# Presentation: 559749

## 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 ***** **

## 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

- 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

## 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

- 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?**

## Newton’s Law in n dimensional space

## Metric perturbation induced at a distance b from the beam,

-                **< h > ~ (4G/c****2****)** **γ****m (N/2****π****R) ln(2****γ****)**
- Bunch length cτB >> 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**** <  M****P****/10****8**** = 10****8**** 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

- A. Melissinos: Fermilab Colloquim, Nov 14, 2007

## Laser Parametric Converter as Gravity Detector

**     ****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**

## 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)

## Numerical estimate of the gravity force

## 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

## 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!