This is true.
However, there exists an infinite number of times in the rest frame such that t'=r/c and x' = r.
Not right, Jack.
The only time and place in the rest frame at which t'=r/c at x'=r is
when $$t=\frac{\gamma r}{c}(1+\frac{v}{c})$$
at $$x=\gamma r(1+\frac{v}{c})$$
When will you learn to apply a Lorentz transform?
This is really old stuff, by the way. Remember this?
Look at the t'= r/c row, in the LR column.
$$\begin{array}{c|cc|cc|cc|cc}
& O(x,\ \ t) & O(x',\ \ t') & O'(x,\ \ t) & O'(x',\ \ t') & LL(x,\ \ t) & LL(x',\ \ t') & LR(x,\ \ t) & LR(x',\ \ t') \\
\hline
t=t'=0 & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) & (0,\ \ 0) \\
\hline
t=\frac{r}{\gamma c} &
(0,\ \ \frac{r}{\gamma c}) &
(\frac{vr}{c},\ \ \frac{r}{c}) &
(\frac{vr}{\gamma c},\ \ \frac{r}{\gamma c}) &
(0,\ \ \frac{r}{\gamma^2c}) &
(\frac{-r}{\gamma},\ \ \frac{r}{\gamma c}) &
(-r(1-\frac{v}{c}),\ \ \frac{r}{c}(1-\frac{v}{c})) &
(\frac{r}{\gamma},\ \ \frac{r}{\gamma c}) &
(r(1+\frac{v}{c}),\ \ \frac{r}{c}(1 + \frac{v}{c}) \\
t=\frac{r}{c} &
(0,\ \ \frac{r}{c}) &
(\frac{-\gamma vr}{c},\ \ \frac{\gamma r}{c}) &
(\frac{vr}{c},\ \ \frac{r}{c}) &
(0,\ \ \frac{r}{\gamma c}) &
(-r,\ \ \frac{r}{c}) &
(-\gamma r(1+\frac{v}{c}),\ \ \frac{\gamma r}{c}(1+\frac{v}{c})) &
(r,\ \ \frac{r}{c}) &
(\gamma r(1-\frac{v}{c}),\ \ \frac{\gamma r}{c}(1-\frac{v}{c})) \\
t=\frac{\gamma r}{c} &
(0,\ \ \frac{\gamma r}{c}) &
(\frac{-\gamma^2vr}{c},\ \ \frac{\gamma^2r}{c}) &
(\frac{\gamma vr}{c},\ \ \frac{\gamma r}{c}) &
(0,\ \ \frac{r}{c}) &
(-\gamma r,\ \ \frac{\gamma r}{c}) &
(\frac{-r}{1-\frac{v}{c}},\ \ \frac{r}{c-v}) &
(\gamma r,\ \ \frac{\gamma r}{c}) &
(\frac{r}{1+\frac{v}{c}},\ \ \frac{r}{c+v}) \\
\hline
t'=\frac{r}{\gamma c} &
(0,\ \ \frac{r}{\gamma^2c}) &
(\frac{-vr}{\gamma c},\ \ \frac{r}{\gamma c}) &
(\frac{vr}{c},\ \ \frac{r}{c}) &
(0,\ \ \frac{r}{\gamma c}) &
(-r(1+\frac{v}{c}),\ \ \frac{r}{c}(1 + \frac{v}{c}) &
(\frac{-r}{\gamma},\ \ \frac{r}{\gamma c}) &
(r(1-\frac{v}{c}),\ \ \frac{r}{c}(1-\frac{v}{c})) &
(\frac{r}{\gamma},\ \ \frac{r}{\gamma c}) \\
t'=\frac{r}{c} &
(0,\ \ \frac{r}{\gamma c}) &
(\frac{-vr}{c},\ \ \frac{r}{c}) &
(\frac{\gamma vr}{c},\ \ \frac{\gamma r}{c}) &
(0,\ \ \frac{r}{c}) &
(-\gamma r(1-\frac{v}{c}),\ \ \frac{\gamma r}{c}(1-\frac{v}{c})) &
(-r,\ \ \frac{r}{c}) &
(\gamma r(1+\frac{v}{c}),\ \ \frac{\gamma r}{c}(1+\frac{v}{c})) &
(r,\ \ \frac{r}{c}) \\
t'=\frac{\gamma r}{c} &
(0,\ \ \frac{r}{c}) &
(\frac{-\gamma vr}{c},\ \ \frac{\gamma r}{c}) &
(\frac{\gamma^2vr}{c},\ \ \frac{\gamma^2r}{c}) &
(0,\ \ \frac{\gamma r}{c}) &
(\frac{-r}{1+\frac{v}{c}},\ \ \frac{r}{c+v}) &
(-\gamma r,\ \ \frac{\gamma r}{c}) &
(\frac{r}{1-\frac{v}{c}},\ \ \frac{r}{c-v}) &
(\gamma r,\ \ \frac{\gamma r}{c}) \\
\hline
\end{array}$$
Jack said:
How did you do with the twins thread?
You failed.
:roflmao:
Have you
read that thread, Jack? Your argument was comprehensively demolished in the first page or two. You spent the rest of the thread with your fingers in your ears saying "La la la I can't hear you!"