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Special Relativity
Special Relativity - Figure 2
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Special Relativity - Figure 3
Special Relativity - Figure 4
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Special Relativity - Figure 5

     This result is a famous equation known as a Lorentz Transformation.  It is a triumph of modern physics, and it is derivable from the most basic mathematical concepts.  Amazingly, it has actually been tested and proven to work exactly.  It is a mathematical proof that time flows differently for each person.