The theory of relativity Phys 343
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Some of the General Relativity Predictions
(1) Gravitational red-shift:
Suppose we measure time with three identical clocks, one placed on the center of a rotating disk, a second placed on the rim of the disk, and the third at rest on the ground.
From the laws of special relativity we know that the clock attached to the center, since it is not moving with respect to the ground, should run at the same rate as the clock on the ground-but not at the same rate as the clock attached to the rim of the disk.
An observer at the center ,on the rotating disk, and an observer at rest on the ground both see the clock on the rim run more slowly than their own clocks. However,
explanations of the difference for the two observers are not the same.
To the observer on the ground, the slower rate of the clock on the rim is due to its motion. The observer on the disk is likely to conclude that the centrifugal force has something to do with the slowing of time. He notices that time is slowed as he moves in the direction of the centrifugal force, outward from the center to the edge of the disk.
By applying the principle of equivalence, which says that any effect of acceleration can be duplicated by gravity, we must conclude that:
As we move in the direction that a
gravitational force acts, time will slow down.
An executive working on the ground floor of a tall city
skyscraper will age more slowly than her twin sister working on the top floor. The difference is very very small.
For larger differences in gravitation, like between the surface of the sun and the surface of the earth, the differences in time are larger.
Generally, A photon emitted near the surface of an extremely massive object will loose energy as it escapes the intense gravitational field. This results in a
gravitational redshift of the photons.
Measurements of time depend not only on relative motion, as we learned in special relativity, but also on the gravity (i.e. on the location
of one point in a gravitational field relative to the other one).
Conclusion:
A clock at the surface of the sun should run measurably slower than a clock at the surface of the earth.
It is interesting to note that the Global Positioning System (GPS) system, while not intended or used as a test of general relativity, does effectively serve as confirmation of the gravitational redshift effect.
If they did not take Einstein's theory into account, (almost 40 microseconds due to gravitational redshift effect at their operating altitude of 20,000 km), GPS trackers in aircraft cockpits would be off by kilometers within a day!
This phenomenon was confirmed in 1959 by Pound-Rebka experiment which measured the relative redshift of gamma rays from two radioactive atoms.
situated at the top and bottom of Harvard University's Jefferson tower
In 1976 NASA mission called Gravity Probe A sent an atomic clock 10,000 kilometers into space, confirming the theory's prediction that gravity slows the flow of time.
(2) The precession of the perihelion of Mercury:
The orbits of the planets about the Sun are not exactly circular, but slightly elliptical.
At one point in its orbit, called aphelion, a planet will be slightly farther than average from the Sun, and at another, called perihelion, slightly closer.
As long as a system is simply one object orbiting another, it is a direct prediction of classical Newtonian gravitation that the same path in space is repeated for ever.
But if anything interferes with that simple interaction, the orbit will precess, (i.e. the points of aphelion and perihelion gradually creep around in a circular fashion).
Newtonian measurements of the rate of Mercury’s precession did not agree exactly with observation. There is still 43 seconds of arc per century missing.
Using general relativity, a correction to the classically expected precession rate of Mercury can be calculated. The result of 43 s of arc per century is in good agreement with observation.
The other planets experience perihelion shifts as well, but, since they have lower orbital velocities, and have less eccentric orbits, their shifts are lower and harder to observe.
For example, the perihelion shift of Earth's orbit due to general relativity is about 5 seconds of arc per century
(3) The deflection of light by the sun:
Rays of light (which are weightless) bend in the presence of a gravitational field , since they travel in a bent space-time geometry.
Einstein predicted that starlight passing close to the sun would be deflected by an angle of 1.75 s of arc, which is large enough to be measured.
Measurements of the deflection of starlight during 1919 sun eclipse had supported Einstein's prediction.
In his General Theory of Relativity Einstein predicted that there must be
gravitational waves which are disturbances in the curvature of spacetime caused by the motions of matter. These waves propagating at (or near) the speed of light.
Though gravitational waves pass straight through matter, their strength weakens
proportionally to the distance traveled from the source. A gravitational wave arriving on Earth will alternately stretch and shrink distances, on an incredibly small scale (by a factor of 10-21) for very strong sources.
No wonder these waves are so hard to detect.
Gravitational Waves:
The existence of these waves considered as a unification between EM and GR.
Gravity Probe B Says Einstein was Right. Again.
Einstein also predicted that the Earth's mass would warp its surrounding spacetime, and that it would
"drag" the fabric of spacetime by a certain degree as it rotates. Those last two predictions are the reason Gravity Probe B was first imagined in 1959 by two Stanford scientists named George Pugh and Leonard Schiff
NASA launched Gravity Probe B in April 2004, and these new results are the culmination of more than 50 years of effort.
After its launch, NASA pointed Gravity Probe B at a single star, IM Pegasi, and collected tons of data to see if the on-board gyroscopes would continue to point in that same direction forever -- as Newton expected -- or whether there would be tiny changes in the direction of their spin in response to Earth's gravitational pull.
the data indicated that Einstein's theory correctly predicts the "geodesic effect" (i.e., how much the mass of the Earth is warping local spacetime) to within around 0.28 percent.
But the scientists were having a bit more trouble with data analysis to measure the much-tinier "frame- dragging" effect (i.e., whether or not, and by what degree, the Earth drags the fabric of spacetime with it as it rotates). The prediction is that the twisting of earth's local spacetime would cause the spin axis to shift by 0.039 arc-seconds, or 0.000011 degrees.
And they can confirm a frame-dragging effect as well, it's confirmed to a 19 percent accuracy.
So, we spent 50 years and $700 million to conclude that Einstein's general theory of relativity is still right. Only time will tell if it was worth the price.
Analysis by Jennifer Ouellette Thu May 5, 2011 09:37 PM ET
