Back in the day, before modern science, time was generally determined by the sun, an hourglass or two, you know, whatever's handy. Then we got into science, which requires measuring things, and then it's nice to make sure everybody is measuring things with the same measuring stick. So there was a long process culminating in basing units of time onthe radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
So, I suppose, perhaps if we get used to this definition, eventually maybe we'll have people saying time radiates outward instead of saying it moves forward, but I doubt it. The sun still moves in the sky and people still anthropomorphize enough to assume it has a front and a back and it is somehow moving forward, which isn't too terrible because we know an object can have a direction because it's in space and time.
So when we measure something in time units we are really measuring one motion by another motion. In order for there to be a motion, there is some object, which does have a direction. The problem comes when we get a bit metaphysical with time. Notice these time travel stories which assume that future and past are places which we could travel to. Does it make any sense? We know the future isn't yet, and the past is no longer there, but our sense of time seems to encourage us to perceive these things as existent somehow.
So, to my mind time can't really have a direction, or if it did any direction it would have all directions, thus rendering the direction of time meaningless. The objects in motion have the direction, and that direction is interestingly dependent on an observer anyway. It is we who say the sun is traveling forward, backward, in a circle, etc...
This has interesting implications for theology by the way.
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