WHERE IS THE HIDDEN MASS OF THE UNIVERSE?
(C)1993 Alan M. Schwartz
The Big Bang was the explosion of space/time that birthed the
universe. The 2.7 kelvin black body microwave radiation
permeating all space is an echo of that singular event. The
large scale distribution of galaxies supports this view. They
are strewn in a truly colossal foam - bubbles of not much bounded
by walls and lines teeming with stuff. The tremendous curvature
of the cosmic egg relaxed over time. Though space appears to be
Euclidian, it does not contain enough overt matter to be so.
If space is filled with a surfeit of matter gravity will overcome
velocity, expansion will eventually cease and then reverse into
collapse. Its overall form would possess positive curvature, the
geometry of Bolyai and Lobachevshy. The sum of the interior
angles of a triangle always would be more than 180 degrees.
There would be no line (shortest path between two points,
geodesic) parallel (never intersecting) to a given line. The
circumference of a circle would be less than the pi(diameter).
The surface of the Earth has positive curvature in two
dimensions. A mile square bounds more than a square mile and
surveyors are elliptic geometers.
If space is filled with the right amount of matter it will expand
at an exponentially decreasing rate, trading kinetic energy for
gravitational potential, and asymptotically approach zero radial
velocity. Its overall form would possess zero curvature, the
geometry of Euclid. The sum of the interior angles of a triangle
would be exactly 180 degrees. There would be just one line
parallel to a given line. The circumference of a circle would be
equal to pi(diameter).
If space is filled with an deficiency of matter it will continue
to expand without limit, there being insufficient gravity to
convert the kinetic energy of expansion into gravitational
potential energy. Its overall form would possess negative
curvature, the geometry of Riemann. The sum of the interior
angles of a triangle always would be less than 180 degrees. There
would be an infinite number of lines parallel to a given line.
The circumference of a circle would be more than pi(diameter).
Observation implies that space is indeed Euclidian but that only
10% of the mass/energy necessary to enforce such a condition
exists. Short of setting up two mirrors and a laser into a
triangle a few billion miles - or light years - on a side to see
what is what, we are left with a quandary. Where is the missing
matter to enforce a flat 3-space?
Astrophysicists postulate cold, dark matter - collections of mass
invisible by direct view but necessary for the studied rotational
dynamics of galaxies. They postulate a tiny neutrino mass which,
given the neutrino soup permeating all Creation, might do the
trick. They postulate families of weakly interacting particles
like WIMPs, non-baryonic matter, rare but hypermassive cosmic
strings and loops born as phase boundary imperfections in the Big
Bang, MACHOs, and still their fevered minds fail to find enough
mass to close reality.
What does not adequately exist might be conveyed like a credit
voucher. Quantum mechanics and its Heisenberg Indeterminacy
Principle allow for the natural creation and uncreation of
mass/energy uplifted from and returned to a seething ocean of
virtual states if the product of the uncertainties of duration
and quantity do not exceed Planck's Constant divided by four pi -
an admittedly minute number: 5.27x10^(-35) Joule-sec. Vacuum
self-energy is experimentally accessible through the mostly
trivial experiment of bringing two exceedingly flat grounded
metal surfaces in a vacuum extremely close together, whereupon
they experience a net attraction by polarizing evanescent "stuff"
which does not exist in classical physics.
That vacuum self-energy, on the average, does not exist does not
remove accountability for the gravity accompanying quantum peeps
into substance. Turning off a flashlight does not affect the
light beam already emitted. The distortion of space/time caused
by mass/energy propagates regardless of the fate of the source.
Stuff may come and go by Heisenberg's rule, but after it pops in
from virtuality its gravity persists though it itself must return
to nothingness.
If the universe were not so empty Heisenberg would allow less of
the virtual maelstrom to surface. Where it even emptier, more
spontaneous creation/uncreation would flare. Nature does indeed
abhor a vacuum, though it must be a very empty vacuum and her
attention shifts from attosecond to attosecond. What a fine
construct the space-time continuum is, materializing from its own
bellybutton and adjusting itself to our convenience over a broad
range of boundary conditions! Either that, or somebody had
better get busy adapting Newton's orbits to Riemann's geometry.