Download Geophysical test of the universality of free fall

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Geophysical tests of
gravitational physics
with
superconducting gravimeters
Sachie Shiomi
Space Geodesy Laboratory,
Department of Civil Engineering,
National Chiao Tung University,
Hsinchu, Taiwan
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Contents
• Introduction
– Superconducting Gravimeters (SGs)
– Examples of applications to gravitational physics
– The global network of SGs
• Application 1: Testing the universality of free-fall
• Application 2: Searching for dilatonic waves
• Summary
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Superconducting gravimeter (SG)
• Sensitive and stable at low frequencies
1m
Hsinchu SG, operated by NCTU and CMS
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Gravimeter Sensing Unit
Working principle
Φ~ 2.5 cm
~4.2 K
• Sphere is levitated
by magnetic fields
induced by currents
in the
superconducting
levitation coils.
• Motion of the
sphere is monitored
by capacitor plates.
J. M. Goodkind, Review of Scientific Instruments 70 (1999)
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Applications to gravitational
physics
Earliest work (1976)
• Search for evidence of a preference frame
(Warburton and Goodkind, Astrophysical Journal, 1976.)
More recent works, e.g.
• Test of the inverse-square law
(Goodkind et al PRD 1993, Baldi et al PRD, 2001)
• Measurement of gravitational constant G
(Baldi et al PRD, 2005)
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The GGP network
• The Global Geodynamics Project (GGP)
network of superconducting gravimeters
(1997~): about 25 operating sites.
• To study geophysical signals in global
nature, i.e. oscillation of the inner core,
polar motion and wobbles.
D. Crossley, Journal of Geodynamics 38 (2004)
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Currently operating
Stopped
To be installed
Newly installed
D. Crossley
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Applications of the global network
to gravitational physics
• We investigate possible applications of the
GGP network to study gravitational
physics.
• One of such applications is testing the
universality of free-fall.
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Testing
the universality of free-fall
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Universality of free-fall
• Every material (point mass) in a given
external gravitational field falls at the same
rate.
http://www.endex.com/gf/buildings/ltpisa/ltpnews/physnews1.htm
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Motivations of testing the
universality
• Fundamental principle
– It should be tested as precisely as possible.
• New physics?
– Theories towards the unification of the four
fundamental forces predict new interactions
that violate the principle.
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Proposed new forces
(spin-independent)
Motivated by
Bosons (Spin) Mass
Charge
References (year)
Conservation of
baryon charge
Vector
bosons (1)
massless
B
Lee and Yang (1955)
Supersymmetry
U-bosons (1)
Massive
(very light)
B, Iz
Fayet(1986)
String theory
Dilatons(0)
massive
Dilatons(0)
massless
Ordinary
matter
B, Iz, E
Moduli(0)
massive
(millimeter
range)
Fujii(1971);Taylor and
Veneziano (1988)
Damour and
Polyakov(1994)
Dimopoulos and
Giudice(1996)
Ordinary
matter
Composition dependent
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Modification of Newton’s law
V(r)
Yukawa-potential type
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Current limits
Fischbach and Talmadge, The Search for Non-Newtonian Gravity (Springer-Verlag, 1999)
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The necessity of variety in
experimental approaches
• The universality has to be tested for
various putative charges, using different
kinds of test bodies, at different ranges.
• To confirm experimental results, it should
be tested by at least two different
experimental methods.
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The concept
Inner
core
Sun
Outer core
Mantle +
Crust
Earth
• If the universality were violated, the inner core
would move relative to the rest part of the Earth.
