On page 26 (RELATIVITY/1962ed/AEinstein) he attempts to explain the equations of time and space motion on a moving train-long vehicle. But he sets aside both precedents: how the light moves (he sets aside the cosmic aether), and how the train moves (he sets aside acceleration). This set-back leaves him integrating zero differential acceleration, to achieve nonzero longitudinal contraction, consistent only with empirical explanations: physics not mathematics. If we reconsider how the train got that way, got moving, we find instead, ....
Suppose we have an ersatz train ready to roll up to the speed-of-light: the train is long, so an additional engine is placed at the (rear) caboose; and the start signal is sent from the station, a point exactly at the center of the train. (This is not crucial, but it'll help visualize the (time) argument). The engines, and all cars and dimensions are perfectly matched (ideal for calculation), so, both ends start simultaneously - we'll presume the middle cars are pushed as much as pulled, and therefor of no numeric concern (unless they should drag the cosmic aether in aether-wake-shielding). Because of the length of the train, the observers, one on the front engine, one on the rear (caboose) engine, each see the other (end) start a tiny fraction of a second late, and so accelerate late; and so in fact, moving very slightly slower for a long while, consequently. This very slight (slowness) difference accumulates: eventually the rear observes (himself) gain on the front, and the front oppositely observes (himself) pull away from the rear: if they check each other's rail position progress - if they check time along the rail, they also observe their own clocks running late (and equally slower), because the clock image from either front or rear, reflected in a mirror at the opposite end, transits a longer path, in the (same) longer time, roundtrip, and this is true at all round-trip lengths, even the size of the atoms in their clocks: in other words, when observing (himself) in a mirror, information has also equally slowed down (internally on the train compared to the outside, or derived from said observed reflections). The net result of all train internal time slowing is some kind of retention, on the average, and some kind of self-distortion, on the average, all observable. Something must give, and it may merely reshape the atoms themselves. Since this arithmetic already shows the full first-order, Special Relativity is specious relativity, a convenient calculatory approximation not replacing true theory(izing).
[The author appends a note with regard to expectations on theory: In Senior High School the author was invited to interview with a panel of teachers for the 'mathematics' entry in the honors' debate in the school district ... (they) asked, who would the author choose as a role model; he answered (possibly not to their expectation, as it was not unknown that he was brought-up as a Christian Scientist) that Albert Einstein was the best role-model for today's school children: the air of response magnetised with breathless surprise (teachers like to be caught by a fresh reply); they asked him, why; he replied (to the effect) that Albert Einstein had advanced science greatly while retaining consistency with his religion. The interview proceeded to other topics, but the teachers must have been wondering what was the meaning behind his words ... there was no 'mathematics' entry that year for the honors' debate, from that school. The author meant that he was proceeding to college (to UCSD for a degree in mathematics) with the full expectation to be learning the best theory of the mathematical substance of the cosmic aether (whether space-time physics defines this aether to be a system of hyperbolic rotation equations, or something airy). That he did not choose Christ Jesus as role model, depended more on the distinctions between Christians and Christ, and between metaphysics and cataphysics [SIC; to coin the word] - not to leave and escape this world but to revise and reform it: the greater works, the Will of the Father done on Earth as it (the Earth must be discerned as already) in heaven ... this very project 'lambhorn' being the current proof of progress. -RKPetry]
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