Unformatted text preview: K = u 2 K = 4 1v 2 /c 2 = 2 + 2 γ yielding γ = 1+ v 2 /c 2 1v 2 /c 2 . Since l = l /γ we ﬁnally obtain l = l 1v 2 /c 2 1 + v 2 /c 2 3. Decompose r into two components: (a) r k = V r · V V 2 , r ⊥ = rr k and similarly for r . Using Lorentz transformations r k = γ ( r k + V t ) , r ⊥ = r ⊥ we get after simple algebra r = γ ( r + V t ) + ( γ1) ( r × V ) × V V 2 , t = γ ± t + r · V c 2 ² (b) Calculating d r and dt as functions of r and t and taking ratio yields v = v + V + ( γ1) V V 2 [( v · V ) + V 2 ] γ ( 1 + v · V c 2 )...
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 Fall '10
 krill
 Special Relativity, inertial reference frame, particle rest frame, 4vector scalar products, ·V c2

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