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shoots a phaser beam at Picard as he sits on the bridge
     of his captain's yacht
    
    
     Calypso,
    
    
     having just engaged the impulse drive (we will assume the inertial dampers are turned off
     for this example)? Picard would accelerate forward, narrowly missing the brunt of the
     phaser blast. When viewed in Picard's frame of reference, things would look like the
     figure at the top of the following page.
    So, for Picard, the trajectory of the phaser ray would be curved. What else would Picard
     notice? Well, recalling the argument in the first chapter, as long as the inertial dampers
     are turned off, he would be thrust back in his seat. In fact, I also noted there that if
     Picard was being accelerated forward at the same rate as gravity causes things to
     accelerate downward at the Earth's surface, he would feel exactly the same force pushing
     him back against his seat that he would feel pushing him down if he were standing on
     Earth. In fact, Einstein argued that Picard (or his equivalent in a rising elevator) would
     never be able to perform any experiment that could tell the difference between the
     reaction force due to his acceleration and the pull of gravity from some nearby heavy
     object outside the ship. Because of this, Einstein boldly went where no physicist had gone
     before, and reasoned that whatever phenomena an accelerating observer experienced would be
     identical to the phenomena an observer in a gravitational field experienced.
    Our example implies the following: Since Picard observes the phaser ray bending when he is
     accelerating away from it, the ray must also bend in a gravitational field. But if light
     rays map out spacetime, then
    
    
     spacetime
    
    
     must bend in a gravitational field. Finally, since matter produces a gravitational field,
     then
    
    
     matter must bend spacetime!
    Now, you may argue that since light has energy, and mass and energy are related by
     Einstein's famous equation, then the fact that light bends in a gravitational field is no
     big surpriseand certainly doesn't seem to imply that we have to believe that spacetime
     itself need be curved. After all, the paths that matter follows bend too (try throwing a
     ball in the air). Galileo could have shown, had he known about such objects, that the
     trajectories of baseballs and Pathfinder missiles bend, but he never would have mentioned
     curved space.
    Well, it turns out that you can calculate how much a light ray should bend if light
     behaved the same way a baseball does, and then you can go ahead and measure this bending,
     as Sir Arthur Stanley Eddington did in 1919 when he led an expedition to observe the
     apparent position of stars on the sky very near the Sun during a solar eclipse.
     Remarkably, you would find, as Eddington did, that light bends exactly
    
    
     twice
    
    
     as much as Galileo might have predicted if it behaved like a baseball in flat space. As
     you may have guessed, this factor of 2 is just what Einstein predicted if spacetime was
     curved in the vicinity of the Sun and light (or the planet Mercury, for that matter) was
     locally traveling in a straight line in this curved space! Suddenly, Einstein's was a
     household name.
    Curved space opens up a whole universe of possibilities, if you will excuse the pun.
     Suddenly we, and the
    
    
     Enterprise,
    
    
     are freed from the shackles of the kind of linear thinking imposed on us in the context of
     special relativity, which Q, for one, seemed to so abhor. One can do many things on a
     curved manifold which are impossible on a flat one. For example, it is possible to keep
     traveling in the same direction and yet return to where you beganpeople who travel around
     the world do it all the time.
    The central premise of Einstein's general relativity is simple to state in words: the
     curvature of spacetime is
    directly determined by the distribution of matter and energy contained within it.