The Holometer: Measurements ofSpacelike Coherent Fluctuations of Space-Time

Ohkyung Kwon
on behalf of the Holometer Collaboration

20th Lomonosov Conference
August 23, 2021
kwon@uchicago.edu

The holographic bound — infrared catastrophes in a definite background space-time
The entropy of a black hole — the amount of information in the system — is proportional to
the 2D “surface area” of its horizon. The information density decreases linearly with scale!

SBH =

kA
4`2P

r=constantIII
II

In local QFT with a definite background,a system of scale R and cutoff m has totalmodes∼ R3 m3
For ΛQCD , gravitational binding energy
exceeded at a generalized Chandrasekhar
radius of 60 km — a third of empty Baikal!

I

t=constantIV

RS

AdS/CFT omits the degrees of freedom in
a Planck resolution background space-time.
[A. Cohen, D. Kaplan, and A. Nelson, PRL 82, 4971] [T. Banks and W. Fischler, arXiv:1810.01671]
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

1 / 22

The cosmological constant as the energy of vacuum
G. Lemaître — PNAS 20, 12 (1934)
ASTRONOMY: G. LEMAITRE

12PROC. N. A. S

EVOLUTION OF THE EXPANDING UNIVERSE
By G. LEMAITRE
UNIVERSITY OF LouvAIN
Read before the Academy, Monday, November 20, 1933

The problem of the universe is essentially an application of the law ofgravitation to a region of extremely low density. The mean density ofmatter up to a distance of some ten millions of light years from us is of
the order of 10-30 gr./cm.3; if all the atoms of the stars were equallydistributed through space there would be about one atom per cubic yard,or the total energy would be that of an equilibrium radiation at the temperature of liquid hydrogen. The theory of relativity points out thepossibility of a modification of the law of gravitation under such extreme
conditions. It suggests that, when we identify gravitational mass andenergy, we have to introduce a constant. Everything happens as though
the energy in zacuo would be different from zero. In order that absolute
motion, i.e., motion relative to vacuum, may not be detected, we must
associate a pressure p = - pc2 to the density of energy pC2 of vacuum.
This is essentially the meaning of the cosmical constant X which corresponds to a negative density of vacuum po according to

'XC2
(1)
10-27 gr./cm.3
47rG
Let us consider the motion of matter symmetrically distributed roundsome fixed point 0. The classical equation of motion under the action of
the modified gravitational field is
2Gm +
(2)
Po = -GYa. B. Zel’dovich and A. Krasinski — Sov. Phys. Usp. 11, 381 (1968)
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

2 / 22

The worst failed prediction in fundamental physics — a boundary condition?
Vacuum energy measured in a lab matches standard QFT.
If we scale this theory to the universe, prediction is 122 ordersof magnitude larger than the actual energy density.

Is a fine-tuned constant needed for cosmic structure?
Proposed explanations: multiverses, or a landscape?
The cosmological constant should be considered an
infrared boundary condition for the total degrees
of freedom in any fundamental theory of quantum
gravity, not a local contribution to the energy density.
[Tom Banks and Willy Fischler, arXiv:1811.00130]

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

3 / 22

Correlations in the space-time vacuum
Claim: Even the low-energy, ground-state limit of quantum gravity cannot be described byperturbative graviton fields on a background metric.
Scaling of information needs nonlocal correlations of space-time at large separations!

Can EFT accommodate the foundational principles needed in a fundamental theory?
Quantum Mechanics: No “local realistic” notions of classical geometrical paths and events
General Relativity: General covariance and background independence“Spukhafte” correlations (in the EPR sense) should exist in flat space-time with no dynamics.
Thermodynamic behavior of BH horizons applies to Unruh horizon entropy in accelerated frames.

Can we understand correlations in a space-time without a built-in boundary like AdS space?
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

4 / 22

A new phenomenological regime

C. Hogan, arXiv:1412.1807
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

5 / 22

The Fermilab Holometer
Holometer/MP8 Laser Lab

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

6 / 22

The Fermilab Holometer

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

6 / 22Extending LIGO technology to nonlocal correlations
LIGO −→ Holometer
Dick Gustafson (Michigan)
Samuel Waldman (SpaceX)
Rainer Weiss (MIT)

Laser interferometers: the most precise indifferential position measurements.
In dimensionless strain units h ≡ δL/L,
the power spectral density reachesqh̃2 (f ) . tP ≡ ~G/c5 ≈ 10−44 sec
LIGO measures local metric fluctuations
and stochastic gravitational waves.
Holometer probes similar stationary noisein space-time position, but at superluminal
frequencies sensitive to both timelike andspacelike correlations across the system.

