Consider the lower right plot in this picture (or many similar ones).
I interpret the angle of the t' axis with respect to the t axis as: From the point of view of the stationary observer, all progress in time for the moving observer will be accompanied by the latter's spatial progress (to the right in this case), so the 'spatial baseline' for the moving observer is angled with respect to that of the stationary observer, as shown. Right? This seems straightforward.
I find it harder to interpret the angle of x' to x. I get that it 'works out' as in how the lightning flash at the carriage's front occurs in the past for the moving observer (red dotted lines). (If the angle of x' to x were the negative of the actual one, then the flash would occur in the future, so it would not be a good representation.) But is there an intuitive equivalent to the interpretation for the t' axis? "From the point of view of the stationary observer, all progress in space for the moving observer will be accompanied by the latter's temporal ..." Somehow I get confused here. Something about the latter's temporal slowing down...? I don't quite see how that speaks from the diagram.
Thanks!
I interpret the angle of the t' axis with respect to the t axis as: From the point of view of the stationary observer, all progress in time for the moving observer will be accompanied by the latter's spatial progress (to the right in this case), so the 'spatial baseline' for the moving observer is angled with respect to that of the stationary observer, as shown. Right? This seems straightforward.
I find it harder to interpret the angle of x' to x. I get that it 'works out' as in how the lightning flash at the carriage's front occurs in the past for the moving observer (red dotted lines). (If the angle of x' to x were the negative of the actual one, then the flash would occur in the future, so it would not be a good representation.) But is there an intuitive equivalent to the interpretation for the t' axis? "From the point of view of the stationary observer, all progress in space for the moving observer will be accompanied by the latter's temporal ..." Somehow I get confused here. Something about the latter's temporal slowing down...? I don't quite see how that speaks from the diagram.
Thanks!
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