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I assume you agree that when a ruler has been rotated,
"the" length of the ruler (i.e. the proper length) is
not changed. If this is a false assumption, please
explain.
By the same token, when a ruler has been boosted, "the"
length of the ruler (i.e. the proper length) is not changed.
Right?
And when a clock has been boosted, "the" time between
ticks (i.e. the proper time) is not changed. Right?
It may be that the /projection/ of the length onto this-
or-that reference frame is changed. It may be that the
/projection/ of the time onto this-or-that reference
frame is changed. But the shadow of a thing does not
behave the same as the thing itself.