+ A Theory of Everything Takes Shape
--String theory was a set of unsolvable equations writeen down in the 60s to
describe collisions of protons in accelerator experiments.
--Later saw equations viewed as describing a new kind of fundamental particle :
infinitesimal, one-dimensional strings which vibrate and interact which accounts
for all known forms of matter.
--Then those equations required the existence of gravity to be consistent ,
which made string theory the sole viable candidate for a single theory uniting
the large-scale realm of gravity and the microscopic realm governed by the other
forces of nature.
--The cases studied were either vastly too simple or complex.
--Theorists have discovered five consistent distince formulations of string
equations, each describing a different type of fundamental string, which for a
supposedly unified theory of everything can be considered moderately
embarrassing. 10dimensional universes. String theorists use compactifications
to hid the 6 superfluous dimensions, leaving them with the 3 of the real world.
But the equations say nothing about how to choose one over another. Thus impasse.
--String theory is rife with dualities, i.e. apparently different formulations
of the theory are actually equivalent. String theorists have learned that their
equations permit the existence of a whole new zoo of potentially fundamental
objects from strings and magnetic monopoles to minuscule black holes and even
five dimensional bubblelike membranes! At the same time, they have found that
all these objects and all five different formulations of string equations appear
to be simply different manifestations of the same underlying theory.
--Dualities are powerful tools, a problem unsolvable in one formulation is
solvable in another.
++ Imperturbable equations.
--The sticking point is that the unification of quantum physics and gravity that
string theory aims to describe can take place only at the plank energy scale
(18 orders of magnitude higher than the energies achieved by the most powerful
accelerators).
--But it does have a "low-energy" side -> supersymmetry. Supersymmetry
postulates a relation between the particles of matter, known as fermions and the
wavelike particles called bosons. that mediate forces. In known physics, those
two classes of particles seem distinct, but supersymmetry holds that for each
existing fermion there must be a matching boson and vice versa.
--But we have yet to discover the superpartners.
--Obstacle :
String theory has remained unamenable to the techniques that physicists studying
quantum theories have traditionally used to calculate physical processes.
--Because of uncertainty inherent in the world of quantum physics, any theory
attempting to describe the interaction of particles and forces has to take into
account an infinite complex of possibilities, which makes the equations
impossible to solve exactly. Only way is to use approximation or perturbation
theory.
--Electromagnetism (quantum electrodynamics) QED, might want to compute what
happens when two electrons approach each other. The most likely thing to happen
is nothing. The next most likely thing is 1 electron will emit a photon and the
other will absorb it and thereby scatter. So in QED, the outcome isthe sum of
these possible interactions, multiplied by ever increasing powers of a number
called the fine structure constant, which is a measure of the probability of
interaction of two particles. --In QED, coupling constant is 1/137. Since
powers of 1/137 approach zero quickly QED agrees with experiment. If the
coupling constant > 1 , (like with strong interactions) like the strong force
that holds quarks. protons, and neutrons together then you're out of luck. A
perturbation expansion will grow with each successive term, never converging on
an answer. QCD the existing theory for the strong force.
--String theory also has to explain strong coupling scenarios like nuclear
binding. Theorists study extremely simplified versions of the equations "toy"
theories not likely to bear much resemblance to reality. 10-dimensional string
theories or 4 dimensional supersymmetry theories that are an ingredient to
string theory. They contain not just one supersymmetric relationship between
fermions and bosons, but lots of them. The relevant mathematics permits up to
eight supersymmetries, and although theories with more than one (known as n=2,
n=4 , or n=8 supersymmetry) are mathematically incapable of generating "real"
physics, they are increasingly easy to study and solve.
--The added symmetries are a powerful tool, but the closer we get to the real
world, the fewer symmetries there are, and the fewer tools we have to analyze the
theory. Need a non-perturbative string theory. Dualities, promises a way to do
just that.
+++Making connections
Does the electron (the fundamental unit of electric charge) have a counterpart
- the monopole? an eliusive and so far undetected particle which carries an
isolated magnetic charge. This "duality" between electric and magnetic charge
was first proposed by British theorist PAM Dirac in the 1930's who wrote it into
the theory of electromagnetism to make the theory consistent with quantum
mechanics. Dirac's monopole had several noteworthy characteristics.
For one, if the electric charge was small, the magnetic charge of the monopole
has to be large and vice versa.
--Dirac's monopoles played little role in physics for the next40 years. In the
early 70's Gerard t'Hooft of the University of Utrecht in the Netherlands and
Alexander Polyakov of Princeton showed that monopoles arose naturally as
solutions of grand` unified theories (GUTs) , which attempt to unify all the
forces of nature except gravity. Their work led Claus Montonen of the
University of Helsinki in Finland and David Olive (U of Wales) to suggest in
1979 that certain GUTs might have aduality between electric and magnetic
charges, similar to the one Dirac has proposed.
