Testing General Relativity in Fermilab:

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

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. Why to Measure Gravity at Microscopic Scale? • 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

4. Newton’s Law in n dimensional space

5. A. Melissinos: Fermilab Colloquim, Nov 14, 2007 Metric perturbation induced at a distance b from the beam, < h > ~ (4G/c2)γm (N/2πR) ln(2γ) Bunch length cτB >> b, γ= E/m, R = Tevatron radius, N = circulating protons If G = GN h ~ 10-40 hopeless!! If gravity becomes “strong” at this highly relativistic velocity G = Gs = GN(MP/MS)2 For Ms < MP/108 = 108 TeV h > 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 MS > 106 TeV

6. A. Melissinos: Fermilab Colloquim, Nov 14, 2007 Laser Parametric Converter as Gravity Detector 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 15 m Optical Cavity 30 m Filled beam buckets The cavity has excited modes spaced at the “free spectral range” f = c/2L = 10 MHz Any perturbation at 10 MHz of dimensionless amplitude h populates the excited modes and gives rise to 10 MHz sidebands Ps = P0 (h Q)2 For reasonable values, Q = 1014 , P0 = 10 W and recording one photon per second, one can detect h ~ 10-24

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  = 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 L Probe mass Probe mass   +d Proton’s beam

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!