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
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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
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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
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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):
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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
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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
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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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