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As a casual science reader, I've always found the implications of relativity (inconsistent clocks after near-light-speed travel and various space-time paradoxes) to be confusing and magical-sounding. Yet I know it's accepted as foundational to modern physics.

What are some of the experiments that have borne out Einstein's theory?

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Possibly related: physics.stackexchange.com/q/9474/2451 –  Qmechanic May 27 '11 at 13:46
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If you're asking for experimental tests of special relativity, arguably the first one is the Michelson-Morley experiment. Subsequent to that, there have been an enormous number of tests that verify it to incredible precision - a comprehensive account with references can be found here:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

But you've tagged your question with general relativity - for which there's a Wikipedia page that summarizes the main predictions (and confirmations) like the precession of Mercury's perihelion, deflection of light by the sun, etc.

http://en.wikipedia.org/wiki/Tests_of_general_relativity

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You can find an extended list of experiments on the Special Theory of Relativity on the following link:

What is the experimental basis of Special Relativity?

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