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An introduction to general relativity
Posted: April 12, 2004

In Einstein's theory of general relativity, space is transformed from the Newtonian idea of a vast emptiness with nothing but the force of gravity to rule the motion of matter through the universe, to an invisible fabric of spacetime, which "grips" matter and directs its course.

Two Observations, One Revolution (From Gravity to Spacetime)

Newton's theory of gravity (1687) is as familiar to us as walking down a hill. As we put one foot in front of the other, the invisible force of gravity reaches out from the Earth and pulls each foot down to the ground. We feel the pull of the force and let our foot fall to the ground and we continue down the hill on our merry way. The same invisible force that keeps us Earth-bound keeps the planets in orbit around the Sun. According to Newton, the Sun's gravity reaches out across empty space and constantly pulls the planets toward it, preventing them from zooming out of our solar system.

This theory remained the strongest explanation for the planetary orbits and the apparent "falling" motion of objects on Earth for several centuries. It was not until the early 20th century when Einstein began working on his theories of relativity that Newton's theory of gravity was seriously challenged.

In 1905 and 1906 Einstein laid out his theory of special relativity in a collection of papers. Central to this theory was his claim that the speed of light in a vacuum (299,792 km/sec) was the speed limit of all matter and energy in the universe. While matter and energy could travel at speeds approaching or equaling the speed of light, they could never surpass it.

With this principle in hand, Einstein turned his attention to Newton's theory of gravity. He focused on two observations that challenged Newton's theory. The first related to the speed limit of light, and its implications for the speed limit of the force of gravity. The second related to the Equivalence Principle.

Observation #1 - Instant Propagation Problem

Newton stated that the attractive force of gravity emanated from all matter, but he did not explain how it physically transmitted from one mass to another, nor how long this transmission took to occur. He simply inferred that the force of gravity traveled instantly across empty space, propagating from one mass to another.

However, Einstein, along with other scientists, began to question this conclusion around the turn of the 20th century. In the 19th century, Maxwell had shown that light and energy, including electricity and magnetism, propagated at the same finite rate in a vacuum - 299,792 km/sec. Einstein's theory of special relativity concluded that this rate was the speed limit for all energy in the universe. If gravity was a force that transmitted between masses in the same way light propagated through space, the force of gravity should be equally restricted to 299,792 km/sec. While crossing nearly three hundred thousand kilometers each second is extremely fast, it is not instantaneous.

Just look at the Sun's light crossing our solar system. Light, in the form of photons, flies out of the Sun at the speed of light toward the inner and outer planets. These photons cross enormous distances very rapidly. But even at this rate, minutes and even hours pass before they reach the planets (~8.3 minutes to Earth; ~5.5 hours to Pluto).

If the force of gravity could travel no faster than the speed of light, then gravity was certainly not traveling instantaneously across space. If the force of the Sun's gravity did not transmit instantly, but instead took a definite amount of time to reach the planets, then something was wrong with the actual orbits of the planets. Instead of following their observed orbits, the paths of the planets should be slightly different.

Was Newton's theory wrong, even though it mathematically agreed with the actual orbits of the planets? Or was Einstein's conclusion mistaken, meaning that gravity was not like other forces and actually could transmit instantly?

Einstein believed that he was not mistaken. Even though Newton's theory explained the planets' orbits to a great extent, it did not tell the whole story. Over the next ten years, Einstein worked to find the answer to the instant propagation problem.

Observation #2 - The Equivalence Principle

A second problem that Einstein encountered was related to the Equivalence Principle. This principle asserts that the motion of objects in the presence of a gravitational field is equivalent to the motion of objects in an accelerating frame of reference. If you drop a hammer on Earth, it falls to the ground at exactly the same rate as when you drop the hammer in an accelerating spaceship.

Let's break this down a bit. In a spaceship accelerating upwards at 9.8 m/s2, any object will fall to the floor at 9.8 m/s2. On Earth, any object you drop will accelerate to the ground at 9.8 m/s2. Since this is true, it raises the question of why things fall at all on Earth. If the objects are simply accelerating down, instead of "falling," could it be that the ground is actually accelerating upwards?

The mere possibility that this could be true was a problem for Einstein. If all motion appeared the same in both frames of reference (the ground and the spaceship) then gravity could not be responsible for both motions. An observer could not tell the difference between gravity and an accelerating frame of reference, so the force of gravity could not be a conclusive explanation for the falling motion of objects in the universe. What exactly was it that caused objects to accelerate towards the ground on Earth?

A New Understanding: Curved Spacetime

In 1916, Einstein addressed these two matters (the instant propagation problem and the equivalence of gravity and an accelerating frame of reference) by reconstructing the theory of gravity. Einstein presented the world with a new understanding of how the universe worked - his theory of general relativity. In this theory, space is not an empty void, but an invisible structure called spacetime. Nor is space simply a three-dimensional grid through which matter, light, and energy move. It is a structure whose shape is curved and twisted by the presence and motion of matter and energy.

