THE NOT SO BIG BANG
(C)1995 Alan M. Schwartz
Is space flat? Will its every triangle sum three interior angles
to precisely and exactly 180 degrees? Astrophysicists and
astronomers have discovered, extrapolated, hypothesized, begged,
borrowed and stolen 10% of the mass mandatory for flat space.
Euclid's space (flat, zero curvature) has less volume/area than
Riemann's space (hyperbolic, negative curvature, triangles
holding fewer than 180 degrees). If space is not flat, astronomy
must be reinterpreted. Learned stomachs acidly smolder in search
of truth, or at least tenure. Whatever the shape of space, it is
avowed that it all erupted in a Big Bang - an explosion of, not
in, space and time to inflate all reality. We look deep into
space with huge, complex and subtle instruments to look back in
time, seeking the cosmic egg. Are we on a fool's errand?
An expanding universe will reveal itself if it retains uniform
physics throughout its substance. As we look deep into it the
objects we espy will recede at radial velocities increasing as
their distance and independent of our observation direction,
characterized as the Hubble Constant. Lightspeed is invariant.
Looking deeper into space is looking backward in time. If space
is hyperbolic rather than flat, the same obtains but at a rate
changed by the degree of curvature. Given the Hubble Constant
and space-time geometry, we can predict the distance of view
needed to reach back to time zero, the Big Bang.
A signal of constant frequency is observed at increasingly lower
frequency the faster its apparent recessional velocity - the
Doppler shift. If we know the Hubble Constant, measure the
Doppler shift of spectral lines, and know the shape of space, we
know how far back in time we are viewing. The Hubble Constant,
if it is constant through the vastness of space, is in legitimate
dispute. The universe got a push start between 5 and 15 billion
years ago. Shall we have a look?
To image an object 5 to 15 billion lightyears away we will need
massive magnification. A vanishingly small area of sky will be
tremendously enlarged until it presents a finite image. The
information-bearing energy within that infinitesimal patch is
negligible. Our optic or antenna must be very large indeed to
capture two kinds of information necessary to create an image:
We need intensity data, proportional to the surface area of our
viewer, to collect the amplitude of signal necessary to raise it
above random noise. We need phase data, proportional to the
extent of our viewer, to give the image form. The Very Long
Baseline Array is ten 25-meter wide microwave dishes spanning
from Hawaii to the Virgin Islands. With clever signal summing
and this antenna some 5,000 miles wide and 52,000 square feet in
area we should be able to look right back to the beginning of
all, except we don't.
The universe is permeated by a whisper of microwave radiation
typical of a 2.7 degree Kelvin blackbody radiator. This is the
echo of the plasma-hot Big Bang cooled by adiabatic expansion of
the universe, said cooling proportional to the cube of the
distance (volume of expansion). As we look back in time to
smaller expansions, we expect the cosmic background to warm up to
increasingly higher frequencies, rapidly! Blackbody emissivity
varies as the fourth power of its temperature (Stephan-Boltzmann
law). As we approach the Big Bang our target will grow much
brighter! As we look deeper into space we expect increasing
Doppler shift to lower frequencies. No matter where in the sky
we look, if we look deeply enough, everything should dribble away
to black save the singular actinic spike of the Big Bang driving
the expanding wedge of reality into... a problem for philosophy.
We can already image distant quasars with much smaller antennas
such as the Very Large Array (27 dishes in Socorro, NM), Merlin
(seven antennas over 200 kilometers in western and central
England) or the Giant Metrewave Radio Telescope (30 45-meter
dishes spread over 25 kilometers at Narayangaon, India).
Measured redshifts, assuming no confounding footnotes, suggest
quasar ages near 14 billion years. Higher estimates of the
Hubble Constant mandated by the Hubble Space Telescope would make
those quasars half as old, but still 90+% of the age of the
universe, said age itself inversely proportional to the Hubble
Constant. Why cannot the leviathan instruments of modern
technology push that little bit deeper, right to the beginning?
Something is very wrong, and in a very big way! Is space
Euclidian? Is the Hubble Constant constant? When all the fudge
factors and diddle constants are firmly in place, where is the
Big Bang?