Re: Galilean Transformation Equations

On Apr 22, 10:13 pm, YBM <ybm...@xxxxxxxx> wrote:
x' = x - vt
y' = y
z' = z
t' = t
These equations are correct for a special case of the Galilean
transformation, but only for this special case. The special case is
that the coordinates of the origin at time t=0 are (0,0,0), and the
velocity in the unprimed coordinate has only one nonzero component (v
in the x-direction only).
If the relative velocity between the two frames is in the x-
direction, and if the origin of the two frames is cospatial at t=0.
If you want to examine the properties of a Galilean invariant
system, you should use an arbitrary velocity vector (components)
v_x,v_y, v_z) and an arbitrary time t_0 when the two coordinates are
cospatial at an initial starting point (x_0, y_0, _z_0).
Of course, the same would apply to the Lorentz transformation.
Usually, people here only talk about the simplest case of the Lorentz
transformation. The simplest case is that the coordinates of the
origin at time t=0 are (0,0,0), and the velocity in the unprimed
coordinate has only one nonzero component (v in the x-direction only).
However, rotations and translations also complicate the form of the
Lorentz transformation.
If you really want to study Yang-Mills et al theory, you may have
to look at cases more general than the one-dimensional cases you are
looking at. However, one-dimensional cases may be a good start.
.

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