on the potential of ste-quest clocks for relativistic geodesy

ON THE POTENTIAL OF STE-QUEST
CLOCKS FOR RELATIVISTIC GEODESY
By Ruxandra Bondarescu (ITP-Zurich)
Collaborators: Mihai Bondarescu (Universitatea de Vest, Timisoara),
Philippe Jetzer (ITP-ZURICH/UZH), Andrew Lundgren (AEI
Hannover), Gyorgy Hetenyi (ETH-Zurich), Nicolas Hollie (ETHZurich), Lapo Boschi (ETH-Zurich/U. Paris), Jayashree Balakshishna
(Harris Stowe State U., USA)
Partly based on Bondarescu et al. Geophys. J. Int. 2012, vol 191,
pages 78-82, arXiv: 1209.2889.
STE QUEST clocks
¨ 
Atomic clock technology progressing at an amazing rate
¤ 
¤ 
Improvement in stability & accuracy of about an order of magnitude a
decade
2012 Nobel Prize: Serge Haroche & David Wineland for particle
control in the quantum world
n 
¤ 
¤ 
¤ 
¨ 
For observing individual quantum systems without destroying them
920 km optical fiber link with accuracy ~ 4 x 10-19 (Predehl et al.,
Science 2012)
BUT still no accurate, stable and portable clocks, which is part of the
promise of STE-QUEST
PTB – Paris first clock comparison to measure geoid planned with (Δf/f
= 10-18 )!!
STE QUEST clock will be portable enough to be flown in space
¤ 
¤ 
What can we can be achieved on Earth with a portable atomic clock of
high stability and accuracy?
What can be achieved in space with such clocks?
Direct Application of General Relativity
Space tells matter how to move.
Matter tells space how to curve.
(Miner, Thorne and Wheeler)
Einstein’s equations
8π G
Gµν = 4 Tµν
c
Space-time curvature = Matter content (Einstein’s equations)
¨  Time does not flow everywhere at the same speed. The
closer an observer is to something heavy, the slower
her clock ticks!
Time near a black hole …
On a black hole horizon time stops altogether.
An observer infinitely close to the horizon will not age at all!.!
Time near a neutron star ..
On a neutron star clocks tick at about half their rate on Earth…
Image Credit: PSU
On Earth …
Ticks faster
Small differences in the speed of time are crucial
to every day life!
Wine stays in the open bottle because the time at
the bottom is slower than at the top.
• 
the difference in time flow between two clocks
placed at 33 cm one above the other has been
measured!
(Chou et al, 2010)
Ticks slower
Current Clocks in Laboratories
¨ 
optical lattice clock: Yb+
5 x 10-16/√τin 1 sec
¤  Measurement uncertainty ~ 10-17
¤  Δf/f = 10-17 corresponds to 10 cm in geoid height
¤  Stability
¨ 
single ion clocks: Al +
stability ~ 3 x 10-15/√τin 1 sec
¤  Measurement uncertainty ~ 7 x 10-18
¤  Relative
Surveying Earth’s Interior with Clocks
¨ 
A clock over a heavy rock will tick slower than one placed
on top of a large empty underground cave.
¤ 
¨ 
¨ 
Portable atomic clocks are sensitive to local, small scale substructure (<< 100 km)
detectable or not? It depends on
¤ 
¤ 
¨ 
¨ 
A portable atomic clock will slow down as it passes over the
rock and speed up as it passes over the cave.
Precision and stability of the clock measurements
size & shape of the anomaly, on the density contrast with the
surrounding material, and on the distance to the observer.
Clocks can measure changes in the gravitational potential on
the local scale due to mineral and petroleum deposits, structure
of tectonic plates, ground water reservoirs and even buildings...
The geoid accounts for the effects of all subsurface density
variations.
Local Measurements of the Geoid
¤ 
Clocks provide the most direct method to determine the geoid locally
(Bjerhammar, 1986)
n 
¤ 
¤ 
¤ 
¤ 
¤ 
¤ 
¨ 
Geoid is the surface of constant gravitational potential that extends the
mean sea level. A ball on the geoid will just sit there. It will not roll up or
down. To measure: one clock at mean sea level and another one anywhere
on the continent.
Tick rate of clocks is constant of the geoid after corrections e.g.,
from tides, etc.
