Picture yourself accelerating to 3/4 the speed of light, taking your girlfriend with you, and leaving your best mate behind, back on earth (with no speed!). At this speed you stop accelerating and continue to travel through space at 0.75c. From this position, you see light travelling at the speed of light and would not know any better than to ASSUME you are stationary, with speed = 0 (even though you are moving away from your stationary friend back on earth). You then send your girlfriend on her way, accelerating her in the same direction you began accelerating from your mate. Relative to you, she accelerates to 0.75c and keeps travelling. But then your friend stops and thinks for a bit. He is not the brightest boy but does a quick calculation and finds that: 0.75c + 0.75c = 1.25c "Wow" he says, that dudes girlfriend is travelling faster than the speed of light. "Is she?" But faster than light travel requires infinite energy! It Isn't possible! Really I can see nothing wrong with this, and if this is a problem, then it raises another question: Couldn't we calculate how fast WE, on earth, and the solar system are travelling through space? As time dilation is not linear (from lorentz factor), we could put a clock on a plane (going really, really fast), and one on earth and calculate the difference in time and from that work out how fast we are actually going! (obviously direction is going to be a big factor here, the earths spin on its axis, earths rotation around the sun, and suns rotation around milky way galaxy). But wouldn't this be possible???