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We solve a very classical problem motivated by considerations in quantum gravity: providing a description of the geometry of a Euclidean tetrahedron from the initial data of the areas of the faces and the areas of the medial parallelograms of Yetter or equivalently of the pseudofaces of McConnell. In particular, we derive expressions for the dihedral angles, face angles and (an) edge length, the remaining parts being derivable by symmetry or by identities in the classic 1902 compendium of results on tetrahedral geometry of Richardson. We also provide an alternative proof using (bi)vectors of the result of Yetter that four times the sum of the squared areas of the medial parallelograms is equal to the sum of the squared areas of the faces. The updated version corrects several errors and provides better historical context for the result.

We investigate looking for black hole starships using very high energy gamma ray telescopes. We find they would be above the threshhold of visibility although there are many unknown factors., Comment: 6 pages contact crane@math.ksu.edu

The I 1 -imidazoline receptor is a novel target for drug development for hypertension and insulin resistance, major disorders associated with type 2 diabetes. In the present study, we examined the effects of a novel imidazoline agonist S43126, on phosphorylation of protein kinase B (PKB/Akt) and extracellular signal-regulated kinase (ERK1/2) in PC12 cells. We further examined the effects of S43126 on insulin stimulated PKB and ERK phosphorylation. PC12 cells were treated with varying doses of S43126 (10 –10 to 10 –6 M) or insulin (10 –10 to 10 –6 M) or combination treatment with insulin (10 –6 M) and varying doses of S43126 (10 –6 – 10 –11 M) for 10 min. Western blot analysis of treated samples showed that S43126 increased both ERK1/2 and PKB phosphorylation by 5 fold. Combination treatment with insulin (10 –6 M) and varying doses of S43126 (10 –6 – 10 –11 M) enhanced phosphorylation of PKB and ERK1/2 above the level of insulin alone, in a dose and time dependent manner. Treatment with siRNA against Nischarin (mouse homologue of I 1 -imidazoline receptor) reduced the phosphorylation of both ERK and PKB following combination treatments. These results indicate that S43126 has the potential to augment insulin action and should be further studied as a possible candidate drug for the treatment of insulin resistance states.

We extend results of Pachner and Casali to give finite sets of moves relating triangulations of PL manifolds respecting filtrations by locally flat manifolds and stratifications in which a finite family of simple local models exists for neighborhoods of strata., Comment: 6 pages

In \cite{C1}, we proposed a new interpretation of the EPRL quantization of the BC model for quantum general relativity using a monoidal functor we call the time functor. In this preliminary draft we apply the theory of modules over monoidal functors \cite{Y1} to the time functor, to propose an extension of the EPRL model which would include the standard model. This is motivated by recent advances in neutrino Physics., 11 pages latex

We discuss a proposal to make small artificial black holes (ABH's) using a huge laser. Because of Hawking radiation, they would be extremely powerful energy sources. We investigate the technical problems of using them to make power plants and starships. The first suggestion is due to Hawking. Next, we consider what challenges the ABH proposal would pose for a future quantum theory of gravity. The form of a theory which would allow us to compute the necessary corrections to classical theory is considered. It is widely believed that every black hole produces a new baby universe on the other side of its singularity. If this is true, ABH technology will involve future humanity in the creation process of universes. Finally, we ponder the effects that the ABH proposal would have on the culture of a future society, particularly if the baby universe theory is correct. The changes in our economic life and understanding of our role in the cosmos would be so profound as to have a "spiritual" aspect., Comment: First prize winner FQXi contest "On the limits of Physics"

This document is the Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008). Please refer to the preface and introduction for more details on the contributions. Keywords: acceleration, artificial cosmogenesis, artificial life, Big Bang, Big History, biological evolution, biological universe, biology, causality, classical vacuum energy, complex systems, complexity, computational universe, conscious evolution, cosmological artificial selection, cosmological natural selection, cosmology, critique, cultural evolution, dark energy, dark matter, development of the universe, development, emergence, evolution of the universe evolution, exobiology, extinction, fine-tuning, fractal space-time, fractal, information, initial conditions, intentional evolution, linear expansion of the universe, log-periodic laws, macroevolution, materialism, meduso-anthropic principle, multiple worlds, natural sciences, Nature, ontology, order, origin of the universe, particle hierarchy, philosophy, physical constants, quantum darwinism, reduction, role of intelligent life, scale relativity, scientific evolution, self-organization, speciation, specification hierarchy, thermodynamics, time, universe, vagueness., 355 pages, Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008) (online at: http://evodevouniverse.com/wiki/Conference_2008) To be published in Foundations of Science. Includes peer-reviewed papers, commentaries and responses (metadata update)

We investigate whether it is physically possible to build starships or power sources using the Hawking radiation of an artificial black hole as a power source. The proposal seems to be at the edge of possibility, but quantum gravity effects could change the picture., Latex document 20 pages

In this paper, we outline a new approach to quantum gravity; describing states for a bounded region of spacetime as eigenstates for two classes of physically plausible gedanken experiments. We end up with two complementary descriptions in which the point set continuum disappears. The first replaces the continuum of events with a handlebody decomposition of loop space. We conjecture that techniques fron algebraic topology will allow us to extend state sum models on spacetime to loop space. The second picture replaces the continuum with a nondistributive lattice; the classical limit seems more tractible in this picture., latex document. Submitted to GRF

