General Relativity and Frame Dragging

In 1687 Isaac Newton (1642-1727) in his ** Principia** mathematically explained how

170 years after the scientific revolution Newton precipitated, James Clerk Maxwell became good friends with Michael Faraday and undertook a decade long task of compiling equations that described Faraday's lines of electric and magnet forces. In the end Maxwell compiled a consistent set of equations that **unified electricity and magnetism** much as Newton had unified equations for heavenly and earthly motions. But unlike Newton's work, Maxwell's equations were based on a mechanism and specified a speed for the transmission of electromagnetic waves as well as electric and magnetic forces. Since visible light was one range of electromagnetic waves and light's speed had been previously measured, this speed remains known as the **speed of light**.

A few years later Albert Einstein (1879-1955) pondered how electric and magnetic forces could generate effects noticed by observers moving at different speeds. In 1905 Einstein wrote three papers, one of which proposed a **theory of Special Relativity** based on the assumption that each observer would measure the same speed of transmission for electric and magnetic effects, the same speed of light. But this assumption would **required that the dimension of space in the direction of motion would be shortened by the motion, and that time would be a term in the equation as if it is a fourth dimension.**

In 1908 **Hermann Minkowski** (1864-1909) had extended the long used theorem of Pythagoras where the speed of any object could be specified by the square root of the sum of the squares of the speed along perpendicular coordinates, **x**, **y**, and **z**. But time multiplied by the speed of light would have similar dimensions and could be subtracted from the sum allowing transformations in time as well as location: **x**^{2} + **y**^{2} + **z**^{2} - **c**^{2}t^{2}.

Einstein suspected that while Special Relativity was formulated on the basis of electricity and magnetism, all forces must be consistent with Special Relativity and the exchange of information at the speed of light. So the remaining force, gravity, would also be governed by similar equations. Einstein was also aware that **inertial mass** that **resists acceleration** in Newtons dynamics, **F** = m**a**, seems to be experimentally equivalent to **gravitational mass** which **causes gravitational force** in Newton's law of gravity: **F** = Gm_{1}m_{2}/**d**^{2}. This seemed to imply an equivalence principle stating that there would be **no experimental way to every distinguish the difference between the effects of gravity and those observed in other accelerated frames of reference.** In 1915 Einstein announced his **general theory of relativity** which suggests that **mass deforms the surrounding space so that,** contrary to Euclid's geometry where the shortest distance between two points is a straight line, **the shortest distance between two locations near any mass would be a curved pathway.** For nearly all situations Einstein's theory makes identical predictions to Newton's theory. But Einstein proposed three distinctions:

- light from a distant star passing a large mass such as the sun would be deflected more by the gravity than Newton's equations would predict.
- light emerging from a massive body would be slightly held back causing a red-shift in the frequency of the light.
- The perihelion of a planet such as Mercury orbiting close to the a massive star such as the Sun would precess.

Observations have been made for each predicted effect and the results found in agreement with Einstein's predictions. But because there are so few distinctions with Newton's theory, Einstein's theory of general relativity remains one of the least tested of scientific theories. Two years after Einstein proposed his theory, Austrian physicists **Josef Lense** and **Hans Thurring** proposed that not only would a mass distort nearby space, but a spinning mass would drag four dimension spacetime similar to how a rotating electric charge creates a magnetic field. While the spinning of the earth should create only a tiny force (gravity is much weaker than electricity), discovery of this gravitomagnetic force is the gravitational equivalent of discovering electromagnetism.

Stanford physicist **Leonard Schiff** and **George Pugh** at the Pentagon independently proposed in 1960 a satellite experiment to attempt to discover the tiny **frame-dragging** effect of this force. At least nine new technologies had to be invented and perfected such as spherical gyroscopes a million times better than any then available, and Super-Conducting Quantum Interference Devices (SQUIDS) to detect changes in gyroscope motions of approximately 1/40,000,000 of a degree. With nearly 100 Ph.D. dissertations written on this project, a satellite called Gravity Probe-B was designed, constructed and finally launched on April 2004.

- Visit the Gravity Probe B experiment web site.