5 ms·

equations can be time-symmetric, or invariant re time reversal. What you're describing is equations being invariant re time reversal.

• bubblyworld 1y ago
  You can call this invariance under time reflection if you like, yeah. Note that the solutions x(t) are not generally time symmetric. We aren't saying that x(t)=x(-t), we are saying that x(t) is a solution to the differential equation if and only if x(-t) is, which is a weaker statement.
  • bonvoyage36 1y ago
    I know what you meant; I've just tried to point out an error in your sentence which pops up sometimes, which may have mislead others. It's all about the time reversal invariance of evolution equations, not solutions.
    • bubblyworld 1y ago
      Oh I see what you mean, it's kinda easy to read my comment as meaning time symmetry. But I do think the phrasing in terms of solutions is correct, provided you interpret it appropriately. As in "is still a solution to the diff eq after transformation" and not "is left unchanged by the transformation".
      • bonvoyage36 1y ago
        It's not a good phrasing to express the point, because "solution is invariant under operation O" has an established meaning, that the solution does no change after the operation. What you mean can be properly phrased as "equations are time-reversal invariant".
        • bubblyworld 1y ago
          You've convinced me =)