Tools for Probing the Universe

from the Smallest to Largest and All Scales In Between

Jeff ScargleSpace Science and Astrobiology Division

NASA Ames Research Center

SETI Institute Colloquium SeriesMarch 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 SpaceInstrumentFermi γ Ray Space Telescope Measurement

Data Space

The Large: Cosmological ScaleHubble: 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

• 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)

QG & the Planck Scale (Ron Adler)

Uncertainty inmeasured length( ) = + G (meffective = Ephoton/c2) / L

Ordinaryuncertaintyprinciple

Spatial distortiondue to mass/energyof the photon

Determine the distance L between two points: measure the

round-trip transit time of a photon of wavelength .

This is + L2planck / --- minimum at = Lplanck

The Small: Planck Scale• Planck length √(G /cℏ 3) = 1.6 x 10 -35 meters• Planck energy = 1.2 × 10 28 electron volts• Planck time = 5.4 x 10 -44 seconds• Planck mass = 2.2 x 10 -8 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Statistical Interlude• Publication bias is large!• Editorial policy: Do not publish a study unless it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 Lomb-

Scargle 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

• 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.

Floating-mean Periodograms

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 floating-parabola 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.

Testing Quantum Gravity Theories

with GLAST

Thanks:

Jay Norris, Johann Cohen-Tanugi, Paul Gazis, Jerry Bonnell, Ron Adler, GLAST Science Teams

Gamma-ray Large Gamma-ray Large Area Space Area Space TelescopeTelescope

Unification of General Relativity & Quantum Mechanics

Modify: GR to fit with QM? QM to fit with GR? Both GR and QM?Seek Observable Effects

Is Lorentz symmetry broken? Lorentz Invariance ViolationWhat 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)?

General Relativity Quantum Mechanics

Scale Large Small

Dynamics Deterministic Probabilistic

Space-time Background Independent Absolute background

Some Approaches to QG TheoryLoop Quantum Gravity hep-th/0601129String theory manyEffective Field Theory hep-th/0407370The World as a Hologram hep-th/9409089Quantum Computation quant-ph/0501135Extra Dimensions hep-ph/9811291Statistical Geometry Myrheim, TH.2538-CERNCategorical Geometry ? gr-qc/0602120 Self-organized criticality hep-th/0412307Random Lattice Field Theory T. D. LeeDynamic Probabilistic Causal Structure ? gr-qc/0509120Causal Sets gr-qc/06 01 069/121Random Walk gr-qc/0403085Regge Calculus gr-qc/0012035Quantum State Diffusion I. Percival

High Energy Astrophysics Tests of Lorentz Invariance Violation

• Dispersion in -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 -rays (Stecker & Glashow 2001).• Long baseline vacuum birefringence (GRB polarization)• Electron velocity (Crab Nebula -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 = F(p, m) particlesE2 = p2 E2 = F( p) 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 energyFind 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 transformedtimes will be smeared out. Hence the entropy of the light curve willbe minimum for the correct value:

optimum = argmin[ Entropy ( histogram( ti + L(, Ei ) ) ]

lag estimate is then just L( optimum, E )

Previous estimate from Cross-correlations

Ellis et al 2002Wavelet method

From Ellis et al.Astro-ph/0510172

Cont

rove

rsy

Random space-time lattice (T. D. Lee)Points: micro-partons?Cells: Planck length cellsBlocks: Elementary Particles

GLAST Source Detection Algorithm

Points: Photons

Blocks: Point sources

Cluster detection algorithm:

Points: Galaxies

Cells: Galaxy Neighborhoods

Blocks: Clusters, filaments, …

10 –35 meters

10 +22 meters

Large Scale Structure

Points: Galaxies

Cells: Voids

Voronoi Tessellations on 3+ Scales