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in much the same way
     that the two rotated observers pictured here view
    
    
     different
    
    
     two-dimensional slices of a three-dimensional space.
    Minkowski imagined that the spatial distance measured by two observers in relative motion
     is a projection of an underlying
    
    
     four-dimensional spacetime distance
    
    
     onto the three-dimensional space that they can sense; and, similarly, that the temporal
     “distance” between two events is a projection of the four-dimensional spacetime distance
     onto their own timeline. Just as rotating something in three dimensions can mix up width
     and depth, so relative motion in four-dimensional space can mix up different observers'
     notions of “space” and “time.” Finally, just as the length of an object does not change
     when we rotate it in space, the four-dimensional spacetime distance between two events is
     absoluteindependent of how different observers in relative motion assign “spatial” and
     “temporal” distances.
    So the crazy invariance of the speed of light for all observers provided a key clue to
     unravel the true nature of the four-dimensional universe of spacetime in which we actually
     live.
    
    
     Light displays the hidden connection between space and time.
    
    
     Indeed, the speed of light
    
    
     defines
    
    
     the connection.
    It is here that Einstein returned to save the day for Star Trek. Once Minkowski had shown
     that spacetime in special relativity was like a four-dimensional sheet of paper, Einstein
     spent the better part of the next decade flexing his mathematical muscles until he was
     able to bend that sheet, which in turn allows us to bend the rules of the game. As you may
     have guessed, light was again the key.

The Physics of Star Trek

CHAPTER THREE
    Shows His Hand
    
    
     “How little do you mortals understand time. Must you be so linear, Jean-Luc?”
    Q
    
    
     to Picard, in "All Good Things... .
    The planet Vulcan, home to Spock, actually has a venerable history in twentieth-century
     physics. A great puzzle in astrophysics in the early part of this century was the fact
     that the perihelion of Mercurythe point of its closest approach to the Sunwas precess-ing
     around the Sun each Mercurian year by a very small amount in a way that was not consistent
     with Newtonian gravity. It was suggested that a new planet existed inside Mercury's orbit
     which could perturb it in such a way as to fix the problem. (In fact, the same solution to
     an anomaly in the orbit of Uranus had earlier led to the discovery of the planet Neptune.)
     The name given to the hypothetical planet was Vulcan.
    Alas, the mystery planet Vulcan is not there. Instead, Einstein proposed that the flat
     space of Newton and Minkowski had to be given up for the curved spacetime of general
     relativity. In this curved space, Mercury's orbit would deviate slightly from that
     predicted by Newton, explaining the observed discrepancy. While this removed the need for
     the planet Vulcan, it introduced possibilities that are much more exciting. Along with
     curved space come black holes, wormholes, and perhaps even warp speeds and time travel.
    Indeed, long before the Star Trek writers conjured up warp fields, Einstein warped
     spacetime, and, like the Star Trek writers, he was armed with nothing other than his
     imagination. Instead of imagining twenty-second-century starship technology, however,
     Einstein imagined an elevator. He was undoubtedly a great physicist, but he probably never
     would have sold a screenplay.
    Nonetheless, his arguments remain intact when translated aboard the
    
    
     Enterprise.
    
    
     Because light is the thread that weaves together space and time, the trajectories of light
     rays give us a map of spacetime just as surely as warp and weft threads elucidate the
     patterns of a tapestry. Light generally travels in straight lines. But what if a Romulan
     commander aboard a nearby Warbird