Now I am sure this is an essential and reasonable premise. It says that
any process (e.g. light propagation) starting at the origin and
developing along the y'-axis in the moving frame (x'=0) obeys, in the
rest frame, the relation x=vt. Einstein should have revealed this. If he
had, applying the special relativity principle would have yielded a
symmetrical premise: Any process starting at the origin and developing
along the y-axis in the rest frame (x=0) obeys, in the moving frame, the
relation x' = -vt'. Let us see what could be deduced from these premises.
Premise 1: x' = ax + by + cz + dt
Premise 2: x' = 0 <-> x = vt
Premise 3: x = 0 <-> x' = -vt'
where A <-> B means "If and only if A then B". Premises 1-3 yield the
following results:
t' = at ; d = -va
If, as is claimed, time dilation has been proved experimentally, we can
introduce a fourth premise:
Premise 4: t' = (1 / gamma)*t
The final transformations are:
x' = (1 / gamma)(x-vt) ; y' = y ; z' = z ; t' = (1 / gamma)*t
If there is no time dilation, we must return to Galilean transformations.
In any event the principle of constancy of speed of light is incompatible
with premises 1-3.