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Originally Posted by darkdev
According to GR, as speed increases, time slows.
I assume that speed is measured as motion across fixed space.
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Hold it right there. That's according to SR, not so much GR. GR says that time also slows as you enter a gravity "field", which is really a curvature in space-time. Which throws an extra monkey wrench into your questions of what we're measuring here on Earth, being also deep into the Earth's, Sun's, and Milky Way's gravity fields.
Quote:
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Originally Posted by darkdev
In case it is not obvious, I am looking for thoughts on speed/time correlation and the actual speed of the earth in space. For instance, if speed and time and gravity/mass have the same relationship as in Ohm's Law (as soo many theories do): V = I * R
Speed = GM / Time
Time = GM / Speed
GM = Speed * Time
GM here means Gravity/Mass, although I'm not sure which is appropriate, or if it should mean gravitional mass... seems somewhat interchangable. Under this equation, speed and time have a inverse relationship for a specific GM, and a change in GM effects both speed and time.
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Contrary to some early impressions I got at a young age, the only M that's affected by the relativistic gamma (that's 1/sqrt(1-v^2/c^2), used in lots of the basic relativistic equations) is the inertial mass. The apparent gravitational pull on or by the fast object seems to remain unchanged. Of course, what that "really" means in relativity is that it's curving space-time around it just as much whether it's going 0 or 0.99993
c.
Anyway, once you figure that gamma, you can figure those speed, time, and mass numbers pretty easily, but they don't share the relationship you suppose above. Observed length (along the same axis as the velocity vector) is length / gamma; observed time is time / gamma; observed mass is mass * gamma. Speed will depend on the direction of motion, since that may change both the gamma and whether it's along the axis of the velocity or not.