Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0,t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S.
b) Now transform the coordinates of the events into the S'frame, which is travelling at 0.6calong the x-axis in a positive direction with respect to the frame S. Hence verify that thespacetime interval is invariant.
Derive the Lorentz transformation connecting a frame S (the lab frame) to a frame S′ that moves with respect to S with a velocity in the xy plane. This velocity makes an angle ϕ with the x axis of SS and has speed v.
In order to solve this, take the route of two successive Lorentz transformations, one along the x axis followed by one along the y axis.
Calculate the interval Δs2 between two events with coordinates (x1 = 55m, y1 = 0m, z1 = 0m, t1 = 1 μs) and (x2 = 125m, y2 = 0m, z2 = 0m, t2 = 1.6 μs) in an inertial frame S. Now transform the coordinates of the events into the S' frame which is travelling at 0.75c along the positive x-axis with respect to frame S, thereby verifying that spacetime interval is invariant.
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- The origins of the two frames coincide at t = t’ = 0 and the relative speed is 0.990 c. Two micrometeorites collide at coordinates x = 100 km and t = 200us according to an observer in frame S. What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame S’? The speed of light in vacuum is 2.998 x 10^8 m/sarrow_forwardSuppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardShow that for a particle is invariant under Lorentz transformations.arrow_forward
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Length contraction: the real explanation; Author: Fermilab;https://www.youtube.com/watch?v=-Poz_95_0RA;License: Standard YouTube License, CC-BY