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Testing General Relativity in Fermilab:

Testing General Relativity in Fermilab:. A Bridge between the Particles Physics and Relativistic Gravity. Sergei Kopeikin University of Missouri-Columbia.

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Testing General Relativity in Fermilab:

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  1. Testing General Relativity in Fermilab: A Bridge between the Particles Physics and Relativistic Gravity Sergei Kopeikin University of Missouri-Columbia

  2. The U.S. program in particle physics is at a crossroads. The continuing vitality of the program requires new, decisive, and forward-looking actions. In addition, sustained leadership requires a willingness to take the risks that always accompany leadership on the scientific frontier. Thus, the committee recommends the thoughtful pursuit of a high-risk, high-reward strategy. Committee on Elementary Particle Physics in the 21st Century, National Research Council (2006) Revealing the Hidden Nature of Space and Time: Charting the Course for Elementary Particle Physics Photograph by Paul Ehrenfest. Image Source: AIP Emilio Segrè Visual Archives .

  3. It seems natural to neglect gravity in particle physics

  4. Tests of Gravity at Macroscopic Distances • Laboratory • Earth/Moon (Lunar Laser Ranging) • Solar System (VLBI, Doppler/radio ranging, GPS) • Binary Pulsars • Black Hole in the Milky Way • Cosmic Microwave Background • Gravitational-wave detectors (bars, interferometers) Gravity regime tested in the solar system: • weak field (U << c²) • slow motion (v << c) Gravity regime tested in binary pulsars: • strong field (U ≤ c²) • slow motion (v << c) • radiation-reaction force 2.5 post-Newtonian approximation

  5. Why Do We Need to Measure Gravity at Microscopic Scale? Over the past 50 years accelerators have explored the energy range from 1 MeV in nuclear reactions up to about 1000 GeV at the Tevatron. We have a remarkably accurate theory to predict and explain what we see at present

  6. Cosmological Evidence for Vacuum Energy

  7. Revolution in Gravity Cris Quigg: Fermi National Accelerator Laboratory

  8. Newton’s Law in n dimensional space

  9. Testing Newtonian 1/r² Law 2- limits on 1/r² violations. [Credit: Jens H Gundlach 2005 New J. Phys.7 205 ] Eöt-Wash 1/r² test data with the rotating pendulum =1; =250 m Casimir force+1/r² law  parameterization of the presumable violation of the Newtonian 1/r² law.

  10. Gravity Field in Fermilab • Weak (U << c²) • Ultra-relativistic (v  c) • Post-Newtonian Possible experiments: • Post-Newtonian gravity force produced by magnetic stresses and mechanical strains • Gravity force at ultra-relativistic velocities (testing standard theory extension, other possible long-range relativistic forces between particles)

  11. The Tevatron Characteristics 6

  12. Local Inertial Reference Frame x³ = Z x² = Y x¹ = X

  13. The metric tensor in the local frame Acceleration of gravity 9.81 m/s² Luni-solar tidal force Angular velocity of the Earth’s rotation

  14. Forces exerted on proton in the beam Protons in the beam falls down to Earth with acceleration of gravity twice as g=9.81 m/s²

  15. Tevatron Magnets • Two main types of magnets: dipole and quadrupole. Dipoles are able to bend a particle beam. Quadrupoles focus the particle beams. • The strength of the magnetic field is determined by the amount of electric current flowing through the coils. The 8-Tesla magnetic field requires current of 12,000 amperes. • The SC magnets rely on a niobium-titanium compound. At ~10 K, the NTC becomes super-conducting and carries electric currents without resistance. • Fermilab operates its 4.4 Tesla magnets. • The magnets are bathed in 4.2-Kelvin liquid helium. Tevatron Magnet Cross Section

  16. Magnetic Field Structure in Tevatron Magnet

  17. Gravity by the Magnetic Stress “Believe it or not, gravity and magnetism are two totally different and really unrelated phenomena.” WikiAnswers http://wiki.answers.com/ • General relativity predicts that gravity should be produced by stress as well as by mass-energy of matter • Magnetic field is a matter field with energy and stresses (Maxwell’s tensor) • Post-Newtonian gravity field of a magnet crucially depends on the magnetic (and mechanical) stress besides the part generated by mass-energy

  18. The Gravity by the Magnetic Stress Why is it important to study? • Astrophysics: the maximum mass of neutron (and quark) stars depends on stress-produced by magnetic field • Gravitational Physics: validity of the principle of equivalence depends on how the stress contributes to the inertial and gravitational masses of a self-gravitating body (motion of binary pulsars, the effacing principle gr-qc/0612017)

  19. Gravity by the Magnetic Stress. • Current circulating in magnet’s coil generates the magnetic force • The magnetic force leads to mechanical deformations that cause stresses in the material of the magnet that are comparable with the magnetic stress • Strain-stress tensor calculation: L. Landau & E. Lifshitz “Electrodynamics of Continuum Media”

  20. Magnetic Strain-Stress Tensor

  21. Gravitational Field of the Magnet

  22. Gravitational Field of a Magnetized Sphere

  23. Gravitational Field of the Magnetized Sphere

  24. Gravitational Force of the Magnetized Sphere

  25. Numerical Estimate and Measurability   

  26. Torsion balance in University of Washington Dr. Eric Adelberger: (a letter from 1/14/2008) The free resonant period of our balances is about 2 mHz. The torsional spring constant is about 0.03 in cgs units and the angular displacement sensitivity is about radians. A typical level arm of our torsion balances is about 2.5 cm. So the force sensitivity is about cgs units or Newtons. The quality factor of our torsion oscillator is about 5000. But if the signal has a definite period (as is the case in all of our experiments so far) one can integrate much for longer longer times (and we do so). To resolve radians of angular deflection (given our noise and other disturbances) we need days of running time.