Around any mass (or energy), spacetime is curved. The presence of planets, stars and galaxies deform the fabric of spacetime like a bowling ball deforms a bedsheet. (Spacetime deforms in four dimensions, so the two-dimensional bedsheet is a limited model. Try visualizing these depressions on all sides of a planet to build a more accurate image of this concept.)

When a smaller mass passes near a larger mass, it curves toward the larger mass because spacetime itself is curved toward the larger mass. The smaller mass is not "attracted" to the larger mass by any force. The smaller mass simply follows the curve of spacetime near the larger mass. For example, the massive Sun curves spacetime around it, a curvature that reaches out to the edges of the solar system and beyond. The planets orbiting the Sun are not being pulled by the Sun; they are following the curved spacetime deformed by the Sun.

The Second Implication: Frame-Dragging

Two years after Einstein submitted his theory of curved spacetime, Austrian physi-cists Joseph Lense and Hans Thirring predicted that a mass could deform spacetime in a second way - through frame-dragging (1918). They proposed that the rotation of planets and stars or any rotating mass twists the structure of spacetime near that mass. Not only is local spacetime curved near the Sun, it is twisted by the Sun's rotation. Lense and Thirring predicted this effect to be extremely small, and would become smaller farther from the rotating mass, but it would occur around every rotating mass, be it a planet, a star, a galaxy, or a person.

Einstein May Be Right, But Newton's Theory is Still Useful

From this description of the differences found in Newton's theory of gravity and Einstein's resolution of them, one may get the impression that Einstein's theory of general relativity completely replaces Newton's theory of gravity. Now that we are in possession of Einstein's concept of spacetime, should we toss "the force of gravity" out of our physics conversations? No. We need to retain both Einstein's theory of curved spacetime and Newton's theory of gravity in order to understand our universe.

Einstein's theory does provide us with a more accurate understanding of the underlying structure of the universe. However, unless one observes phenomena moving near or at the speed of light (e.g., starlight, radio waves, quasar jets) or near enormous masses (e.g., neutron stars, galaxies, black holes), the actual effects of curved spacetime and frame-dragging are barely distinguishable from those predicted by Newton's theory of gravity. In our common physical experience on Earth, where the fastest phenomena rarely reach 0.0001% of the speed of light, Newton's theory of gravity suffices. Its mathematics are much, much simpler than the mathematics of motion in curved spacetime, and it provides a functional picture of our physical world.

Previous Tests of General Relativity

Einstein was well aware that scientists would want empirical proof if they were to accept his theory of curved spacetime. He offered three specific phenomena that curved spacetime could explain - starlight deflection, the error in Newton's description of Mercury's orbital precession, and the gravitational redshift. Over the past century, scientists have closely observed these phenomena, in addition to examining a fourth phenomenon known as the Shapiro time-delay.

Starlight Deflection

The central premise of Einstein's general theory of relativity is that all matter and energy moving through the universe are affected by curved spacetime. This includes the path of light rays as they emerge from distant stars and make their way across the universe to our Earth-based telescopes and eyes. When their light passes near a massive body, such as a galaxy or our Sun, its path is deflected slightly.

In 1919, merely three years after Einstein published his theory, Frank Dyson (Great Britain's Astronomer Royal at that time), Charles Davidson, and Arthur Eddington took on the challenge of observing and measuring this phenomenon. They compared photographs of a selected area of the night sky with photographs taken of the same area during a solar eclipse. Looking at these photographs, it became apparent that stars that should have been behind the Sun were actually visible during the eclipse. Their light was bending through curved spacetime around the Sun's mass. The result was limited by the short amount of time available to make the measurement during an eclipse (about four minutes), but it confirmed Einstein's prediction to within about 20%.

In 1920, Arthur Eddington wrote a book entitled: "Space, Time, and Gravitation," which described this phenomenon. Since then, the results have been reproduced to higher and higher precision, as the technology for observing stars has improved.

Between 1969 and 1975, twelve measurements were made using radio telescopes to measure the deflection of radio waves from a distant quasar around a galaxy. These measurements matched general relativity's predictions to within 1%, and now the results are good to about 0.1%.

Mercury's Perihelion Precession

As Mercury orbits the Sun, it does not follow the exact same elliptical path each year. As it goes around, Mercury's orbit slowly turns, or precesses, in the direction of its revolution around the Sun. Its perihelion point (the point of orbit closest to the Sun) shifts slightly each time around. Astronomers have observed that over every one hundred years Mercury's orbit has precessed another 574 arcseconds around (0.16).

Newton's theory of gravity largely accounted for this phenomenon and explained that it is caused by the gravitational perturbations of the other planets. But it did not completely account for what is observed. Each century, Mercury's orbit precesses a little farther than Newton's equations predicted - 43 arcseconds more, to be precise.

When Einstein's equations were applied to the orbit of Mercury, it was a precise success. Einstein's calculations predicted that Mercury's orbit would precess 43 arcseconds/year more than Newton's equations predicted. This matched the astronomers' observations exactly. The additional 43 arcseconds were a natural effect of Mercury's motion through the spacetime curved by the Sun.

