Hawking and Hartle propose to calculate the wave-function of the universe using the sum-over-paths method, which begins with the assumption that the universe has all possible histories. Moreover, they would calculate this sum in imaginary time, not ordinary time. This is because imaginary time travels at right angles to ordinary time and "meets" with the three spatial dimensions to create a smooth surface similar to the surface of the earth. This eliminates the singularities (points of infinite curvature) present in ordinary time, allowing the history of the universe to be reliably calculated. Also unlike ordinary time, imaginary time has no beginning or end, so progression through it is determined entirely by physical laws.
The extract above is from the Oracle ThinkQuest foundation, which unfortunately no longer exists in this time dimension, but most probably does somewhere else. Time, as the fractal image demonstrates, is not confined to singular dimensions - that would be impossible, for if it was, there would be no future options available other than one. Clearly, options are open to us all the time, and even the most passionate determinists of fate would be hard pressed not to concede that the existence of multiple dimensions and/or Universes gives Opportunity an open pathway no matter which way you look at it.
Time is perfectly entitled to be flat, here in this Universe, so that the bumps in it can give us an idea of where we are in relation to everything else. Without flatness and bumps, the distance to stars and the outer reaches of the Universe would be impossible to define. Most of the cosmic high-energy particles travel in straight lines, so they travel through flat time without any trouble at all. We see curvature from our perspective because of the way gravity and light converge to illuminate time. The more curvature, the more time has lapsed.
The Universe, on the other hand, is full of round things. Everywhere we look, things are round. Orbits keep the Universe in motion. An entity which contains mostly round things and loads of energy, ranging from ground state to light speed, has no business whatsoever in being flat. It would be out of sorts with itself in no time.
Time is not bothered about ranges of speed and energy, it just is. Time is so damn reliable we can measure it with clocks. We can put our puny parameters on time and it doesn't mind in the slightest. Time does not plague us with paradoxes and uncertainties; it has polarity, as everything must, and it has a tiny secret relationship with infinity. Infinity, as we know, is the scourge of the serious physicist.
I'm rather excited about Hawking-Hartle Wave functions, and will pursue the matter later.
I'm rather excited about Hawking-Hartle Wave functions, and will pursue the matter later.
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