Question

Two events, A and B, occur in the frame S at spacetime 4-vector coordinates (0;500,10,10) and (600;2000,10,10) respectively. All coordinates are given in meters. (a) What is the spacetime interval between these events? What type of interval is it? (b) How fast must an observer be moving along the x axis for the two events to be simultaneous and what is the spatial separation between the events in this case? (c) Could event B precede event A for some observer?

Answer 1

IN FRANCE S, EVENT A (ct_1: x_1, y_1, z_1) = (0: 500, 10, 10) EVENT B (ct_2: x_2, y_2, z_2) = (600: 2000, 10, 10) downarrow ALL COORDINATES IN METER (a) delta s^2 = (c delta t)^2 + delta x^2 + delta y^2 + delta z^2 = -[c(t_2 - t_1)]^2 + (x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2 = -(600 - 0)^2 + (2000 - 500)^2 + (10 - 10)^2 + (10 - 10)^2 - 600^2 + 1500^2 + 0 + 0 = 1890000 Delta S = 1374.8 m SPARE - TIME INTERVAL HERE Delta s^2 > implies delta x^2 > c^2 Delta t^2 therefore SPATIAL SEPARATION IS GREATER THAN THE DISTANCE LIGHT TRAVELS AND HENCE SPACE TIME INTERVAL IS SPACE - LIKE. (b) LET S� MOVES WITH SPEED V ALONG times A times 15 T_MAT t_2� - t_1� = 0 (SIMULTANEOUS) y(t_2 - v x_2/c^2) - y(t_1 - v x_1/c^2) = 0 t� = y(t - VX/C^2) y = 1/squareroot 1 - v^2/c^2 (t_2

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