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Galilean Transformation

The Galilean transformation is used to transform between the coordinate of two reference frames which differ only by constant relative motion within the construct of Newtonian physics. This is a passive transformation point of view. In special relativity the Galilean transformations are replaced by Lorentz transformations.

The notation that can be found below describes the relationship under the Galilean transformation between the coordinates (x, y, z, t) and (x’, y’, x’, t’) of a single arbitrary event as measured in two coordinate systems S and S’, in uniform relative motion in their common x and x’ directions, with their spatial origins coinciding at t=t’=0.

x’ = x – vt
y’ = y
z’ = z
t’ = t

The transformation can also be considered a shear mapping and is described with matrix acting on a vector. When the motion is parallel to the x-axis, the transformation acts on only two components:

(x',t')= (x,t)(1  0)

                 (-v 1)

With this matrix representation are not strictly necessary for Galilean transformation, they provide the means for direct comparison to transformation methods in special relativity.

Galilean transformation and electromagnetic waves

(See attached for full problem description) If electromagnetic wave equation for vacuum is where W is either magnetic B or electric E field vector, show that by using Galilean transformation wave equation will be changed to which has completely different form than given wave equation. Hence, Galilean transformation violate

Relativity

In the old west, a marshal riding on a train traveling 50m/s sees a duel between two men standing on the earth 50m apart parallel to the train. The marshal's instruments indicate that in his reference frame the two men fired simultaneously. (a) Which of the two, the first one the train passes (guy A) or the second (guy B), shoul