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

7 / 22

Design principles
First-generation Holometer (2011 - 2016)

Cross-spectral density with two interferometers:h̃2 (f ) ≡∞−∞δLA (t) δLB (t−τ )e−2πiτ f dτL
Lt

Spacelike coherence: e.g. one Planck scale jitter
per Planck time, each generating a flat responseover system scale L/c due to its delocalized nature.
Variance scales like a random walk over L = 39 m:∆x2 P ≈ `P L ≈ PSD tP L2 × Bandwidth c/L
PSD ≡ h̃2 (f ) · L2 is shot noise limited and reaches:h̃2 (f ) ≈ tP ≈ 10−44 s

The sampling rate and bandwidth must far exceed
the 7.7 MHz inverse light crossing time.

Isolated and independent: optics, vacuum systems, electronics, clocks, and data streams.
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

8 / 22

Measured Sources of Environmental Noise

Exclusion of correlated environmental noise

Realtime Monitoring of Laser Noise andRadio-Frequency (RF) Environment

INPUT SIDE
Lasers & Active Optics• Correlated optical intensity noise• Correlated optical phase noiseContinuously measured during
data acquisition

OUTPUT SIDE
Detectors & Readout Electronics• Correlated electronics noise• Cross-channel signal leakage
Measured offline using opticalsources of independent white
noise (incandescent light bulbs)

Ohkyung
Kwon
Jonathan Richardson

Four RF environmental channels arecross-correlated with the interferometer
output channels (8x8 correlation matrix)• Lomonosov
HolometerNov. 17, 2017
- FNAL PAC

Aug 23, 2021
33

9 / 22

SpectralSpectral Density Ma

10
10−40
10−41
10−42
10−43
10−44

10−43

Cross Power(real part) [tP ]

1.0
0.5

Cross Power(imag. part) [tP ]Cross Power(imag. part) [tP ]Cross Power(real part) [tP ]1st-gen Holometer: a verified symmetry at 0.25 10Planck scale

0.0
−0.5
1.0
0.5

−44

1.0
0.5
0.0
−0.5
1.0
0.5
0.0
−0.5
0

0.0
−0.5
0

1

2

3
4
5
Frequency [MHz]

6

7

8

145 hour data — PRL 117, 111102 (2016)704 hour data — CQG 34, 165005 (2017)
Instrumentation — CQG 34, 065005 (2017)

Clean null test for exploring general geometries.
Ohkyung Kwon

1

2

3
4
5
Frequency [MHz]

6

7

8

Left: Independent bins at 1.9 kHz resolution.
Right: Rebinned to 100 kHz, Planck units.
At 100 kHz, uncorrelated noise is averaged downover 2.5 × 1011 independent measurements.
Cross-power spectral density in δL/L, normalized
to L = 39 m, reaches an upper limit below 0.25 tP .

Holometer • Lomonosov

Aug 23, 2021

10 / 22

What are the symmetries and degrees of freedom?
1st-gen Holometer — CQG 33, 105004 & 34, 075006 • E. Verlinde & K. Zurek, arXiv:1902.08207|dA/dτ|= |dA+ /dτ + dA− /dτ|,

Radial arms in two orthogonal directions from the beamsplitter.

a sum of the rotational components in the two directions, so that
(Ξ(τ) + constant) =P dA/cdτ.

All light propagation along null (lightlike) directions frommeasurements, following the boundary of a causal diamond.

τ), the swept area rate is simply related to the signal correlation by
PR

Poincaré symmetry

1/ 2tion to the exotic signal correlation at each
ined by closure of the circuit, is also ﬁxed by a projection onto the path, in thise (Eqs. 26, A13) :Lorentz boosts•

2) + constant) = ∆ x ⊥R (τ) sinθ =Lorentz symmetry

Translations

RotationsdA± /dτ = sin θdA± /dt = R (τ) sin
τ via dt/dτ

2nd-gen Holometer: Models on covariant structures — CQG 34, 135006 & 35, 204001
Correlations respect exact causal structure (in radial directions from the observer’s world line)
Correlations must be along these surfaces: e.g. transverse ones with rotational symmetry
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

