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

Detection of body postures and movements in ambulatory adults with cerebral palsy: a novel and valid measure of physical behaviour

BACKGROUND: Accurate measurement of physical behaviour is paramount to better understand lifestyle, health, and functioning, particularly in adults with physical disability as they may be at higher risk of sedentary lifestyle and subsequent negative health consequences. This study aimed: 1) to evaluate the criterion validity of a novel and clinically applicable activity monitor (AM, Activ8), in the detection of body postures and movements in adults with spastic cerebral palsy (CP); and 2) to evaluate the extent that the AM's positioning affects validity. METHODS: In this cross-sectional study, 14 ambulatory adults with CP [9 men; mean (SD) age, 35.4 (13.1) years] performed standardized activities while wearing three Activ8 monitors - frontolateral thigh (primary position), frontal thigh, and pant pocket - and being video recorded (criterion measure). AM activity output was compared to synchronized video recordings. Absolute (seconds) and relative [(video time-AM time)/mean time, %] time differences between methods were calculated. Relative time differences of < 10% were indicative of good validity. Comparison of AM attachment positions was completed using Spearman Rho correlation coefficients and Meng's tests. RESULTS: Criterion validity of the AM (frontolateral thigh) was good (average relative time differences: 0.25% for sitting, 4.69% for standing, 2.46% for walking, 1.96% for upright activity, 3.19% for cycling), except for running (34.6%). Spearman Rho correlation coefficients were greater between video/frontolateral thigh position than video/frontal thigh position and video/pant pocket position for body posture and movement categories sitting, standing, walking, and upright activity (p < 0.01 for all). CONCLUSIONS: The AM, positioned on the frontolateral thigh, demonstrated good criterion validity in ambulatory adults with CP. Though the Activ8 offers potential as an objective measure of physical activity, appropriate positioning is paramount for valid measurement

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Measurement of the Lambda(b) cross section and the anti-Lambda(b) to Lambda(b) ratio with Lambda(b) to J/Psi Lambda decays in pp collisions at sqrt(s) = 7 TeV

The Lambda(b) differential production cross section and the cross section ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/Psi Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and Lambda to proton pion, using a data sample corresponding to an integrated luminosity of 1.9 inverse femtobarns. The product of the cross section times the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls faster than that of b mesons. The measured value of the cross section times the branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06 +/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively.Comment: Submitted to Physics Letters

Measurement of isolated photon production in pp and PbPb collisions at sqrt(sNN) = 2.76 TeV

Isolated photon production is measured in proton-proton and lead-lead collisions at nucleon-nucleon centre-of-mass energies of 2.76 TeV in the pseudorapidity range |eta|<1.44 and transverse energies ET between 20 and 80 GeV with the CMS detector at the LHC. The measured ET spectra are found to be in good agreement with next-to-leading-order perturbative QCD predictions. The ratio of PbPb to pp isolated photon ET-differential yields, scaled by the number of incoherent nucleon-nucleon collisions, is consistent with unity for all PbPb reaction centralities.Comment: Submitted to Physics Letters

Search for new physics in events with opposite-sign leptons, jets, and missing transverse energy in pp collisions at sqrt(s) = 7 TeV

A search is presented for physics beyond the standard model (BSM) in final states with a pair of opposite-sign isolated leptons accompanied by jets and missing transverse energy. The search uses LHC data recorded at a center-of-mass energy sqrt(s) = 7 TeV with the CMS detector, corresponding to an integrated luminosity of approximately 5 inverse femtobarns. Two complementary search strategies are employed. The first probes models with a specific dilepton production mechanism that leads to a characteristic kinematic edge in the dilepton mass distribution. The second strategy probes models of dilepton production with heavy, colored objects that decay to final states including invisible particles, leading to very large hadronic activity and missing transverse energy. No evidence for an event yield in excess of the standard model expectations is found. Upper limits on the BSM contributions to the signal regions are deduced from the results, which are used to exclude a region of the parameter space of the constrained minimal supersymmetric extension of the standard model. Additional information related to detector efficiencies and response is provided to allow testing specific models of BSM physics not considered in this paper.Comment: Replaced with published version. Added journal reference and DO

Thorium speciation in seawater

Author Posting. © The Authors, 2006. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Marine Chemistry 100 (2006): 250-268, doi:10.1016/j.marchem.2005.10.024.Since the 1960’s, thorium isotopes occupy a special place in the oceanographer’s toolbox as tracers for determining rates and mechanisms of oceanic scavenging, particle dynamics, and carbon fluxes. Due to their unique and constant production rates from soluble parent nuclides of uranium and radium, their disequilibrium can be used to calculate rates and time scales of sinking particles. In addition, by ratio-ing particulate 234Th (as well, in principle, other Thnuclides) to carbon (and other elements), and linking this ratio to the parent-daughter disequilibrium in the water column, it is possible to calculate fluxes of carbon and other elements. Most of these applications are possible with little knowledge of the dissolved chemical properties of thorium, other than its oxidation state (IV) and tendency to strongly sorb to surfaces, i.e., its “particle- or surface-activity”. However, the use of any tracer is hindered by a lack of knowledge of its chemical properties. Recent observations in the variability of carbon to 234Th ratios in different particle types, as well as of associations of Th(IV) with various marine organic biomolecules has led to the need for a review of current knowledge and what future endeavors should be taken to understand the marine chemistry of thorium.The writing of this paper was supported, in parts by NSF (OCE-0351559; OCE-0350758, and OCE 0354757)