Clocks measure geopotential differences at the location of the
clock
ALL current methods that determine the geoid measure derivatives
of the potential – vectors or tensors that need to be integrated. The
integration is typically ill defined.
Geoid known to 30-50 cm (locally from gravimeters + leveling)
GOCE & GRACE – satellite measurements of geoid (poor spatial
resolution: 100 km; geoid height ~ 1 – 2 cm)
On the ground: PTB – Paris first clock comparison to measure geoid
planned at Δf/f = 10-18 !!!
Complementary to measurements from gravimeters and
accelerometers
¤ 
independent measurements with very different characteristics
naccuracy corresponds to a change
and
are the
vitational
constant,
RE m
−18
2 −2
≈ 0.1
s M.EThe
!U
= c2 10
For the standard values of RE ≈
de Earth.
height
can be computed by
as24
2 −2
× 10 kg and !U = 0.1 m s , one
ght RE + !h and RE , respectively,
minute and degree) spatial resolution. While the oceanic crust is
3
Simple example: Buried Sphere
id height of !h ≈ 1 cm.
(Turcotte & Schubert 2002)
thoughttwo
to be simpler
both in synthetic
and in density
variations for a joint
In this
study, we gravity
take
simple
examples
accurate
instruments,
alone
is structure
insufficient
to map subsur4π Gb !ρ
than the continental crust, the amplitude of geoid anomalies in the
,
!U (x) =
ocean
due to the
underlying
mantle
structure (see
reach uplater)
to a heightand a buried
gravity–geopotential
survey:
a
buried
sphere
(x
)
3
+
h
face structures. This is ofdue
to the non-uniqueness of the inverse
100 m (Marsh & Martin 1982). On continents, a resolution of
where !ρ = ρ − ρ is the d
1
cm
in
geoid
height with unlimited Information),
spatial resolution, which isboth
3-D rectangular
slablocal
(see the
Supporting
of conto
its surroundings, b is its ra
problem.
Combining
gravity
with
direct,
local
geopotential
achievable considering current technological advances, will theresurface measured
from the c
foreWe
be largely
sufficient
to add significant details
existing geoid
stant density anomaly.
then
investigate
thetoextent
to which
the
anomaly
in
the
z-direction
is
measurements
reduces some
of
this
degeneracy
(i.e.
depth
determimaps derived from satellite measurements. These direct measuredegeneracy of the inverse
is reduced
ments ofproblem
geopotential differences,
leading to aby
morehaving
direct conti-both gravity
4π Ghb !ρ
=
.
!g
nation) and is able to provide
inversion
results.
In(x)pracnental geoidmeaningful
as outlined earlier (Section
1), will not only provide
the
(x
)
3
+
h
and geopotential measurements.
first, high-resolution geoid map per se, but will also reveal density
2
1
2 /2
1
0
3
z
2
3
2 /2
a synthetic example,
anomalies
from large to small,
mantle- to crustal-scale
sources, in- andAsfuture
tical terms, using already
available
relative
gravimeters
1.5 km) piece of mantle or m
cluding structure of the lithosphere, fluid reservoirs in the crust and
the shallow upper crust (ρ
dense ore deposits.
inverse method
approaches looking
portable atomic clocks, joint
fieldMoreover,
surveying
becomes
a conceivable
h = 2 km, which is a relativ
to map structural and/or density variations of the Earth’s interior
per
cent. Such a scenario (F
will
further
benefit
from
the
joint
geopotential
and
gravity
surveys.
4.1 Buried sphere
approach.
S
¨  Depth to the center ofInthe
buried
this
study,awe
take two
simple
synthetic
examples
a joint
at a for
depth
h in
We
assume
spherical
body
of density
ρ 1 buried
nal constant, RE and M E are the
nh.be
known
at
relatively
high
(between
gravity–geopotential
survey:
a
buried
sphere
(see
later)
and
a
buried
sphere
a medium of density ρ 0 . The corresponding geopotential anomaly
For the standard
values of RE ≈
3-D(Turcotte
rectangular
slab (see2002)
the Supporting
Information), both of con4l resolution. While the oceanic
2 −2 crust is
& Schubert
is
kg and !U
=
0.1
m
s
,
one
¨  and
Radius
ofradius
the
h in structure
density
variations
Figure
2. in
Minimum
ofsphere
a buried sphere
radius b that
atomic clocks
ableinvestigate
resolve, as a function
of depthtoh and
relative
stantofdensity
anomaly.
