alan@oz.nm.paradyne.com (Alan Lovejoy) (01/08/90)
For more information on the life and work of Roger Penrose, I HIGHLY recommend
the book "Superstrings and the Search for the Theory of Everything" by
F. David Peat (Contemporary Books, 1988 ISBN 0-8092-4637-6).
Penrose is researching very fundamental questions regarding space, time and
quantum processes. His original insight (or hunch) was that quantum
particles are not born into a background space-time, but rather space-time
is created as a result of even more primitive quantum processes. In other
words, space-time is merely an effect of more fundamental relationships
between quantum particlces. In particular, in Penrose's formulations,
each quantum particle creates its own space-time and defines its own geometries.
That is, not only is space and time considered to be relative, but so is
geometry itself. Just as relativity theory introduced a new invariant (the
speed of light) to replace the dethroned ones (space and time), so does
Penrose: the "light ray" or "null line," which is a creature of complex
number spaces. A null line is the path taken through space by a massless
particle, such as a photon. Null lines have "zero length" (an observer who
travels at light speed always experiences a trip time of zero, since his clock
is not running). Penrose postulates that such null lines are the only "real"
directions. The geometry of a space in which only null lines exist is said to
exhibit a property called "conformal invariance," which means that the geometry
is invariant under scale and/or distance transformations. Mass and energy
can only exist in a universe whose geometry permits the conformal invariance
symmetry to be broken (since only massless particles can travel along null
lines.)
Penrose has constructed (created out of whole cloth) a geometry based on
null lines and spaces with complex dimensions. (Chaos theory is based on
spaces with real-number dimensions; classical geometry is based on spaces
with integer dimensions). The key to this geometry is an object called
a "twistor," which evolved from "spinors." Spinors are used in quantum theory
to describe the behavior of particles with angular momentum ("spin"). Twistors
have both angular and linear momentum, which may be the key to unifying gravity
and quantum mechanics. The coordinates of a twistor in twistor space are
complex numbers. In twistor space, a twistor is a point. By projective
geometry, it is possible to translate objects in twistor space into their
real-space equivalents. The real space equivalent of a twistor whose helicity
("twistyness") is zero
[ helicity(Z) = Z/2 * Z (where Z is any twistor) ]
corresponds in real-space to a null line. Points in real space correspond
to lines in twistor space ALL OF WHOSE "POINTS" ARE TWISTORS WITH ZERO
HELICITY! (Not all twistors have zero helicity.) This could be thought
of as a proof that all points in real-space are intersected by null lines!
Note the nonlocalities that are inherent in the relationships between
real-space and twistor space--and the non-locaclities which cause so much
puzzlement in quantum theory. Penrose is trying to prove that the primitive
geometry of quantum particles is a four-dimensional twistor space, and that
Einstenian space-time is a large-scale effect of quantum interactions in
twistor space. Certain transformations or processes in twistor space turn
out to be equivalent to quantum processes in space-time. And, as with
any transformation, the basic geometrical untis become interchanged. In this
case, a quantum transform of twistor space mixes up the twistors. But since
points in space time are defined in terms of the conjunctions of these
twistors (a series of points in twistor space) this means that the space-time
point WILL SMEAR OUT. At the quantum level, the twistor space picture
suggests that points in space-time lose their distinction and become "fuzzy."
Just like quantum particles.
A twistor with a positive helicity corresponds to a collection of null lines
in space-time which twist around each other in a right-handed sense. A twistor
with negative helicity corresponds to a collection of null lines in space-time
that twist around each other in a left-handed sense. Chirality (handedness)
in space-time can thus be seen as a function of the helicity (twistiness)
of twistors in twistor space.
Penrose would like to be able to model both gravity and quantum processes
by means of interactions among twistors in twistor space. He has found many
intriguing indications that gravity (space-time curvature) can be modelled
by quantum-like operations on twistors in twistor space.
Edward Witten at Princeton (Mr. Superstrings) thinks that twistor space may
be the proper starting point for a quantum theory of gravity.
____"Congress shall have the power to prohibit speech offensive to Congress"____
Alan Lovejoy; alan@pdn; 813-530-2211; AT&T Paradyne: 8550 Ulmerton, Largo, FL.
Disclaimer: I do not speak for AT&T Paradyne. They do not speak for me.
Mottos: << Many are cold, but few are frozen. >> << Frigido, ergo sum. >>