  27. Long range forces and spontaneous violation of the Lorentz symmetry One may expect that the Lorentz invariance for gravity field is spontaneously broken. Theories with spontaneous local Lorentz and diffeomorphism violation contain massless Nambu-Goldstone modes, which arise as field excitations in the minimum of the symmetry-breaking potential. If the shape of the potential also allows excitations above the minimum, then an alternative gravitational Higgs mechanism can occur in which massive modes involving the metric appear (see discussion of a class of bumblebee models by A. Kostelecky et al. gr-qc 0712.4119)

  28. Local Lorentz Invariance [Credit: Clifford M. Will] The limitsassume a speed of the solar system of 370 km/srelative to the mean rest frame of the universe that is considered as a preferred frame. However, a genuine test of the Lorentz invariance of gravity must not rely upon this assumption (requires an experiment in a variable gravitational field)

  29. The speed-of-gravity VLBI experiment with Jupiter(Kopeikin, ApJL, 556, 1, 2001;Fomalont & Kopeikin, ApJ., 598, 704, 2003) Position of Jupiter from JPL ephemerides (radio/optics) gravity-unperturbed position of quasar 5 1 Position of Jupiter as measured from the gravitational deflection of light by Jupiter 4 2 3 Measured with 20% of accuracy, thus, proving that the fundamental speed in General Relativity (the speed of gravity) equals the speed of light. 10 microarcseconds= the width of a typical strand of a human hair from a distance of 650 miles !

  30. Relativity in high-energy accelerators Fermilab’s Tevatron: CERN’s Large Hadron Collider

  31. The Minkowski geometry of the gravity force measurement at ultra-relativistic speed In general relativity ultra- relativistic gravity force behaves similar to the synchrotron EM radiation World line of the detector World line of the proton bunch time space

  32. What makes it plausible to measure the ultra-relativistic force of gravity in Tevatron? • The bunch consists of N=3×10¹¹ protons • Ultra-relativistic speed = large Lorentz factor  =1000 • Synchrotron character of the force = beaming factor gives additional Lorentz factors • Spectral density of the gravity force grows as a power law as frequency decreases • The gravity force is a sequence of pulses (45000 “pushes” per second  36 bunches =1,620,000)

  33. Einstein-Maxwell Equations

  34. The Reissner-Nordström Metric (an exact solution of Einstein-Maxwell equations) The RN metric is a black hole that is electrically charged but non-rotating (q<<m). A Reissner-Nordström black hole has two separate event horizons; the more charge the black hole carries, the closer are its event horizons. If q>>m, the two horizons disappear and the singularity becomes a naked one. Many physicists believe that such a situation can't arise: there is a principle of "cosmic censorship", which prevents naked singularities from ever forming. Theories with super-symmetry usually guarantee that such "super-extremal" black holes can't exist. Main features of a Reissner-Nordstrom black hole. Credit: N. Rumiano

  35. Electromagnetic-Gravitational Field Model in a post-Minkowskian Approximation • Gravity field potentials • Lorentz – de Donder gauge • Linearized field equations =

  36. Electromagnetic Lienard-Wiechert Potentials Retarded time s=s(t,x)

  37. Electromagnetic Stress-Energy Tensor

  38. Gravitational Lienard-Wiechert Potentials Gravitational mass of the particle Inertial mass of the particle

  39. The frame used for calculation of the gravity force Y X  O Gravity force detector (torsion balance)  X-Z plane is the plane of the Tevatron ring. Y axis is a local vertical. Z

  40. Equations of Motion of a Mechanical Detector Braginsky V.B. and Manukin, A.B., “Measurement of Weak Forces in Physics Experiments”, Univ. Chicago Press, 1977 Braginsky, V.B., Caves, C.M. & K.S. Thorne, “Laboratory experiments to test relativistic gravity”, PRD, 15, 2047-2068, 1977 Braginsky, V.B., “Experiments with Probe Masses”, PNAS, 104, 3677-80, 2007

  41. Gravitational versus Lorentz Force Tensor force Vector force

  42. Gravitational versus Lorentz Force

  43. Gravity Force in ultra-relativistic approximation

  44. Motion of the particle in the beam

  45. The Dipole Approximation

  46. The ultra-relativistic approximation

  47. Fourier Transform of the Gravity Force Fourier frequency

  48. Fourier Transform in The Ultra-relativistic Approximation

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