As 2013 approaches, one may be left wondering where all the marvelous 2015 inventions of Back to the Future 2 are. It seems the motorized Nike's worn by Marty McFly do exist (as Nike Air MAGs), but as of now cost a pretty penny to purchase. However, the shoes aren't even the coolest invention featured in the movie, as hoverboards steal the spotlight in the 1989 film.
Let's suppose hoverboards may be possible. How will they work? Could they be a type of antigravity device? Antigravity turns out to be quite natural in extended supergravity theories, as pointed out by the late Joel Scherk. The supergravity multiplet in the N=2,8 cases contains in addition to the graviton, a spin-1 vector field (graviphoton) and in the N=8 case, a graviscalar. The graviphoton behaves like a massive photon, prone to couple with gravitational strength, and unlike the graviton may provide a repulsive (as well as attractive) force, giving rise to a type of antigravity. Could a real life hoverboard operate using graviphoton fields? Perhaps real life hoverboards will employ superconductor/topological insulator pairs to accomplish the needed levitation effect. Stay tuned.
Jim Gates is back with another paper on Adinkras, which are graphs describing supersymmetric equations. Just as a weight-space diagram is a graphical representation that
precisely encodes the mathematical relations between the members of
SU(3) families, so an adinkra is a graphical representation that
precisely encodes the mathematical relations between the members of
The extra fun comes from seeing SUSY through the lens of error correcting codes. In the figure below, pick the bottom dot as a starting point and assign it an address
of (0000). To move to any of the dots at the second level requires
traversing one of the coloured links. There are four distinct ways in
which this can be done. To move to any dot at the third level from the
bottom dot requires the use of two different coloured links, and so on
for the rest of the adinkra. In this way, every dot is assigned an
address, from (0000) to (1111). These sequences of ones and zeros are
binary computer words.
To accomplish the folding that maintains the SUSY property in the
associated equations, we must begin by squeezing the bottom dot together
with the upper dot. When their addresses are added bit-wise to one
another, this yields the sequence (1111). If we continue this folding
process, always choosing pairs of dots so that their associated "words"
sum bit-wise to (1111), we can transform the adinkra on the left-hand
side to the one on the right in the figure below.
Thus, maintaining the
equations' SUSY property requires that the particular sequence of bits
given by (1111) be used in the folding process. The process used to meet
this criterion happens to correspond to the simplest member of the
family containing the check-sum extended Hamming code.
Motivic homotopy theory is the homotopy theory for algebraic
varieties and, more generally, for Grothendieck's schemes which is based
on the analogy between the affine line and the unit interval. Ultimately, motivic homotopy theory is expected to provide
techniques to solve problems in algebraic geometry such
as various standard conjectures on algebraic cycles, Beilinson-Soule
vanishing and rigidity conjectures, the Bloch-Kato conjecture etc.
Unlike many other approaches tried in the past decades, motivic
homotopy theory aims to understand the category of algebraic
varieties internally, i.e. without explicit use of such
constructions as Betti cohomology or Hodge structures which require external topological or analytic tools.
In its current state, motivic homotopy theory has as its primary objects of study categories of three types: the unstable A1-homotopy categories, the stable A1-homotopy
categories and the triangulated categories of motives. Each of these
types consists of a family of categories depending on the base scheme
and in the two latter cases on the ring of coefficients.
It's only natural that motivic homotopy theory will have applications in quantum gravity. Perhaps there are immediate applications through the study of twistor string scattering amplitudes, which already make use of mixed Tate motives.
Cachazo, Mason and Skinner have given a formula (and its proof) for the complete tree-level S-matrix of N=8 supergravity, using twistor techniques. As is known, the BCFW recursion relations were initially used to study gluon amplitudes. Later it was shown that gravity amplitudes also obey such recursion relations. In N=4 super Yang-Mills BCFW decomposition is related to performing a contour integral in the moduli space of holomorphic maps so as to localize on the boundary where the worldsheet degenerates to a nodal curve. The summands on the right hand side of the recursion relation correspond to the various ways the vertex operators and map degree may be distributed among the two curve components (see above picture).
The formula is a big step in moving towards a motivic formulation of gravity. Moreover, as N=8 supergravity in four dimensions can be recovered from a toroidal compactification of M-theory, it would be interesting to understand the formula in an 'oxidized' context in eleven dimensions.
The CERN CMS team reports a combined significance of over 5 sigma! ATLAS also reports 5 sigma evidence. A new "Higgs-like" boson particle has been discovered. But is the new 125 GeV particle a Standard Model Higgs? (Note: If Standard Model is valid up to GUT or Planck scale, with top quark mass 174 GeV, 130 GeV is a lower limit on the Higgs mass from the requirement of vacuum stability. Whereas, with the Minimal Supersymmetric Standard Model (MSSM), for example, the lightest Higgs must necessarily be lighter than 130 GeV.) Stay tuned...
An official CERN video appeared on posts at viXra log and TRF, turning the Higgs rumors into solid evidence for a new particle. As stated in the video, this new boson has an even numbered spin and behaves very much like a Higgs particle (with 125 GeV mass). So the question remains: is this a Standard Model Higgs boson? As noted by John Ellis, the present electroweak
vacuum is unstable for a light Higgs in the range 114-135 GeV, requiring new physics to stabilize it (see TRF for a detailed discussion).
