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Motion Is Not Symmetric In This Case...

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Posted by Mark on October 31, 2001 20:18:16 UTC

Because of the symmetry of motion, relativity teaches us that all inertial frames are equally valid in measuring or observing a law of physics in action (experiment). Because of this, you cannot tell whether or not it is you that is actually in motion; all you can say is "motion with respect to...". On Earth it is most convenient to measure motion with respect to ground. However in space, since there is no "special reference frame", and since all frames must measure the invariant speed c to be c regardless of "relative state of motion"... several consequences must inevitably follow to preserve this notion.

One of these consequences of relativity is time dialation.

In my reference frame, I will perceive myself to be at rest while it is everything else that is in motion. To preserve the invariance of speed c, a particle of light emitted from a frame [in motion as compared to my frame with velocity v] must not move with speed c + v, as is implicated in Gallilean relativity theory (and Newtonian mechanics). Because of verification of c invariance in Michelson/Morely experiment, Lorentz was led to conclude that there is some sort of distortion of length in the direction of motion, such that the resulting distortion allows for additional term v in c+v to vanish. There is a function of v which does just that, and it is called the Lorentz Transformation Factor (or something to that effect). Because speed c is intrinsic to this distortion factor, then it follows that there is a corresponding distortion in time (t = d/c). This "time dilation" is symmetric to all inertial frames, because motion is symmetric to all inertial frames [(x',y',z',t') = (x,y,z,t)]. Simply stated, I can say I'm at rest and you're in motion, while you can say that I'm in motion while it is you that is at rest; seemingly paradoxically, neither of us is inaccurate... it's all relative hence the name relativity. Since we both conclude that it is ourself at rest, then we both conclude accurately that it is the other that ages slower.

However how can it be so, that we are each two years older than eachother after a high speed trip?

The resolution lies in the breaking of symmetry. Since one must undergo acceleration, and hence "feel" motion (felt by G-forces)... it is that person that must conclude that he is in motion. When he reverses direction to come back to Earth (deceleration or negative acceleration) there is yet another perceived change in state of motion. Because the two reference frames are no longer symmetric, on concludes that it is the one who felt the acceleration that is younger. Mathematically, the resulting term of acceleration could be visualized geometrically as a "curved spacetime path".

Of course, if you never bring the twins back together again (and there was no initial rocket blast from Earth), then you never have to say who is actually younger and who is actually older. If you reestablish symmetry, then in order to preserve this symmetry one is required to keep the twins spatially separated since neither can ever turn around and come back. To the degree that a communication signal takes appropriate time to cross space and reveal age... paradox is once again resolved because of delay due to finite speed of light. Each can rightfully conclude that it is the other who is younger.

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