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

Einstein's equations, in fact, provide simply the strict mathematical relation between
     curvature on the one hand and matter and energy on the other:
    What makes the theory so devilishly difficult to work with is this simple feedback loop:
     The curvature of spacetime is determined by the distribution of matter and energy in the
     universe, but this distribution is in turn governed by the curvature of space. It is like
     the chicken and the egg. Which was there first? Matter acts as the source of curvature,
     which in turn determines how matter evolves, which in turn alters the curvature, and so on.
    Indeed, this may be perhaps the most important single aspect of general relativity as far
     as Star Trek is concerned. The complexity of the theory means that we still have not yet
     fully understood all its consequences; therefore we cannot rule out various exotic
     possibilities. It is these exotic possibilities that are the grist of Star Trek's mill. In
     fact, we shall see that all these possibilities rely on one great unknown that permeates
     everything, from wormholes and black holes to time machines.
    The first implication of the fact that spacetime need not be flat which will be important
     to the adventures of the
    
    
     Enterprise
    
    
     is that time itself becomes an even more dynamic quantity than it was in special
     relativity. Time can flow at different rates for different observers even if they are not
     moving relative to each other. Think of the ticks of a clock as the ticks on a ruler made
     of rubber. If I were to stretch or bend the ruler, the spacing between the ticks would
     differ from point to point. If this spacing represents the ticks of a clock, then clocks
     located in different places can tick at different rates. In general relativity, the only
     way to “bend” the ruler is for a gravitational field to be present, which in turn requires
     the presence of matter.
    To translate this into more pragmatic terms: if I put a heavy iron ball near a clock, it
     should change the rate at which the clock ticks. Or more practical still, if I sleep with
     my alarm clock tucked next to my body's rest mass, I will be awakened a little later than
     I would otherwise, at least as far as the rest of the world is concerned.
    A famous experiment done in the physics laboratories at Harvard University in 1960 first
     demonstrated that time can depend on where you are. Robert Pound and George Rebka showed
     that the frequency of gamma radiation measured at its source, in the basement of the
     building, differed from the frequency of the radiation when it was received 74 feet
     higher, on the building's roof (with the detectors having been carefully calibrated so
     that any observed difference would not be detector-related). The shift was an incredibly
     small amount about 1 part in a million billion. If each cycle of the gamma-ray wave is
     like the tick of an atomic clock, this experiment implies that a clock in the basement
     will appear to be running more slowly than an equivalent atomic clock on the roof. Time
     slows on the lower floor because this is closer to the Earth than the roof is, so the
     gravitational field, and hence the spacetime curvature, is larger there. As small as this
     effect was, it was precisely the value predicted by general relativity, assuming that
     spacetime is curved near the Earth.
    The second implication of curved space is perhaps even more exciting as far as space
     travel is concerned. If space is curved, then a straight line need not be the shortest
     distance between two points. Here's an example. Consider a circle on a piece of paper.
     Normally, the shortest distance between two points A and B located on opposite sides
    of the circle is given by the line connecting them through the center of the circle:
    If, instead, one were to travel around the circle to get from A to B, the journey would be
     about
    
    
     1 1/2
    
    
     times as long.