Surface gravity changes
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Test bodies: inner core and the rest
• Chemical composition
– Density [kg m-3]
• Inner core (iron, nickel): ~ 13000
• The rest (silicon oxides): ~ 5400
• Gravitational binding energy
– Inner core: -3.7 ×10-11
– The rest: -4.2 ×10-10
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Best observation points
N
Taiwan
SG
Sun
Earth
S
Summer
• In Spring and
Autumnal
equinox points:
on the equator
SG
• In Summer and
Winter solstices:
on Tropic of
Cancer or
Capricorn
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Equation of motion of
the inner core
Gravitational
stiffness
Damping effect
Violation effect
S. Shiomi, Physical Review D 74, 027101(2006)
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Forced oscillation
When the damping coefficient (k) is sufficiently small:
Surface gravity changes
10-12 ms-2
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Expected sensitivity
Current limits: a few parts in 1013
;nearly four orders of magnitude
improvement is necessary.
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Improving the sensitivity (1)
• Carrying out coincidence measurements at
two observatories located opposite side of
the Earth near the equators.
Concepcion,
Chile
Inner
core
Hsinchu,
Taiwan
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Improving the sensitivity (2)
• Development of the data analysis
method to extract weak signals.
e.g.
Non-Linear Damped Harmonic Analysis
method (S. Rosat et al, J. Geodyn. in press)
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Summary: expected signals
Direction
along the Earth-Sun line
Frequency
• once per day
• once per year
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Future works
• Improving noise reduction methods
– Identification of environmental noise
– Data analyses to extract weak signals
• Figuring out the optimum scheme of global
observations
– e.g. coincidence measurements
• Improvements of the sensitivity of SGs
• Application of elaborate Earth models
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Conclusions
• The universality of free-fall can be tested
using a superconducting gravimeter
installed near the equator to ~10-9.
• Some improvements can be expected
from global observations and applications
of advanced data analysis methods.
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Search for
composition-dependent
dilatonic waves
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Introduction
• String theory predicts the existence of relic
background of the dilaton (a scalar partner
of the graviton).
• Ordinary macroscopic test masses have
dilatonic charges, which depend on their
internal compositions.
• The response of the test masses to
dilatonic waves is non geodesic.
M. Gasperini, Phys. Lett. B 470, 67 (1999)
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The concept
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Estimation of upper limits (1)
Spectrum of the displacement ( l ) at resonance
Dimensionless energy density for massless dilaton
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Estimation of upper limits (2)
From residual gravity data,
an upper limit on the displacement is
1.1 ×10-4 m Hz-1/2 at 7 ×10-5 Hz.
(S. Rosat et al, J. of Geodyn. 38 (2004))
Effective viscosity: 10-3 ~ 1012 Pa s
(R.A. Secco, A Handbook of Physical Constants)
S. Shiomi, “Geophysical search for dilatonic waves” (submitted in 2007)
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• Nucleosynthesis and measurements of
cosmic microwave background:
Ωh2100 ≤ 10-5
• To reach this limit, the effective viscosity
has to be smaller than ~ 2 × 106 Pa s.
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Conclusions
• Dilatonic waves can be searched for using
superconducting gravimeters.
• The sensitivity is currently limited by the
uncertainty in the Earth model.
• If the effective viscosity were determined
to be smaller than ~ 2 × 106 Pa s, this
method would provide an upper limit better
than the astrophysical limits.
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Other possible future applications
• Improved tests of the existence of a
preference frame and an anisotropy of the
gravitational constant.
• Direct detection of gravitational waves
using the Earth as the receiver.
• Measurement of G
– Tests for a distant dependence, time
dependence and a spatial anisotropy.
• Improved tests of the inverse square law.
J. M. Goodkind, Review of Scientific Instruments 70 (1999)
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Summary
• Superconducting gravimeters have been proved
to be stable and sensitive in geophysical studies
and also they have been used to study
gravitational physics since 1970’s.
• The global network of superconducting
gravimeters has been developed to study the
Earth’s interior. By using the Earth as the test
body, we investigate possible applications of the
network to gravitational physics.
• We have discussed the geophysical test of the
universality of free-fall and the search for
dilatonic waves.
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Thank you.
Any new ideas for possible
applications of SGs are welcome.