- #1

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## Main Question or Discussion Point

In discussion with my friend, we reached a conclusion that transformation formula of velosity v to another IFR moving V, i.e.

[tex]v'=\frac{v+V}{1+vV/c^2}[/tex]

is valid even if v is hypothetical velocity,i,e,

[tex]v=\frac{x_2-x_1}{t_2-t_1}[/tex]

[tex]v'=\frac{x'_2-x'_1}{t'_2-t'_1}[/tex]

where interval of ##(t_1,x_1)\rightarrow (t'_1,x'_1)## and ##(t_2,x_2)\rightarrow (t_2',x_2')## are time-like, space-lile, null, it doen't matter.

For example when ##t_2-t_1=0## ,##v=\pm \infty## is trandformed to

[tex]\pm \infty \rightarrow \frac{\pm \infty + V}{1+\pm \infty V/c^2}=\frac{c^2}{V}[/tex]

Of course it is over c but it seems to work describing change of synchronicity.

I have never thought of such an application of the law so appreciate your comment whether it is OK or No Good.

[tex]v'=\frac{v+V}{1+vV/c^2}[/tex]

is valid even if v is hypothetical velocity,i,e,

[tex]v=\frac{x_2-x_1}{t_2-t_1}[/tex]

[tex]v'=\frac{x'_2-x'_1}{t'_2-t'_1}[/tex]

where interval of ##(t_1,x_1)\rightarrow (t'_1,x'_1)## and ##(t_2,x_2)\rightarrow (t_2',x_2')## are time-like, space-lile, null, it doen't matter.

For example when ##t_2-t_1=0## ,##v=\pm \infty## is trandformed to

[tex]\pm \infty \rightarrow \frac{\pm \infty + V}{1+\pm \infty V/c^2}=\frac{c^2}{V}[/tex]

Of course it is over c but it seems to work describing change of synchronicity.

I have never thought of such an application of the law so appreciate your comment whether it is OK or No Good.