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Holographic Noise

Craig Hogan

Fermilab and U. Chicago

1AEI, May 2009


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Are time and space infinitely smooth?

Einsteins theory assumes spacetime is a classical manifold,infinitely divisible

This may be just an approximate behavior Can we measure the minimum interval of time?

2AEI, May 2009


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The smallest interval of time

Quantum gravity suggests a minimum (Planck) time,

~ particle energy 1016 TeV

seconds

ma

ss

length

quantum

gravity

3AEI, May 2009


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Two approaches to the Planck scale

mass

length

quantum

gravity

4AEI, May 2009

position

momentum


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Best microscopes vs best microphones

CERN/Fermilab: TeV-1~10-18 m: particle interactions

LIGO/GEO600: ~10-18 m, coherent over

~103 m baseline: Positions of massive

bodies

5AEI, May 2009


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A new phenomenon?: holographic noise

The minimum interval of time may affect interferometers Transverse uncertainty much larger than Planck scale in

holographic theories

precise, zero-parameter prediction of Holographic Noise

Planck diffraction limit at L

is >> Planck length

x ~ L

6


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Spatial frequency limit causes transverse indeterminacy:transverse position wavefunction at distance L

AEI, May 20097

L

L


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Indeterminacy in difference of orthogonal transverse positions

AEI, May 20098


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GEO-600 (Hannover): best displacement sensitivity

9AEI, May 2009


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Mystery Noise in GEO600

Prediction: CJH, arXiv:0806.0665

(Phys Rev D.78.087501)

Data: S. Hild (GEO600)

Total noise: not fitted

zero-parameter prediction for

holographic noise in GEO600(equivalent GW strain)

tPlanck

/

10AEI, May 2009


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Measurement of holographic noise

Holographic wave geometry predicts a new detectable effect:"holographic noise

Not the same as zero-point field mode fluctuations Spectrum and distinctive spatial character of the noise is predicted

with no parameters

It may already be detected An experimental program is motivated

CJH: arXiv:0806.0665 Phys Rev D.78.087501 (2008)

CJH: arXiv:0712.3419 Phys Rev D 77, 104031 (2008)

CJH and M. Jackson, Phys. Rev. D in press, arXiv:0812.1285

11AEI, May 2009


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This is what we found out about Naturesbook keeping system: the data can be written

onto a surface, and the pen with which the

data are written has a finite size.

-Gerard t Hooft

Everything about the

3D world can be

encoded on a 2D null

surface at Planckresolution

12AEI, May 2009

Holographic Theories of Everything


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Holographic geometry: a phenomenological layer

AEI, May 200913

Fundamental theory (Matrix, string, loop,)

Holographic geometry (paraxial waves, diffraction, transverse

spacetime wavefunction, holographic uncertainty)

Observables in classical apparatus (effective beamsplitter

motion, holographic noise in interferometer signals)


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Holographic Quantum Geometry: theory

Black holes: entropy=area/4

Black hole evaporationEinstein's equations from heat flowClassical GR from surface theoryUniversal covariant entropy boundExact state counts of extremal holes in large DAdS/CFT type dualities: N-1 dimensional dualsMatrix theoryAll suggest theory on 2+1 dimensional null surfaceswith Planck frequency bound

Beckenstein, Hawking, Bardeen et al.,

'tHooft, Susskind, Bousso, Srednicki,

Jacobson, Padmanabhan, Banks,

Fischler, Shenker, Unruh14AEI, May 2009


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Holography 2: Black Hole Evaporation

Hawking (1975): black holes radiate ~thermal radiation, loseenergy and disappear

evaporated quanta carry off degrees of freedom (~1 perparticle) as area decreases

States on 2D event horizon completely account for informationof evaporated states, assembly histories

Information of evaporated particles=entropy of hole= A/4

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black hole evaporation can obey quantum mechanics if

distant, nearly flat space has transverse indeterminacy

If the quantum states of the evaporated particles allowed relativetransverse position observables with arbitrary angular precision, at

large distance they would contain more information than the hole

17AEI, May 2009


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~ One particle evaporates per Planck areaposition recorded on film at distance Lwavelength ~ hole size Rstandard position uncertaintyParticle images on distant film: must have fewer pixels than holeRequires transverse uncertainty at distance L independent of R

Uncertainty of flat spacetime independent of black hole massSimilarly for number of position states of an interferometer

x > L

Holographic uncertainty and black hole evaporation

(L /x)2 < (R /)2

x > R

18AEI, May 2009


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Holography 3: nearly-flat spacetime

Unruh (1976): Hawking radiation seen by accelerating observer Appears with any event horizon, not just black holes: identify

entropy of thermal radiation with missing information

Jacobson (1995): Einstein equation derived fromthermodynamics (~ equation of state)

Classical GR from 2+1D null surface (Padmanabhan 2007)

