General Relativity Talk

Emiliano Garcia

Outline

• Brief Introduction

• Basics of General Relativity

• Gravity Probe B

Brief Introduction

• Newton’s Universal Law Of Gravity – Two bodies attract each other with a force that is

directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Brief Introduction

• Special Relativity

• Einstein published his first paper on relativity in 1905.– First Postulate: The laws of physics are the

same to all inertial observers– Second Postulate: The speed of light is the

same to all inertial observers

Brief Introduction

• Conflict– No signal can travel faster than light, but in

Newton's theory, gravity is a force transmitted instantaneously over vast distances.

– Example: Masses at the ends of the universe– What’s wrong?

Basics of General Relativity

• Mach’s Principle– Newtonian inertial frames not rotating with

respect to the “fixed” stars– Inertial properties are determined by the

presence of other bodies in the universe

Basics of General Relativity

• Principle of Equivalence– “We shall therefore assume the complete

physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame.”

Basics of General Relativity

• Principle of Covariance– In special relativity, all inertial observers

equivalent– Here, all observers observe the same laws of

physics.– Laws of physics can be expressed in terms of

tensors, since tensors are defined independent of any coor. system

Basics of General Relativity

• Correspondence Principle– In weak gravitation fields with velocities<<c ,

general theory should correspond with the predictions of Newtonian mechanics

– As gravitational fields go to zero, general theory should corresponds with the predictions of special relativity

Basics of General Relativity

• Principle of minimal gravitational coupling– No terms explicitly containing the curvature

should be added when going from special to general

Basics of General Relativity

• Leads to the idea that space-time is curved• Field Equation; where Rik is the Ricci curvature tensor, R

is the scalar curvature, gik is the metric tensor, Λ is the cosmological constant, Tik is the stress-energy tensor describing the non-gravitational matter, energy and forces at any given point in space-time

Basics of General Relativity

Gravity Probe B

• Proposed by Stanford University Physicist Leonard Schiff

• The experiment will measure how space and time are warped by the presence of the Earth, and how the Earth's rotation drags space-time around with it.

Gravity Probe B• A gyroscope (actually four) and telescope will be placed in

a satellite and sent into a polar orbit 400 miles (640 km) above the Earth .

• The telescope and the gyroscope’s spin axis will be perfectly aligned, and both will point at a distant star (IM Pegasi).– Classically, the underlying principle of a gyroscope is that

rotating systems, free from disturbing forces, should stay pointing in the same direction in space.

– However, as mentioned before, space-time is warped -- and may even be set in motion by moving matter. A gyroscope orbiting the Earth will find two space-time processes acting on it-- frame-dragging and the geodetic effect -- gradually changing its direction of spin.

Gravity Probe B

• Frame Dragging– In 1918, Josef Lense and Hans Thirring

predicted that masses in space-time would not only curve the structure of space-time around them, but would also twist the local space-time around them if they are rotating

– This twisting would alter measurements of distance, time and direction in local space-time

– Example: Racquetball in honey….

Gravity Probe B

• The Geodetic Effect– When a mass “sits” in space-time, it causes

the space-time “fabric” to deform, changing the space and altering the passage of time around that object.

– In the case of the Sun’s “dip”, as the planets travel across space-time, they respond to the “dip” and follow the curve in space-time and travel around the Sun.

Gravity Probe B

Gravity Probe B

• Note: Why IM Pegasi?– Stars are not fixed in the sky. – IM Pegasi was chosen because it is one of

the brightest stars in the sky, in the microwave range.

– Very-Long-Baseline Interferometry (VLBI) measurements since 1997 were used to map IM Pegasi’s motion in the sky.

Gravity Probe B

• Note: Perfect Gyroscopes– In order for GP-B to measure anything, its

gyroscopes must be nearly perfect– Must not wobble or drift more than 1e-11

degrees in an hour while its spinning, since the predicted twist in space-time is on the order ~ 1e-6 degrees each year.

Perfect Gyroscopes

• Must be near perfect spherically and homogeneity

• Gyro Size: 1.5 inches of fused quartz

• Sphericity: <40 atomic layers from perfect

Perfect Gyroscopes

• Quartz Purity: Within 2 parts per million

• Gyro Spin Rate: ~10,000 rpm

• Gyro Drift Rate:

<10e-12 degrees/hour

Gravity Probe B

• Note: How do you measure the twist?

• Superconductivity– Gyroscopes coated with a sliver thin layer

(1270nm) of niobium.– As the gyroscope spins, the niobium layer

generates a magnetic field, whose axis is exactly aligned with the spin axis.

Superconductivity

• A thin superconducting metal loop encircles each gyroscope.

• The loop is connected to an external SQUID (Superconducting Quantum Interference Device)

• If and when the gyro tilts, the magnetic field changes with it, which affects the current in the loop

Superconductivity

Gravity Probe B

• According to Einstein’s theory , the gyroscope should turn in two directions simultaneously. As it travels through curved space time , it will turn slightly along one axis . As “frame -dragging” occurs, it will also turn slightly along a perpendicular axis.

• Schiff calculated that at a 400-mile altitude, space time curvature would turn the gyroscope 6.6 arcseconds per year in one direction, and the “frame-dragging ” will turn at .042 arcseconds per year in a perpendicular direction.

Gravity Probe B

Conclusions

• Conflicts between the Newton’s Universal Law of Gravity and Einstein’s Special Theory of Relativity lead to the formalization of General Relativity

• GP-B is almost 34 weeks in orbit, and is scheduled to orbit for a little over a year.

Sources

• Gravity Probe B – einstein.stanford.edu• Goldstein Poole & Safko, Classical Mechanics

3rd Edition. Addison Wesley, 2002• Steven Weinberg, Gravitation and Cosmology.

John Wiley & Sons, Inc.,1972• Tim Maudlin, Quantum Non-Locality & Relativity

2nd Edition. Blackwell Publishing, 2002• Wikipedia entry on “General Relativity” –

wikipedia.org