The Physics of Star Trek by Lawrence M. Krauss Read Free Book Online Page A

However, let me draw this circle on a rubber sheet, and distort the central
     region:
    Now, when viewed in our three-dimensional perspective, it is clear that the journey from A
     to B taken through the center of the region will be much longer than that taken by going
     around the circle. Note that if we took a snapshot of this from above, so we would have
     only a two-dimensional perspective, the line from A to B through the center would look
     like a straight line. More relevant perhaps, if a tiny bug (or two-dimensional beings, of
     the type encountered by the
    
    
     Enterprise)
    
    
     were to follow the trajectory from A to B through the center by crawling along the surface
     of the sheet, this trajectory would appear to be straight. The bug would be amazed to find
     that the straight line through the center between A and B was no longer the shortest
     distance between these two points. If the bug were intelligent, it would be forced to the
     conclusion that the two-dimensional space it lived in was curved. Only by viewing the
     embedding of this sheet in the underlying three-dimensional space can we observe the
     curvature directly.
    Now, remember that we live within a four-dimensional spacetime that can be curved, and we
     can no more perceive the curvature of this space directly than the bug crawling on the
     surface of the sheet can detect the curvature of the sheet. I think you know where I am
     heading: If, in curved space, the shortest distance between two points need not be a
     straight line, then it might be possible to traverse what appears
    
    
     along the line of sight
    
    
     to be a huge distance, by finding instead a shorter route through curved spacetime.
    These properties I have described are the stuff that Star Trek dreams are made of. Of
     course, the question is: How many of these dreams may one day come true?
    WORMHOLES: FACT AND FANCY: The Bajoran wormhole in
    
    
     Deep Space Nine
    
    
     is perhaps the most famous wormhole in Star Trek, although there have been plenty of
     others, including the dangerous wormhole that Scotty could create by imbalancing the
     matter-antimatter mix in the
    
    
     Enterprise's
    
    
     warp drive; the unstable Barzan wormhole, through which a Ferengi ship was lost in the
    
    
     Next Generation
    
    
     episode "The
    Price"; and the temporal wormhole that the
    
    
     Voyager
    
    
     encountered in its effort to get back home from the far edge of the galaxy.
    The idea that gives rise to wormholes is exactly the one I just described. If spacetime is
     curved, then perhaps there are different ways of connecting two points so that the
     distance between them is much shorter than that which would be measured by traveling in a
     “straight line” through curved space. Because curved-space phenomena in four dimensions
     are impossible to visualize, we once again resort to a two-dimensional rubber sheet, whose
     curvature we can observe by embedding it in three-dimensional space.
    If the sheet is curved on large scales, one might imagine that it looks something like
     this:
    Clearly, if we were to poke a pencil down at A and stretch the sheet until we touched B,
     and then sewed together the two parts of the sheet, like so:
    we would create a path from A to B that was far shorter than the path leading around the
     sheet from one point to another. Notice also that the sheet appears flat near A and also
     near B. The curvature that brings these two points close enough together to warrant
     joining them by a tunnel is due to the global bending of the sheet over large distances. A
     little bug (even an intelligent one) at A, confined to crawl on the sheet, would have no
     idea that B was as “close” as it was, even if it could do some local experiments around A
     to check for a curvature of the sheet.
    As you have no doubt surmised, the tunnel connecting A and B in this figure is a
     two-dimensional analogue of a