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Derive the approximate expression for the lab-frame speed

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Reference no: EM13945192

The lab-frame speed of light propagating along arm A in the aether theory would satisfy

c2 = v'2A + V2 + 2v'A V cos ?,

where V~ is the velocity of the lab relative to the aether and ? is the angle between V~ and ~v' A. Use this to derive the approximate expression for the lab-frame speed

v'A ? c (1 - ß cos ? - ½ ß2 sin2?,

where ß = V/c. You can drop any terms involving ß3 or higher powers of ß.

Reference no: EM13945192

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