Archimedes Experiment A Feasibility study for the measurement of the Archimedes force of vacuum

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Archimedes Experiment A Feasibility study for
the measurement of the Archimedes force of vacuum

• INFN_sezione di Naples Laboratorio Fisica della
  Gravitazione Univ. Federico II
• INFN sezione di Roma1 Univ. La Sapienza Roma
• Naples Seconda Università
• Université de Aix-Marseille Centre de Physique
  Théorique de Luminy
• Institut Universitaire de France

E. Calloni - Rencontres de Moriond 2015-03-25
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Scientific motivations and goal of the experiment

• The scientific problem addressed is within the
  interaction of vacuum fluctuations with gravity
  -- cosmological constant problem why the
  universe exhibits a vacuum energy density much
  smaller than the one resulting from application
  of quantum mechanics and equivalence principle?

The first calculation of the radius of the
universe as expected by applying general
relativity and a energy density as foreseen by
zero point fluctuations - with a cut off to
highest frequencies/wavelenghts equal to the
electron radius dates back to Pauli 1931 that
found R 31 km ! Many remarkable and
important theoretical attemps since then but not
a direct experiment Does vacuum fluctuations
gravitate or not? Does vacuum pressure
red-shift ?
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The Casimir effect is a macroscopic
manifestation of vacuum fluctuations. It is
derived considering the zero point e.m. energy
contained in a Casimir cavity, i.e. in the volume
defined by two perfectly reflecting parallel
plates
If the plates are perfectly reflecting the modes
that can oscillate must have discrete
wavenumbers on vertical axes kz np/a while
all values are allowed for kx e ky
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The regularization is made by determing the
Casimir Energy as the change in energy when
the plates are at distance a with respect to
the plates having a?infinity

• Casimir Energy

1.3x10-3 N/m2
(1mm/a4)

• Casimir Pressure

First prediction Casimir 1948 First measure
(force) Sparnay 1956 Presently tested (force)
with an accuracy of 0.5 (Mohideen 2005) (No
problems in QFT in flat space-time)
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Weighing the vacuum
The idea is to weigh a rigid Casimir cavity when
the vacuum energy is modulated by changing the
reflectivity of the plates. The forces along z are
difference of gravitational potential between the
plates
The total force is directed upward an it is equal
to the weigh of the vacuum modes that are removed
from the cavity
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Pressure red-shift
A simple summation of the lower force and upper
force on the plates would bring to a somewhat
unespected result
The lower vacuum photons must exert a bigger
force because the force will be red-shifted when
reaching the same level of upper plate ? in the
experiment the sum must be done taking into
account the red-shift becuase the cavity is rigid
and hanged in a unique point - (for this effect
our measurement is a null measurement)
E. Calloni et.al. Phys. Letters A, 297,
328-333, (2002) G. Bimonte, E. Calloni , G.
Esposito, L. Rosa - Phys. Rev D 74, 085011
(2006)
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S. A. Fulling et al. Phys. Rev. D76025004
(2007) K.A. Milton et al. J. Phys. A
41164052 (2008) G. Bimonte, E. Calloni et.
al. Phys.Rev.D76025008, (2007)
On interpretation of Tolman-Ehrenfest effect C.
Rovelli, M. Smerlak Class. Quant. Grav. 28 (2011)
075007 Hal M. Haggard and Carlo Rovelli,
arXiv1302.0724
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Experimental problem modulate Casimir energy
without exchanging too much energy with the
system (to not destroy the possibility of
measurement and control) and measure it.
Modulation of Casimir energy with superconductors
(type I)
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Use of superconductors

• The condensation energy is very small so it can
  be expected that the variation of Casimir energy
  at the transition for a superconductor inside a
  cavity can be of the same order, or even
  dominates, the total transition energy

N metal
Diel
N/S
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The change in energy can be calculated following
the Casimir energy calculation in case of real
plates with complex conductivity s
modulation factor with respect perfect
reflectivity
N metal
Re(s)
Diel
N/S
Plot of real part of conducibility s normalized
to zero frequency Drude conducibilty s0 for
different temperatures T Tc (Drude)
T/Tc 0.9
T/Tc 00.3
The conducibility changes only in the very low
frequency region (microwave) so the modulation
depth (if Tc is of the order of 1 K) is expected
to be small for small Tc
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..but also the energy exchanged with the system,
besides the vacuum energy, is expected to be
small being linked to the condensation
energy which is (roughly) proportional to Tc2 .
Better to use low Tc superconductors. If the two
energy variations are comparable then it is
expected that vacuum fluctuations modifies the
transition
Is there a way to measure DFc?
Superconductivity is destroyed by a critical
magnetic field .
The proposed way to measure DFc consists in
placing the cavity in a parallel magnetic field
and measuring the critical field that destroys
the superconductivity of the film.
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Results and references on energy modulation
Aladin Experiment
The data are not in contrast with the theory and
the region of energy of different behaviour is
the expected one
2008
G. Bimonte et Al. - J. Phys. A Math. Theor. 41
164023 (2008) A. Allocca et Al. Jour. Of.
Supercond. And Novel Magnetism. 25, 2557-2565
(2012)
 

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Proposal for the weight measurement Use of Type
II superconductors

1. Use high_Tc layered superconductors as natural
   multi Casimir-cavities
2. Profit of the fact that in normal state the plane
   (that will become superconducting) is a very poor
   conductor ? high variation of Casimir energy at
   the transition

