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These theories have augmented earlier approaches, such as [[Galilean Relativity]].

These theories have augmented earlier approaches, such as [[Galilean Relativity]].

While virtually all scientists accept relativity, it has been met with much resistance in some quarters.  In fact, it is unlikely that college faculty tenure, or a Ph.D degree, would be awarded to any critic of the theory.  Perhaps its most famous detractor was Louis Essen [1908-1997], the man credited with determining the speed of light.  He wrote many fiery papers against it such as ''Relativity and Time Signals''<ref>http://gsjournal.net/Science-Journals/Journal%20Reprints-Relativity%20Theory/Download/3297</ref> and ''Relativity - Joke or Swindle?''<ref>http://www.ekkehard-friebe.de/Essen-L.htm</ref>.  Perhaps the most famous website opposing relativity is this one, with its [[Counterexamples to Relativity]] page.  The cornerstone item in that page involves the experimental measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error.

The theory of relativity is defended with religious-like zeal, such that no college faculty tenure, Ph.D degree, or Nobel Prize is ever awarded to anyone who dares criticize the theory, as the example of denying a Nobel Prize to the most accomplished physicist of the 20th century, [[Robert Dicke]], illustrates.  Another critic of the theory was Louis Essen [1908-1997], the man credited with determining the speed of light.  He wrote many fiery papers against it such as ''Relativity and Time Signals''<ref>http://gsjournal.net/Science-Journals/Journal%20Reprints-Relativity%20Theory/Download/3297</ref> and ''Relativity - Joke or Swindle?''<ref>http://www.ekkehard-friebe.de/Essen-L.htm</ref>.  Perhaps the most famous website opposing relativity is this one, with its [[Counterexamples to Relativity]] page.  The cornerstone item in that page involves the experimental measurements of the advance of the perihelion of Mercury that show a shift greater than predicted by Relativity, well beyond the margin of error.

Unlike most of physics, the theories of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value.  For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

Unlike most of physics, the theories of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value.  For example, the limit of momentum as mass approaches 0 and velocity approaches the speed of light is not equal to the momentum of (massless) light.<ref>Discontinuities in General Relativity are also well-recognized. See, e.g., [http://www.springerlink.com/content/u47l341u2q555455/]</ref>

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury.  There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun.  These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century.  This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

*The second "classical" test of general relativity was the advance of the perihelion of the orbit of Mercury.  There are many complex effects contributing to this, including gravitational perturbations from other planets and the effect of the oblateness of the Sun.  These are hard to calculate accurately, but, by 1900 it was known quite accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of 43 arc seconds per century.  This is a very tiny effect, but astronomical measurements were sufficiently accurate by that time to show it clearly.

:This created quite a problem&mdash;physicists by then were accustomed to having their theories check out very accurately.  One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2.  He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>.  By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year.  While the loss of the ability to get a simple result from the integration with an exponent of 2 would be regrettable, physicists would would have been willing to put up with that if it gave the right answer.  But it didn't.  As can be seen from the formula above, whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies.  The value chosen by Newcomb was "tweaked" for Mercury, but it got wrong values for the precessions of other planets, and, most notably, for the Moon.  The Newcomb-Hall hypothesis was soon discarded.  As can be seen from the table below, the measured values of the anomalous precessions of other planets agree well with the predictions of general relativity but poorly with those predicted by Newcomb and Hall.

:This created quite a problem&mdash;physicists by then were accustomed to having their theories check out very accurately.  One proposal that was made, by Simon Newcomb and Asaph Hall, was that the exponent of the radius in the gravitational formula wasn't exactly 2.  He showed that, by choosing an exponent of <math>2+\delta</math>, the precession, as a fraction of a full orbit per planet's year, is <math>\delta/2</math>.  By setting <math>\delta</math> to .000000157, that is, an exponent of 2.000000157, Newcomb was able to get a precession of .000000078 revolutions per Mercury year, or 43 arcseconds per Earth year.  Whatever value is chosen for <math>\delta\,</math>, it gives the same precession, per revolution, for all orbiting bodies, but gravitational effects from other planets diminish that effect the further the planet is from the sun.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.

:While Newcomb's theory, and general relativity, don't lead to closed-form solutions, both theories can be solved numerically to as much precision as one desires.