Relativity and Lorentz Transformations?

Question

Mary sees two pulses of light emitted 3 microseconds apart from what she observes as the same place. Micheal is moving and observes the same light pulses emitted 9 microseconds apart. Part A asks: What is Michael's relativistic speed?

Part B asks: How far apart do the light pulses appear to Michael.

The question is the first one asked under the section of Lorentz Trans., so I assume its using the basic equations and not the Lorentz Velocity Trans.

I got .95*c for part A. Nothing for B.

Thanks!

- David

Answer 1

Part B is easy:

The pulses of light travel at speed of light c with respect to Micheal, and are 9 microseconds apart with respect to Micheal.

How far apart do the light pulses appear to Michael?

L = Δt c = 9e-9 x 3e8 = 2.7 meter apart

Note that solution of part B ignores the very existence of Mary.

*****

Part A is indeed troublesome, if you want to do it through Lorentz transformation. Normally I would simply use formula for Doppler red shift, which is

9 mcs/ 3mcs = 3 = √[(v+c)/(c-v)]

v = 4/5 c