Chinglu, you calculated both position and time of events Q and R in frame Σ and in Σ'. What is the law of nature that says a flash of light can't be at two different positions at two different times? What is the speed of light moving from Q to R in frame Σ? What is the speed of light moving from Q to R in frame Σ'?
First off, I never claimed there was a law of nature that would not place a light flash at two different places at two different times. Further, I am assuming light is c to all frames and observers. So, your post above is meaningless.
The issue here is to determine under all SR calculations where the light flash is located when C' and M are co-located. This is but one time in each frame and I proved that and with great difficulty got you to accept that.
Where I am deeply concerned is that you did not answer my extremely simple post. Now, if you are not able to handle it, simply admit it.
Here it is again. Try to keep in mind all conclusions and calculations are based on M and C' being co-located.
When C' and M are co-located, event Q is valid for the frame Σ. (This assumes LP is correct)
When C' and M are co-located, event R is valid for the frame Σ'. (This assumes LP is correct)
When C' and M are co-located, event LT(Q) is valid for the frame Σ'. (This assumes LT correctly translates)
When C' and M are co-located, event LT(R) is valid for the frame Σ. (This assumes LT correctly translates)
However, LT(Q) != R and LT(R) != Q. (This show LP and LT do not agree when M and C' are co-located)
Hence, if C' and M are co-located, Q is valid for the frame Σ and so is LT(R).
Hence, if C' and M are co-located, R is valid for the frame Σ' and so is LT(Q).
Therefore, SR claims when C' and M are co-located, the light flash is at Q and LT(R) with LT(R) != Q, so 2 different places.
Therefore, SR claims when C' and M are co-located, the light flash is at R and LT(Q) with LT(Q) != R, so 2 different places.