In a frame S, two events are observed: event 1: a pion is created at rest at the origin and event 2: the pion disintegrates after time τ . Another observer in a frame S′ is moving in the positive direction along the positive xaxis with a constant speed v and observes the same two events in his frame. The origins of the two frames coincide at t = t′ = 0. (a) Find the positions and timings of these two events in the frame S′ (a) according to the Galilean transformation, and (b) according to the Lorentz transformation.

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)