7. For the Lorentz matrix P = use a? – 32 = 1 and v = B/a to verify that a = 1/vi – v² and 3 = v//1– v². Conclude that 1 P = Ly = 1 V1- v2 For this reason it is called the Lorentz matrix for the...

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Extracted text: 7. For the Lorentz matrix P = use a? – 32 = 1 and v = B/a to verify that a = 1/vi – v² and 3 = v//1– v². Conclude that 1 P = Ly = 1 V1- v2 For this reason it is called the Lorentz matrix for the velocity v. (hint: Substitute 3 = va in a² – 32 = 1 and solve for a.) %3D 8. Compute L, for v = 4/5, i.e., 80% of the speed of light. 9. What is the range of possible values for v in the formula for L„? What physical fact does this correspond to? -[: : - а в 10. If L, = % and Le, = are Lorentz matrices, show that the product Lu, Lva is a Lorentz matrix Lvz where vi + v2 V3 = 1+ vị v2 (hint: Why does this product have determinant 1? Use að + Be ae + Bồ ae + B8 að + ße Lv, Lvz XE + B8 að + ße to compute v3. Dividing the top and bottom of by að will help.) The presence of this denominator1+ v1v2 # 1 indicates that in Special Relativity, velocities are not additive!