The challenging concept of time in quantum mechanics

Jafari Matehkolaee, Mehdi

"slamic A#ad uni$ersity of %hahrood, %harood, "ran

Time plays a peculiar role in quantum mechanics. What makes this concept so interesting is the question “what can quantum mechanics tell us the about the nature and role of time?” and conversely, “what can time tell us about the structure of quantum theory?” In standard quantum mechanics probabilities are assigned to measure the outcomes of a given observable at a given moment of time. Time enters the Schrodinger equation as an external parameter, and not a dynamical variable. It is not a standard quantum mechanical observable. But in concepts such as the time of arrival , the time-energy uncertainty relation , tunneling time , and time in quantum gravity , time can no longer be viewed as a mere parameter. This survey explores various attempts made in order to treat time as a dynamical variable (observable) and hence measure it.