> In sum,
>
> THIS is what observer A sees:
> _________
> B's ruler: ||||||||||| = smaller (-)
> |_________|
> ___________________
> A's ruler: | | | | | | | | | | | = larger (+)
> |___________________|
Oops! There you go again! A's ruler is *0* relative to A! So you get:
___________________
A's ruler: | | | | | | | | | | | = larger (0)
|___________________|
which, unfortunately for you, doesn't sum right.
Think about what chart you'd get with these values:
A B
A + -
B - +
Missing something? Oh, yes, the 0s that are supposed to go down the
diagonal! What ever happened to those?
>
>
> THIS is what observer B sees:
> ___________________
> B's ruler: | | | | | | | | | | | = larger (+)
> |___________________|
No, B sees B's ruler to be 0.
> _________
> A's ruler: ||||||||||| = smaller (-)
> |_________|
>
>
> There are in total, 4 measure entries. Notice
> that for each "+" there is a corresponding "-."
Very funny. You mean for each 0 there is a corresponding -.
> Because a measure of relative size is simply a
> measure of difference, we could've ascertained
> a priori that the change in size would sum to
> 0 by observing that as a rule, the sum of
> all differences between all numerical
> measurements always equals zero:
>
> 0 1 2 3
> ____________
> 0 | 0 1 2 3 |
> | |
> 1 |-1 0 1 2 |
> | |
> 2 |-2 -1 0 1 |
> | |
> 3 |-3 -2 -1 0 |
> --------------
Shame it breaks down under special relativity. Back to the drawing board,
eh?