COMING SOON TO YOUR STELLAR NEIGHBORHOOD - MANKIND!
(C)1993 Alan M. Schwartz
Newton's physics and his and Leibniz' calculus are analytic
bedrock. All but "pathological" functions yield to delta-epsilon
decomposition, precursor of integration (containment) and
differentiation (rate of change). Singularities can be cleverly
massaged or approached asymptotically. The universe ran like
clockwork as the 19th Century waned, a Berne patent clerk
wondered about light, and Bohr fretted over his atoms.
Postulating that information cannot convey at speeds beyond that
of light, Albert Einstein declared Relativity. Experimentalists
suspected something was odd about reality, hence the Michelson-
Morely experiment and Lorenz' contraction. Maxwell's equations
relating charge, current, magnetism and electromagnetic radiation
were covariant with Relativity. Extant physicists were horrified
by rubber rulers, variable clocks and cause and effect that were
not strictly ordered. Einstein may not be complete, but he is
accurate beyond refutation - by experiment and observation.
Quantum mechanics appeared as Bohr's crude rationale where
Newton's physics failed - on the atomic sale. It evolved into a
world described by wavefunctions, virtual states and transition
probabilities. Quantum entities were slippery, being neither
bounded particles nor diffuse waves. Action became granular as
it yielded to quantized descriptions. Reality was only defined
upon observation. It ran counter to common sense. It was
verifiable to seven decimal places and more. Einstein went to
his grave denying it as his detractors had denied him.
Mankind is aggressive, rich with culls and waste, and running
short of assets and elbow room. Humanity is too fragile to keep
all its eggs in one Terran basket. Our best will move into space
for conquest and reproduction throughout our galaxy. Relativity
requires a state initially below lightspeed to approach a
mathematical singularity at lightspeed. Mass goes to infinity,
dimension in line of travel goes to zero, and time stops as
viewed by external observers. Given the size of the universe,
the speed of light and our lifespan, we are solidly stuck at
home. We either finesse Relativity or we are quarantined.
Planet-sized nuclei, neutron stars, are no hurdle for Relativity.
Transient mass densities so great that neutrinos are reflected,
the nascent rebound of the outer layers of an exploding Type II
supernova, hardly disturb the continuum. A Black Hole gives it a
good thump, but we are lacking samples within reach. Particle-
antiparticle accelerators recreate ultramicroscopic conditions
near those postulated for the Big Bang. Einstein prevails.
Where Relativity and quantum mechanics claim the same turf with
different predictions - the Einstein-Podolsky-Rosen Paradox and
the Bell Inequality - quantum mechanics wins. Inciting a pair of
photons to thumb their noses at old Albert is a good start.
Interstellar colonization will require something rather larger.
A decimal point followed by an infinite string of ones can be
more succinctly conveyed as the fraction 1/9. Newton's seven
refractive colors - red, orange, yellow, green, blue, violet and
indigo - were born of the concept of the octave in a god's
perfect universe. No pristine Terran culture has been discovered
that so partitions the spectrum. Idiom defines perception.
Quantum event models are contained within a Newtonian universe of
well-behaved functions. Infinities are tamed by renormalization.
Classical functions are dulled by quantum mechanics' tight weave.
Breaking the structure of a universe swaddled in dense virtual
assemblages of particles and states requires a chisel whose edge
cannot be blunted by the infinite magnifications of delta-epsilon
analysis or the finite intervals of quantized action. Quantum
mechanics might better reflect fractal and chaos theories wherein
evolving structure is intrinsic to the description itself. No
magnification will disclose a simplification of form. Our chisel
will be unceasingly self-sharpening, always outracing its target.
Quantum particles with half integral spins are fermions. No two
fermions may share all the same quantum numbers. Fermion arrays
stack into serially higher energy levels, each containing a spin
up/spin down pair. The Earth does not collapse into a plum-sized
lump and then the zero dimensional singularity of a black hole.
Its atoms' electrons stay inflated in their orbits and its atoms'
nucleons in their nuclei likewise, supported by the ghostly hand
of Fermi statistics. Fermion pairs arise from the symmetries of
the array of functions that are the model of half integral spin.
In one dimension we know mathematics wherein bifurcation is an
intrinsic property of the system - the Verhulst process. It
delivers the eerie Feigenbaum number, 4.6692016091029906718532038...
the limiting ratio of successive generations of iterations'
across a staggering and apparently unrelated set of physical
phenomena varying from turbulence onset in fluid flow to
population dynamics. Chaos contains vast and powerful dominions.
The Keplerian triumph of planets' heliocentric orbits was not in
its initial accuracy - epicycles did marginally better when
circular orbits were assumed - but in the remarkable simplicity
inherent in using better language. An eight-lobed rose in
Cartesian coordinates, (x^2+y^2)^5=16a^2(x^3y-xy^3)^2, lacks the
grace of its form in polar coordinates: r=a(sin 4[theta]). Is
quantum mechanics the modern equivalent of a summation of
epicycles waiting to be cast out by a single well-placed ellipse?
Is heterodox thought worth pursuing? A variation of the Bell
Inequality experiment races a pair of quantum-correlated photons:
one flies through free space only, the other also tunnels through
a classically impenetrable barrier. On those occasions when both
photons arrive, the one that did the tunneling arrives first.
Traversal of a classically forbidden energy region appears to be
instantaneous, if only probabilistic (poor publicity for an
interstellar cruise ship).
Prompt travel across our galaxy would pale even "Star Trek."
With no time in which to lay in course corrections or abort
transmission, recoverable errors will be the stuff of legend.
Prompt travel would also support a very lopsided game of "Last
Tag" with a belligerent opponent. If they discover us, we are in
trouble. If we discover them, they are in trouble.
The future holds no berths for those who have grown comfortable
within their ancestors' nightmares. Our culture of physicists,
scientists and mathematicians is supported by government grants
awarded by peer review to orthodox standard bearers. I believe
that it is worth a pause and an investment to look at how we are
looking in addition to looking at what we are seeing. We will
all be damned if it is not a human serving the unlawful detainer
when God is displaced in his Heaven by a worthier competitor.