--If the duality really existed, they added, the inverse relation between the
monopole's charge and the electric charge implied that excchanging monopoles
for electrically charged bosons would also flip-flop a theory from strong
coupling- which was not amenable to perturbation expansion - to weak coupling,
which was. In other words, if a theorist came across an unsolvable strong
coupling scenario in one GUT formulation, he could look at its inverse in the
weakly coupled formulation and solve the equations that way - on the other hand
Montonen and Olive managed to produce little evidence that GUTs really had this
electric-magnetic duality and for the next 10 years everybody forgot about it.
--In 1989 electric magnenetic duality began attracting new interest from string
theorists , who by then were at an impasse. Harvey & Atish Dabolkhar of Caltech
said electrically charged string could be dual to solitons - hypothetical
particlelike objects that include magnetic monopoles. That same year
Strominger proposed an even more bizarre duality : between strings and objects
called five-branes. A Five-brane is a five-dimensional analog to a string
(five-brane is short for "five-dimensional supermembrane"), and Strominger found
that this 5-dimensional object is a solution to the equations of string theory and
could be a fundamental object justl ike a string. The equations also suggested
that in some way these 5-branes were dual to 1-dimensional strings in the
same way that electric charges and magnetic charges were dual in Montonen and
Olive's conjecture.
--The dualities proliferated when Duff made an excursion from the 10 dimensions
to 6 dimensions. Duff suggested that if a 5-brane were wrapped around a
4-dimensional space known as a manifold in a six-dimensional universe, what
would be left would a 1 dimensional object - a string, one of the five varieties
described in string theory's various formulations. If , as strominger has
suggested another species of string was dual to these five-branes-turned-strings,
there might be a duality between two different types of strings, albeit one that
only existed in a six dimensional universe.
--The pieces fell together. Ashoke Sen of TaTa Institute in India showed that
electric-magnetic dualities Montonen and Olive had proposed for GUTs really exist
in a 4-dimensional supersymmetry theory. Then N. Seiberg of Rutgers with Ed
Witten of Princeton showed that these dualities could open the way to analyzing
a supersymmetric theory plagued by strong coupling.
--Chris Hull of QMC in London and P. Townsend of Cambridge conjectured that the
electric-magnetic dualities not only exist in a 6-dimensional string theory, but
are much more powerful than ever before imagined. In this case the dualities
link not electrons and monopoles but two of the five different kinds of strings
that theorists have envisioned, iknown as heterotic and type II Strings.
--Earlier, string theorists had written off type II strings as part of a theory
of everything because these strings implied a universe without charged particles.
To solve this problem, Hull and Townsend invoked the possibility of another
duality. Their hypothetical charge-bearer is called an extremal black hole- the
theoretical end of the line for charged black holes, which are believed to
evaporate gradually through Hawking radiation. Hull and Townsend suggested, that
these black holes might be dual to strings, in the same way that magnetic
monopoles are dual to electrons in the four-dimensional theory.
++Web of dualities
Witten wrote a paper in March 1995. He provided new evidence and
codified how many of these things ought to work and discarded other things which didn't work.
On the one hand, the dualities seemed to have opened the way
for the fundamental particles of string theory to be almost anything - any of the various string formulations, monopoles or five-branes, or even the extremal black holes. Much of the
present excitement was generated when Strominger and Morrison showed the black
holes could turn into strings and vice versa (Science 23 June p1699).
The unique positions that strings occupied has somehow vanished, since strings, black holes and
membranes - all these higher dimensional extended objects - have a part to playi n the big picture.
--What once appeared to be five distinct theories we now know are all equivalent to each other. It is now clear there is just one string theory which is nice, since only one known theory consistent with gravity and quantum mechanics. We only need one.
--We now have the tools to explore theories with less supersymmetry and greater realism.
Witten and Vafa were writing paper for theory with n=1 supersymmetry.
--Its like a primitive society finding some advanced tool left behind by some other culture. You push one
button it does one thing, push another it does something else.
+ Isolation of the Heterofullerene C59N as Its dimer(C59N)2
The heterofullerene ion C59N+ is formed efficiently in the gas phase during fast
atom bombardment mass spectroscopy of a cluster -opened N-MEM (N-methoxyethoxy
methyl) ketolactam. This transformation is shown to occur also in solution in
the presence of strong acid, affording biazafullerenyl (C59N)2 in good yield.
It is proposed that the azafullerene dimer is formed upon in situ reduction of
the highly reactive azafulleronium ion. The isolation and characterization of
biazafullerenyl opens a viable route for the preparation of other
heterofullerenes in solution
+ A Stable high-index surface of Silicon: Si (5 5 12)
A stable high-index surface of silicon Si (5 5 12) .
This surface forms a 2x1 reconstruction with one of the largest unit cells ever
observed, 7.7 angstroms by 53.5 angstroms. Scanning tunneling microscopy (STM)
revals that the 68 surface atoms per 2 x 1 unit cell are reconstructed only on a
local scale. A complete structural model for the surface is proposed,
incorporating a variety of features known to exist on other stable silicon
surfaces. Simulated STM images based on this model have been computed by first-
principles electronic-structure methods and show excellent agreement with
experiment.
--fin