We are
then
the extent
which
thedensity a
3
ht
of
!h
≈
1
cm.
2
−2
4πmGb
2, 5 of
andgeoid
20 per anomalies
cent. Here we in
usethe
an accuracy of !U max = 0.2
s !ρ
, that is the double of the expected accuracy, to take into account pote
the amplitude
degeneracy
of
the
inverse
problem
is reduced by having both gravity
,
(3)
!U
(x)
=
errors.
The upper left
part of the diagram, shaded in brown, corresponds
¨  Density
contrast
1/ to spheres touching the ground; therefore the detection thresh
g mantle structure
reach up to a height and geopotential
2 + h2) 2
3 (xmeasurements.
calculated for this domain.
ME !h
,
(2)
2
Unkowns
TRYE T O D I R E C T G E O I D
0
n 1982). OnReduce
continents,
a resolution
of
the
degeneracy
of
the!ρinverse
anomaly of the sphere compared
where
= gravimeters
ρ 1 − ρ 0 is the density
2 −2
h unlimited both
spatial
resolution,
is m s ) and relative
atomic
clocks (!Uwhich
important to note that eqs (3) and (4) have differen
max ≈ 0.25
to its surroundings,
is its radius
x is
distance
onperformed
the
problem
by
gravimetric
≈E
12.6
The primary
limitation
comes&from bthe
(!g
ings:and
due to
thehorizontal
relative nature
of easily
maxadvances,
rent
technological
will thereO D
IRE
Cz T
G
O mGal).
I combining
D
4.1 surface
Buriedmeasured
sphere from the centre
h the
of
sphere.
The
gravity
atomic
clock sensitivity
since
relative gravimeters
have sensitivities
mentsanomaly
in
the
field,
well
asrelated
to!gg
the
properti
Figure 1. (a) Geopotential
!U (solid
line)as
and gravity
anomaly
(dashed
line) as a function
of displace
z inherent
add significant
details
to
existing
geoid
atomic
clock
measurements
a density contrast of 20 per cent with respect to the surrounding crust buried with its centre at a depth of h = 2 km. T
as
in the range of µGal. We then consider
ratio of a
!U
and
!gz threshold
two
will
provide
anomaly
in
the
z-direction
of is
!U the
0.1
m s methods
for atomic clocks
with frequency
of 10 . (b) To determine
the d
atinaccuracies
a independent
depth
h in measu
assume
spherical
body
of =density
ρ 1 buried
e measurements.
These direct measure- Wethe
displayed as function of horizontal position. The
resulting curve is a parabola with its minimum located at the sear
a function high
of x:
their different sensitivity that will allow better d
nown at leading
relatively
3 . The corresponding geopotential anomaly
erences,
to a more(between
direct conti- a medium of density
ρ
4π Ghb !ρ
0
h b
subsurface structures.
2
Geo
!U
x
(x)
=
.
(4)
!g
ution.
While1),the
oceanic
crust
is h. (Turcotte
z
lier (Section
will
not only
3/
& Schubert
2002)
=h+
≈ hprovide
for x # the
(5)
2 is
2
2
3 (x + h )
h variations
ructure
inz density
map perand
se,!g
but
will also
reveal density
4π Gb3 !ρ
example, we
consider
aU spherical
(radius b =
mall, mantleto crustal-scale
mplitude
of geoid
anomaliessources,
in the in- !U (x)As=a synthetic
5
C
O
N
C
L
S
I
O
N
S
,
(3)
In this simple case, the
above
ratio
can
be
used
to
determine
the
2
−3
1
Δf/f
≈ΔU/c
/
1.5 km) piece of mantle or magma (ρ 1 ≈ 3200 kg m ) located in
osphere,
fluid
reservoirs
in athe
crust and
tle structure
reach
to
height
depth
h to up
the centre
of the anomaly (see Fig. 1b).3 (x 2 + h 2 ) 2
Mapping
geoidkg
directly
ρ crust ≈the2670
m−3 )and
at alocally
depthwith
of portab
the shallow
upper
crust
ver,On
inverse
method
looking
2).
continents,
aapproaches
resolution
of of our method,
To illustrate
the sensitivity
we compute
from
eq. (ρ 0 =
is a dramatic application of General Relativity to o
−
ρ
is
the
density
anomaly
of theof
sphere
where
!ρ
=
ρ
= 20
h
=
2
km,
which
is
a
relative
density
anomaly
!ρ/ρcompared
ensity
variations
of
the
Earth’s
interior
1
0
(3)
the
radius
of
the
smallest
detectable
sphere
as
a
function
of
mited spatial resolution, which is
which is becoming possible withcrust
improving techno
max
2 −2
−18
in the range of µGal. We then con
a function of x:
!U
x2
=h+
≈ h for x # h.
