Dear Colleague,
I shall be very grateful if you read the following short note and answer the question posed at its end. You may state your opinion just by writing TRUE or FALSE.
"Consider two reference frames, F and F′, moving along with respect to each other with constant velocity v. A “stationary” observer in frame F defines events with coordinates: x, y, z, t. Another observer in F′ defines events using the coordinates x′, y′, z′, t′. For simplicity, assume that the coordinate axes in each frame are parallel (x is parallel to x′, y to y′, and z to z′). Now consider the case in which a physical occurrence (an event in time) takes place at the point of origin in F′ and F [i.e., at (x′, y′, z′) = (x, y, z)= (0, 0, 0)], and that it starts at time t'1, and ends at time t'2 (as measured by a clock at F′), lasting for a period of Δt' = t'2 - t'1
The observer at F has no direct way for knowing the times t'1 and t'2 (and Δt'). He/she receives two signals, traveling with the same constant velocity Vs emitted from the point of origin of F′ where the occurrence took place, indicating the start and end of the occurrence, respectively. The signal can be of any modality (light, sound, seismic waves, etc.), provided that Vs > v.
Assume that the first, and second signals arrive to the observer at F at times t1, and t2 , respectively (according to the clock at F). Denote the time difference between the two arrival times by Δt (Δt = t2 - t1 ).
I argue that the following inequalities are always true:
If F′ is departing from F, then Δt > Δt'
And
If F′ is approaching F, then Δt < Δt'
Question: Are the above inequalities (combined) TRUE or FALSE?
Many thanks in advance,
Ramzi Suleiman
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