1. Testing General Relativity in Fermilab: Sergei Kopeikin - University of Missouri Adrian Melissinos - University of Rochester Nickolai Andreev - Fermilab Nikolai Mokhov - Fermilab Sergei Striganov - Fermilab Working Sub-Group: Relativistic Gravity in Particle Physics

2. Gravity regime normally tested: weak field (U << c²) slow motion (v << c) Gravity regime for LIGO: strong field (U ≤ c²) fast motion (v  c) Problem – identification of signal with the source Gravity regime for Fermilab: Weak field (U << c²) Fast motion (v  c) Advantage – experimental parameters are controlled

3. Understanding of mass: is the inertial and gravitational masses of the particles the same? Understanding of anti-matter: does anti-matter attract or repeal? Understanding mechanism of the spontaneous violation of the Lorentz symmetry Possible window to extra dimensions Understanding of various mechnisms for extention of the standard model Why to Measure Gravity at Microscopic Scale?

4. Newton’s Law in n dimensional space

5. Metric perturbation induced at a distance b from the beam, ~ (4G/c 2 ) γ m (N/2πR) ln(2 γ ) Bunch length cτ B >> b, γ = E/m, R = Tevatron radius, N = circulating protons If G = G N h ~ 10 -40 hopeless !! If gravity becomes “strong” at this highly relativistic velocity G = G s = G N (M P /M S ) 2 For M s 10 -24 The effect is detectable in 100 s of integration ! Noise and false signal issues could be severe A 1986 Fermilab expt used a s.c. microwave parametric converter and set a limit M S > 10 6 TeV A. Melissinos: Fermilab Colloquim, Nov 14, 2007

6. Wish to measure the gravitational field of the Tevatron beam! Modulate the proton beam to λ = 2L ~ 30 m. At some distance from the beam line, install a high finesse Fabry-Perot cavity of length L ~ 15 m Any perturbation at 10 MHz of dimensionless amplitude h populates the excited modes and gives rise to 10 MHz sidebands P s = P 0 (h Q) 2 For reasonable values, Q = 10 14, P 0 = 10 W and recording one photon per second, one can detect h ~ 10 -24 Optical Cavity 15 m 30 m Filled beam buckets The cavity has excited modes spaced at the “free spectral range” f = c/2L = 10 MHz A. Melissinos: Fermilab Colloquim, Nov 14, 2007 Laser Parametric Converter as Gravity Detector

7. 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)

8. Numerical estimate of the gravity force

9. Laser Interferometer for Gravity Physics at Tevatron   L  = 999.5 m d = 0.07 m L = 16.7 m Current technology of LIGO coordinate meters allows us to measure position of test mass with an error  +d Probe mass Proton’s beam Probe mass

10. Problems to solve: Theory – solving gravity field equations without a small parameter v/c (the post-Newtonian approximations fails). Synergy with LIGO. Re- consider LIGO expectations – the gravity signal is anisotropic (synchrotron gravitational radiation) Experiment – shielding against the background noise and parasitic signals Thank You!