!gz
h
Radius of sphere vs. depth
In this simple case, the above r
depth h to the2 centre
of the anoma
ΔUmax = 1 m /s2
To illustrate the sensitivity of o
(3) the radius
of the smallest de
-17
Δf/f = 10
depth,
density contrast and clock
"
!
3h!Umax 1/3
,
b=
4π G!ρ
24
/ = 100%
/ = 50 %
/ = 20 %
/ =5%
/ =2%
/ =1%
Touching the ground
22
20
18
b [km]
16
14
12
10
8
6
4
2
0
10
1
10
h [km]
2
10
where !U max = !U(x = 0).
Fig. 2 displays b for density con
1 to 20 per cent as a function of de
rors or noise is not yet known, but f
curacy ratio two times higher than
Fig. 2 shows the dashed lines abov
detect buried objects for each den
spheres are considered. At large !
radius sphere is detectable down
sity contrast of 1 per cent, a 10
Volcanoes
¨ 
Clocks can measure changes inside the volcano
BEFORE the ground moves!
¤  How
large in the magma chamber? Is it partially filled?
Is it empty?
¤  Dikes are closer to the surface
¨ 
Combine with existent measures
¤  For
Etna, e.g., slow ground movement: a few millimeters
per year via GPS
¤  Takes > 10 years to measure
¨ 
Combine with gravity measurements?
Movie by Thomas Glauninger (IT University of Zurich)
Water, Oil and Minerals
¨ 
¨ 
Detectable with clocks?
Depends on the size of the
deposit/water reservoir
and on the density contrast
Oil has roughly the same
density as water
¤  Lower
density contrast
because of the porosity of
the surrounding material: 1%
- 2%
¨ 
Some minerals are mixed in
with other materials =>
small density contrast
Reference clock
Portable clock
Tick rate is faster
Over oil/gas deposit
Reference clock
Portable clock
Tick rate goes back up
Reference clock
Atomic Clocks in Space
¨ 
Can clocks be part of future GRACE/GOCE missions? When are they
accurate enough? What would a clock provide?
¤ 
A very stable frequency reference.
n 
n 
¤ 
Reduce oscillator noise?
Improve tracking of space crafts?
Multiple space-craft setup of future GRACE
n 
4 clocks: second derivative of the gravitational potential?
n 
¤ 
Accelerometers have a drift noise ~ 1/f that limits their low frequency
performance.
n 
¤ 
¨ 
Could be important for geoid measurements
Clocks are better at resolving low multipoles perhaps without so much
averaging
LISA Pathfinder technology could be our precedent for exporting GR
testing technology to relativistic geodesy/geophysics
Atomic clocks have been steadily improving since the 1950s. No end
in sight yet! Important to use their full potential!
Conclusions
¨ 
Atomic clocks provide the most direct local geoid measurements
¤ 
¤ 
¤ 
¨ 
¨ 
¨ 
They measure potential differences at the location of the clock
Add detail to satellite maps
Calibrate satellites?
The measurements are non-instantaneous – there are corrections that
have to be considered, e.g., from tidal effects
Provides an independent measurement from gravimeters,
accelerometers with independent sources of errors
Can be combined with local gravimetric & InSAR/GPS & other
measurements to reduce the degeneracy of the inverse problem
¤ 
¤ 
Different scaling, different systematics, etc.
Gravimeters are more accurate. However, they measure the gradient of
the potential, which is a vector. Its integral is poorly defined since its
direction is not known accurately.
Atomic clocks get a grip on gravity - physics-math - 30 Sept...
http://www.newscientist.com/article/mg21528844.200-atomic...
In the press ….
Atomic Clocks To Measure Earth's Geoid From The Ground -...
