In a galilean transformation, what do the variables stand for in x'=x-vt?

Question

This seems to be an increasingly large gap in my education. Thorough explanations appreciated instead of cryptic one-line explanations.

Answer 1

If a reference frameO'XÝ'is moving with a uniform velocity v with respect to a reference fram OXY ,the velocity being parellel to the and along the positiveX-axis and the origin O'of primed reference coincides with the origin O of the unprimed reference frame at t=0.At time t,let the x-coordinateof an event be x'&x in the primed and unprimed reference frame, the the relation between x'& x is given bythe Galilean transformation, :
x'=x-vt.
I am sorry for not being more precise as I have written just from what I remember in the head and I have not revised or gone through this stuff for many years(10 yearssince I retired as a university professor).

Answer 2

First, you need to have a clear idea of what a Galilean transformation is.

Suppose you have two scientists, Alice and Betty. Each scientist wishes to describe the events around her, and uses a coordinate system to describe locations of those events. Let's call Alice's coordinates x, y, z, and t (standing for position east, position north, position up, and time). Now Betty has her own coordinate system, but we can't call her coordinates x,y,z, and t anymore, because we've already used those symbols. So we'll call her coordniates x', y', z', and t'.

Betty's coordinates need not match Alice's, because she may choose a different origin, and she might be moving with speed v relative to Alice. So if Alice measures that an event happens at location (x,y,z) and time t, Betty's measurement (x',y',z') and t' may be different, even though they measured the same event.

x' = x-vt describes how to get Betty's x-coordinate from Alice's in the special case where the x and x' axes are parallel, the origins of the two systems coincide at time t=0, and Betty moves to the right with speed v in Alice's reckoning.

Answer 3

x'=x-vt is an equation from Galilean Transformation in one-dimension, the x direction. In this case a variable in the second reference frame is denoted by a prime ('), whereas the variables in the first reference frame lacks a prime. So x is the vector displacement in the x direction of the first reference frame, and x' is the vector displacement in the x direction in the second reference frame. In one dimension t'=t, y'=y, and z'=z. Likewise the velocity in the y direction is equal in both reference frames, And the velocity in the z direction is equal in both reference frames. Since Galilean Transformations are used within the purview of Newtonian Physics, the velocity of the second reference frame is considered to be in moving with a constant velocity, v, with respect to the first.