A great articulation of why people find it hard to adopt a naturalistic worldview

Stabilizer

[You can] reverse T without violating any laws providing you also (1) replace particles with antiparticles and (2) reverse all the spatial coordinates.

Well, yes, but we in fact have a universe with a bunch of particles in particular coordinates! Given the particles there is an arrow of time, that is, you can tell the difference between forward and backwards evolution.

I do not think what most people mean by an explanation of the arrow of time is a way of distinguishing the history of the universe from a T-reversed version, given that under CPT symmetry this is equivalent to a way of distinguishing the history of the universe from a CP-reversed version.

By way of illustration, here's an actual cosmologist: Sean Carroll, in his book "From eternity to here".

The lesson of all this is that the statement "this theory is invariant under time reversal" does not, in common parlance, mean "you can revers

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4entirelyuseless9y

Reversed spatial particles look the same to us as unreversed; and the names "matter" and "anti-matter" are arbitrary. So those differences are not helpful in explaining an arrow of time. They will not make any large scale difference in how the universe evolves.