Let an object move with velocity relative to S' frame and let its velocity as determined is S frame be
, then what is the relation between and ?
Velocity of an object measurable in
Velocity of that object measured in S' - frame
Velocity of S' frame relative to S- frame.
The validity of equations (1) and (2) for motions of objects
familiar to us in every day life is a fact without reservation.
At very high speeds it is not necessary that Equations (1) and (2)
be valid. The validity of Equations (1) implies that of equation
(2) and conversely. However, if measurements of speed of an object
is S and S' frames do not confirm to Equation (2) then it necessarily
implies that Equations (1) are also invalid.