Jacobson: points=2D surfaces19AEI, May 2009


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Holography 4: Covariant (Holographic) Entropy Bounds

't Hooft (1985): black holes are quantum systems 't Hooft, Susskind et al. (~1993): world is "holographic",

encoded in 2+1D at the Planck scale

Black hole is highest entropy state (per volume) and setsbound on entropy of any system (includes quantum degrees of

freedom of spacetime)

All physics within a 3D volume can be encoded on a 2Dbounding surface ("holographic principle")

Bousso (2002): holographic principle generalized to "covariantentropy bound" based on causal diamonds: entropy of 3D lightsheets bounded by area of 2D bounding surface in Planck units

Suggests that 3+1D geometry emerges from a quantum theoryin 2+1D: light sheets

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Holography 5: Exact dual theories in N-1 dimensions

Maldacena, Witten et al. (1997): AdS/CFT correspondence N dimensional conformal field "boundary" theory exactly maps

onto (is dual to) N+1 dimensional "bulk" theory with gravity and

supersymmetric field theory

Is nearly flat 3+1 spacetime described as a dual in 2+1?

AEI, May 2009 21


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Holography 6: string/M theory

Strominger, Vafa (1996): count degrees of freedom ofextremal higher-dimension black holes using duality

All degrees of freedom appear accounted for Agrees with Hawking/Beckenstein thermodynamic count Unitary quantum system Strong indication of a minimum length ~ Planck length What do the degrees of freedom look like in a realistic system? Matrix theory: wavefunctions of transverse position Matrix

Hamiltonian (CJH& M. Jackson)

AEI, May 2009 22


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Holographic geometry implements holographic entropy

bound in emergent 3+1D spacetime

3+1D spacetime from 2+1Dbuilt on light sheets: covariant formulationfewer independent modes than field theoryindependent pixels in 3D volume~ area of 2D null surface elementbandwidth limit of spacetime states

t

z

1

2

1

2

z

x

k = lP

k

y

23AEI, May 2009


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Theories with holographic noise

Two conditions are sufficient:

1. Maximum Planck frequency in any frame2. Planck wavelength resolution on light sheets

AEI, May 2009 24


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AEI, May 2009

1

2

y

x

t

3

25

1D segment of length L on

null wavefront

Sweeps out 2D surface:

independent position

degrees of freedom

Position variance in 2D

x2 Ll

P

(L /x)2 L / l

P


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Example: Matrix theory

Banks, Fischler, Shenker, & Susskind 1997: a candidate theoryof everything

Fundamental objects are 9 N x N matrices, describing N D0branes (particles)

Dual relationship with string theory Gives rise to 10 space dimensions, 1 compact, plus time

AEI, May 2009

R=size of Mdimension

D0 branes= KK modes

9 larger dimensions

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3+1D spacetime

emerges from

2+1D: lightsheet with z=t

2

1 2z

t

z

1

x

y

AEI, May 2009

Only 2 of the 9 space dimensions survive to be macroscopicThe third space dimension is virtual, swept out by 2D null sheet

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Holographic spacetime: wave theory from M theory

N D0 branes, N x N matrices Xi, , i= 1 to 9, compact Mdimension with radius R ~ Planck length

Hamiltonian from Banks, Fischler, Shenker, & Susskind:

Notions of position, distance emerge on scales >>R local in 2+1 D, incompressible on Planck scale: holographic Center of mass position of macroscopic body, x= trX Macroscopic longitudinal position encoded by first (kinetic)

term,conjugate momenta to position matrices

CJH & M. Jackson, arXiv:0812.1285AEI, May 2009 28


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Macroscopic wave equation from M theory

M Hamiltonian stripped to macroscopic essentials

substitute

AEI, May 2009 29

tr2 h22/x2,

H ih/z+,

H=R

2htr2

R k1 = /2


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Macroscopic wave equation from M theory

becomes

Schrodinger equation, with z+as time dimension Quantum mechanics without Plancks constant

AEI, May 2009 30

2u

x2+

4i

u

z+= 0

H= R2h

tr2


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Solutions of wave equation mix dimensions

Solutions display diffusion, diffraction:

AEI, May 2009 31

2

ux2

+ 4i

uz+

= 0

u(x, z+) =

k

Ak expi[k+z+ kx]

k =

4k+/


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New uncertainty principle: widths of wavepackets

AEI, May 2009 32

2ux2

+ 4i

uz+

= 0

x2 > L+/2

x2k2 162

L+ (4/)(2/k2)


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Nonlocal modes connect longitudinal and transverse positions

