Changes

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.  The significance of that equation, however, remains debatable as nothing in [[quantum mechanics]] depends on it.

Another prediction of special relativity was time dilation in rapidly moving objects.  This has been verified in the anomalously slow decay of relativistic cosmic muons.  In fact, time dilation must be taken into account in all high-energy nuclear physics experiments.

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.

Predictions of general relativity turned out to be more obscure and difficult to test.  The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.  The first of these was famously tested during a total eclipse in 1919.  That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used <ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref>.  The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome.  His analysis techniques would not pass muster today.

Predictions of general relativity turned out to be more obscure and difficult to test.  The two most famous predictions were the bending of light in a gravitational field and the precession of the perihelia of orbiting planets.  The first of these was famously tested during a total eclipse in 1919.  That test was somewhat muddled by an incorrect initial calculation, by several people including Einstein himself, of what the effect would be, and some "cherry picking" of the data to be used <ref>''Einstein's Luck'', John Waller, Oxford University Press, ISBN 0-19-860719-9</ref>.  The data selection could be considered "manipulation" or "fudging", by a person (Arthur Eddington) who had a personal stake in the outcome.  His analysis techniques would not pass muster today.

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.  Also, some people may have objected because it ruined the very elegant integral that is obtained when the exponent is exactly 2.  Newcomb's approach was abandoned.

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.  While other orbits do not have a similar precession, Mercury experiences a gravitational pull far higher than any other planet in the solar system due to its proximity the Sun.  Mathematicians falsely claimed that the exponent must be precisely 2 in order to make the integrals work properly, and Newcomb's approach was abandoned.

General relativity predicts 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.  There is some controversy over whether general relativity's results are really accurate in terms of modern observations.

General relativity predicts 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.  There is some controversy over whether general relativity's results are really accurate in terms of modern observations.