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Home | Physics & Math | Tech | News
VIEW // COMMUNICATIONS
Atomic clocks get a grip on gravity
Atomic Clocks To Measure Earth's Geoid From
The Ground
Updated 14:55 02 October 2012
Magazine issue 2884. Subscribe and save
Prospecting for Oil or Gold? Check the Time - IEEE Spectrum
Satellites
http://spectrum.ieee.org/tech-talk/at-work/test-and-measureme...
give a rough picture of the Earth's geoid. Now physicists say atomic
issue
clock technology is ready to This
giveweek's
a better
picture from the ground
MEASURING Earth's hidden structures could soon be as simple as looking at
your watch - provided it's a super-accurate atomic clock.
BLOGS
3 comments
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// TECH TALK
Such clocks are nearly good enough to deliver a detailed geoid, says Ruxandra
THE PHYSICS ARXIV BLOG
Prospecting
for
Oil or ofGold?
theand
Time
Bondarescu at the
University
Zurich, Check
Switzerland,
her colleagues. The
Monday, September 17, 2012
POSTED BY: DOUGLAS MCCORMICK / WED, NOVEMBER 14, 2012
geoid is a model
of Earth's density variations - from the surface down to the
mantle - as revealed by anomalies in the planet's gravitational pull. Knowing
Clocks low in the gravity well run slower than those higher up. That’s just a relativistic fact of life—one that we take
the geoid's shape can aid studies of deeply buried geological structures and
advantage of every time we use the Global Positioning System. (I remember how cool I thought it was when I first
show how mass is being redistributed over time, such as by the melting of polar
learned that clocks in orbiting GPS satellites have to be programmed to correct for relativistic time dilation.) Within theResearchers say atomic clocks now good enough to measure E...
ice sheets.
past year, experimentalists comparing the speeds of widely
separated atomic clocks (connected via fiber optic cable)
have shown
that current
chronometers,
with uncertainties
Geoid measurements use satellite readings of Earth's
gravitational
field,
but
around 10-16, are sensitive enough to detect the change in
they are limited to a resolution of about 400 kilometres.
time’s flow that accompanies a shift of a meter or less in
relative elevation.
Quantum Physics
06 October 2012
Researchers say atomic clocks now good
enough to measure Earth's geoid
ADVERTISEMENT
General relativity tells us that clocks run slightly faster above sea level due to
Thean
geoid
is the
Earth-swaddling
higher gravitational potential – the potential energy
object
has
based on itssurface of equal
potential
that more or less coincides with global
position in a gravitational field – and slower belowgravitational
due to lower
gravitational
mean the
sea level.
Or, from
thealso
chronometric viewpoint, the
potential. That means an atomic clock carried around
surface
could
October 1, 2012 by Bob Yirka
surface on which all clocks tick at the same rate.
The geoidLatest news
More
measure the geoid, Bondarescu says. The team's
calculations show that large
isn’t smooth. As we have known for years (and continue to
clocks in labs are already accurate enough to determine geoid heights to the
prove with increasing detail), the geoid undulates.Manipulators
Its rise and
of quantum world win
nearest centimetre (arxiv.org/abs/1209.2889).
fall betray details of objects and events far below the surface.
physics Nobel
Writing in Geophysical Journal International (the paper is also available on arXiv.org), a team of researchers from
The clocks still need to be more portable, but Roger Haagmans at the
Switzerland, the United States, and Romania shows that clocks accurate to within 10-18 could map the geoid to within
European Space Agency says miniaturised versions are feasible.
http://phys.org/news/2012-10-atomic-clocks-good-earth-geoid...
Enlarge
Credit: ESA
15:26 09 October 2012
(Phys.org)—Researchers from the University of
Zurich say that atomic clock technology has
sufficiently progressed to the point that it should now
be feasible to use them to measure the Earth's geoid,
thereby producing more accurate geophysical
estimates of oil and mineral deposits, as well as water
reservoirs. The team, led by Ruxandra Bondarescu
Bondarescu and her co-workers New
show Scientist
that a clock with 10-18 accuracy can easily detect and locate a 1.5-kilometerwrite in their paper published in Geophysical Journal
radius, high-density sphere centered 2 km below the surface. It could also unmask a 4 km-radius sphere 45Black-hole
km below
laser
edges
closer
to
testing
Not just a website!
International, that atomic clock accuracy now
our feet. Time changes can reveal subtler differences, too—such as a 1 percent density anomaly 10 km in radius
Hawking
centered 37 km underground. Subscribe to New Scientist and get:
approaches a frequency ratio inaccuracy of 10-18 which they say should provide an accuracy
11:48 08 October 2012
in measuring a equipotential surface area equivalent to just one centimeter.
