Hey Nonlinear. I've got a question for you. First let's examine this example:
LtGoose wrote:
Suppose, for a moment, that you are alighting from a spaceship. Suppose, too, that you are a twin travelling on your own, and that you have whizzed away from Earth for ten years at 0.9 times the speed of light before turning round and whizzing back. Einstein's "Special Theory of Relativity" has some implications for you.
One is that you think you have been away from 20 years and are therefore 20 years older than when you left---making you 45 years old if, say, you were 25 when you set off. But your confused twin thinks you have been away for 46 years, making him 71. This, the "twin paradox", is all a consequence of various inadequacies in Sir Issac Newton's belief that space and time were absolute concepts that existed independently of the Universe. Einstein was the first to jot down what now seems so obvious---that the Universse should be considered as a continuum with both spatial and temportal dimensions.
Ok. All very clear. But let's say you didn't just fly around in a big circle, but rather traveled directly to a fixed point in space and back (like another star). How far away was that point?
What I'm getting at here is that we measure distances between stars in light years, right? But that's a measure of how long it takes light to travel to a point and back. Presumably, that measurement is taken by someone sitting at a single stationary point. Does this example mean that the distance is actually different for the guy at the starting point and the guy who was traveling? Something in the distance/time/velocity equation has to give here, or (at least relative to the moving observer) it has to actually be possible to travel faster then light.
Look at it another way. We measure the distance between ourselves and our nearest neighboring star(s) at about 4 LY. That's presumably the time it takes for light to travel from that point to us. Presumably also, if we set up a big mirror and shined a laser at it, it would take 8 years from our stationary perspective to travel to Alpha Centauri and back, right?
But if a round trip would take longer to the stationary observer then to the person making the trip, then how long did the trip take to the light? So assume for a second that I could travel in my spaceship at light speed. To someone on earth, it would take me 8 years to travel there and back. But relativity says that it's going to take somewhat less time from my perspective.
Wouldn't that apply to percentage C speeds as well? In the example given above, I'm traveling at .9C. Presumably that means that if it takes me 10 years to get to a point in space, that point is actually 9 LY away. Thus, it would take light 18 years to make the round trip, right? Are we measuring that .9C velocity purely from the perspective of the guy moving? Clearly, if the object is actually 9LY away, and it actually takes 46 years from the observer's point of view for someone to travel there and back, then the traveler wasn't going anywhere near the speed of light from that observer's perspecitve.
If we measure the objects distance from the stationary observers perspective, and the traveler is moving relative to that same stationary observer, and we measure the travelers speed relative to the stationary observer, then if it takes that traveler 46 years to make the trip at .9C, the object was actually 20.2 LY away, right? If that's the case, and the traveler made the round trip in just 20 years from his perspective, wasn't his rate of speed from his perspective a bit over twice the speed of light?
I'm sure I'm missing something. I just kinda thought this up after reading the thread last night. Haven't given it a ton of thought, but figured I'd see what answer you'd give. It just seems to me that we most certainly do measure distances based on the percieved speed of light to a stationary point, and I'd just assumed we'd measure speeds relative to C in the same way. That second assumption could clearly be wrong (and would "fix" things nicely), I just wanted to make sure.