A Simple and Possibly New Way to Deduce Special Relativity

Imagine an object some distance in front of you moving toward you also imagine a second object moving in a line perpendicular to the line of motion of the first with the two on a collision course with that point of collision some distance in front of you. If we assume that the motion of light obeys Galilean Relativity then what we will observe of the collision is the first object being deflected with the second object still some distance away from the first. This seems to me to be an uncomfortable situation as I prefer to believe that cause and effect should always be observed. Thus we may consider to assume a principle of "conservation of the observation of causality" and thus insist that the light from the two objects at the moment of collision reach our eyes at the same time which requires that the speed of light be constant.

|

v

o obj 0    ---

    .

    .

y     .

.     .    d t=0

.     .

obj 1 .             .

-> o        + ··· x    ---

     | . . . . . . . . d t=0 . . . . . .  | + == origin

.        .

    .        .

       .        .

           .            theta       . theta is angle formed by line from observer to obj 1 and line from observer to origin

               .                .

               .

      o observer stationary wrt origin

     /|\

     / \ 

assume Galilean Relativity

speed of light in a rest frame == c

v == speed of each object relative to origin

d == distance of each object from origin at time zero

obj 0 vy = -v   

observed y(t) 

y = (-v+c)*t + d

for obj 0 t at time of collision which occurs at origin can be solved for

t = d/(v+c)

obj 1 vx = v

observed x(t)

x = (v+sin(theta)*c)*t + -d

for obj 1 t at time of collision which occurs at origin can be solved for

sin(theta) = op/hyp = x/sqrt(x^2+d^2)

x = (v+x/sqrt(x^2+d^2)*c)*t + -d

0 = v*t + -d

t = d/v

from the two final results we see that obj 0 will be observed to be at the origin by a time prior to having observing obj 1 at the origin but of course they are each there at the same so called "universal" time as per ancient Galilean thought which means that the two objects must each be deflected upon the actual collision which means that our observer will observe obj 0 being deflected while our observer has yet to observe object 1 at the collision point. this contradicts my presumed assumption that causality must be observed therefore we can conclude that Galilean Relativity is not correct and so introduce the notion of the constancy of the speed of light which resolves the matter

- Just a paltry thought