A coupleof things:
You begin by describing time translation invariance, even relating it to space translation invariance. This is all well and good, except that you then you ask:
“Does it make sense to say that the global rate of motion could slow down, or speed up, over the whole universe at once—so that all the particles arrive at the same final configuration, in twice as much time, or half as much time? You couldn’t measure it with any clock, because the ticking of the clock would slow down too.”
This one doesn’t make as much sense to me. This is not just a translation but is actually a re-scaling. If you rescale time separately from space then you will have problems because you will qualitatively change the metric (special relativity under t → 2t no longer uses a minkowski metric). This in turn changes the geometric structure of spacetime. If you rescale both time and space then you have a conformal transformation, but this transformation is not a lorentz transformation. I’m not so sure physics is invariant under such transformations.
The electroweak force has been observed to violate both charge conjugation symmetry and parity symmetry. However, any lorentz invariant physics must be symmetric under CPT (charge conjugation + parity + time reversal). Thus if our universe is lorentz invariant, it is not time-reversal invariant. So you will at least need to keep the direction of time, even if you are able to otherwise eliminate t.
“@Stirling: If you took one world and extrapolated backward, you’d get many pasts. If you take the many worlds and extrapolate backward, all but one of the resulting pasts will cancel out! Quantum mechanics is time-symmetric.”
Um… no. As I explained above, lorentz invariance plus CP violation in electroweak experiments indicate that the universe is not invariant under time-reversal. http://en.wikipedia.org/wiki/CP_violation
Eh… correction. Quantum Mechanics may be time-symmetric, but quantum field theories including weak interactions are not.
The even/odd attribute of a collection of marbles is not an emergent phenomenon. This is because as I gradually (one by one) remove marbles from the collection, the collection has a meaningful even/odd attribute all the way down, no matter how few marbles remain. If an attribute remains meaningful at all scales, then that attribute is not emergent.
If the accuracy of fluid mechanics was nearly 100% for 500+ water molecules and then suddenly dropped to something like 10% at 499 water molecules, then I would not count fluid mechanics as an emergent phenomenon. I guess I would word this as “no jump discontinuities in the accuracy vs scale graph.”