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Tools for Probing the Universe from the Smallest to Largest and All Scales In Between Jeff Scargle Space Science and Astrobiology Division NASA Ames Research Center SETI Institute Colloquium Series March 11, 2009 Real Space Data Space The Largest Scales in the Universe The Smallest Scales in the Universe Data Segmentation: Voronoi tessellation Large scale: structure of the Universe Medium scale: Extra-solar Planets Small scale: Space-Time? Real Space Instrument Fermi γ Ray Space Telescope Data Space Measurement The Large: Cosmological Scale Hubble: 500 km/s/Mpc The Large: Cosmological Scale The Large: Cosmological Scale Concordance Cosmology Hubble constant = 71 Size of the visible Universe: R = 14,224,900 pc = 4.4 x 10 28 cm = 2.7 x 10 61 Planck lengths QG & the Planck Scale (Ron Adler) • • • • h = 1.054 x 10 –27 g cm 2 / sec (Quantum Mechanics) c = 2.998 x 10 10 cm / sec (Special Relativity) G = 6.670 x 10 –8 cm 3 / g sec 2 (Gravity/General Relativity) Only one combination of these variables is a length LPlanck = ( hG / c3 )1/2 = 1.616 x 10 –35 m (10-17 electroweak scale) Determine the distance L between two points: measure the round-trip transit time of a photon of wavelength . ( ) = + G (meffective = E Uncertainty in measured length 2) / L /c photon Ordinary uncertainty principle Spatial distortion due to mass/energy of the photon This is + L2planck / --- minimum at = Lplanck The Small: Planck Scale • • • • Planck length √(Gℏ/c3) Planck energy Planck time Planck mass = 1.6 x 10 -35 = 1.2 × 10 28 = 5.4 x 10 -44 = 2.2 x 10 -8 meters electron volts seconds kilograms – ℏ from quantum mechanics – c from special relativity – G from general relativity • Generalized Uncertainty Principle: The smallest possible space-time measurements are at the Planck scales: Adler, R.J., & Santiago, D.J. 1999, Modern Physics Letters A, 14, 1371. Scales: small to large Bayesian Blocks: Construct best-fit piecewise constant model to the data. Voronoi Tessellation of data in any dimension Construct Voronoi cells to represent local photon density density ~ 1 / cell area Statistical Interlude • Clinical studies usually small and expensive • “Meta-analysis” – Increase significance by combining statistical summaries of published studies (not re-analysis of original data) • Role of publication bias (PB) • Assess potential for PB with Rosenthal formula Statistical Interlude • Publication bias is large! • Editorial policy: Do not publish a study unless it achieves a 3-sigma positive result • Rosenthal formula: Completely wrong! Used to justify hundreds of “meta-analytic” results in medicine, and psychology (real and para-) Not a single applied scientist questioned the validity of the formula • Many medical studies, especially those relevant to decisions about safety of drugs to be released to the market, are based on this statistical blunder. Statistical Interlude • Rosenthal, R. (1979) The "file drawer problem" and tolerance for null results. Psychological Bulletin, 86, 638-641. • Publication Bias: The “File-Drawer” Problem in Scientific Inference, J. D. Scargle. Journal of Scientific Exploration, Vol. 14, No. 1, pp. 91– 106, 2000. • A Generalized Publication Bias Model, P. H. Schonemann and J. D. Scargle, Chinese Journal of Psychology, 2008, Vol. 50, 1, 21-29. Statistical Interlude • Pre-election radio interview with the president of a major political polling organization (“Dr. Z”). • Caller: “I hang up on polling phone calls – intrusion of my privacy.” • Discussion of this as a potential bias. • Dr. Z: “I don’t worry about such biases. We just get a larger sample.” • JS calls the radio show and tries to verify Dr. Z’s belief that increased sample size can fix a bias. • Dr. Z does not understand; responds by puffing up the reliability of his polling organization. Planetary Detection Periodograms (Marcy et al.) • Similar to a power spectrum, or discrete data analog of a Fourier transform. • The periodograms used here are closely related to the LombScargle Periodogram. • A measure of the improvement of fitting a single sinusoid plus a constant to the data over fitting only a constant. • Each peak has a width of ~1/T in frequency space, where T is the time spanned by the data. • Periodogram power z(ω) is evaluated for a grid of orbital frequencies, separated here by 1/(4T). • Highest peaks are optimized to increase precision in the corresponding orbital frequency or period. Cumming et al. 1999 Floating-mean Periodograms • For N = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200 observations, left to right, top to bottom. – Vertical line represents correct period. – Horizontal lines for detection thresholds corresponding to FAP’s of F = 0.1 (lower) and F = 0.01 (upper). – Initial decrease in FAP is probably due to increase in number of independent frequencies. 