Established methods (like those used
in Scientist
a recently published
report
linking variations
in the Earth’s magnetic field to
New
magazine
delivered
every week
Unlimited online access to articles from over
Bondarescu, et al maintain that chronometric mapping of the geoid presents some distinct advantages. Clock readings
500 back issues
measure the potential surface directly. The researchers point out that force (the first derivative of the potential) must be
A novel laser could confirm
Stephen
Hawking's theory
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1 comment
Haroche and Wineland
about a centimeter and show the sizes and locations of mass variations far below the surface. Since the accuracy of
found ways to handle
standard reference clocks has increased at a steady order-of-magnitude-per-decade since the 1950s—and since newly
quantum objects without
The
penultimate
paragraph
of
this
article
has
been
edited
since
it
was
first
built optical atomic clocks and proposed designs for highly charged ion and nuclear clocks promise to increase that rate
destroying them, paving the
posted
substantially—it is clearly time prepare for an age in which we can map the crust and mantle by watching way
time slip
for by.
today's atomic clocks and quantum
computing
Imagine a bubble of magma 20 percent denser than the surrounding rock. University of Zurich physicist Ruxandra
mass flows deep under the Atlantic and Indian Oceans) use satellites to detect variations in gravitational force.
New on Technology Review
that black holes emit light –
and find practical
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Предложен новый метод определения формы Земли
01 октября 2012 года, 19:04 | Текст: Александр Березин | Послушать эту новость
Земля — геоид (а масло — масляное, но об этом в другой раз). При помощи спутников мы можем
относительно точно измерить глубину его впадин и высоту выступов. Собственно говоря, эта работа уже
ведётся. И она весьма интересна практически, ведь в тех точках геоида, где гравитация сильнее, чем
обусловливает его форма, близко к поверхности находятся залежи необычно тяжёлых или очень лёгких
веществ.
Но чтобы всё корректно посчитать при помощи спутников, их измерительные инструменты нуждаются в
частой калибровке. А обработка данных требует колоссальных вычислительных мощностей.
Услуги
Managed
Services от
IBM — это
оптимизация
затрат, улучшение
качества и скорости
ведения бизнеса в
России.Подробнее
Звёзды вокруг чёрной
дыры и звёзды,
выбрасываемые из
нашей Галактики,
имеют одно
происхождение
In Reichweite: Genaue Vermessung des Geoids vom Erdboden
Zürich
(Schweiz) – Die wahre physikalische Form der Erde – das sogenannte Geoid – lässt sich grob durch die
Возникло подозрение,
что «Вояджер-1» von Satellitenbahnen bestimmen. Eine sehr viel genauere Vermessung des Geoids mithilfe von
Untersuchung
вышел за пределы
Atomuhren
am Erdboden sei in greifbarer Nähe, so ein internationales Forscherteam im Fachblatt „Geophysical
Солнечной системы
Journal
International“. Eine detaillierte Kenntnis des Geoids ist für die Geophysiker von großer Bedeutung, da
Любители томатов
страдают от
sieреже
beispielsweise
Rückschlüsse auf Dichteanomalien im Inneren der Erde erlaubt.
инсульта
Самцы
австралийских
„Das
Geoid
entspricht etwa der mittleren Meeresoberfläche“, so Ruxandra Bondarescu von der Universität
квакш квакают друг для
Zürich
und
ihre
Kollegen, „doch im Bereich von Kontinenten ist das Geoid schwerer zu bestimmen.“ Beim
друга, но
не для
самок
КОМПЬЮТЕРРА
heutigen
Standardverfahren
messen
Forscher die Abweichungen von Satellitenbahnen von der Idealform.
Древнего паука
застали
за атакой
на наездника Computermodelle
Mithilfe
komplexer
rekonstruieren die Wissenschaftler daraus ein Geoid, das möglichst genau
Google готовит
10-дюймовые
планшеты с Dieses Geoid extrapolieren sie dann über die Landmassen
чтения в
mitНавыки
der mittleren
Meeresoberfläche
übereinstimmt.
разрешением выше, чем у
детском возрасте
der
Erde
hinweg.
