Be clear.
What is "completely false" and where is the evidence and line of reasoning that shows it to be false? Here are some possibilities for what you mean by "this" (unclear antecedent):
- Did you mean (in the [POST=3198449]OP[/POST] when you wrote "when M and C' are co-located, one lightning strike is located at 2 different positions along the positive x-axis in both coordinate systems, which of course is inconsistent with nature") that somewhere you explained how $$x_Q \neq x_R$$ was "inconsistent with nature" when it has been show that the two different locations also corresponded to two different times, $$ t_Q \neq t_R$$, because you were using two different definitions of "when", $$t=t_P$$ and $$t'=t'_P$$ and since motion is not inconsistent with nature there can be nothing a priori wrong with calculating two different positions? Because I really think you have not shown how this is inconsistent with nature. Indeed, in [post=3199677]post #30[/post], you agreed with me and said "I never claimed there was a law of nature that would not place a light flash at two different places at two different times." And even in the [POST=3198449]OP[/POST] you explicitly calculate $$t_Q$$ and $$t_R$$ to be different.
- Did you mean that $$\color{red} (x_Q - x_O) - c(t_Q - t_O) \neq (x_R - x_O) - c(t_R - t_O)$$? Because if you could show that then I would be completely wrong about "Events Q and R ... happen in different positions and times in every frame ...on a light-like line." Using your own numbers, it appears however that $$(x_Q - x_O) - c(t_Q - t_O) = (x_R - x_O) - c(t_R - t_O)$$.
- Did you mean there was a response to my observation that you have confused $$t = t_P = t_Q$$ with $$t' = t'_P = t'_R$$ in the [POST=3198449]OP[/POST] where you used the phrase "when C' and M are co-located" ? With two different definitions of this phrase, $$t = t_P$$ with $$t' = t'_P$$, it's obvious that you should expect two different events, with different times and different locations, Q and R.
- Did you mean that special relativity says $$t = t_P$$ has the same meaning as $$t' = t'_P$$ and that I was wrong to criticize your ability to work within the assumptions of special relativity? If so, please demonstrate the logical equivalence of the two statements.
- If you have not responded to these, then it must be that you mean that failure to respond does not indicate insincerity. But I argue that it does, because you are responding to my post activity but not the content of the posts. Instead you would rather repeat demands for questions already answered and ignore questions directed at you. That's peculiar behavior for someone who is sincere.
In conclusion, the charge of "This is completely false" is vague and unsupported.
No, it doesn't. The [POST=3198449]OP[/POST] asks "when C' and M are co-located, where is the lightning along the positive x-axis for both frame coordinate systems?"
Working in the domain of SR requires acknowledging that "when" has no absolute meaning. $$t=t_O$$ does not have the same meaning as $$t' = t'_O$$. Likewise $$x = x_O$$ does not have the same meaning as $$x' = x'_O$$, so locations have no absolute meaning. And yet $$(x - x_O) = c (t - t_O)$$ does have the same meaning as $$(x' - x'_O) = c (t' - t'_O)$$. When you asked your question in the [POST=3198449]OP[/POST], you used two definitions : "when C' and M are co-located ... for both frame coordinate systems" thus guaranteeing you would get two answers in space-time, not one. To complain that you get two answers and blame SR and not your question is a misrepresentation. SR is self-consistent -- it is not consistent with the question as you wrote it giving one answer.
It's obvious that [post=3198606]post #2[/post] covers all of this. If you didn't understand post #2, you should have asked more questions.
Someone with a cursory knowledge of the physical world and special relativity knows that a space-time event is of zero duration, "speed of light" is a term of art in special relativity, light in vacuum travels at the "speed of light" (and very close to this speed in air), lightning is an electrical discharge of finite (but short by human standards) duration which causes intense heating of the air through which it travels, resulting in light and sound, and (finally) electrical discharges move slower than light (typically, much slower than light in air). In English usage the atmospheric electrical discharges
and the accompanying flashes of light are both referred to a "lightning" which is a mass noun. So to count (or refer to single events of) electrical discharges one has to refer to "lightning strikes" (or strokes) and to count emissions of light, one has to refer to "lightning flashes." So according to the [POST=3198449]OP[/POST] what happens at event O is "lightning strikes their [common] location" which refers to a single electrical discharge of idealized zero duration. What propagates at the speed of light through events Q and then R is not electricity but a portion of flash of light. Since you aren't referring to the entirety of the light emitted by the lightning strike, but only the portion that propagates parallel to the +X axis, we are talking about a single light-speed, particle-like, propagating phenomenon so "light" or "flash of light" seems preferable to "flash of lightning" but all are preferred to the construction you used was just "lightning".
