Author: PhysNeophyte (---.bct.bellsouth.net)
Date: 04-11-02 08:45
I think you're getting there Curt.
But not only will your measurements of time differ from L\'s, your measurements of space will differ. Let\'s say that you tell L that R moved x miles in y hours, according to your measurements. If L wants to convert that information into a velocity for R, he must first convert those measurements into the measurements he would have taken if he could see R for himself. According to him, your clock is running slow. (YOU will think that HIS clock is running slow. More about that below.) So he will increase the time measure that you give him. On the other hand, he will think that the distance measure you give him is too big. He will reduce it. Both of these results combine to reduce the velocity of R relative to him. More time plus less distance means lower velocity. Of course, you could just give him R\'s velocity relative to you and he could plug that into an equation, but discussing the measurements of time and distance seperately does seem instructive.
If that answers your question comfortably, no need to read further. On the other hand, there were a few things I thought I\'d try to clear up. Again, as a Neophyte I\'m not claiming expertise or even correct information here or anywhere else. Just my best shot.
First of all, I\'m a bit uncomfortable with your use of the term \"accelerating\" in the previous post. In physics, accelerating means a change of velocity -- slowing down (decreasing velocity magnitude) speeding up (increasing velocity magnitude) or even a change of direction. You seemed to grasp this. However, accelerating frames of reference are not considered \"equal\" to non-accelerating frames of reference in relativity. Let\'s just say L and R are moving at uniform velocities with respect to you at the time of this scenario. Of course, they could have accelerated to their current velocities at some point in the past.
I believe another poster said something about acceleration being necessary for differences in time between different reference frames to occur. Let me just tell you how I see it, using a famous thought experiment. If I get it wrong, remember I\'m the physNeophyte (as in Neophyte!).
In the famous twin paradox, one twin flies off into space at nearly light speed while his brother stays home. Let\'s call the earthbound twin E and the space-traveler S. S returns many years later but is still a young man. E is old. The explanation for this is that time passed more slowly for S than for E. The problem is, if E saw S fly off into space, then didn\'t S (the space-traveler, remember) equally see E (the earthbound twin) fly away in the opposite direction? Like people on a train claiming that they aren\'t really moving, it\'s the rest of the world that is moving. In relativity, where all frames of reference are equal (that is, everybody\'s measurements are equally valid), isn\'t that a valid point? And therefore, why shouldn\'t S return to find that his brother is the young one? From S\'s viewpoint, he\'s not the one who went on a near-light-speed trip, it\'s the rest of the world.
Well this is a real pickle. The way it is resolved is to point out that S is the one who underwent acceleration, not E. A detailed analysis shows that although E appears to be aging slowly to S on the outbound trip, E appears to age rapidly when S turns around and returns to earth, more than making up for the apparent slow aging in the beginning. S, on the other hand, really does come back to earth still young. So the acceleration S undergoes makes his measurements less valid than his brother\'s. Whew.
So, all that comes to just this point: let\'s not talk about acceleration, shall we?
Now, from your comments you seem to know already that time measurements will differ between L and yourself. Did you know that spatial measurements will differ as well? If L is a humanoid, he will look curiously flat to you. Of course, you will look flatened to him as well. This has absolutely nothing to do with acceleration; there is no acceleration. Both of your measurements are valid. Let\'s say that L is moving very fast not just with respect to you, but with respect to the stars. We are all moving with respect to the stars, right. We are on a planet rotating on its axis and revolving around a sun which is itself orbiting the galactic center....there\'s quite a lot of acceleration in that, actually. Let\'s ignore it :)
Let\'s say that basically, compared to L, the earth is in a relatively fixed position with respect to the stars... and pretty much the rest of the universe. Then L will not only see YOU as flat, but the rest of the universe as well. If he is VERY close to light speed, the universe may look like a small place to him indeed, at least in his direction of travel. So, not only will your measurements disagree on time, but on distance as well. Oh well. I\'m repeating myself at this point... see ya Curt.