Doch
dieses
Verfahren
liefert oft mehrere mögliche Varianten, die dann subjektiv ausgewählt
зависят от развития
нового iPad
мозга müssen. Außerdem ist die räumliche Auflösung mit etwa 400 Kilometern zu gering, um den vielfältigen
werden
Эти фотографии,
Acer Iconia W510:
Dichteschwankungen
in der kontinentalen
Erdkruste und darunter gerecht zu werden.
записанные на пластинах,
планшет с
Atom-процессором п/у
EsWindows
gibt allerdings
eine
8
расскажут о нас через
лет so Bondarescu und ihr Team, die viel genauere Ergebnisse liefern kann
andereмиллиард
Methode,
und
die dank
des Fortschritts beim
Bau ultrapräziser Atomuhren schon bald anwendungsreif sein könnte. Das
В Австралии
Ролевой
экшен Fable:
The Journey поступил в
сформулированы
Geoid
ist – physikalisch gesprochen
– eine Fläche, auf der die Schwerkraft der Erde konstant ist. Die Allgemeine
продажу
уравнения для движения
Relativitätstheorie Albert Einsteins
zeigt,
dass
die Zeit nicht überall gleich verläuft, sondern umso langsamer, je
быстрее
скорости
света
Проведено лазерное
stärker
das Gravitationsfeld ist. Deshalb lässt sich mit genauen Atomuhren der Verlauf des Geoids bestimmen:
сканирование
Фотографии с «Игромира
Стоунхенджа
Oberhalb
dieser Fläche laufen2012»:
die Uhren
schneller,
darunter langsamer.
игры, игроки
и всё
Algiz X10:
То, что гравитационное поле Земли неоднородно, известно давно, но вот использовать такую
неоднородность для поиска полезных ископаемых ещё не удавалось. (Здесь и ниже иллюстрации Ruxandra
Bondarescu et al.)
Группа исследователей из Цюрихского университета (Швейцария) во главе с Руксандрой Бондареску
предложила более простой и, кажется, весьма точный метод определения формы геоида и даже
гравитационных аномалий при помощи всего одного типа инструментов. Правда, в помощь инструменту
придётся придать теорию относительности.
Как все помнят, из последней вытекает, что время быстрее течёт выше уровня моря и медленнее —
ниже него (из-за более высокой гравитации). Согласно проведённому моделированию, уже
существующие атомные часы вполне способны зафиксировать с высокой точностью как высоту земной
остальное
«внедорожный»
Die
besten Atomuhren sind soМеханика
präzise,
dass sie im Verlauf von zwanzig Milliarden Jahren nur um eine Sekunde
планшет с диагональю
в электронике:
тачскрина
10 дюймов
falsch
gehen
würden. Mit dieser
Genauigkeit
растянутый
кремнийlassen
станет sich Höhenabweichungen von nur einem Zentimeter
Горький вкус
инфекции, existieren основой
messen.
Allerdings
derart будущих
genaue Atomuhren bislang nur im Labor unter genau kontrollierten
микросхем
или Как вкусовые
Bedingungen.
Doch die Entwicklung gehe weiter, so Bondarescu und ihre Kollegen. So plant die europäische
рецепторы защищают
Raumfahrtbehörde
2014 eine Atomuhr an Bord der Internationalen Raumstation zu installieren, die bereits eine
нас от бактерий
Samsung Galaxy Music:von einer Sekunde
Ganggenauigkeit
pro 200 Millionen Jahren hat. Es sei also nur eine Frage weniger Jahre, bis
iBUSINESS
смартфон для
ausreichend
genaue Atomuhren
auch außerhalb kontrollierter Laborbedingungen verfügbar sind. „Wir denken,
аудиофилов
Иран на пороге
dies
ist der richtige Zeitpunkt für
die Geophysiker,
über mögliche Anwendungen dieser neue Technik zu
гиперинфляции:
как это
«1С-СофтКлаб» издаст
работает и куда ведёт?
diskutieren.“
игру Worms: Revolution
Разрабатывается
iOS-версия Crazy Taxi
Задуман новый проект
по доставке на Землю
лунного грунта
Почему ИТ-компаниям
сложно сочетать
устойчивость и развитие
Informationen zur Nachricht
Super Talent выпускает
бюджетные
Лучше бы государство не
Go STE-QUEST!
The End
Underground water level changes
Movie by Thomas Glauninger (IT University of Zurich)