Towards the Unification of Gravity and other Interactions: What has been Missed?

Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$ associated with matter configurations. We consider general relativity in ${\cal C}$. In spacetime, which is a 4-dimensional subspace of ${\cal C}$, we have not only the 4-dimensional gravity, but also other interactions, just as in Kaluza-Klein theories. We then consider a finite dimensional description of extended objects in terms of the center of mass, area, and volume degrees of freedom, which altogether form a 16-dimensional manifold whose tangent space at any point is Clifford algebra Cl(1,3). The latter algebra is very promising for the unification, and it provides description of fermions.Comment: 11 pages; Talk presented at "First Mediterranean Conference on Classical and Quantum Gravity", Kolymbari, Crete, Greece, 14-18 September 200

The Secant Conjecture in the real Schubert calculus

We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real, if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for it as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some phenomena we observed in our data.Comment: 19 page

Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime

A theory in which 4-dimensional spacetime is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza-Klein theory. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U(1)xSU(2)xSU(3) of the standard model. The generalized spin connection in C-space has the properties of Yang-Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb-Ramond fields.Comment: 57 pages; References added, section 2 rewritten and expande

A Novel View on the Physical Origin of E8

We consider a straightforward extension of the 4-dimensional spacetime $M_4$ to the space of extended events associated with strings/branes, corresponding to points, lines, areas, 3-volumes, and 4-volumes in $M_4$. All those objects can be elegantly represented by the Clifford numbers $X\equiv x^A \gamma_A \equiv x^{a_1 ...a_r} \gamma_{a_1 ...a_r}, r=0,1,2,3,4$. This leads to the concept of the so-called Clifford space ${\cal C}$, a 16-dimensional manifold whose tangent space at every point is the Clifford algebra ${\cal C \ell }(1,3)$. The latter space besides an algebra is also a vector space whose elements can be rotated into each other in two ways: (i) either by the action of the rotation matrices of SO(8,8) on the components $x^A$ or (ii) by the left and right action of the Clifford numbers $R=$exp [\alpha^A \gam_A] and $S=$exp [\beta^A \gam_A] on $X$. In the latter case, one does not recover all possible rotations of the group SO(8,8). This discrepancy between the transformations (i) and (ii) suggests that one should replace the tangent space ${\cal C \ell}(1,3)$ with a vector space $V_{8,8}$ whose basis elements are generators of the Clifford algebra ${\cal C \ell}(8,8)$, which contains the Lie algebra of the exceptional group E$_8$ as a subspace. E$_8$ thus arises from the fact that, just as in the spacetime $M_4$ there are $r$-volumes generated by the tangent vectors of the spacetime, there are $R$-volumes, $R=0,1,2,3,...,16$, in the Clifford space ${\cal C}$, generated by the tangent vectors of ${\cal C}$.Comment: 14 page

Large Coherence Area Thin-Film Photonic Stop-Band Lasers

We demonstrate that the shift of the stop band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film

AD Leonis: Radial Velocity Signal of Stellar Rotation or Spin–Orbit Resonance?

AD Leonis is a nearby magnetically active M dwarf. We find Doppler variability with a period of 2.23 days, as well as photometric signals: (1) a short-period signal, which is similar to the radial velocity signal, albeit with considerable variability; and (2) a long-term activity cycle of 4070 ± 120 days. We examine the short-term photometric signal in the available All-Sky Automated Survey and Microvariability and Oscillations of STars (MOST) photometry and find that the signal is not consistently present and varies considerably as a function of time. This signal undergoes a phase change of roughly 0.8 rad when considering the first and second halves of the MOST data set, which are separated in median time by 3.38 days. In contrast, the Doppler signal is stable in the combined High-Accuracy Radial velocity Planet Searcher and High Resolution Echelle Spectrometer radial velocities for over 4700 days and does not appear to vary in time in amplitude, phase, period, or as a function of extracted wavelength. We consider a variety of starspot scenarios and find it challenging to simultaneously explain the rapidly varying photometric signal and the stable radial velocity signal as being caused by starspots corotating on the stellar surface. This suggests that the origin of the Doppler periodicity might be the gravitational tug of a planet orbiting the star in spin–orbit resonance. For such a scenario and no spin–orbit misalignment, the measured v sin i indicates an inclination angle of 15°̣5 ± 2°̣5 and a planetary companion mass of 0.237 ± 0.047 M Jup

Independent Review Of Social And Population Variation In Mental Health Could Improve Diagnosis In DSM Revisions

At stake in the May 2013 publication of the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5), are billions of dollars in insurance payments and government resources, as well as the diagnoses and treatment of millions of patients. We argue that the most recent revision process has missed social determinants of mental health disorders and their diagnosis: environmental factors triggering biological responses that manifest themselves in behavior; differing cultural perceptions about what is normal and what is abnormal behavior; and institutional pressures related to such matters as insurance reimbursements, disability benefits, and pharmaceutical marketing. In addition, the experts charged with revising the DSM lack a systematic. way to take population-level variations in diagnoses into account. To address these problems, we propose the creation of an independent research review body that would monitor variations in diagnostic patterns, inform future DSM revisions, identify needed changes in mental health policy and practice, and recommend new avenues of research. Drawing on the best available knowledge, the review body would make possible more precise and equitable psychiatric diagnoses and interventions