angular size
with redshift for distant galaxies.  I followed the trail here, to
Hypatia, and found the secret of the Redshift !   And, wildly,
unbelievably, the answers to Gravity and the Quasars lay here as well.


In this posting I will relate this tale of discovery, and support it
with examples from the published literature in which an esteemed
researcher, Charles Steidel, unknowingly gives decisive evidence for
this cosmological model.  He had the evidence, but in the end it was I
who was fortunate enough to understand the picture it painted.

Allow me to preface this discussion with a discussion of the clue
which started all this:    At the frontiers of the observable cosmos,
there is an evident inverse correlation between angular size (theta)
and redshift (z).  Many authorities have mapped this correlation, but
it is ignored in today's theoretical thinking as there is no physical
model for such a relationship.  And yet, this relationship is the
cleanest, best-mapped aspect of the distant cosmos.   In a definitive
paper overviewing current cosmological methodologies, 1993 ApJ
413:453-476, Nilsson et al assembled data from many studies, mapped
these together, noted (p469) that "the line of LAS (theta) - z ... in
fact agrees well with the data", and then, before reviewing other
studies, qualified:  "The crucial assumption here is that the linear
size - redshift correlation, if it exists, can be neglected."   

Thus did Nillson et al choose to ignore the clearly-mapped
correlation, and all other studies have done the same.  However, once
upon a time Einstein took a difficult-to-understand precept (the
invariant speed of light) and turned this into a postulate which
revolutionized physics.  Armed with Einstein's example, I have
followed the same course with the inverse-z relationship.  Here's what
I found, and how it led to complete understanding of the Redshift,
Gravity, and the Quasars.

In a normal Euclidean geometry we expect theta (angular size) to be
linearly inverse with distance, i.e. twice as far away, half the
angular size.  Observations show that at great distance, the role of
distance is replicated by redshift.  The only static physical model
that allows this is that of distance being progressively supplanted by
the redshift until at far distances redshift increases with little
change of distance, and yet the "shells of space" continue to increase
in volume with redshift.  This is consistent with a hyperbolic
geometry in which there is a maximum distance of travel but space
broadens more widely than 360 degrees in the long run.  A
little-publicized aspect of hyperbolic geometry is that distant
hyperbollically-expanded shells of space appear smaller (i.e. more
distant) to our eyes because of the required mapping into the
360-degree Euclidean space.

In such a space, you must aim carefully at which distant galaxy you
are travelling to, because if you miss-aim even a little, you will
find at the conclusion of your voyage that you are no closer to your
target!  Lest you deride such a space, Einstein himself postulated
just such a hyperbolic static universe.  However, he did not contain
such a space.  I specify that this space is contained by a
hypersphere, so that the curvature of space resembles the curvature of
a bead, inside & out.  A fine illustration is found at night by
looking through a certain type of frosted bathroom window at a light
source outside -- you will see an admirable hyperbolic curvature in
the center of a sphere (well, obloid) which curves around the exterior
to bound that sphere.  It's quite pretty.

For the rest of this article, I refer to the "surface of the
hypersphere" as though we are looking at its outside, but the
hyperbolic curvature originates from within.  It's no matter.  Let's
move on.

Now, the idea that our universe is shaped as the surface of a
hypersphere is quite common, even typical.  But little attention has
been given to what effect this fourth spatial dimension would have on
our little universe.  It is commonly illustrated that we could be
plucked out of our world into the fourth dimension, rotated, and put
back into our world in reverse!  You'd have to learn to read
backwards, but would probably die of starvation first (since food is
left-rotation oriented).  And yet, it is assumed without thought that
the 4-D curvature of our universe over the surface of the hypersphere
somehow does not affect us.  But here, in this article, we do think
about this.  And just as we can be rotated in hyperspace as in the
above example, so do I postulate that there is a 4th-dimensional
orientation dependent on your position on the hypersphere,
corresponding to polarization.  A 4th-dimensional polarization, or
hyperpolarization.

This will, of course, not stop us from travelling about the
hypersphere (as we do just by travelling within our universe).  As we
move, our polarization re-orients according to the hypersphere's
orientation, and so all is well.  But there is a notable, major
exception to this rule.  And that is those particles which travel at
the speed of light, i.e. photons and neutrinos.

Following the results of the delayed-choice test which conclusively
show that photons do not exist in their own flight paths, John Wheeler
commented "We have no right to speak of the attributes of the photon
before it registers".  We strengthen this point to posit that the
photon has no classical existence between emission and absorption.
Therefore, the photon, when it strikes, will *showcase the 4-D
orientation that it had upon emission*.  

