Consider the two observers O and

O′
at the origins of the frames of reference
S
and
S′
respectively, which are in relative motion at constant velocity
v
along the x-axis as illustrated in figure TMA 1_Fig1. Suppose the origins
O
and
O′
as well as the axes of the coordinates of these frames are coincident at an initial time
t=t′=0
. The two observers are equipped with measuring instruments to determine the coordinates of the event at P. Measurements made in the
S
frame are related to those made in the
S′
by the following EXCEPT
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x′=x−vt
y′=y
z′=z+vt
t′=t

The equation x' = x - vt is not correct. The correct equation should be x' = x - vt', where t' is the time in the S' frame.

To determine which equation is NOT related to the measurements made in the S frame to those made in the S′ frame, we need to examine each equation's relationship to the relative motion along the x-axis.

1. x′=x−vt: This is the equation for the translation of the x-coordinate from the S frame to the S′ frame. The velocity v is multiplied by the time variable t to account for the relative motion along the x-axis. This equation is valid and related to the measurement in the S frame.

2. y′=y: This equation states that the y-coordinate in the S frame is equal to the y-coordinate in the S′ frame. It means that there is no relative motion or transformation along the y-axis. This equation is also valid and related to the measurement in the S frame.

3. z′=z+vt: This equation describes the transformation of the z-coordinate from the S frame to the S′ frame. Similar to the first equation, the velocity v is multiplied by the time variable t to account for the relative motion along the x-axis. This equation is valid and related to the measurement in the S frame.

4. t′=t: This equation states that the time in the S frame is equal to the time in the S′ frame. It means that there is no time transformation due to the relative motion along the x-axis. This equation is also valid and related to the measurement in the S frame.

Therefore, the equation that is NOT related to the measurements made in the S frame to those made in the S′ frame is: y′=y.