Time Dilation Calculation

• Use Pythagorean Theorem:

w

v t2

v t2

c t2

c t2

(c t2)2 = (v t2)2 + w2

t2 = w / sqrt(c2 - v2) ???t2 = ? w/ c

Compare this with the proper time measured in the rest frame: T = 2w / c

Total time: T2 = 2 t2 ? T2 = ? 2w /c

• Result: Moving clocks run slow! T2 = ? T

• But wait! According to observer in rest frame, observer 2 is moving! Do we have a problem?

? =

1

sqrt(1 - v2 /c2 )

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