Pavol VALKO Dept. of Physics, Slovak Technical University Ilkovičova 3, Bratislava

 J. Tate, S. B. Felch, B. Cabrera: Determination of the Cooper-pair mass in niobium Physical Review B, 42 (1990) 7885  The Gravity Probe B team: Post Flight Analysis Final Report, March 2007  H. Hayasaka, S. Takeuchi: Anomalous Weight Reduction on a Gyroscope’s Right Rotations around the Vertical Axis on the Earth Physical Review Letters 25(1989) 2701  E. Podkletnov, R. Nieminen: A possibility of gravitational force shielding by bulk YBa 2 Cu 3 O 7-x superconductor Physica C 2O3 (1992)  R.H. Koch, D.J. van Harlingen, J. Clarke: Measurements of quantum noise in resistively shunted Josephson junctions Physical Review B, 26 (1982) 74

 Prediction ◦ Cooper mass smaller than 2m e by 8 ppm  Result ◦ measured 84 ppm larger than 2m e  with 21 ppm accuracy (5 ppm statistical)  Just comment ◦ measured effect is only ~4.5  ◦ with new Planck constant value (NIST)  used value h= (40)x J.s  current NIST value h= (33)x J.s ◦ the result should be 83 ± 20 ppm (small change but...)

 experimental “nightmare” ◦ electrostatic charging of the rotor  “It proved impossible to ground the rotor continuously.”  “The charge build up over the period of hours and discharged somewhat over a period of days if the rotor was not spun.”  (accumulation of charge in weak spots - patches?)  “Once the rotor was coated with a thin metallic film, the sign of  reversed but then gradually (over weeks) headed towards zero, and became positive again.”  in experiment  varied between and

 To keep in mind ◦ this experiment was spin-off experiment from GPB with expected major sources of errors  rotor position shift in housing ± 16 ppm  nonuniform charge distribution in rotor ± 5  detection loop area ± 8.86 ◦ further possible problems discussed in paper  vortex trapping in niobium ???  after GPB results we know that all listed effects are important

 observed experimental “problems” ◦ polhode motion (without periodicity pattern) ◦ small classical torque (and associated energy dissipation)  caused by (primarily) ◦ electrostatic patches on gyro (and housing) metal coating  niobium sputtered in 64 steps - with clearly observed effect of the last coating step ◦ trapped flux in superconducting niobium  sputtered niobium is hard Type-II superconductor  high T c of niobium (larger than shielding lead)  is there (any) significance of GPB observations for Tate, et al. experiment?

 weak but clearly detectable shielding effect against the gravitational force at the temperatures from 20 to 70 K  the sample with the initial weight of g was found to loose about 0.05% of its weight when placed over the levitating disk without any rotation  when the rotation speed of the disk increased, the weight of the sample became unstable and gave fluctuations from -2.5 to +5.4% of the initial value  at certain speeds of rotation and at certain frequencies of electromagnetic field in the rotation magnets the weight of the sample stabilized and decreased by 0.3%.  the readings in the stable regions were recorded several times with good reproducibility

 basically identical superconductor levitation set-up  different acceleration measurement method  changes in acceleration were measured to be less than 2 parts in 10 8 of the normal gravitational acceleration

 subset of the Podkletnov conditions examined here does not produce gravity modification measurable with our equipment (a resolution of the order of ±0.004%)

 some sources of inspiration ◦ V. Braginsky, C.M. Caves, K.S. Thorne: Laboratory Experiments to Test Relativistic Gravity, Physical Review D 15 (1977) 2047 ◦ J. Anandan: Relativistic Thermoelectromagnetic Gravitational Effects in Normal Conductors and Superconductors, Physics Letters 105A (1984) 280 ◦ J. Argyris, C. Ciubotariu: A Proposal of New Gravitational Experiments, Modern Physics Letters A, 12 (1997) 3105 ◦ C.M. Will: The Confrontation between General Relativity and Experiment, arXiv:gr-qc/ v1, 12 Mar 2001

 select the most important (or promising) effect for test  confront theoretical predictions with available experimental sensitivity  design experiment in detail  method of measurement  differential measurement if applicable  results with periodic pattern, etc.  perform experiment  at genuinely variable experimental conditions  with variable materials but identical geometry  and vice versa  cross check results via deliberately strengthening effect of major error sources

 can be done (already performed) ◦ with different superconductors (and more than one)  lead, mercury, tantalum, vanadium, bulk niobium ◦ better experimental sensitivity  new, more sensitive DC SQUIDs are now commercially available ◦ how to made this measurement differential?  periodic measurements in superconducting and normal state  in close vicinity of T c (fine tuned Pb-Hg) alloys  known sources of major experimental errors ◦ electrostatic charges (ionization will make them extreme) ◦ flux trapping (must be tested under controlled conditions)

 can be done up to some frequency ◦ maximum frequency required (2 THz) not achieved yet ◦ various superconducting materials available  aluminum, indium, lead, tantalum, niobium ◦ running at different temperatures experiment became semi-differential (predicted temperature behavior)  the effect of quasiparticle current shot noise must be addressed ◦ quasiparticle sub-gap characteristics of junctions should be known prior to RSJ measurement

 utilizing flux interference ◦ interference is very powerful method of measurement  since times of Michelson-Morley....  SQUID or superfluid 4 He interferometer sensor ◦ DC SQUID could be calibrated by magnetic flux  rotating superconductors (or simple superconducting current) as a source of gravitomagnetic field ◦ magnetic vs. gravitomagnetic cross-check could be performed by shielding sensor by superconducting or usual (cryoperm) shield  in the case of quasistatic experimental set-up

 if rotating Earth is a source of gravitomagnetic field  if gravitomagnetic field causes phase shift of superconducting condensate in that case  very weak gravitomagnetic field (~ rad/s) ◦ could be tested with cutting edge SQUID technology  noise better than  0 (Hz) -1/2 ◦ with ~10 4 m 2 total SQUID input coil area  which must be sufficiently (absolutely) magnetically shielded

 there are several examples when experiments went wrong due to unknown (unclear) reasons  even the results of the best ones could be questioned  there are several (although not many) possibilities to push resolution (sensitivity) further  there are many (although unknown yet) possibilities for a “new” physics experiments using ◦ advanced SQUIDs, superfluid 4 He ( 3 He) interferometers