The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

Localization and symmetries

The violation of the Noether relation between symmetries and charges is reduced to the time dependence of the charge associated to a conserved current. For the U(1) gauge symmetry a non-perturbative control of the charge commutators is obtained by an analysis of the Coulomb charged fields. From this, in the unbroken case we obtain a correct expression for the electric charge on the Coulomb states, its superselection and the presence of massless vector bosons; in the broken case, we obtain a general non-perturbative version of the Higgs phenomenon, i.e. the absence of massless Goldstone bosons and of massless vector bosons. The conservation of the (gauge dependent) current associated to the U(1) axial symmetry in QCD is shown to be compatible with the time dependence of the corresponding charge commutators and a non-vanishing eta' mass, as a consequence of the non locality of the (conserved) current.Comment: Invited contribution to ``The Quantum Universe'', dedicated to G. Ghirardi for his 70th birthda

Reflections on the four facets of symmetry: how physics exemplifies rational thinking

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to examine closely the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with others disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields

New broad-spectrum resistance to septoria tritici blotch derived from synthetic hexaploid wheat

Septoria tritici blotch (STB), caused by the ascomycete Mycosphaerella graminicola, is one of the most devastating foliar diseases of wheat. We screened five synthetic hexaploid wheats (SHs), 13 wheat varieties that represent the differential set of cultivars and two susceptible checks with a global set of 20 isolates and discovered exceptionally broad STB resistance in SHs. Subsequent development and analyses of recombinant inbred lines (RILs) from a cross between the SH M3 and the highly susceptible bread wheat cv. Kulm revealed two novel resistance loci on chromosomes 3D and 5A. The 3D resistance was expressed in the seedling and adult plant stages, and it controlled necrosis (N) and pycnidia (P) development as well as the latency periods of these parameters. This locus, which is closely linked to the microsatellite marker Xgwm494, was tentatively designated Stb16q and explained from 41 to 71% of the phenotypic variation at seedling stage and 28–31% in mature plants. The resistance locus on chromosome 5A was specifically expressed in the adult plant stage, associated with SSR marker Xhbg247, explained 12–32% of the variation in disease, was designated Stb17, and is the first unambiguously identified and named QTL for adult plant resistance to M. graminicola. Our results confirm that common wheat progenitors might be a rich source of new Stb resistance genes/QTLs that can be deployed in commercial breeding programs

Signal transduction underlying the control of urinary bladder smooth muscle tone by muscarinic receptors and β-adrenoceptors

The normal physiological contraction of the urinary bladder, which is required for voiding, is predominantly mediated by muscarinic receptors, primarily the M3 subtype, with the M2 subtype providing a secondary backup role. Bladder relaxation, which is required for urine storage, is mediated by β-adrenoceptors, in most species involving a strong β3-component. An excessive stimulation of contraction or a reduced relaxation of the detrusor smooth muscle during the storage phase of the micturition cycle may contribute to bladder dysfunction known as the overactive bladder. Therefore, interference with the signal transduction of these receptors may be a viable approach to develop drugs for the treatment of overactive bladder. The prototypical signaling pathway of M3 receptors is activation of phospholipase C (PLC), and this pathway is also activated in the bladder. Nevertheless, PLC apparently contributes only in a very minor way to bladder contraction. Rather, muscarinic-receptor-mediated bladder contraction involves voltage-operated Ca2+ channels and Rho kinase. The prototypical signaling pathway of β-adrenoceptors is an activation of adenylyl cyclase with the subsequent formation of cAMP. Nevertheless, cAMP apparently contributes in a minor way only to β-adrenoceptor-mediated bladder relaxation. BKCa channels may play a greater role in β-adrenoceptor-mediated bladder relaxation. We conclude that apart from muscarinic receptor antagonists and β-adrenoceptor agonists, inhibitors of Rho kinase and activators of BKCa channels may have potential to treat an overactive bladder