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math3.nb
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math3.nb
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Thus the full equation for position looks like this:\
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(Note that \[Gamma] appears twice in this equation; do the proper \
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Thus: compute how much proper time \[Tau] elapses for reference time t given \
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Cell["\<\
The trickiest question is: given that we know the worldlines of two \
accelerated objects (A and B), how do we transform one worldline (A) onto the \
reference frame of the other (B)? The answer is to use the Lorentz \
transformation at each point along B\[CloseCurlyQuote]s worldline to select \
the correct point along A\[CloseCurlyQuote]s worldline.
This is the procedure: for each point on B\[CloseCurlyQuote]s worldline (as \
seen from intertial frame), draw a line representing everything that B sees \
at that proper time. Find the hyperbolic segment from A\[CloseCurlyQuote]s \
worldline that intersects this line, then compute the intersection. Finally, \
transform the intersected point back into B\[CloseCurlyQuote]s coordinate \
system using the Lorentz transform.
An identical way of saying this is: for each point on B\[CloseCurlyQuote]s \
worldline, transform A\[CloseCurlyQuote]s worldline into B\[CloseCurlyQuote]s \
reference frame using the Lorentz transform for B\[CloseCurlyQuote]s \
instantaneous velocity. Then, the correct location of A for that proper-time \
point is where the world line crosses t=0.\
\>", "Text",