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(SR) Lorentz t', x' = Intervals
Section - 12. Summary

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Top Document: (SR) Lorentz t', x' = Intervals
Previous Document: 11. Intervals versus the Twins Paradox.
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A.  t'=t/g and x'=x/g can be almost 'just coordinates'
    in the sense that the values obtained may not be
    of much use except in the most primal and useless
    way: how long and how far since/from the time/
    place they were zero. Even here, however, the zero
    points within each of the two scale pairs (t',t) 
    and (x'.x) must have been lined up.  If the zero
    points have been intelligently selected (such as
    at the starting point and time of a trip) they 
    can be rationally used 'as is' in any valid sci-
    entific equation.

B.  Even the interval scale t'=t.z' - xv/gcc + t/g and 
    x'=x.z' - vt/g + x/g are not 'just coordinates'. They 
    can be used to good effect by establishing the relevant 
    starting times/points and using (t'-t.z'+xv/gcc) and 
    (x'-x.z'+vt/g), as the situation may require.

C.  When you see vx/gcc or vt/g in use in any guise with non-zero
    values, you know the resultant t' or x' is a degraded, interval
    scale value.

E-X: Anytime you do not see what amounts to t.z' and xv/gcc in
     the time case, or x.z' and vt/g in the distance case, you
     know that the t' and/or x' in use are intervals. Period.

Y:   Either set your clock to zero at the start of the relevant
     time interval, or use (t-t0), with both being readings on
     the same clock. Either move your x-axis origin to the starting
     end or point, or use (x-x0), with both being readings on
     the same axis.

Z:   In _(SR) Lorentz t', x' = Degraded (Interval) Scales_ we see 
     that t' and x' satisfy the mathematical tests for/of interval
     scales when -vt and -vx/cc are not zero; thus, they must
     be intervals. When -vt and -vx/cc are zero, t' and x'
     satisfy the much better mathematical definition of 
     ratio scales, and are thus not just mere intervals,
     but (rescaled) good ones.

Eleaticus

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! Eleaticus        Oren C. Webster         ThnkTank@concentric.net  ?
! "Anything and everything that requires or encourages systematic   ?
!  examination of premises, logic, and conclusions"                 ?
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Top Document: (SR) Lorentz t', x' = Intervals
Previous Document: 11. Intervals versus the Twins Paradox.

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Last Update March 27 2014 @ 02:12 PM