GENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLE

GENERAL RELATIVITY NEEDS TESTS of the EQUIVALENCE PRINCIPLE

THE OBSERVABLE to be MEASURED for TESTING the EQUIVALENCE PRINCIPLE The most direct experimental consequence of the Equivalence Principle is the Universlaity of Free Fall (UFF): in the gravitational field of a source mass all bodies fall with the same acceleration regardless of their mass and composition The observable to be measured is the differential acceleration of different composition test masses in the gravitational field of a source body (i. e. Earth, Sun. . ): if UFF, hence the Equivalence Principle and GR hold (Eötvös parameter)

EQUIVALENCE PRINCIPLE TESTS ARE by far the MOST POWERFUL TESTS of GENERAL RELATIVITY the superior probing power of UFF (hence EP) tests is beyond question !!! In simple terms, this expresses the fact that EP is the founding “principle” of GR: “hypothesis” of complete physical equivalence (Einstein 1907)

EQUIVALENCE PRINCIPLE TESTS: WHAT’s ON The best ground tests (with slowly rotating torsion balance) provide: Proposed and ongoing experiments for EP testing : GG (I) 250 kg; STEP (USA) 1000 kg- LEO Torsion balances (USA)

GG: configuration for EQUATORIAL ORBIT s/c configuration for equatoriial (VEGA launch; operantion from ASI ground station in Malindi)

GG: the SPACE EXPERIMENT DRIVING CONCEPTS (I)

GG: the SPACE EXPERIMENT DRIVING CONCEPTS (II) Fast rotation of whole spacecraft around symmetry axis for high frequency modulation (2 Hz) Large test masses to reduce thermal noise (with 10 kg test mass at room temperature the ratio T/m is the same as in STEP) High level of symmetry Small total satellite mass (250 kg) - determined in Phase A Studies with industry But people were scared to set large macroscopic test masses in rapid rotation !!!!!

GG DIFFERENTIAL ACCELEROMETR

GG ACCELEROMETERS: SECTION ALONG THE SPIN AXIS

GG ACCELEROMETERS CUTAWAY

GGG vs GG design

GGG labin INFN lab ) GGG 2005 (March

RESULTS from TILT MEASUREMENTS Automated Control of Low Frequency Terrain Tilts-0. 9 Hz spin rate Low frequency terrain tilts are strongly reduced: the control loop works very well. Work in progress to reduce thermal variation effects on the zero of the tilt sensor.

DIFFERENTIAL MOTION of ROTATING TEST CYLINDERS from Rotating Capacitance Bridges: improvements since 2002 GGG operation in INFN lab started in 2004:

AUTOCENTERING of GGG TEST CYLINDERS vs SPIN FREQUENCY Experimental evidence of autocentering of the test cylinders in supercritical rotation: relative displacements of the test cylinders in the rotating frame (X in red, Y in blu) decrease as spin frequency increases and crosses the resonance zones (shown by dashed lines) …. . See next slide….

AUTOCENTERING of GGG TEST CYLINDERS in the ROTATING PLANE Experimental evidence of autocentering of the test cylinders in supercritical rotation: in the horizontal plane of the rotating frame the centers of mass of the test cylinders approach each other as the spin frequency increases (along red arrow) from below the first resonance (L), to between the two resonances (M), to above both resonances (H). The equilibrium position reached is always the same (determined by physical laws. . ), thus allowing us to set the electric zero of the read out

QQMEASUREMENTS @@ NATURALFREQUENCIES (I) MEASUREMENTS NATURAL FREQUENCIES Q measured from free oscillations of full GGG system at its natural frequencies –see blu lines- with system not spinning: 0. 0553 Hz (18 sec) 0. 891 Hz (1. 1 sec) 1. 416 Hz (0. 7 sec) Q of GGG apparatus at frequencies other than the natural ones (e. g. at 0. 16 Hz) can be measured (during supercritical rotation at that frequency) from the growth of whirl motion….

Q in SUPERCRITYICAL ROTATION Rotordynamics theory states that in supercritical rotation (defined by spin frequency > natural frequency) whirl motions arise at each natural frequency whose growth is determined by the Q of the full system at the SPIN frequency of the system (not at the natural frequency …. . ) High Q means slow whirl growth, and Q at higher frequencies is larger …. ok In supercritical rotation thermal noise also depends on Q at the spin frequency (not at the –low- natural one) and this is a crucial advantage. .

Q MEASUREMENT from GROWTH of WHIRL MOTION (data of fixed electronics) Spin period 6. 25 sec (0. 16 Hz), whirl period 13 sec (O. 0765 Hz), whirl control off

Q MEASUREMENT from GROWTH of WHIRL MOTION (data of rotating electronics) Spin period 6. 25 sec (0. 16 Hz), whirl period 13 sec (O. 0765 Hz), whirl control off Measurements of whirl growth made with 2 different read-outs give the same value of Q at 0. 16 Hz: this is the relevant Q for operation at that spin rate

ETA in GGG: In the field of the Earth from space (GG orbit) with natural differential period of TMs

The GREAT ADVANTAGE of WEIGHTLESSNESS The sensitivity to differential accelerations between the test masses (sensitivity to EP tests), is inversely proportional to the square of their natural differential period: The natural differential period is inversely proportional to the stiffness of their coupling: In space, thanks to weightlessness, the stiffness of coupling can be weaker than on Earth by many orders of magnitude… From GG Phase A Study (ASI 1998; 2000), as compared to GGG, we see that the factor gained in absence of weight is:

ETA in GG: In space we gain: 1500 (weaker suspensions in absence of weight, longer differential period - quadratic improvement) 10 (no motor , no motor noise…) 10 (no terrain tilts – the whole satellite spins together and spin energy is so large that disturbing torques are ineffective…)

GG SIMULATIONS During Phase A and Advanced Phase A Studies

GG MISSION PROGRAMMATICS GG included in ASI National Space Plan recently approved – VEGA launch foreseen