Time-energy uncertainty does not create particles

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation, and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.
Comment: Forthcoming in Journal of Physics: Conference Proceedings, Mathematical Foundations of Quantum Mechanics in Memoriam Paul Busch