The Arrow of Time

The presence of an arrow pointing from past to future is apparently determined by numbers (Imaginary numbers?).

Imagine a pool table, partitioned in two equal halves by a wooden board, on which one lonely cue ball moves without friction, elastically bouncing off the walls and the separation board, confined to its half of the table.

This scene is filmed from on top.

Now a hand appears and removes the separation board. The result is that the ball now has the entire surface to move about in its Brownian motion.

If this film is played back in reverse, there will be no way to tell if the hand has removed the separation or inserted it originally!
But if there are many cue balls moving, one can tell which sense of film projection corresponds to the order in which it was recorded

• When you see the balls suddenly conspiring to collect in one half of the table just prior to a hand inserting the separation, you are watching a very unlikely scenario. The more balls, the more unlikely it is that they would all collect on one side.
• When you see the separation removed, followed by a spreading out of the balls over the whole surface, then the correct direction of time becomes visible.

There must be some connection between the influence of numbers on the flow of time and the influence of numbers on the spacetime continuum.

In a "universe" consisting only of the earth in an otherwise empty spacetime continuum

• it would be meaningless to speak of "motion" for the earth. Its absolute speed could be v=c or null and
• time would have an entirely different meaning. No matter means no gravity. No gravity means no time.

With nearly no matter in the Universe, geometry would be nearly Euclidean. Would its size then be close to infinite?

If all objects recede from each other due to the expansion of spacetime, would that imply that because of the curvature of spacetime they will eventually converge?

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