We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In the process of constructing a quantum topos for quantum gravity, we propose a new, operational approach to the problem of the obervables in quantum gravity, which leads to a new mathematical point of view on the state sum models., Comment: 25 pages, latex file

We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its interpretation, and connect with the construction of causal sites., Comment: Contribution to the Cambridge University Press volume on Quantum Gravity

We give the construction modulo normalization of a new state sum model for lorentzian quantum general relativity, using the construction of Dirac's expansors to include quantum operators corresponding to edge lengths as well as the quantum bivectors of the Barrett-Crane model, and discuss the problem of its normalization. The new model gives rise to a new picture of quantum geometry in which lengths come in a discrete spectrum, while areas have a continuum of values., Comment: 11 pages latex

We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with Lorentzian signature., 11 pages, 3 pictures

We show that the sum over geometries in the Lorentzian 4-D state sum model for quantum GR in [1] includes terms which correspond to geometries on manifolds with conical singularities. Natural approximations suggest that they can be interpreted as gauge bosond for the standard model, plus fermions plus matter., Comment: 9 pages, latex no figs

We propose a new line of attack to create a finite quantum theory which includes general relativity and (perhaps) the standard model in its low energy limit. The theory would emerge from the categorical approach. A structure is observed on the category of unitary representations of the lorentz group which we call hypergravity. This, combined with a study of the relationship between Feynman diagrams and words in tensor categories, leads to the proposal., Comment: 16 pages, latex

We propose a new 4D state sum model, related to the balanced model, which is constructed using the octonions, or equivalently, triality. An effective continuum physical theory constructed from this model coupled to the balanced model would have a non-vanishing cosmological constant, chiral asymmetry, and a gauge group related to the octonions., 9 pages, Latex

We propose a model for the quantum theory of gravity. the model has diffeomorphism invariance, a natural length scale, and (plausibly) propagating modes. in the new addendum, we alter the model in a way which makes the propagating modes much easier to approach., 11 pages, latex, important addendum

We discuss the interpretation of the state sum of Barrett and Crane., Comment: 4 pages latex

We define the cohomology and formal deformation theories for algebra and bialgebra categories. We suggest some approaches to finding nontrivial deformations of the categories associated to the quantum groups by the work of Lusztig., 12 pages latex

We provide, with proofs, a complete description of the authors' construction of state-sum invariants announced in [CY], and its generalization to an arbitrary (artinian) semisimple tortile category. We also discuss the relationship of these invariants to generalizations of Broda's surgery invariants [Br1,Br2] using techniques developed in the case of the semi-simple sub-quotient of $Rep(U_q(sl_2))$ ($q$ a principal $4r^{th}$ root of unity) by Roberts [Ro1]. We briefly discuss the generalizations to invariants of 4-manifolds equipped with 2-dimensional (co)homology classes introduced by Yetter [Y6] and Roberts [Ro2], which are the subject of the sequel. (citations refer to bibliography in the paper), 46 pages

We consider the implications of some simple assumptions about the nature of the quantum theory of gravity which are plausible for a class of possible theories I have been attempting to construct. The simple assumptions turn out to have surprizingly wide implications of a type one might call philosophical. The paper is short and nontechnical. ( This builds on recent unpublished work of Lee Smolin, but comes to opposite conclusions)., Comment: 5 pages, latex document

Recent work of Roberts has shown that the first surgical 4-manifold invariant of Broda and (up to an unspecified normalization factor) the state-sum invariant arising from the TQFT of Crane-Yetter are equivalent to the signature of the 4-manifold. Subsequently Broda defined another surgical invariant in which the 1- and 2-handles are treated differently. We use a refinement of Roberts' techniques developped by the authors in hep-th/9309063 to show that the "improved" surgical invariant of Broda also depends only on the signature and Euler character, 4 pages (revised to state correctly Lemma 1--the correct lemma was proved, and used throughout, but the original statement jumbled some phrases--and add an explanatory footnote on an abuse of language)

We provide an explicit formula for the invariant of 4-manifolds introduced by Crane and Yetter (in hep-th 9301062). A consequence of our result is the existence of a combinatorial formula for the signature of a 4-manifold in terms of local data from a triangulation. Potential physical applications of our result exist in light of the fact that the Crane-Yetter invariant is a rigorous version of ideas of Ooguri on B wedge F theory., 4 pages

I propose a new mathematical form for the quantum theory of gravity coupled to matter. The motivation is from the connection between CSW TQFT and the Ashtekar variables. I also connect the algebraic structure of TQFT with some thoughts about the interpretation of quantum mechanics in a general relativistic setting., 9 pages amstex

We construct a four dimensional topological Quantum Field Theory from a modular tensor category. We complete the proof in the case of SU(2)q at a root of unity. Our construction may be important in the physical interpretation of the Chern Simons state in the Ashtekar variables., Comment: 11 pages

We show that the construction of Ocneanu, which yields 1 for any 4D manifold, is not identical to our construction, which gives different numbers for different manifolds., Comment: 2 pages

Motivated by the similarity between CSW theory and the Chern Simons state for General Relativity in the Ashtekar variables, we explore what the universe would look like if it were in a state corresponding to a 3D TQFT. We end up with a construction of propagating ststes for parts of the universe and a Hilbert space corresponding to a certain approximation. The construction avoids path integrals, using instead recombination diagrams in a certain tensor category., Comment: 10 pages to appear in Knots and Quantum Gravity ed John Baez, Oxford University Press Latex document