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Oct 2, 2014 at 21:49 comment added user4552 Another way to see that it can't be of interest physically is to consider the case where $v=c$, which is intermediate between $v<c$ and $v>c$. You get nonsense for $v=c$.
Jul 25, 2014 at 22:02 vote accept fimas
Jul 25, 2014 at 22:02 comment added fimas I guess that answers it then, an imaginary/complex speed value does not make sense since it breaks physics.
Jul 25, 2014 at 17:48 comment added garyp The experimental results for time dilation show that an observer moving relative to a clock sees the hands of a clock moving more slowly than an observer stationary with respect to the clock. Your analysis shows the opposite. Note that in your notation, $T'$ is the time interval between two clock ticks in the stationary frame. Your analysis does not describe the time dilation that is actually observed. It does not describe a physical phenomenon.
Jul 25, 2014 at 17:25 comment added fimas The physical phenomenon it describes is the time dillation $T'$ between two objects moving relative to eachother. The relative differense in speed between them is $i$. I.e. object $a$ travels away from object $b$ at the speed of $i$ units for 1 unit of time. The speed unit used defines the speed of light in a vacuum as 2. How much does the time differ from $a$ and $b$? In the case above it differs by $\sqrt{\frac{5}{4}}$ units of time.
Jul 25, 2014 at 16:55 history answered garyp CC BY-SA 3.0