ThomasT
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There's no dispute, afaik, about the existence of an arrow of time. You might think of the nature of time as changes in the configuration of a group of objects. Suppose you take a bunch of snapshots of a group of objects (eg., a basketball game) and number them sequentially.
As you review your snapshots after the game you notice that they're all different.
This individual uniqueness and the fact that each snapshot more closely resembles the ones that immediately precede and follow it in the sequence than any others suggests an irreversibility wrt the evolution of the game, and this apparent irreversibility is called the arrow of time.
A clearer way to see the arrow of time is via the evolution of an expanding wavefront. Waves in any medium always proceed omnidirectionally (more or less) away from a point (or points) of disturbance. Just drop a pebble or whatever into some calm water. Or drop a hula hoop flatly into some calm water and you'll see waves traveling both inward and outward away from the disturbance. This is called the radiative arrow of time, and it's also apparent in the motion of very large scale cosmological structures.
The inferred isotropic expansion of the universe is called the cosmological arrow of time and it carries with it a number of auxilliary inferences -- one of which is that the universe was denser and hotter at an earlier time and as it expands it gets less dense and cooler. No end and no reversal of this trend is in sight and this sort of dispersal and dissipation is called the thermodynamic arrow of time as any system tends to evolve toward equilibrium.
Although there's little doubt that there is an arrow of time, its deep cause is a matter of speculation.
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