Understanding Galilean Transformation: A Troubleshooting Guide

[xiankai]

i have trouble taking the equations given, that is the conversion of one coordinate frame to another.

lets assume at the starting point there are two observers (coordinates (x,y,z,t)).

one observer moves in the x direction and the other observer stays still. the observer that moves has the coordinates of x',y',z',t' at any time.

the stationary observer sees an object in the x-direction, n units ahead. for the moving observer, at a particular instant of time, he sees it as n-vt ahead, where v is the relative velocity between the two frames of reference, and t is the time elapsed from the start till the instant.

as the coordinates of object are (x+n,y,z,t) or (x'+n-vt,y',z',t')

hence..

x+n = x'+n-vt

x = x' - vt

x' = x + vt

which isn't the result to be arrived at. can someone help me? i tried doing a search but it seems to elementary a problem to feature as a major stumbling block, couldn't find any topics on it. ><

 

[Doc Al]

the stationary observer sees an object in the x-direction, n units ahead. for the moving observer, at a particular instant of time, he sees it as n-vt ahead, where v is the relative velocity between the two frames of reference, and t is the time elapsed from the start till the instant.

as the coordinates of object are (x+n,y,z,t) or (x'+n-vt,y',z',t')

You seem to be confusing the meaning of x and x'. If the stationary observer sees the object at x = n, the moving observer sees the object at x' = x - vt = n - vt.

The coordinates of the object are simply (x, y, z, t) and (x', y', z', t'), related by the usual Galilean transformation.