State of the art in the knowledge of Casimir
energy in superconductors

• Approximate theory for high_Tc superconductor
  (plasma sheet no dissipation zero temperature)
  Kempf hyphotheis (based on order of magnitude
  estimation) the contribution to free energy is
  comparable to condensation energy in particular
  layered superconductors like YBCO
• In the final experiment also if the actual
  contribution were only of few percent we could
  ascertain if it gravitates or not
• The Casimir Signature the dependence of the
  effect from layers separation is known the
  verification of the effect is by changing the
  layers separation possible with standard
  techniques

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The key points to be addressed

• Seismic isolation a seismic isolation of about
  10(-4) in the 10-30 mHz region does not yet
  exist
• A complete theory of the Casimir effect in type
  II superconductors does not yet exist
• An efficient modulation system by temperature
  or external field is needed and must be
  designed from scratch

Archimedes Experiment
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Present experiment

• 2 years feasibility study Objectives
• Theoretical implications of the measurement
  (Naples-Marseille)
• Theoretical evaluation of contribution to
  condensation energy (Naples-Rome)
• Evaluation and choice of best-experimental
  material (Naples-Roma)
• Design and construction of balance prototype with
  resonance frequency in the 10 mHz range (Naples)
• Design and construction of prototype optical
  read out (Naples)
• Design and test of temperature modulation
  actuator (Rome - Naples)
• Study of pre-attenuation stage suspension (Pisa)

The Archimedes crew
E. Calloni (Univ. Naples), S. Caprara (Univ.
Roma), G. Esposito (INFN Naples), M. Grilli
(Univ. Roma), E. Majorana (INFN Roma), G. P. Pepe
(Univ. Naples), S. Petrarca (Univ. Roma), P.
Puppo (INFN Roma), F. Ricci (Univ. Roma), L.
Rosa (Univ. Naples), C. Rovelli (Univ.
Marseille), P. Ruggi (EGO-Pisa), N. Saini (Univ.
Roma), C. Stornaiolo (INFN Naples), F. Tafuri (II
Univ. Naples)
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Seismic attenuation

• The experiment is made in the framework of
  gravitational wave detectors expertise
  particularly at low frequencies and within the
  improvements in
• seismic isolation systems
• low loss mirror suspensions systems
• control systems
• low temperatures techniques in small force
  detectors
• Virgo has reached the best sensitivity at low
  frequency during past runs and now LIGO is
  comparable

The resonance frequency of the first stage is 30
mHz
Transfer function of the Virgo Super-Attenuator
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The balance
Scheme of the balance With suspended samples
Zoom on the flexural joints where The balance
will be suspended
The center of mass must lie within few micron
from the flexural rotation point (bending
point).
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The superconductor
YBCO Prototype on a 7.5 cm diameter sapphire
substrate (Ceraco) Transition Temperature 87
K Total volume of the superconductor (final
experiment) 30 cm3 Two possibilities under
study 1) deposition on a sapphire substrate 2)
Crystals Frequency of modulation (final) 5-10
mHz Expected Weight modulation 410-16
N Differential measurement respect to phononic
contribution different doping Other materials
are under evaluation BSCCO
Gold plated face of YBCO
View from the substrate face
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A side-measurement the weight of the entropyT
Difference in internal energy for a transition
at fixed temperature
Difference in entropy for a transition at fixed
temperature valid for BCS approximatively for
layered type II
Disregarding in this particular discussion the
contribution of Casimir effect the weight of the
entropy (times Temperature) can be considered as
an interesting side-measurement of the final
experiment. This weight is classical (no question
on it) but never measured
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Final experiment balance and local detection

• Seismically isolated balance
• Temperature modulation around Tc
• Balance tilt possibly read with an optical lever

Signal and Sensitivity expected signal amplitude
under Kempf hypotesis for a fixed modulation
frequency (blue curve) and integration time of
1.5 months - total noise for interferometric
detection (black curve) and optical lever (pink
dashed curve) (seismic noise evaluated from J.
Harms et al. Phys.Rev. D88 (2013) 12, 122003)
E.Calloni, M.De Laurentis, R. De Rosa, F. Garufi,
L. Rosa, L, Di Fiore,G. Esposito, C.Rovelli, P.
Ruggi, F. Tafuri Towards weighing the
condensation energy to ascertain the Archimedes
force of vacuum Phys. Rev. D 90, 022002 (2014)
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A curious citation
In the framework of quantum engineering
propulsion for the futures spacecrafts our
result has been cited in the paper
A gedanken spacecraft that operates using
the quantum vacuum (Dynamic Casimir
Effect) Foundations of
physics 34, pag 477 (2004) our result is
proposed ..to make lighter and modulate the
weight of
the future spacecrafts..
Is the author of this paper a visionary ?
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Conclusion

• Archimedes is a two years feasibility study
  concerning
• Theory and on modulation of vacuum energy in
  layered Supercondutoring systems
• Experimental Improvement of seismic
• performances at low frequency
• Experimental Improvements of high quality
  superconductors temperature modulation

The horizontal double-torsion pendulum in
construction at the Laboratorio di Fisica della
Gravitazione
Measure the Archimedes force of vacuum in
a Macroscopic system
The Project is within the Whats next activity
of INFN Fundamental Physics
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Spares
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A discussed paper explicitely commenting us
We confirm that suitably modified ALADIN has the
correct conditions (superconductors, casimir
cavity, measure of casimir energy contribution)
and that it did not have the sensitivity to
distinguish among the two theories
(On the gravitational waves vacuum fluctuation
contribution to weight