Aha! You have finally come right out and said it. This is not in accord with SR, but, if it makes you feel any better, that is exactly how I considered it when I first learned this stuff, and everyone with whom I have discussed SR in an introductory setting has had this same ill-conceived consideration. This is the crux of the misconception. This is also the reason why I have emphasized that SR posits an ontology, that ontology being the events themselves, not the reception thereof. I wonder if it will ever be possible to communicate this position of SR, saving the student from this difficulty. I have tried conveying this in several different ways, but they never seem to make the point clear. A stubborn cleaving to the Gallilean conception of space and time seems quite inevitable, and only after a somewhat painful abandonment can an appreciation of the Minkowski character be gained.
Length contraction and time dilation are part of the solution to the principle of relativity (in the restricted sense) playing nicely with the constant isotropy of c. Of course, as you obviously realize, this leads to problems exactly in the instance of simultaneity. The answer that every serious student seems to naturally conjure: length contraction must be anisotropic. Einstein's answer (if you read way into it): simultaneity is (ontologically) relative. Of course, at the same time, Einstein, being somewhat of a physicist, confounds the distinction between a theoretical ontology (which most certainly exists in SR as the events in space-time) and a physical ontology (of which the discipline of physics is absolutely devoid, always admitting mere physical epistimology in its results, and never extending itself to the philosophical bost of ontology).
I will superficially agree with you. I occasioned to read Relativity last night from the beginning through Chapter IX: "The Relativity of Simultaneity." I now quite understand your position. Were I to be trying to understand SR from these writings, I would be so completely confounded by not only his wandering style (I suppose this is to what you were referring with "peripatetic"), but also by the manner in which he attempts to elucidate the conceptual problems, the theoretical conflicts, and the solutions. With particular attention to Chapter VIII, the opening remarks present the reader with a problem:
The text goes on with a concourse between Einstein and some imaginary you for whom he takes the privelage of speaking. Finally, the two of you come to a tentative agreement on the mechanism for determining simultaneity. Unfortunately (and this is one of the many things that I believe he has underemphasized) Einstein still maintains some subtle residual disagreement:
In my opinion, this is quite obsesively picky. Even Einstein admits in the next few lines:
But, it is nevertheless the absolutely necessary removal of this final inevitable residue at the end of the chapter that presents the solution to your problem, I believe:
I do not believe that Einstein endows that last bit (that I have put in bold) with sufficient emphasis. This is a huge part of understanding the structure of relativity, and it presents you with an alternative to your thought experiment, an you would so allow. I suggest that you maintain your embankment with clocks, so nearly adjacent as to form a virtual continuum line of them, and that their tick markings form a virtual continuum to the limit of the practical purposes of this experiment. (Let us assume, further, that this stipulation is always possible to achieve in principle.) Then, have two clocks on the train (separated by as great a distance as is practical).
Make two further arrangements:
1) All clocks on the embankment are synchronized, and the two clocks in the train frame are synchronized. That is, they all simultaneously display the same tick mark in their corresponding frames.
2) Each embankment clock is set to stop at some common tick mark (so that they all stop simultaneously in the embankment frame) and, in so stopping, send a trigger pulse through some mechanism (the details of which are forfit in this thought experiment in the interest of clarity, and the only stipulation is that the transmission path of the triggering signal is negligible for the timescale of the experiment) to the point in the train directly above it that effects a clock at that point in the train (should there be one present) to also stop.
Now, let us imagine that this experiment has run its course, and we are to assess the outcome. The train comes to a halt at the station, we board it, and proceed on our long walk to examine the aft clock. We can do this by obvious means of simply walking to its location on the train and visually inspecting its face. It gives us some reading (frozen by the experiment and so allowing us to take our time, no pun intended) which we write down on our clip boards. Then, we proceed to examine the fore clock, which can be accomplished in the same manner. Upon examination of these two records, we find that the fore clock had stopped previously to the aft clock (in the thought experiment). Thus, without any intimate connection to a particular type of signal, we have (thought) experimentally demonstrated the relativity of simultaneity.
Absolutely. Space-time diagrams are absolutely indespensible, if for nought else than their pedigogical utility. I do not believe that SR can be properly communicated without somewhat of an appeal to geometry. And, in this special case (that is, this "special theory of relativity"), the geometry may delightfully be concretely associated with graphical representation. Perhaps this site may be a tremendous help to you:
http://casa.colorado.edu/~ajsh/sr/sr.shtml