1. Archimedes Experiment A Feasibility study for the measurement of the Archimedes force of vacuum E. Calloni - Rencontres de Moriond 2015-03-25  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

2. 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? 2 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 ?

3. 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 x y z a L If the plates are perfectly reflecting the modes that can oscillate must have discrete wavenumbers on vertical axes k z = n  /a while all values are allowed for k x e k y

4. 4 Casimir Energy Casimir Pressure = 1.3x10 -3 N/m 2 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) 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 E reg = E(a) – E( ) (1  m/a 4)

5. Weighing the vacuum 5 x y z a L 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 The total force is directed upward an it is equal to the weigh of the vacuum modes that are removed from the cavity difference of gravitational potential between the plates

6. Pressure red-shift 6 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) A simple summation of the lower force and upper force on the plates would bring to a somewhat unespected result: 555 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) S. A. Fulling et al. Phys. Rev. D76:025004 (2007) K.A. Milton et al. J. Phys. A 41:164052 (2008) G. Bimonte, E. Calloni et. al. Phys.Rev.D76:025008, (2007) On interpretation of Tolman-Ehrenfest effect: C. Rovelli, M. Smerlak Class. Quant. Grav. 28 (2011) 075007 Hal M. Haggard and Carlo Rovelli, arXiv:1302.0724

7. 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. LASER The energy E sent to the film is about 5x10^(5) J The variation of casimir energy  E cas is about 2.5x10^(-19) J The efficiency is  =  E cas /E = 10^(-14) Modulation of Casimir energy with superconductors (type I)

8. 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 8 N metal Diel N/S

9. : modulation factor with respect perfect reflectivity Plot of real part of conducibility  normalized to zero frequency Drude conducibilty  0 for different temperatures: T = Tc (Drude) T/Tc = 0.9 T/Tc = 00.3 N metal Diel N/S Re(  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 T c … The change in energy can be calculated following the Casimir energy calculation in case of real plates with complex conductivity  9

10. The proposed way to measure  Fc consists in placing the cavity in a parallel magnetic field and measuring the critical field that destroys the superconductivity of the film. The proposed way to measure  Fc consists in placing the cavity in a parallel magnetic field and measuring the critical field that destroys the superconductivity of the film. Is there a way to measure  F c ?..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 T c 2. Better to use low T c superconductors. If the two energy variations are comparable then it is expected that vacuum fluctuations modifies the transition Superconductivity is destroyed by a critical magnetic field.

11. 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 T 0 - T (  K) 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) 2008

12. Proposal for the weight measurement: Use of Type II superconductors 12 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 1)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 2)In the final experiment also if the actual contribution were only of few percent we could ascertain if it gravitates or not 3)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

13. 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 13 Archimedes Experiment

14. 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) 14 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)

15. 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 15 The resonance frequency of the first stage is 30 mHz Transfer function of the Virgo Super-Attenuator

16. The balance 16 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).

17. The superconductor 17 YBCO Prototype on a 7.5 cm diameter sapphire substrate (Ceraco) Transition Temperature : 87 K Total volume of the superconductor (final experiment): 30 cm 3 Two possibilities under study: 1) deposition on a sapphire substrate 2) Crystals Frequency of modulation (final): 5-10 mHz Expected Weight modulation : 4*10 -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

18. A side-measurement : the weight of the entropy*T 18 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

19. Final experiment: balance and local detection 19  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)

20. A curious citation “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 ? In the framework of quantum engineering propulsion for the futures spacecrafts our result has been cited in the paper: R. L. Forward realized the first prototype of interferometric gravitational wave detector ! 1972 (Malibu laboratiores – California) R. L. Forward – J. Maclay

21. 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 «What’s next» activity of INFN – Fundamental Physics

22. Spares 22

23. A discussed paper explicitely commenting us 23 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