Actually, Lorentz assumed a preffered reference frame of the eather when originally diriving these equations. Einstein showed that the assumption of a prefferred reference frame is not needed with SR.
The process of this outline is from
http://en.wikipedia.org/wiki/Lorentz_transformation
If one assumes that space is linear with time relative to velocity in an inertial frame (space is flat) then the following observations can be made:
(let [t,x,y] be in observer 1's frame and {t,x,y} be in observer 2's frame)
1) [t,Vt,0] = {t,0,0} - Invariance of the motion of observer 2
2) [t,0,0] = {t,-Vt,0} - Invariance of the motion of observer 1
The transformation will be a matrix A(V). Symmetry implies A(-V)=A
-1(v).
This is enough to find that A must take the form:
g=1/(1+k*V^2)^1/2
[t] = g*{t} + k*V*{x}
[x] = -g*{t} + g*{x}
[y] = {y}
for some k.
k=0 this becomes the Galilean transforms. MANY studies show that k = -1/c^2. This is a fundamental property of our space-time, which becomes the Lorentz equations you started with, without assuming that c is constant.
Your question is to now show that c must be constant if these transforms apply.
