I understand that Einstein derived his Special Theory from two assumptions: 1. That classical physics holds in all inertial frames 2. That the speed of light will always be measured to be the same. So, what I was trying to do was to derive the equations starting out from these two assumptions. I got a bit messed up though. Consider this: Three particles are lined up: . . . The top one (a photon, if you will) travels at the speed of light. The middle one travels at some velocity v<c. And the bottom one stays still. Now what if the middle and bottom particles are holding a ruler? After some time t, the picture will look like this: -------------. -------._____________ ._____________ (I put the hyphens in so it would come out right; the underscore is the ruler) The distance along its own ruler the bottom particle measures the photon to have traveled will be d=c*t, since it observes the photon's velocity to be c. Now what the bottom particle observes to be the distance the photon has traveled along the middle particle's ruler is c*t - v*t, or (c-v)t. So, since the middle particle has to observe the photon's speed to be c, we can argue that its flow of time is altered: c*t = (c-v)t' t'= tc/(c-v) where t' is from the bottom particle's perspective how much time appears to pass for the middle particle during a unit time interval (in its own frame). Not only is this an incorrect formula for time dilation, we could go the other way and say that the ruler contracts for the moving particle by a factor k, instead of saying time is altered: c*t=k(c-v)t k=c/(c-v) And this is obviously an incorrect formula for Lorentz contraction. The last thing is that instead of assuming either time is slowed or the ruler contracts (from the still reference frame), couldn't one say both happened to some extent? Obviously I'm doing something really wrong here, since there usually is no confusion about time dilation/length contraction, and my formulas are messed up. But I'm trying to get it from first principles instead of following along a text, so here I am.