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Isaac Newton defined how we think of time: as a flowing river moving at constant speed from the past to the future, never deviating, never changing. We are born, we live, we die. A tree is planted, grows, is felled, cut up, and becomes a house. Snow and rain fall in the mountains, gather into brooks and streams, merge into rivers that flow into oceans. Tectonic plates collide, mountains emerge, are assaulted by wind, rain, and rising water, and eventually erode back to the plains from which they arose.

Time is one-way, an arrow, immutable in its inexorable progress...or so it seems.

When Albert Einstein published his Special and General Theories of Relativity in the early 1900s, he said to the world, "Wait a moment. Time is not so constant as Newton said; it meanders, and speeds up and slows down around stars and galaxies."

We came to think of time as just another dimension in a four-dimensional space-time continuum. We began to understand that time's flow is entirely dependent on our own motion through the other three dimensions. We even discovered that we could use this new knowledge to improve our lives through the application of modern physics and its step-child, electronics.

Through all of this new understanding, however, time still flowed in one direction. True, it meandered a bit, and speeded up and slowed, depending on circumstances, but it only went that way, toward the future.

In 1949 Kurt Goedel decided to spend some quality time reviewing Einstein's relativity equations. To put this event into context, you should know that Goedel was arguably the finest mathematician and logician of the last millennium. When he tackled Einstein's General Relativity equations, he discovered a solution that had eluded Einstein. Einstein's solutions describe an expanding universe in which time flows only one way, albeit with turns and speed variations. Goedel's solution describes a rotating universe where time twists back on itself, so that if somehow you were to go all the way around the universe, you would arrive back where you started before you got underway. In Goedel's universe, time has whirlpools, which scientists call "closed time-like curves."

Einstein was not happy with several developments that flowed from his original work with Relativity. He was especially bothered by the implications of the Heisenberg Uncertainty Principle which says, in effect, that on the very small scale, it is impossible to know for a particle both its exact position and the precise time

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