Speed of Light
Out of context: Reply #76
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- bk_shankz0
When it comes to comparing distances, as well as times, measured in frames moving at high speeds with respect to one another, things get more complicated. Lorentz transforms and a new form of Pythagoras theorem involving time needs to be developed, and phenomena like length contraction and frame-dependent simultaneity need to be understood. Although we don't have time to treat these here, one of the complications is that relative velocities can no longer be calculated by simple addition. In fact, only in this way is it possible for light in a vacuum to travel at the speed of light relative to all observers, even if the observers are traveling at high speeds with respect to each other.
There is a simple way to keep track of these effects. Note from above that proper-velocity w can be written in terms of coordinate velocity as w = ?v = v/Sqrt[1-(v/c)2]. If one object is moving rightward with coordinate speed v1 in the frame in which you measure distances, and a second object is moving leftward toward the first with speed v2 in that same frame, then the proper-velocity of the first object in the frame of the second is w12 = ?1?2(v1+v2). In other words, when calculating relative proper velocities, the coordinate velocities add while the gamma values have to be multiplied. This expression then allows one to calculate the relative speeds and energies attainable when throwing objects (like elementary particles) at each other at relativistic speeds from opposite directions.
What is the relative proper-velocity, in lightyears per traveler year, of two 70 GeV electrons in head-on collision trajectories? This may be the "relative-speed record" for objects accelerated by man.
My old stomping grounds.