Wave solutions: Holographic geometry Transverse gaussian beam solutions from wave optics New macroscopic behavior, not the same as field theory limit

x

z,tAEI, May 2009 33


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Wave Theory of Spacetime

Adapt wave optics to theory ofspacetime wavefunctions

transverse indeterminacy fromdiffraction of Planck waves

Allows calculation of holographicnoise with no parameters

34AEI, May 2009


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Paraxial wave equation

phasors in wavefronts: wavefunction relative to carrier wave equation in each transverse dimension x

Basis of laser wave optics Solutions display diffraction: e.g. laser cavities reinterpret as a position wavefunction

AEI, May 2009 35

2u

x2 4i

u

z = 0


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Gaussian Beam solutions

AEI, May 2009 36


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Rayleigh range and uncertainty of rays

Aperture D, wavelength : angular resolution /DSize of diffraction spot at distance L: L/Dpath is determined imprecisely by wavesMinimum uncertainty at given L whenaperture size =spot size, or

( )D L/D

L

D = L37AEI, May 2009


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Indeterminacy of a Planckian path

Classical spacetime manifold defined by paths and eventspath~ ray approximation of waveIndeterminacy of geometry reflects limited information contentof band-limited waves

38AEI, May 2009


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holographic approach to the classical limit

Angles are indeterminate at the Planck scale, and becomebetter defined at larger separations:

But uncertainty in relative transverse positionincreases atlarger separations:

Not the classical limit of field theory Indeterminacy and nonlocality persist to macroscopic scales

39AEI, May 2009


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Holographic Noise in Interferometers

Nonlocality: relative positions at km scale Fractional precision: angle < 10-21, > "halfway to Planck" Transverse position measured in Michelson layout Heavy proof masses, small Heisenberg uncertainty (SQL):

positions measure spacetime wavefunction holographic noise appears in signal

40AEI, May 2009


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Measurement of holographic geometry requires coherenttransverse position measurement over macroscopic distance

CERN/FNAL: TeV-1

~10-18

m

LIGO/GEO600: ~10-18 m

over ~103 m baseline

41AEI, May 2009


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Signal phase~ difference ofintegrated distance along two

orthogonal arms

Beamsplitter

Beamsplitter and signal in Michelson interferometer

42AEI, May 2009


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Signal: random phase differenceof reflection events from

indeterminate position differenceof beamsplitter at the two events

reflection

events at two

timesseparated by

2L/c

Holographic noise in the signal of a Michelson interferometer

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Quantum uncertainty of transverse positions of beamsplitter

Position wavefunctionwidths of beamsplittter at

reflection events given byGaussian beamwidth

apparent arm lengthdifference is a random

variable, with variance

this is a new effect predicted with no parameters44AEI, May 2009

L/


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Wavefunction and wavefronts

AEI, May 2009 45

In an optical cavity of any size, theholographic transverse uncertainty is

smaller than the beam waist by a factor

P

/laser


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Interferometer with Planck radiation

AEI, May 2009 46

Beamsplitter mass limited to Planck surface densityNo better measurement is possible


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Power Spectral Density of Shear Noise

At f=c/2L, shear fluctuations with power spectral density

Uncertainty in angle ~ dimensionless shear

47AEI, May 2009


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Universal Holographic Noise

flat power spectral density ofshearperturbations:

general property of holographic quantum geometryPrediction of spectrum with no parametersPrediction of spatial shear character: only detectable innonlocal relative transverse position observablesDefinitively falsifiableBetter estimate at low frequencies in interferometers:

48AEI, May 2009

h(f) = N1/L2 = N12

tP/ = N

12.6 1022/

Hz


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Holographic noise does not carry energy or information

~ classical gauge mode (flat space, no classicalspacetime degrees of freedom excited)~sampling or pixelation noise, not thermal noiseBandwidth limit of spacetime relationshipsNecessary so the number of distinguishable positionstates does not exceed holographic bound ondegrees of freedom

No curvatureno strain, just shearno detectable effect in a purely radial measurement

49AEI, May 2009


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Normal incidence optics: phase signal does notrecord the transverse position of a surface

But phase of beam-split signal is sensitive to transverseposition of surface

( )

50AEI, May 2009


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GEO-600 (Hannover)

51AEI, May 2009


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Large power

cycles through

beamsplitter,

adds transverseholographic

noiseK.Strain

52AEI, May 2009


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Noise in GEO600 over time

H. Lck, S. Hild, K. Danzmann, K. Strain

K.Strain

AEI, May 2009 53


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S. Hild, GEO600, May 2008

54AEI, May 2009


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S. Hild, GEO600

55AEI, May 2009

h =

tP/ = 1.3 1022/

Hz


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Mystery Noise in GEO600

Prediction: CJH, arXiv:0806.0665

(Phys Rev D.78.087501)

Data: S. Hild (GEO600)

Total noise: not fitted

zero-parameter prediction for

holographic noise in GEO600(equivalent GW strain)

tPlanck /

56AEI, May 2009


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Why doesn't LIGO detect holographic noise?