The significance of this comes when you we recognize that we 3-D
dwellers can only perceive our own particular 4-D orientation, and
other orientations are invisible to us.  Thus the photon will be
hyperpolarized, and we see only that part of the photon which
corresponds to our own orientation.  The rest returns to the
hypersphere.  Calculations show that as sin^2 + cos^2 = 1, so the
cos^2 component of the photon is seen by us, and the sin^2 component
is returned to the hypersphere.  Thus, redshift is as:
		z = tan^2 A
where A is the hyperangle between the photon's point of emission and
absorption.  This is the cause of the redshift -- it's just 4-D
polarization.

Now, I've spoken of the cos^2 part of the photon returning to the
hypersphere (and so do the Sun's "missing" neutrinos).  Such a concept
seems to blur the distinction between our universe and the
hypersphere.  Our universe is a self-contained entity, is it not?  NO!
The hypersphere is no dead shell, it is a dynamic ecosystem which is
inseparable from our universe.  The fact that a fraction of the light
"returns" to the hypersphere shows that there is interaction.  There
is therefore, clearly, two-way interaction.  Perhaps, if we re-define
our universe to include the hypersphere, then this would be a closed
system.  (Or perhaps not.)

The next step, when entertaining the concept of a "living"
hypersphere, is to gauge the place of its surface in our universe's
scheme of things.  An immediate connection springs out:  the surface
of the hypersphere is Einstein's gravitationally-bending surface where
General Relativity rules.  Thus mass weighs heavily on the
hypershere's surface, depressing it.  Therefore, black holes, when
dropping their mass out of this universe, simply drop it back into the
hypersphere.  

With these thoughts, we are attacked by Occam's Razor.  The apple
drops to Earth due to Earth's gravity.  Even if the apple did not
gravitate, still it would fall.  But now we see that black holes cause
mass to drop out of our universe into the hypersphere.  The
hypersphere is pulling the mass of our universe!  It is the Earth and
we are the apple!!  And so we shout EUREKA!  This is why gravity
cannot be united with the other three forces into a unified theory.
This is why quantum gravity will not work.  It is because gravity is
not a force of this universe!  Gravity is a force of the hypersphere,
and so external to this universe!  This is the secret of GR's success,
as Einstein had the vision to map the surface of the hypersphere even
though he did not see the bigger picture.  And this is why no unifying
theory will work, as you cannot unify within our universe a force
which belongs to the hypersphere without. 

Thus, Gravity is solved as being a feature of the hypersphere.  The
closer to the hypersphere's center, the stronger the gravitational
force.  But that means there are regions of greater & lesser
gravitational potential on the hypersphere's surface, depending where
there are valleys & hills, etc.  And these valleys & hills will roll
as the hypersphere will determine.  Thus this is how a static universe
retains its distribution of galaxies -- gravitational potential shifts
around.  The consequences are immediate -- the "Great Attractor" is an
empty region which has slumped to become a valley on the hypersphere's
surface.  The "Great Wall" is a long-standing valley.  And empty
regions in space are, on average, "highlands" on the hypersphere's
surface.   

What about the CMB?  Ah, it's just the ambient temperature of the
hypersphere, or perhaps a ghostly shadow of radiation which is
traversing our universe as it radiates in a 4-D direction outwards.
But the CMR's radiation certainly contributes to the forming of new
atoms of matter in deep space, as per the usual
virtual-particle-to-real-particle method.  So is that it, is that how
the hypersphere returns matter to our universe -- just with the CMB?
Certainly not.

Note that when gravity deforms the surface of the hypersphere, the
hyperangle between nearby places increases.  Thus we have a
gravitational redshift.  Now, cosmologists have only ever thought of
massive objects gravitationally depressing the surface of the 4-D
manifold.  However, now we know that the 4-D manifold is just the
surface of the hypersphere, the vibrant thumping hypersphere.  If
black holes donate clumps of matter to the hypersphere, will the
hypersphere return the favor?  Certainly.  Volcanoes.

Just as with Earth, we can posit that a hypersphere such as we have
described will push matter back into our universe, volcano-style.  But
volcanoes are not depressions, but mighty towers!  Could the
hypersphere push huge towers of gravitational potential into our
universe, from there to spew mighty loads of matter?  Certainly!
There are the Quasars.   What, you jeer at my claim?  I will *prove*
it, using the research of Charles Steidel.

First, let's carefully predict the qualities of such Quasars, then see
if they conform to observation better than current models.  The quasar
will be an emission of mass & light which rush downhill, pouring down
into our universe from the apex of high gravitation potential.  The
first point is that this cone of high gravitational potential will be
seen (by nearby galaxies) to be highly redshifted as the angle tan^2
will be large due to the peak of high gravitational potential (like
the high slope of a volcano).  The second, and key, prediction is that
of General Relativity.  Just as light bends around a gravitational
well, so would light reflect off a gravitational tower.  This means
that a volcanic quasar will bear, on its slopes, the shrunken images
of optically nearby galaxies.  Do we see such things?  Yes we do!!
Let us consult the research of Charles Steidel.

