Quantum Geometry and Interferometry

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Quantum Geometry and Interferometry

Craig Hogan

University of Chicago and Fermilab


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Quantum Field Theory

Classical Geometry (space-time)

ynam ca u no quan um

Responds to classical average of particle/field energy

Quantum particles and fields

,

background

Space-time geometry is assumed to be classical : it is not part of

the quantum system

Approximation explains all experiments with particles

But cannot be the whole story about geometry


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The Planck scale: gravity + quantum

equivalent Planck length ~10 -35 meters

5


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Gravity is thermodynamical

Theory suggests a statistical entropic origin of gravityar een e a . aws o ac o e ermo ynam cs

Beckenstein- Hawking black hole evaporation

Unruh radiation

Jacobson formulation of GR

Verlinde entropic formulation of gravity

Metric does not describe fundamental degrees of freedom

Classical space-time is a statistical behavior of a quantum system


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Physical states are holographic

Information encoded with Planck density on 2D bounding surfaces

,

Maldacena ADS/CFT dualities in string theory

Bousso covariant entropy bound: causal diamonds

Banks theory of emergence

States must have new forms of spatially nonlocal entanglement


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Macroscopic effects of new Planck scale physics

Quantum field theor assumes classical s ace-time; redicts thatPlanck scale effects are highly suppressed at large scales

Also true in string theory, using fields for macroscopic limit

But real geometry may have quantum effects on larger scales

,

New a rox im ation : c las s ic al m atter u an tum eom etr

10


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Requirements for a macroscopic quantum geometry

Consistent quantum theory

e.g. sa s y aco en es

Consistent with classical geometry

Formulate as a theory of position operators for massive bodies

Unidirectional plane wave modes should propagate along a nearlyclassical dimension

Holographic density of states

For thermodynamic GR, entropic gravity:Number of eigenstates = surface area in Planck units

Consistent with current experiments


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Wave interpretation

Spacelike-separated event intervals are defined with clocks and lightBut transverse positions defined by phases of Planckian waves are

,Lct

P

muc arger an e anc eng

Lct P

Wigner (1957): quantum

P

Add transverse dimension andPlanck fre uenc limit:m s w one space e

dimension and physically-realizable clocks

transverse position uncertainty


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Quantum-geometrical uncertainty and fluctuations

~ ct LTransverse uncertainty >> Planck length for large L

fluctuations in transverse position


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Interferometers as Probes of Planckian Quantum Geometry

CJH, Phys Rev D 85, 064007 (2012)

ovar an acroscop c uan um eome ry

CJH, arXiv:1204.5948

Phenomenon lies beyond scope of well tested theory

There is reason to suspect new physics at the Planck scaleMotivates an experiment!

Physics is an experimental science --I. I. Rabi


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Pioneer of precision experiments

Invented a device to measure position differences in space andtime with extraordinary precision:

Michelson Interferometer

Albert Michelson


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Michelson interferometer

Albert Michelson reading interference fringes


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Mi h l d t i b b Chi i t 1924


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Michelson and team in suburban Chicago, winter 1924,with partial-vacuum pipes of 1000 by 2000 foot

interferometer, measuring the rotation of the earth with

g rave ng n wo rec ons aroun a oop

28C. Hogan, January 2013


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I l h i h l i


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Intense lasers have precise phase resolutionand can make recise osition measurements

Amplitude 2 = N Large Nmp u e=sqr

ma

Photon number-phase uncertainty relation

N =1/2

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Interferometers can reach Planckian sensitivity

Over short (~ size of apparatus ~ microsecond) time intervals,interferometers can reach Planck precision (~ attometer jitter)

Fractional random variation in differential frequency or positionbetween two directions over time interval

Compare to best atomic clocks (over longer times):

C. Hogan, January 2013 32


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Space-time of Michelson interferometer

3 world lines: beamsplitter andtwo end mirrors

,cylinders

4 events contribute tointerferometer signal at onetime

,nonlocal in space and time,includes ositions in two

noncommuting directionsC. Hogan, January 2013 34


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Interferometer position noise spectrum, including transfer function

Quantum- eometrical noise

37 C. Hogan, January 2013


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GEO600 noise (2011) and predicted noise


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h O f d li h i i


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In the Oxford English Dictionary

43C. Hogan, January 2013


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E i t C t


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Experiment Concept

Measurement of the correlated optical phase fluctuations in a pair ofisolated but collocated power recycled Michelson interferometers

exploit the spatial coherence of quantum-geometrical noise

measure a g requenc es z w ere o er corre a e no se s sma

Sensitive to nonlocal entanglement of quantum-geometrical position states

Overlapping spacetime volumes -> correlated fluctuations

i m e

World lines of beamsplitters

space



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relative to GW

Seismic noise spectrum

measured at Fermilab

The exotic noise measurement can be made at high frequencies whereseismic noise is negligible e o ograp c no se s pre c e o e w e or


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Distinguishing exotic noise from

Normalization of spectrum scales as arm length L 2

Interferometer response function cuts off at f=c/2L Conventional RF backgrounds are usually frequency dependent

(narrow lines, ~1/f, etc.)

such as AM radio stations. Experimental knobs:

Orientation of two interferometersNested for maximum correlation

- -(information then travels along independent paths)

Change arm length to verify scaling with L.

Correlations of two interferometers


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Correlations of two interferometers

Overlapping spacetime volumes collapse into the same state

orre a es s gna s o near y co- oca e c e son n er erome ers

Non-overlapping configurations are uncorrelated

time Causal diamonds of

50space

eamsp er s gna s

C. Hogan, January 2013

Top view of one interferometer


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Top view of one interferometer

L configuration of 2 interferometers

Highly correlated signals

Causal diamonds are independentNo entanglement or signal correlations 51


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Ben Brubaker bolting the holometer vacuum system together


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Pipes are insulated with 4

fiberglass +


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Bake in situ to 200C by flowing 200A current through stainless steelvacuum pipe

East arms North arms


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Laser launch


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,

Nd:YAG laser

to lock the laser tothe instantaneous

frequency of theinterferometercavit .

Telescope formode-matching tothe 40m cavity.

Active PZT-basedsteering.

Separate launchfor eachinterferometer


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e erm a o ome er eam

Fermilab:

A. Chou (co-PI, project manager), C. Hogan, C. Stoughton, R.

Tomlin, J. Volk, W. Wester MIT LIGO:

M. Evans, S. Waldman, R. Weiss

.

S. Meyer (co-PI)U. Michigan LIGO

D. Gustafson

Northwestern

.

Training 4 PhD students, and providing research experience to numerous,

Status of the Fermilab Holometer


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Currently under commissioning at FermilabFunded mostly by A. Chou Early Career Award

Power-recycled 40m interferometers operating with high finesse

Developing & testing detectors, electronics, control systemsacuum sys ems o o n er erome ers are comp e e

Cross-correlation spectrum has been measured

Upgrades to subsystems still pending

Planckian sensitivity expected in a year or two



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Not a test of the holographic principle!


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Not foamlike!

o a e e ge o euniverse!


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Quantum Geometry and Interferometry