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

• 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?

Newton’s Law in n dimensional space

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

A. Melissinos: Fermilab Colloquim, Nov 14, 2007

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

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

Optical Cavity

15 m

30 mFilled 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

mass 2mass 19 2

0

charge mass2 2 3charge 23 20

2 3/20

40 0

44.4 10 cm/sec

6.8 10 cm/sec( )

at the fundamental beam-revolution frequency 2 2.3 10 rad/sec,

grav pgrav

grav gravgrav

F GNma

M d

F FNrGN ea

M Mc d d

d

3

12

160

10 cm - minimal distance between the beam and detector,

= 1 km - radius of Tevatron,

=10 - the Lorentz factor,

10 - number of protons in bunch,

1.54 10 cm - radius of proton.

N

r

Laser Interferometer for Gravity Physics at Tevatron

16 18(10 10 ) cm/L Hz

L = 999.5 md = 0.07 mL = 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

16 18

3

13

15

cm (10 10 )

For the detector frequency 10 Hz

4.4 10 cm

3.2 10 cm

m

LHz

x

L

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!