On the arrow of time; See Y. Strauss, J. Silman, S. Machnes, and L.P. Horwitz, Comptes Rendus Mathematique 349, 1117 (2011)

On the E,t uncertainty relations:
Yes, the best derivation I know is that of Schwinger, who assumes an H and H_0. H generates transitions in the levels of H_0, and he estimates the time for moving Delta E in H_0 to be Delta E over hbar. Certainly not rigorous. In relativistic quantum theory (e.g. my book with Springer 2015) it is established…[Read more]