However, before Einstein died, he was faced with an embarrassing problem. Einstein's neighbor at Princeton, Kurt Goedel, perhaps the greatest mathematical logician of the past 500 years, found a new solution to Einstein's own equations which allowed for time travel!

The "river of time" now had whirlpools in which time could wrap itself into a circle. Goedel's solution was quite ingenious: it postulated a universe filled with a rotating fluid. Anyone walking along the direction of rotation would find themselves back at the starting point, but backwards in time!

In his memoirs, Einstein wrote that he was disturbed that his equations contained solutions that allowed for time travel. But he finally concluded: the universe does not rotate, it ex- pands (i.e. as in the Big Bang theory) and hence Goedel's solution could be thrown out for "physical reasons." (Apparently, if the Big Bang was rotating, then time travel would be possible throughout the universe!)

Then in 1963, Roy Kerr, a New Zealand mathematician, found a solution of Einstein's equations for a rotating black hole, which had bizarre properties. The black hole would not collapse to a point (as previously thought) but into a spinning ring (of neu- trons). The ring would be circulating so rapidly that centrifugal force would keep the ring from collapsing under gravity.

The ring, in turn, acts like the Looking Glass of Alice. Anyone walking through the ring would not die, but could pass through the ring into an alternate universe.

Since then, hundreds of other "wormhole" solutions have been found to Einstein's equations. These wormholes connect not only two regions of space (hence the name) but also two regions of time as well. In principle, they can be used as time machines.

Recently, attempts to add the quantum theory to gravity (and hence create a "theory of everything") have given us some insight into the paradox problem. In the quantum theory, we can have multiple states of any object. For example, an electron can exist simultaneously in different orbits (a fact which is responsible for giving us the laws of chemistry). Similarly, Schrodinger's famous cat can exist simultaneously in two possible states: dead and alive. So by going back in time and altering the past, we merely create a parallel universe. So we are changing someone ELSE's past by saving, say, Abraham Lincoln from being assassinated at the Ford Theater, but our Lincoln is still dead. In this way, the river of time forks into two separate rivers.

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