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Originally Posted by ObieX
I know im going off on a slight tangent here, but I'm still not sure how objects cant keep accellerating. I know there's the "the faster you get to the speed of light the more massive you become" arguement, but since speed is relative this makes little sense to me. For example, say i was traveling at 99% the speed of light relative to a small rock floating in space. Now lets say here comes the earth speeding toward me, for simpliscity i'll just say that earth in this case is moving at 2% the speed of light. Now relative to the earth im traveling faster than the speed of light (99% + 2% = 101%). Another example, say im in a rocket, i accellerate to 50% the speed of light relative to a rock floating in space (lets assume that space in this instance is a vaccume except for the rock, my ship, and my fuel), and i turn off my rockets. Now everything in the space ship, fuel included, has "caught up" and we're all moving at the same speed. Now if i were to reignite my engines how would i not gain a new momentum and accelleration ability? Sure i can only go as fast as my thrusters can push out of the back of my ship, but relatively speaking i gained a new starting point for starting accelleration. Another example, we're all traveling around the sun, on earth, at lets say 30000mph (not the real # im just using it as an example) Relative to the eart we arent moving yet, we havent left the launch pad. Now lets say we blast off in the direction the earth is moving, increasing our speed relative to the sun. Lets assume our rocket can accellerate to 156283.4mph. This would put us 1mph over the speed of light relative to the sun, right? Why cant we use methods similar to this to travel faster than light? Say we build a space station that is constantly moving at 50% the speed of light, and use that as a launch pad to gain speed over the speed of light relative to earth. Is everything just limited to some relative speed to the very fabric of space-time? Does space-time have a speed? Can we measure and use this speed of space-time in some way to over-come this drawback? Like finding a way to move whol sections of space-time? (actually now that i think about this i think this is how warp drive in startrek is supposed to work, warping space-time around the ship to make a bubble of spacetime, the enterprise wouldnt actually be moving in "real" space-time they create their own little bubble of space-time that moves in the greater space-time.. i think, anyway)
WeEEeEe! My brain hurts!
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First of all, in SR you measure all velocities relative to you. You just can't say a space station is moving at 50% of the speed of light, it has to be moving that speed relative to something else. Second, and here's the non-intuitive part, you can't just add velocities like you are trying to do. Lets take your first example:
You have three different frames of reference in the example, the one where the rocket is stationary, the one where the rock is stationary and the one where the earth is stationary. All the speeds you gave were from the rock's frame of reference.
So, in the rock's frame of reference, the rocket is moving at .99c, and the earth is moving at .02c. We can then ask what the earth's velocity will be in the rocket's frame of reference. The rock's velocity will, obviously, be .99c, but the earth's velocity will not be 1.1c, because the formula for adding velocities is actually w = (u+v)/(1+(uv/c^2)). This comes out to approximately .9904c. So the rocket is travelling at 99.04% of the speed of light relative to the earth, not the 101% one would naively assume.
EDIT: added more digits to make it more clear that the relative velocity between the rocket and the earth is larger than between the rocket and the rock.