The proper time is defined as tex2html_wrap121 . In newton's equation, you replace t with tex2html_wrap122 : tex2html_wrap123 .

setup: tex2html_wrap124 then tex2html_wrap125 Then tex2html_wrap126 . Then tex2html_wrap127 . Can reparameterize s as tex2html_wrap122 . Then tex2html_wrap129 . tex2html_wrap130 is a contravariant 4-vector which is the analog of velocity. If particle velocity is tex2html_wrap131 , then tex2html_wrap132 . From this, tex2html_wrap133 .


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