1. Floating-parabola periodogram • All peaks within some fraction (we use e-1/2 ≈ 0.607) of the highest peak are considered. – A detection threshold can be used as an additional criteria. – Only one peak qualifies here. It has periodicity P = 39.855 days. 1. Single-Keplerian fit • We evaluate the floatingparabola periodogram and fit a single Keplerian orbit as in the single-planet case. – Don’t decide on trend; we keep a parabola for now. • Peaks higher than both e-1/2 of the highest peak (dashed line) and a detection threshold corresponding to an FAP of F = 0.01 (dotted line) are considered. – The 2 qualifying peaks in this example are marked with asterisks. 2-dimensional Periodogram • Measures the improvement in fitting 2 sinusoids plus a floating constant/trend over fitting a floating constant/trend. – The first periodicity (days) is plotted against the second. – Regions where the power is lowest appear black and those with the most power appear red. – The highest peaks are marked with x’s. • Most useful where there are two planets with similar velocity amplitudes. • Has problems with highly eccentric orbits. Gamma-ray Large Area Space Telescope Testing Quantum Gravity Theories with GLAST Thanks: Jay Norris, Johann Cohen-Tanugi, Paul Gazis, Jerry Bonnell, Ron Adler, GLAST Science Teams Unification of General Relativity & Quantum Mechanics General Relativity Quantum Mechanics Scale Large Small Dynamics Deterministic Probabilistic Space-time Background Independent Absolute background Modify: GR to fit with QM? QM to fit with GR? Both GR and QM? Seek Observable Effects Is Lorentz symmetry broken? Lorentz Invariance Violation What about other symmetries (translation and scale invariance, CPT, supersymmetry, Poincaré, …)? Is space-time discrete/chunky, affecting photon/particle propagation? Is this quantum foam at the Planck scale (10-35 m; 1019 GeV)? Some Approaches to QG Theory Loop Quantum Gravity hep-th/0601129 String theory many Effective Field Theory hep-th/0407370 The World as a Hologram hep-th/9409089 Quantum Computation quant-ph/0501135 Extra Dimensions hep-ph/9811291 Statistical Geometry Myrheim, TH.2538-CERN Categorical Geometry ? gr-qc/0602120 Self-organized criticality hep-th/0412307 Random Lattice Field Theory T. D. Lee Dynamic Probabilistic Causal Structure ? gr-qc/0509120 Causal Sets gr-qc/06 01 069/121 Random Walk gr-qc/0403085 Regge Calculus gr-qc/0012035 Quantum State Diffusion I. Percival High Energy Astrophysics Tests of Lorentz Invariance Violation • • • • • • • • • • Dispersion in g-rays from GRBs & AGN Photon decay (Coleman & Glashow 1999, Stecker & Glashow 2001) Vacuum Cherenkov radiation (Coleman & Glashow 1999; Stecker & Glashow 2001) Shifted pair production threshold constraints from AGN g-rays (Stecker & Glashow 2001). Long baseline vacuum birefringence (GRB polarization) Electron velocity (Crab Nebula g-ray spectrum;Jacobson, Liberati & Mattingly 2003). Ultrahigh energy cosmic ray spectrum GZK effect (Coleman & Glashow 1999; Stecker & Scully 2005). Photon phase coherence (diffraction patterns of distant point sources) Dispersion in neutrinos from GRBs (Jacob and Piran, hep-ph/0607145) Modified dispersion relation – white dwarf Fermi temperatures – neutrino oscillations and pulsar kicks – Pulsar rotation periods Time-of-Flight Measurements (Mattingly, gr-qc/0502097) Is the speed of light a function of photon energy? Postulate: E2 = m2 + p2 E2 = p2 E2 = F(p, m) E2 = F( p) particles photons “Since we live in an almost Lorentz invariant world (and are nearly at rest with respect to the CMBR), in the preferred frame F(p,m) must reduce to the Lorentz invariant dispersion at small energies and momenta. It is therefore natural to expand F(p,m) about p = 0 ...” E2 = m2 + p2 + Eplanck f(1) |p| + f(2) |p|2+ f(3) |p|3 /Eplanck + ... (particles) ∆t / T = 0.5 ( n – 1) f(n) (∆ E / Eplanck) n-2 (photons) where n is the order of the first non-zero term in the expansion. More complete and cogent analysis in “High-energy Tests of Lorentz Invariance, Coleman and Glashow, hep-ph/9812418. Even if there is dispersion, it may be masked by the Pulse Asymmetry / Energy-shift Paradigm, Norris, Marani, and Bonnell, astro-ph/9903233 Low energy High energy How best to measure Energy-Dependent Lags? The data: time and energy tagged -- ti Ei i = 1, 2, ... , N Usual approach: Bin the data in both time and energy Find peak in cross-correlation function (across E bands) Entropy approach define transformation of time: t'i = f( ti ) = ti + L(, Ei ) (lag L is a function of a parameter ) If is other than the correct value, the light curve for the transformed times will be smeared out. Hence the entropy of the light curve will be minimum for the correct value: optimum = argmin[ Entropy ( histogram( ti + L(, Ei ) ) ] lag estimate is then just L( optimum, E ) Previous estimate from Crosscorrelations Ellis et al 2002 Wavelet method From Ellis et al. Astro-ph/0510172 Voronoi Tessellations on 3+ Scales Random space-time lattice (T. D. Lee) Points: micro-partons? Cells: Planck length cells Blocks: Elementary Particles GLAST Source Detection Algorithm 10 –35 meters Points: Photons Blocks: Point sources Cluster detection algorithm: Points: Galaxies Cells: Galaxy Neighborhoods 10 +22 meters Blocks: Clusters, filaments, … Large Scale Structure Points: Galaxies Cells: Voids