A typical transformation between our frame and the frame of such an observer would be the map \(S\) defined by \((t',x') = (x,t)\), simply swapping the time and space coordinates. Our sun’s world-line might, for example, be orthogonal to hers, in which case the sun would not appear to her as an object in motion but rather as a line stretching across space, which would wink into existence and then wink back out. (Never mind that the stars, which pass in front of and behind the spaceship, should actually be a million times larger than it.) Actually such an observer would consider her own world-line, which we call spacelike, to be timelike, while the world-line of a star such as our sun, which we consider timelike, would be spacelike in her opinion. This is because if two observers differ in velocity by \(c\), then the Lorentz transformation between them is not a one-to-one map, which is physically unacceptable.īut what about a superluminal observer, one who moves faster than \(c\)? With charming naivete, the special-effects technicians for Star Trek attempted to show the frame of reference of such an observer in scenes where a field of stars rushed past the Enterprise. We recall from Section 3.4 that special relativity doesn’t permit the existence of observers who move at \(c\). Explain the phenomenon of faster-than-light motion in relativity.
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