By later this year, the identity of the newly found particle should be known. And if we're lucky, another particle could be found (e.g. a Z' boson), telling us more about which models are best suited for describing our universe.
As research into quantum gravity continues, it is wise to look at the mathematical issues at hand. Most would agree that ordinary algebraic geometry is not sufficient to tackle the problem in its ultimate form. The theory of motives, at least in its commutative form, is only recently finding applications in the study of scattering amplitudes and Calabi-Yau compactifications. Noncommutative algebraic geometry and its generalized motives, as an extension of Grothendieck's dream of building a gateway between algebraic geometry and the assortment of Weil cohomology theories (de Rham, Betti, l-adic, crystalline, etc.) seems to be a more appropriate tool in the study of quantum geometry. In the noncommutative framework, the role of algebraic varieties and classical Weil cohomologies is played by differential graded categories and numerous functorial invariants. The gateway category Mot, through which all invariants factor uniquely, is the category of noncommutative motives and the different invariants (the Grothendieck, higher K-theory, and cyclic homology groups, etc.) are simply different representations of the motivic category.
In the recent Prometheus trailer (Alien prequel), Peter Weyland in his 2023 TED talk mentions M-theory as one of mankind's great accomplishments. M-theory isn't yet complete, but I'm pretty certain it (or its completion) will be complete by 2023. Either way, it's entertaining to imagine the status of high energy physics 11 years from now.
While all eyes are on the LHC to discover new, interesting particles species, condensed matter physicists have been working hard in attempts to detect Majorana fermions and Magnetic Monopoles in solids. In today's talk at the American Physical Society’s March meeting in Boston, Massachusetts, Leo Kouwenhoven presented findings that Majorana fermions have been detected in an indium antimonide nanowire apparatus. Indium antimonide nanowires are connected to a circuit with a gold
contact at one end and a slice of superconductor at the other, and then
exposed to a moderately strong magnetic field. Measurements of the
electrical conductance of the nanowires showed a peak at zero voltage
that is consistent with the formation of a pair of Majorana particles,
one at either end of the region of the nanowire in contact with the
superconductor. As a sanity check, the group varied the orientation of
the magnetic field and checked that the peak came and went as would be
expected for Majorana fermions.
Although other groups have previously reported circumstantial evidence
for the appearance of Majorana fermions in solid materials, Jay Sau, a
physicist at Harvard University in Cambridge, Massachusetts, who
attended Kouwenhoven’s talk, says that this is a direct measurement. “I
think this is the most promising-looking experiment yet,” he says. “It
would be hard to argue that it’s not Majorana fermions.”
Multiple schemes have been proposed in which Majorana fermions act as
the 'bits' in quantum computers, although Sau cautions that it’s not yet
clear whether those created by Kouwenhoven will be long-lived enough to
be used in that way.
As the LHC's
Higgs hunt continues, it's worthwhile to reflect on the current state
of cutting-edge experimental particle physics, as a whole. Indeed the Higgs boson is
a prediction of the Standard Model of particle physics, but as former CERN theoretical physicist John Ellis admitted,
in the range 114-135 GeV the "present electroweak vacuum would be
unstable for such a light Higgs in the Standard Model" forcing one to
come up with new physics to stabilize it. By "new", this means physics
beyond the Standard Model, such as for example, supersymmetry. Yet,
let's pretend the Standard Model is nice and stable with a ~125 GeV
Higgs particle. Does it tell us about every type of matter in the
universe? Sadly, it doesn't. Ordinary matter accounts for only 4.6% of
the mass-energy content of the observable universe, while mysterious
dark matter makes up about 23%. The rest of the mass-energy content, about 72.4%, is in the form of dark energy. So cosmologically, the Standard Model doesn't seem so standard after all.
So what kind of model explains the physics of dark energy and dark matter (the 95.4% of the universe), along with the 4.6% nicely described by the Standard Model? Many theorists would agree such a model must come from a complete theory of quantum gravity. The leading contender for such a theory is M-theory, the theory underlying the 10-dimensional string theories and 11-dimensional supergravity. There also exist other theories, such as Loop Quantum Gravity, which essentially aims to "quantize" space via Wilson loop operators. Ultimately, the goal is unification of all forces and matter in the universe, using just a single theory. And this theory, in turn, should describe 100% of the universe.
Are we close to figuring out a complete theory of quantum gravity, hence a theory of all matter and forces? There are hints that we are, but as always, many hurdles are mathematical. Historically, Newton had to invent Calculus to describe motion properly. Einstein had to invoke the tools of Riemann's Differential Geometry to describe space-time curvature. And will it now be Connes' Noncommutative Geometry that will serve as the magic bullet for quantum gravity? There is evidence that it might, as the coordinates of branes in string/M-theory are naturally noncommutative. Erik Verlinde has even proposed a model for dark energy and dark matter, which as a matrix model, is an application of noncommutative geometry. From a historical perspective, the use of new geometrical mathematics has proven fruitful, so we may very well be on the verge of a new physics revolution.