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Mar8-12, 07:18 PM
If you parameterize your curve with the proper time in seconds, and your proper distances are measured in meters, don't you necessarily get the norm condition in U to be c?
What I mean is, if you use units of distance the same as your units of time, aren't you necessarily setting c=1?
No. The conventions:
position: (t, x/c, y./c, z/c)
line element: d tau^2 = d t^2 - (dx^2 + dy^2 + dz^2)/c^2
and the consequence that U = d(position) / d tau has norm 1
in no way have c=1.