11 / 22

Light cones as the basic quantum elements of space-time“Just as the proper recognition of this atomicity requiresin the electromagnetic theory a modification in the useof the field concept equivalent to the introduction of theconcept of action at a distance, so it would appear thatt and τ via dt/dτ =insin
and the swept
via be able intheθ,gravitational
theory area
we should±

principle to dispense with the concepts of space/dτ = sin θdA± /dt = R(τ) sinθ,and time and take as the basis of our description(30)
of nature the elementary concepts of world line

n to the exotic signal correlation at eachτ, apart from a constant oset ﬁxed
and light cones.”
ed by closure of the circuit, is also ﬁxed by a projection onto the path, in this— J. A. Wheeler(Eqs. 26, A13) :1/ 2

constant) = ∆ x 2⊥ R (τ) sinθ =P R(τ) sinθ.

(31)), the swept area rate is simply related to the signal correlation by

American Philosophical Society

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

12 / 22

Two
TwoLayouts,
Layouts,Same
SameTechnique
Technique
The Holometer research programFirst-Generation
First-GenerationHolometer
HolometerFirst-generation
Holometer (2011 - 2016)(2012-2016)(2012-2016)

Second-Generation
Second-GenerationHolometer
Holometer

Second-generation
Holometer (2017 - 2020)(2017)(2017)

90°90°armarmbendbend

Bendmirror added.
Unmodified:
optics, electronics, control
system,toanddata acquisition chain.
Sensitivity
Sensitivity
torotationalrotational
Sensitivity
Sensitivity
tototranslationaltranslational

fluctuations.
fluctuations.
Ohkyung Kwon

fluctuations.
fluctuations.

Holometer • Lomonosov

Aug 23, 2021

13 / 22

The Holometer research programFirst-generation Holometer (2011 - 2016)

Second-generation Holometer (2017 - 2020)
38.91 mBeam
Splitters

LASER

LASER

40 m

38.91 m

LASER
LASER

PD
PD

0.635 mPD
PD

PD

0.63 mPD

Y End Mirrors

PD

0.635 mBeamsplitter
stations

East
End Stations

North
End Stations

1m

Interferometer 1

40 m

Interferometer 2PD

18.45 m19.99 m90º
Bend
Mirrors

X End Mirrors

0.905 m20.46 m0.63 m

18.92 mBend mirror added. Unmodified: optics, electronics, control system, and data acquisition chain.
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

13 / 22

2nd-gen Holometer: measuring angular rotation (1-axis) at Planck diffraction resolution!
Measuring the rotation of the Earth with light traveling in two directions around a loop.
Albert Michelson, winter 1924, suburban Chicago.

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

14 / 22

10

5

10

4

10

10−36
IFO 1 AutoIFO 2 AutoIFO 1-2 Cross

10−37
10−38

Cross Statistical
Model Spectrum
Aux. Chn. Veto

103
102

10

−39

101

10

−40

10

0

10−41

10−1

0

2

4

6

8 10 12 14
Frequency [MHz]

16

18

20

1098 hour data — PRL 126, 241301 (2021)
For a nominal model of rotational fluctuations withspacelike coherence on light cones, the data sets a
0.25 tP upper bound on the normalization.
Ohkyung Kwon

2

0.2

0

0.0

−2

−0.2

2

0.2

0

0.0

−2

−0.2



Cross Power 10−41 m2/Hz
Imag. Part
Real Part

Rotation-Sensitive Configuration 106

−35

0

2

4

6

8 10 12 14
Frequency [MHz]

16

18

20

Strain Noise Power Spectral Density [tP ]10−34

Strain Noise Power Spectral Density [tP ]Spectral Density Magnitude m2/Hz

2nd-gen Holometer: 1-axis rotational fluctuations constrained at 0.25 Planck scale

Left: Independent bins at 9.92 kHz resolution.
Right: Rebinned to 496 kHz, real & imaginary.
At 496 kHz, uncorrelated noise is averaged downover 1.96 × 1012 independent measurements.

