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It is important to be aware that it is fairly rare for an experiment to '''prove''' a theory.  In general, experiments can only '''refute''' a theory.  They can also '''be consistent with''' a theory.  When enough experiments, especially experiments that investigate a wide variety of phenomena, are shown to be consistent with a theory, it lends credence to that theory.  When no other plausible theory can explain those observations, we can say that they '''validate''' the theory.  The Mercury observations are just one phenomenon.  By themselves they couldn't validate or prove GR.  And there was at one time another competing theory—the Newcomb-Hall exponent-fudging theory.  That one didn't hold up for things other than Mercury.  No other theory has come up explaining the phenomenon; GR has withstood the test of time.  That goes a long way toward validating GR.  There are many other observations and experiments, covering a wide variety of phenomena, described below—bending of light, gravitational time dilation, gravitational waves, geodetic precession, Shapiro effect, etc.  It is these widely disparate observations, and the lack of any alternative theories explaining any of them, that lead people to say that GR is "experimentally validated".

It is important to be aware that it is fairly rare for an experiment to '''prove''' a theory.  In general, experiments can only '''refute''' a theory.  They can also '''be consistent with''' a theory.  When enough experiments, especially experiments that investigate a wide variety of phenomena, are shown to be consistent with a theory, it lends credence to that theory.  When no other plausible theory can explain those observations, we can say that they '''validate''' the theory.  The Mercury observations are just one phenomenon.  By themselves they couldn't validate or prove GR.  And there was at one time another competing theory—the Newcomb-Hall exponent-fudging theory.  That one didn't hold up for things other than Mercury.  No other theory has come up explaining the phenomenon; GR has withstood the test of time.  That goes a long way toward validating GR.  There are many other observations and experiments, covering a wide variety of phenomena, described below—bending of light, gravitational time dilation, gravitational waves, geodetic precession, Shapiro effect, etc.  It is these widely disparate observations, and the lack of any alternative theories explaining any of them, that lead people to say that GR is "experimentally validated".

There's also the matter of simply "accepting" something, when a phenomenon is consistent with a theory that is already known to be valid.  The recoil from a gun is an example of this.  Everyone knows that there is a backward recoil when a gun is fired.  This is explained to people when they are first being taught how to use a gun, and they get used to it with practice.  The reason for the recoil is that it is an obvious consequence of Newtons' laws of motion.  But people don't specifically think about Newton's laws, or consider this to be a "proof", when they are firing a gun.  They just accept that the recoil is a known consequence of those laws.  Newton's laws of motion have been validated through thousands of experiments much more focused than the firing of a gun. The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]] is another example of this kind of acceptance.  The results are consistent (to within 5% when analyzed carefully) with Special Relativity, and many people consider it to be a validation of SR.  But there were too many other things going on, such as the use of the newly-invented particle accelerator, to make it a definitive test.  In any case, Special Relativity had already been validated through more focused and definitive tests.

There's also the matter of simply "accepting" something, when a phenomenon is consistent with a theory that is already known to be valid.  The recoil from a gun is an example of this.  Everyone knows that there is a backward recoil when a gun is fired.  This is explained to people when they are first being taught how to use a gun, and they get used to it with practice.  The reason for the recoil is that it is an obvious consequence of Newtons' laws of motion.  But people don't specifically think about Newton's laws, or consider this to be a "proof", when they are firing a gun.  They just accept that the recoil is a known consequence of those laws.  Newton's laws of motion have been validated through thousands of experiments much more focused than the firing of a gun.

 

The [[Cockcroft and Walton Experiment|Cockcroft/Walton experiment]] is an example of this kind of acceptance.  The results are consistent (to within 5% when analyzed carefully) with Special Relativity, and many people consider it to be a validation of SR.  But there were too many other things going on, such as the use of the newly-invented particle accelerator, to make it a definitive test.  In any case, Special Relativity had already been validated through more focused and definitive tests.  It is important to note that there are no known alternative theories explaining this result.

 

The anomalous behavior of the timing signals from [[GPS]] satellites is another example.  The phenomenon is well known—the system compensates for this; otherwise it wouldn't work—and the phenomenon is known to be a consequence of both special and general relativity.  But the GPS system should not be considered and experiment to test relativity.  No sensible person would build the GPS system as a test of relativity, if only because it exhibits two phenomena (time dilation of special relativity, 7 milliseconds per day, and time compression of general relativity, 45 milliseconds per day) that work against each other.  No one would design and experiment that tests two phenomena working against each other.  But the effect of both, 38 milliseconds per day, is well known, as is the reason for this.  It is important to note that there are no known alternative theories explaining this result.

While the experimental tests for General Relativity are rather esoteric, those for Special Relativity are fairly straightforward.  So much so that the Michelson-Morley experiment could be said to have single-handedly established the case for SR—the logical syllogism leading from Michelson-Morley to SR and the Lorentz transform was fairly clear once people saw it.

While the experimental tests for General Relativity are rather esoteric, those for Special Relativity are fairly straightforward.  So much so that the Michelson-Morley experiment could be said to have single-handedly established the case for SR—the logical syllogism leading from Michelson-Morley to SR and the Lorentz transform was fairly clear once people saw it.