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The different effects predicted by special relativity, compared to classical formulations, are extremely tiny.  Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans.  The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second&mdash;such speeds are called ''relativistic''.  (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity.  The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny.  Most relativistic effects are negligible at the speeds of ordinary phenomena observed by humans.  The effects only become significant when the speeds involved are a significant fraction of the speed of light, which is <math>3 \times 10^8</math> meters per second&mdash;such speeds are called ''relativistic''.  (However, it's worth noting that ordinary magnetism can be considered an effect of relativity, dictated by the need for electrostatic theory to be correct under relativity.  The speed of light in fact appears in the formulas ([[Maxwell's Equations]]) governing electricity and magnetism, though these equations were developed long before relativity was proposed.)

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.  In fact, at the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity. The significance of that equation, however, remains debatable as nothing in [[quantum mechanics]] depends on it.

Because the effects of relativity are so tiny, scientists have been devising sophisticated and sensitive tests ever since the theory was formulated in 1905.  In fact, at the end of Einstein's original 1905 paper [http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ "Does the Inertia of a Body Depend its Energy Content?"], he speculates on the possibility that the equation <math>E = m c^2</math>, which would normally be very hard to verify, could be verified with the extremely high energies of the newly-discovered phenomenon of radioactivity.<ref>This is perhaps the most famous, most widely quoted, and least understood equations ever written.  It is not related to [[quantum mechanics]].</ref>

Another prediction of special relativity was time dilation in rapidly moving objects.  Some have suggested that this effect is verified in the anomalously slow decay of relativistic cosmic muons, but other explanations are possible for this effect.  Similarly, the assertion that time dilation must be taken into account in all high-energy nuclear physics experiments is rarely backed up by specific examples with data.

Another prediction of special relativity was time dilation in rapidly moving objects.  Some have suggested that this effect is verified in the anomalously slow decay of relativistic cosmic muons, but other explanations are possible for this effect.  Similarly, the assertion that time dilation must be taken into account in all high-energy nuclear physics experiments is rarely backed up by specific examples with data.

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, 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 = .000000157</math>, 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.  Unfortunately, any such fudging of the exponent gives the same precession, per planetary year, for ''any'' orbiting object.  This would have given the Moon a very noticeable precession, which was not observed.  There may have been another effect working against Newcomb's theory.  There is sometimes "intellectual inertia," a reluctance to accept new theories.  This would have been particularly evident in the case of Newtonian gravitation, because the Newtonian formula, with its exponent of exactly 2, can be integrated exactly, in closed form.  In fact, the invention of calculus, and mathematical physics in general, was largely founded on Newton's exact closed-form solution for an inverse square force field, and the demonstration that it exactly matched Kepler's laws.  Mathematical physics would have had a very rocky start if this weren't the case.  Giving up the exact Newtonian formulation, with its exponent of exactly 2, did not come easily.

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.  Unfortunately, any such fudging of the exponent gives the same precession, per planetary year, for ''any'' orbiting object.  This would have given the Moon a very noticeable precession, which was not observed.  There may have been another effect working against Newcomb's theory.  There is sometimes "intellectual inertia," a reluctance to accept new theories.  This would have been particularly evident in the case of Newtonian gravitation, because the Newtonian formula, with its exponent of exactly 2, can be integrated exactly, in closed form.  In fact, the invention of calculus, and mathematical physics in general, was largely founded on Newton's exact closed-form solution for an inverse square force field, and the demonstration that it exactly matched Kepler's laws.  Mathematical physics would have had a very rocky start if this weren't the case.  Giving up the exact Newtonian formulation, with its exponent of exactly 2, did not come easily.

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.

General relativity was developed to predict this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.  But more accurate, modern measurements of Mercury's precession disproves general relativity, as it predicts values incorrect by more than measurement error.

General relativity was developed to predict this extra precession, in the amount of <math>3{}v^2/c^2</math> revolutions per planet's "year", where <math>v</math> is the planet's average orbital speed.<ref>That is a simple approximation, designed to relate the precession to the planet's speed relative to the speed of light.  A more accurate approximation is <math>\frac{3GM}{c^2 a(1-e^2)}</math>, where a is the semi-mahor axis and e is the eccentricity.</ref>  More accurate, modern measurements of Mercury's precession differ slightly from the calculated combined effects of planetary perturbation, equinoctial precession, solar oblateness, and general relativity.  The reason for this is not known.

The following table show some approximate parameters for the planets.  Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull.  Precession of planets other than Mercury is very hard to measure.

The following table show some approximate parameters for the planets.  Note that Mercury has the smallest orbit, the fastest speed, and the highest gravitational pull.  Precession of planets other than Mercury is extremely hard to measure, but measurements of the actual anomalous precessions are in good agreement with the last column of the table.<ref>http://www.mathpages.com/rr/s6-02/6-02.htm</ref>

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