Holometer • Lomonosov

Aug 23, 2021

15 / 22

Cross-interferometer limits on environmental noise correlations

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

16 / 22

General hypothesis for future research program: Quantum coherence on causal horizons
All causal horizons are universal boundaries of coherent quantum information, where
the decoherence of space-time happens for the observer.
G. ’t Hooft’s models of black hole information —arXiv:1605.05119, Found. Phys. 46: 1185, 48: 1134, arXiv:1804.05744, 1809.05367, 1902.10469
Because of gravitational frame dragging / backreaction, entire horizon is a coherent quantum
object, with antipodes entangled. Horizon is a quantum-classical boundary for information.
E. Verlinde & K. Zurek, arXiv:1902.08207, JHEP 2020: 209 / K. Zurek, arXiv:2012.05870
Reproduces the same angular correlations as the ’t Hooft BH models for causal diamonds inflat space (conformal Killing horizons), and the random walk scaling of Planckian fluctuationsas probed by the Holometer, using topological BH mapping and tools from AdS/CFT.
T. Banks & K. Zurek, arXiv:2108.04806 — Conformal description of near-horizon vacuum states
T. Banks & W. Fischler, arXiv:1109.2435, 1810.01671, IJMPD 27: 1846005, Front. Phys. 8: 111
Holographic Space-Time — Localization of information: Causal diamonds are Hilbert spaces,intersecting / nested ones are tensor products / subspaces. “Fast scrambling” at the boundaries.
Causal order superpositions, Nat. Commun. 10: 3772 • Wigner’s friend paradox, arXiv:1902.09028
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

17 / 22

General hypothesis for future research program: Quantum coherence on causal horizons
Standard quantum limit for mass m, duration τDE∆x2 ? ~ τ /mr=constantIII
II

Coherent quadrupolar distortions needed for a BH
horizon of radius R = c τ to radiate at the standard
Hawking flux, one graviton of λ ∼ c τ per time τ
DE(δR/R)2 ∼ tP /τFluctuations of this scale exist on causal
diamonds in flat space (conformal Killing
horizons) of radius R = c τ and duration τ .

I

t=constant

IV

RS

Thermodynamic behavior of BH horizons applies
to Unruh horizon entropy in accelerated frames.
The coherence on all null surfaces gives rise to an estimate larger than conventional EFT by ∼ τ /tP .

In frequency space, corresponds to strain power spectral density tP over bandwidth 1/τ .
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

18 / 22

What are the symmetries and degrees of freedom?
1st-gen Holometer — CQG 33, 105004 & 34, 075006 • E. Verlinde & K. Zurek, arXiv:1902.08207|dA/dτ|= |dA+ /dτ + dA− /dτ|,

Radial arms in two orthogonal directions from the beamsplitter.

a sum of the rotational components in the two directions, so that
(Ξ(τ) + constant) =P dA/cdτ.

All light propagation along null (lightlike) directions frommeasurements, following the boundary of a causal diamond.

τ), the swept area rate is simply related to the signal correlation by
PR

Poincaré symmetry

1/ 2tion to the exotic signal correlation at each
ined by closure of the circuit, is also ﬁxed by a projection onto the path, in thise (Eqs. 26, A13) :Lorentz boosts•

2) + constant) = ∆ x ⊥R (τ) sinθ =Lorentz symmetry

Translations

RotationsdA± /dτ = sin θdA± /dt = R (τ) sin
τ via dt/dτ

2nd-gen Holometer: Models on covariant structures — CQG 34, 135006 & 35, 204001
Correlations respect exact causal structure (in radial directions from the observer’s world line)
Correlations must be along these surfaces: e.g. transverse ones with rotational symmetry
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

11 / 22

General hypothesis for future research program: Quantum coherence on causal horizons
Light cones as coherent quantum objects

2 D quantum fluctuations(2 transverse rotational axes)

1+1D fluctuations: Emergence of proper time
2D fluctuations: Emergence of local inertial frame
2-spheres

Decoherence happens on causal diamonds!
Dirac’s light cone function for relativistic quantum commutators

1+1 D quantum fluctuations

Toy model: “directional” eigenstates of proper time
On light cone —τ̂i , τ̂j

= i ijk τ̂k tPModel of correlations on inflationary horizon:
C. Hogan, PRD 99, 063531 and CQG 37, 095005
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

19 / 22

General hypothesis for future research program: Quantum coherence on causal horizons
Light cones as coherent quantum objects
1+1D fluctuations: Emergence of proper time
2D fluctuations: Emergence of local inertial frame
Decoherence happens on causal diamonds!
Dirac’s light cone for relativistic quantum commutators