LIGO design is not as sensitive to transverse displacementnoise as GEO600

relationship of holographic to gravitational wave depends ondetails of the system layout

Transverse position

measurement is not

made in FP cavities

57AEI, May 2009


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LIGO noise (astro-ph/0608606)

Measured LIGO noise spectrum (GW strain

equivalent, rms power spectral density)

(if shear=strain)

holographic noise

spectrum (shear)

58AEI, May 2009

2.6 1022

/

Hz


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holographic noise prediction for LIGO: reduced by

~arm cavity finesse

about 100 times less

59AEI, May 2009

N12.6 1022/Hz


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Beamsplitter position indeterminacy inserts holographicnoise into signal

system with GEO600 technology can detectholographic noise if it exists

Signatures: spectrum, spatial shear

Interferometers can detect quantum

indeterminacy of holographic geometry

CJH: Phys. Rev. D 77, 104031 (2008); arXiv:0806.0665

60AEI, May 2009


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Current experiments: summary

Most sensitive device, GEO600, sees noise compatible withholographic spacetime indeterminacy requires testing and confirmation! H. Lck: "...it is way too early to claim we might have seen

something.

But GEO600 is operating at holographic noise limit LIGO: current system not sensitive enough, awaits upgrade Proof: new apparatus, coherence of adjacent systems

AEI, May 2009 61


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Dedicated holographic noise experiments:

beyondGW detectors

f ~100 to 1000 Hz with GW machinesf ~ 3 MHz possible with new apparatus on ~40m scaleEasier suspension, isolation, optics, vacuum, smallerscale

Correlated holographic noise in adjacent paths:signature of holographic effect

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Two ~40m Michelsoninterferometers incoincidence

~1000 W cavity

holographic noise= laserphoton shot noise in ~5

minutes (1 sigma)

Conceptual Design from Rai Weiss

Currently discussing: Fermilab (CJH, Chou, Wester, Steffen,

Ramberg, Gustafson, Stoughton, Tomlin, Ruan, Bhat), MIT (Weiss,

Waldman), Caltech (Whitcomb), UC (Meyer)

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Status of the Fermilab Holographic Interferometer

Team so far: Fermilab (CJH, Chou, Wester, Steffen,Ramberg, Gustafson, Stoughton, Tomlin, Ruan, Bhat),

MIT (Weiss, Waldman), Caltech (Whitcomb), UC (Meyer)

Building tabletop prototype Planning around Weiss design Sites on site available and surveyed: ~40m arms possible

(partially outdoors), seismically acceptable

Invited by Director Oddone to move forward Internal R&D proposal in preparation, decision in ~June

AEI, May 2009 64


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Candidate site on old neutrino beamline

AEI, May 2009 65


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Science of Holographic Noise

Measure fundamental interval of time Measure all physical degrees of freedom: explore physics

from above

Study holographic relationship between space and time,emergence of spatial dimensions

Precisely compare noise spectrum with Planck time derivedfrom Newtons G: test fundamental theory

Test predictions for spectrum and spatial correlations:properties of holographic geometry

66AEI, May 2009


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Projects in phenomenology

Calculate spectrum via a different argument

Exact numerics of black hole/flat space system: normalizationof value of effective lambda to black hole physics

Full quantum wave model of apparatus, spacetime, signal Numerically evaluate displacement spectrum at all f Numerically evaluate signal spectrum from displacement

correlation function for various devices

Develop theory of cross correlation for arbitrary interferometeroffsets and orientations, numerical predictions

AEI, May 2009 67


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Projects in Theory

Use Matrix theory interpretation to bridge to strings

Secure lambda normalization to black hole entropy Generalize to curved spacetime backgrounds What happens inside black holes Relation to field theory Effect on inflationary modes (scalar, vector, tensor) Effect on quantum field modes (zero point energy) Cosmological observables (CMB, DE) Corrections to quantum processes Effect for masses less than M_P (atom interferometers)

AEI, May 2009 68


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Holographic geometry: part of new dark energy physics?

Holographic blurring is ~0.1mm at the Hubble length

~(0.1mm)^-4 is the dark energy density Nonlocality length for dark energy is holographic

displacement uncertainty, scaled to Hubble length

(literature on holographic dark energy centers on samenumerology)

Does not explain dark energy!

69AEI, May 2009


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Items to discuss at the Hannover workshop

What is the status of the GEO600 mystery noise? What are the prospects for GEO600 to test the holographic

noise hypothesis?

Are the theoretical arguments strong enough to motivate anew, dedicated high-frequency experiment, independent of the

results from GEO600?

What are the optimal design choices? (configuration, size,power,...)

Will there be two experiments? (Fermilab and Hannover?) If so, what will be the similarities and differences betweenthem? What about LIGO?

AEI, May 2009 70

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