Dr. Steidel has been trying for years to map the influence of
galaxies' haloes on the light from quasar 3C336.  In 1992 he published
(with Mark Dickinson) the paper ApJ 394:81-86 where he carefully
mapped the visual environment of this quasar (at z=.9265) and tried to
identify a set of small galaxies almost obscured by the quasar's glow.
In the event it proved very difficult, but Steidel tentatively
concluded two of the little galaxies were of the observed z-values of
z=.656 and z=.8912.  But two of the more optically distant galaxies
have just these redshifts!  Are the "little" galaxies reflections of
the quasar's gravitational tower?  And why were 3 of Steidel's
observed redshifts just resonances of eachother? 

In 1997 Steidel et al published a further paper on 3C336 (1997
ApJ...480...568S) which uses HST observations and others to get to the
bottom of this mystery.  But it still makes no sense.  Steidel
forlornly writes "Previously published reports of a cluster around
3C336 were largely misled by the presence of many foreground galaxies
seen in projection near the QSO.  It is possible that a reported
measurement of weak shear gravitational lensing in this field may be
produced by the QSO cluster itself, since there appear to be no other
groups or clusters in the foreground."  Steidel is saying that there
is *no other collection* of "foreground galaxies" like the one wrapped
around 3C336, anywhere nearby!  Steidel follows the standard belief of
positing that the quasar is further away than the galaxies, and
wonders why "foreground" galaxies (of varying z-values) appear to be
clustering around the more distant 3C336 (he is evidently even
considering some type of "gravitational shear" to rescue this
conundrum!).  Note that other studies also find this same dilemna,
clusters of small "nearby" galaxies of different redshift optically
oriented around the more distant quasar, without similar such
clusterings elsewhere.

But we have the solution!  The quasars are not more distant, they are
nearby objects!!  The clusters of small galaxies are images of more
distant galaxies reflecting off the quasars' gravitational towers, as
General Relativity prescribes!  The mystery is solved, and quasars are
revealed to be modest objects located not too far from our own galaxy.
Observe that this even handles those magnificent photos where we see
apparently distant quasars' light bent around both sides of some
distant intervening galaxy.  In fact, the quasar is not distant, and
the galaxy is just a shrunken image of an optically nearby galaxy
which has been reflected off the quasar's gravitational tower right
down the middle.  What a trickster you are, General Relativity!! 

Now the life cycle of the quasar is clear to see.  The hypersphere
pushes matter against our universe, and a swelling ensues,
volcano-style.  This selling builds a great gravitational mountain.
Eventually the matter erupts from the mountain, and this cataclysmic
eruption is probably signalled by the gamma-ray bursts -- that is, the
gamma-ray bursts signal the birth of quasars.  The Quasar first erupts
at high-redshift values, due to the high gravitational slope (and
resultant high tan^2 value).  As the matter disgorges, the quasar
slowly loses its gravitational potential (i.e. the mountain gets
smaller) and so the redshift reduces.  Eventually, when the quasar is
depleted the newly-injected matter, if there's enough of it, will be
able to form a proto-galaxy.  Note that young small galaxies will
retain some of the gravitational plateau left over from the quasar,
and so will be somewhat more red-shifted than larger older nearby
galaxies -- in accordance with observation.

Of course, you know what this means:  Halton Arp is right about
quasars!!  He was right all along.  But I had no idea, when I set out
on my journey, that I would come to this result -- I had been quite
convinced, by those spectacular photographs of galaxies splitting
"background" quasars' images, of the opposite.  So does the tide of
events spin us about.

Another point is the fate of the Sun's "missing" neutrinos.  These
neutrinos are emitted near the Sun's core, and thus bear the
gravitationally-sourced hyperangle found there.  The neutrinos appear
to respond to the hyperangle with transmission percentages, akin to
normal 3-D polarization.  Thus the number of neutrinos which disappear
into the hypersphere go as mass(sun)/mass(minimum black hole).  This
is in accordance with observation once again.

So, by realizing that the universe's hypersphere is no dead object,
but a "living" contributing member of the universal eco-system, we
have found many secrets.  It all makes sense now, gravity, quasars,
redshift, black holes, the Great Attractor, neutrinos, and the CMB as
the hypersphere's signature.  The hypersphere is the steward of our
universe, just as the Sun is the steward of our solar system.  

The Sun has a name (Sol), and the hypersphere deserves a name also.
Hypersphere, what shall I name thee?  Hyp- something, to be sure.  Ah,
I have it.  Hypersphere, I name thee HYPATIA, after the 6th century
Greek mathematician & scientist who died for the cause of rational
thought.  May her tradition of rational thought live forevermore in
eternal HYPATIA.

Eric Flesch  (copyright of text & ideas)
Nelson, New Zealand
January 9, 1998.