Toy model: “directional” eigenstates of proper time
On light cone —τ̂i , τ̂j

= i ijk τ̂k tPModel of correlations on inflationary horizon:
C. Hogan, PRD 99, 063531 and CQG 37, 095005
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

19 / 22

Cosmic microwave background anomalies may contain concordant signatures!
Cosmic structure is an image of primordial quantum states —the fluctuations “froze in” at the inflationary horizon!
CMB anomalies after Planck

6000

3

Planck, A&A 594, A16

102

after Planck

3000

101

2000
1000

3

10

50

`max

0
600

DT T

100

Probability [%]

4000

10‒1

DT T [µK2 ]

5000

15
Hagimoto, Hogan, Lewin, and Meyer, ApJL 888, L29

Figure 7. Parity asymmetry in the Planck 2015
data [7].
Shown is thep-value significance, basedon a power-spectrum statistic sensitive to parity forthe four foreground cleaned
Planck maps (Commander, NILC, SEVEM and
SMICA) as a function of
the maximum multipole
used in the analysis.

60
Odd multipolesof WMAP maps was extended
by [63,the even and odd parity maps,
30
dominate
up 64,
to 65] who studied

300
0
-600
2

ℓ ≈ 280 T (ê) T ( ê)T (ê) + T ( ê),T (ê) =-30
.
(10)
2
2
Using a suitably defined power spectrum statistic – -60
the ratio of the sum over multipoles
10
30
1500
2000
2500
of 500
D` for the 1000
even map tothat for the
odd map– they found a 99.7% evidence for the!
violation of `parity in WMAP7 data in the multipole range 2  `  22. The analysis[43, 7], who• confirmed
the results from [63] based on
Ohkyung Kwon was finally extended to Planck byHolometer
Lomonosov

T + (ê) =-300

Aug 23, 2021

20 / 22

Cosmic microwave backgroundanomalies
mayCMB
containconcordantSignificanceof theseanomalies
is limitedsignatures!
by cosmic variance
But smallhintquantum
that standard
is missing something
Cosmic structure is an imageof p-values
primordialstatesinflation—
the fluctuations“froze inin”detailat the inflationary horizon!
Spooky predictions
can be tested
CMB
anomalies
after Planck
BENNETT CQG
ET AL. 33, 184001

rophysicalJournalSupplement
WMAP,
ApJS
192, 17Series, 192:17 (19pp), 2011 February 1

featurein angular space
low variance (Nside = 16)2-pt correlation 2 (✓ > 60 )2-pt correlation S1/2
2-pt correlation S1/2

p-values of various
l=2 + l=3
anomalies, from1510.07929

l=2

l=3

re. Unambiguous evidence for power asymmetry would
rofound implications for Ohkyung
cosmology. Kwon

l=2 + l=3
superposed over ILC!39

2-pt correlation S1/2 (larger masks)
hemispherical variance asymmetry
cold spotin harmonic spacequadrupole-octopole alignment` = 1, 2, 3 alignment
odd parity preference `max = 28
odd parity preference `max < 50 (LEE)
dipolar modulation for ` = 2 – 67

p-valuedatare 0.5%
 3.2%
 0.5%
 0.3%

Planck 15
Planck 15
Planck 15
Planck 13 &WMAP 9yr
Planck13
WMAP 9yr
Planck 15
Planck 15

Tab
Tab
Tab

Planck 13
Planck 13
Planck 15
Planck 15
Planck 15

Tab
Tab
Fig

 0.1%
 0.1%
 0.1%
 1.0%
 0.5%
 0.2%< 0.3%
< 2%
 1%

Tab
Tab

Tab
Tab

Table 1. P-values in per cent of various unexpected features. In this tablea Gaussian window, and added extra white noise. These process-the sense of p-values such that a small value means that it is unexpected
Holometer
Aug 23, 2021
20 / 22ing steps implicitly defined
a weighting•inLomonosovl, where the powerWe are finally ready to probe a general 3D geometry!
The class of theories motivated by recent lessons requires entangling all three dimensions —e.g. measuring two orthogonal rotational axes corresponding to incompatible observables.
O. KwonO. KwonUK QTFP ST/T006331/1 at Cardiff University: CQG 38, 085008 • Theory manuscript forthcoming!
Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

21 / 22

Thanks to...

Ohkyung Kwon

Holometer • Lomonosov

Aug 23, 2021

22 / 22

We are building a team to commission the next design. Collaborate with us!