Is quantum mechanics really timeless?

Abstract

In this paper, I shall put into question a widely-held claim in the discussion on the arrow of time in quantum mechanics: since the Schrödinger equation is evidently time-reversal invariant, there is no room for a fundamental arrow of time in quantum mechanics. I shall first show that there are two ways to define a time-reversal operator in quantum mechanics. Next, I shall argue that the rationale to get rid of one of these time-reversal operator may be challenged.