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==Fallacious Claims of Experimental Verification of Relativity==

==Fallacious Claims of Experimental Verification of Relativity==

The different effects predicted by special relativity, compared to classical formulations, are extremely tiny.  Most relativistic effects would not occur except at speeds near the high speed of light, <math>3 \times 10^8 m/s</math> relative to ordinary phenomena observed by humans.  (However, it's worth noting that ordinary magnetism can be considered a relativistic effect, 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.  The significance of that equation, however, remains debatable as nothing in [[quantum mechanics]] depends on it.

Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

Nevertheless, it has been verified with ever-increasing precision in subsequent eclipses, and in the observations of quasar 3C273.

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 effect of the oblateness of the Sun.  These are hard to calculate accurately, but, by 1900 it was known reasonably accurately that there was an "anomalous" precession, that is, a precession beyond all other known effects, of about 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 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 floated, by Simon Newcomb, was that the exponent of the radius in the gravitational formula wasn't exactly 2.  By choosing a value of 2.000000157, Newcomb was able to fit the observed behavior of Mercury.  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.

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.

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.

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[sun]] is delayed slightly.]]

[[Image:Cassini-science-289.jpg|right|thumb|The Shapiro effect: A spacecraft signal dipping into a gravity well around the [[Sun]] is delayed slightly.]]

As the 20^th century progressed, more tests of general relativity were proposed.  One was the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of a planet.  Various spacecraft have confirmed this.

As the 20^th century progressed, more tests of general relativity were proposed.  One was the ''Shapiro effect'', involving time delay in radio signals passing through the gravity well of the Sun or a planet.  Various spacecraft have confirmed this.

Another is ''gravitational time dilation''.  This is an effect separate from the time dilation of special relativity.  It was tested by the Pound-Rebka experiment in 1959.

Another is ''gravitational time dilation''.  This is an effect separate from the time dilation of special relativity.  It was tested by the Pound-Rebka experiment in 1959.