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Class notes from professor Bao, Xiaoyi
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Testing General Relativity● General Relativity is a great success by the criterion of predictions, with all of its
predictions proving correct despite being tested to incredibly high levels of
accuracy. The perihelion of Mercury problem, the bending of light beams, the
gravitational redshift and the radar echo delay problem are all tests of Relativity.
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Mercury’s Perihelion Problem: First Test
● The perihelion of Mercury problem was solved by General Relativity, when its
predictions were found to be almost exactly 42′′ larger than Le Verrier's
Newtonian-based work.
● Newton's law of gravity assumes that two masses experience their mutual forces
of gravity without any mediator being involved to convey those forces between
the masses. Changes in the mutual interaction occur instantaneously.
● Mercury's gravitational force on the Sun changes as the separation of the two
bodies changes and as Mercury moves around its orbit. These changes occur
simultaneously and are inherent to Newtonian gravitational theory.
● Before Relativity, several attempts were made to calculate what would happen if
changes in gravitation propagated at some speed less than infinity. One result
reduced, but not eliminated, the 42′′ discrepancy in Mercury's orbit.
PAGE 31
● When Einstein conceived of 4D space-time, the 42′′ discrepancy between
Newton's and Einstein's predictions for Mercury's orbit disappeared when the
speed of gravity was set equal to the speed of light.
● General Relativity's solution of the precession of Mercury's perihelion point
required the use of obscure mathematics known as tensor analysis.
● Einstein used tensors to deal with multiple masses in 4D space-time interactions,
and made mistakes. Tullio Levi-Civita helped him out with his tensor problems,
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