Gravitational Redshift

Another phenomenon predicted by Einstein's general theory of relativity is that light loses energy as it emerges from a gravitational field. When light loses energy, its wavelength becomes longer and the color of the light shifts toward the red end of the spectrum (thus called the "redshift").

Two key tests of the gravitational redshift are the Pound-Rebka Experiment and NASA's Gravity Probe A. In 1960, physicists Robert Pound and Glen Rebka were able to detect the redshift of high-energy gamma rays in an elevator shaft at Harvard University. They sent gamma rays up from the bottom of the shaft to a sensor 74 feet high. As the gamma rays climbed the 74 feet out of Earth's gravitational field, they lost a minuscule amount of energy (~ 2 parts in a trillion), which Pound and Rebka were able to detect. Their measurement agreed with Einstein's predictions to within 10%, later improved to about 2%.

A more precise test of the redshift was conducted by Gravity Probe A in 1976, a rocket-based experiment, also known as the Vessot-Levine test. In this experiment, a hydrogen-maser clock was launched to an altitude of 6,000 miles. The frequency of the clock in flight was compared to the frequency of a matching clock on the ground. The experiment revealed that the frequencies of the clocks differed slightly, matching Einstein's predictions to within 70 parts per million.

Shapiro Time-Delay

In 1964, Irwin Shapiro, an astrophysicist at Harvard University, identified another phenomenon that Einstein's curved spacetime should cause: the apparent reduction of the speed of light (or electromagnetic waves) when it passes through a gravitational field.

Since 1964, a systematic program has been in place to test the presence of this phenomenon to a greater and greater precision. Scientists have used radio telescopes to perform "radar ranging" on various objects whose distance is precisely known. They began by bouncing signals off of Mercury and Venus.

When the line of sight between the Earth and Mercury was far from the Sun, the travel time of the signal was barely delayed, if at all. But as the line of sight neared the Sun, the delay increased. Scientists predicted that, according to Einstein's equations, the signal would be delayed by 200 microseconds if it traveled right next to the Sun. When performing the experiment, the result matched this prediction.

In addition to bouncing signals off of Mercury, astronomers have bounced signals off of Venus and off the Mariner 6 and Mariner 7 spacecrafts as they orbited Mars. In one of the most precise measurements of this time-delay effect, scientists used a transponder left on the surface of Mars by one of NASA's Viking landers. This experiment confirmed Einstein's prediction to within 0.1%.

Most recently, in June, 2002, Italian physicists B. Bertotti, L. Iess, and P. Tortora bounced radio waves, as they passed near the Sun, off the Cassini spacecraft - a joint NASA and Italian Space Agency satellite and probe en route to a rendezvous with Saturn in July, 2004. Their observations confirmed Einstein's prediction to within 20 parts per million.

Why Perform Another Test of General Relativity?

We wonder about the stars, about our universe, and about how things work - wonder is an important part of human life. Gravity is the most fundamental force in nature; it affects all of us all the time. But even though we've placed men on the Moon, gravity is still an enigma - we still don't completely understand it. Einstein's 1916 general theory of relativity forever changed our notions of space and time, and it gave us a new way to think about gravity.

But, although general relativity has become a cornerstone of modern physics, it remains one of the least tested theories in physics. The frame-dragging effect has never been directly experimentally verified, and none of the previous tests of the geodetic effect come close to the precision that will be achieved by the gyroscopes and SQUID readouts of Gravity Probe B. If we are to continue to advance our knowledge of fundamental laws of nature and the universe, we must experimentally test and verify the predictions of our theories.

Gravity Probe B is one of the most sophisticated physics experiments ever attempted. Over 40 years in development, it has required the efforts of dozens of scientists and engineers at Stanford University, Lockheed Martin Space Systems Company, NASA's Marshall Space Flight Center and the Harvard-Smithsonian Center for Astrophysics, along with many others. It has spawned numerous advances in navigation technology and materials precision. Most importantly, it will provide us a glimpse into the sublime structure of our universe.

Will Gravity Probe B Verify or Refute Einstein?

Will the results of Gravity Probe B verify Einstein's theory of curved spacetime and frame-dragging, or will Einstein's theory be refuted? If the former proves true, then we will have made the most precise measurement of the shape of local spacetime and confirmed the mathematics of general relativity to a new standard of precision. If the latter proves true, then we may be faced with the challenge of constructing a new theory of the universe's structure and the motion of matter.

Will Gravity Probe B Reveal Where "Inertia" Comes From?

One of the fundamental concepts of our physical world is that all objects at rest or in motion have inertia, or a tendency to keep doing whatever they are doing. But where does this tendency or property come from? Does is come from within matter itself? Or is it related to the underlying universe?

In the late 1800's, Austrian physicist Ernst Mach proposed that the property of inertia comes from the motion of matter in the distant universe. The reason an object resists changes in motion is because it is somehow connected to the motion of all the other matter in the universe. It is a gravitational interaction that creates the property of inertia.

Gravity Probe B's investigation of frame-dragging will contribute to this question, because for distant matter to affect local matter, there has to be a gravitational link between the two. Einstein's theory of the geometry of spacetime and the effects of frame-dragging could explain this link.