The spacetime interval s is defined by the equation
s2 = x2 - c2 t2
The interval in spacetime and its analogy to the concept of distance in ordinary space are discussed at the spacetime analogy page.
Now that you understand spacetime and the definition of the interval, apply it to time dilation.
Find the length of the interval in the lab and the rocket#1 reference frames for one "tick" of the clock at rest in rocket#1. Are the intervals the same? Should they be?
Now, try the same thing with the Lorentz contraction. Find the intervals between the emission of the flash and its arrival at the detector in both lab and rocket frames. Again, are they the same? Should they be?
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