chinglu said:
Light can be located at 2 different places given 2 different times. But, this make no difference in the OP.
The OP notices that given C' and M are co-located, the primed frame light postulate places the light at $$(d',0,0,d'/c)$$. This is the only correct answer.
No it isn't; the correct answer includes which observer sees the event at $$(d',0,0,d'/c)$$, you have failed to specify this, so you aren't describing special relativity but something else.
However, given C' and M are co-located, the unprimed frame applies LP and LT and puts the light at primed frame $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$.
Again, the correct answer includes an observer, there are two of these, one for each frame. Which observer are you (intentionally not) referring to?
Therefore, LT gets the answer wrong.
No, chinglu got the answer wrong, or came to a completely false conclusion. You have, in fact, only demonstrated that, given a vague enough description of simultaneity, you can get all kinds of wrong answers.
Now, you are applying scales and all that, except LT takes all that into account and LT was used by the OP. So, that is a non-argument on your part.
Further, the OP proved the co-located event was unique since it was proven both frames agreed on the clock times at C' and M for the co-location event.
You haven't defined what you mean by "unique", and it is not something you find described in special relativity. There are no unique events, or times, or distances; what the hell are you doing introducing a term that has nothing to do with the physical reality? Wait, don't answer that.
So, LT simply gets the answer wrong. Remember, the job of LT is to translate into the other frame in terms of what it deems to be true. LT failed to do that.
What you seem to be incapable of comprehending is that each observer sees what they "deem to be true", and truth is not unique (how can it be?).
You are also getting the direction wrong in the logic. You are claiming the OP starts with two different primed frame times and claims light should be at the same place. That is not at all what is going on. The OP shows given the unique configuration of the coordinate systems where C' and M are co-located, SR claims light is at 2 different space-time coordinates in the primed frame and that is wrong. Given C' and M are co-located the light pulse is at one space-time coordinate.
SR doesn't "claim" anything, observers do.
It doesn't matter what a Lorentz transform "says" about where another observer moving relative to a stationary frame will see an event; the stationary observer sees the event in their own system of coordinates, the moving observer does too. It doesn't matter what they calculate about their relatively moving counterpart or how many transforms they try, they cannot, and will never, see what the other sees.
That's why your attempt at discrediting Einstein is so pathetic; you think the transform can "do something" or something . . .
You are a complete idiot.