With "lightning" being a mass noun, there is literally no problem with it being in multiple locations at the same time -- this distracts from the question you were trying to explore.
In detail he wrote:
or with our current notation:
Since he had just finished giving the coordinate transformation, he is talking about a single event in space-time, O, with coordinates $$\left( x=0, \; y=0, \; z=0, \; t = 0, \;x'=0, \; y'=0, \; z'=0, \; t' = 0 \right)$$ -- He didn't assume $$t = 0$$ and $$t' = 0$$ had the same meaning universally. He didn't assume that "when the origin of the co-ordinates is common to the two systems" had a meaning other than at the place and time that those origins met. He limited his discussion to the portion of space time for which both were true because he was trying to talk about an event in the geometry of space-time before 1908 when Minkowski unified relativity and geometry.
This blurring of "when" [at what time] as used in a discussion of space-time and "when" [under what circumstances] as used to introduce assumptions in logic conflates two different senses of the same word and is a fallacious argument.
http://www.oxforddictionaries.com/us/definition/english/when
http://en.wikipedia.org/wiki/Equivocation 一詞多義
This does not allow you to change the question asked in the OP.
You can't use "if" here -- Because the assumption that C' is not at rest relative to M, any such co-location happens only at discrete event P, not as some universal truth suitable for predicate logic. What you want is first-order logic where the universe of discussion is limited to space-time events and coordinates given to space-time events. [post=3198606]Post #2[/post] is simple to read in the context of first-order logic.
A second reason you can't use "if" here is because if "if" is read to mean "under such circumstances that at some event in space-time C' and M happen to be co-located" then the location of the flash of light doesn't have
two answers -- it has the answer "every location on the + X axis" because the answer is not the x or x' value of an event, but the x-coordinate value of a half-line, ℓ, that starts at the event O. But because you don't understand what a logical predicate is, I include this only for completeness, not for your personal edification.
You are missing a comma, because I will not answer a "where" question with yes or no. If you were to ask "Are you finally going to answer this, yes or no?" I would point out that "this" is a question predicated both on assuming special relativity and assuming universality of the truth of simultaneity of non-co-located events, so no simple answer suffices. Where a complex answer suffices, I refer you to [post=3198606]post #2[/post], when I answered over two weeks ago.
Your use of "lightning" and "distance" is problematic, because you said the lightning struck the common (well, "command", but everyone assumes you meant "common") location of M' and M. So to the distance to M is logically zero if you are talking about the lightning strike. If you are talking about the lightning flash, the above comments about "when" and relativity of simultaneity apply. Finally, "distance" between events doesn't have any universal meaning. You could talk about the space-time interval if you wanted something with universal meaning.
You are still talking about three events, P, Q and R. Until you start over and actually label the things you are talking about you will make no progress towards asking questions that make sense. You continue to suffer the delusion that you have a right to demand answers when you pretty much make a hash out of your own discussion and contribute nothing positive to the reputation of this forum.
No you can't because the propagating flash of light never passes through event P. At most you can ask where is the propagating flash of light under the circumstances that apply to the propagating flash of light. Event Q is the answer to where the flash of light is under the circumstance that $$t_Q = t_P$$. Event R is the answer to where the flash of light is under the circumstance that $$t'_R = t'_P$$.
Geometrically, the same way to say this is that Q is the intersection of lines j and ℓ; R is the intersection of lines k and ℓ. Everything else is frame-dependent dross without universal meaning.
Again, you have tried to equivocate the meaning of "when" and substitute "if" as if predicate logic could be substituted for first-order logic. What you need to do is stop pretending you understand the subject matter better than textbooks when you can't even follow the geometry when described in [post=3198606]post #2[/post] or drawn for you in [post=3204088]post #192[/post] and [post=3204151]post #199[/post].
I know I'm only a minion at this game, but I did pick up with the non absolute nature of space and time early in the event, and chinglu's usual refusal to recognise it.