Hence x(0) = ct(0) and x(v) = ct(v)
or t(0) = x(0)/c and t(v) = x(v)/c
In this time Oo sees Ov move a distance vt(0) and Ov is now x(v) units from Z which is seen by Oo as x(v).L(v) by *EQ6
x(0) = vt(0) + x(v)L(v) or
The observers now have formulae for calculating the position from Z from each others perspective.
Also since there is no motion in the y direction y(0) = y(v), substituting *EQ8 into *EQ9
Next consider that the point Z is moving with velocity Ux(0) and Ux(v) in the x direction, and Uy(0) and Uy(v) in the y direction, relative to Oo and Ov respectively.
How are the velocities of Z related? In Newtonian Physics
Ux(v) = Ux(0) v
but now things are different.
the inverse of
NOTE: In the y direction Ux(0) = dx(0)/dt(0) = 0. Also, since v is constant, L(v) is a constant with respect to time.
Hence *EQ10 becomes
and Uy(v) = Uy(0).L(v) *EQ11
This result indicates that objects externally observed as approaching at a combined speed in excess of c will appear to each other to be approaching at less than c. In particular if the approach speed Ux(0) = -c, then Ux(v) also is c, i.e. principle 1.
This document was created on 23 August 1995
last modified on 23 August 1995
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