Dynamical nonlocality in quantum time via modular operators

Quantum clock frames: Uncertainty relations, non-Hermitian dynamics and nonlocality in time

“…We have utilized it above to find new time-energy uncertainty relations pertaining to the interplay between internal and external clocks during the process of energy measurement [17]. We have also employed it to introduce the phenomenon of dynamical nonlocality in quantum time, which is further exemplified in [16]. Finally, we have identified what seems to be a general feature of this approach, namely, the appearance of non-Hermiitan dynamics when non-inertial clocks are used.…”

“…Below we elaborate on these two works as well as on a different result obtained lately within the Page-Wootters framework: dynamical nonlocality in time [16]. Following our earlier studies of dynamical nonlocality in space [21,22,23,24,25], an interesting notion which seems to deserve more exploration [26], we shall study equations of motion which depend on two remote points in time.…”

“…We have shown in [54] that kinematic nonlocality (even in theories beyond quantum mechanics) will not violate relativistic causality if generalized uncertainty relations are obeyed, which could be interesting to compare with the dynamical case. Additional analysis and specific examples are given in [16].…”

“…Time, then, becomes a dynamical quantum variable rather than a mere parameter. The Page-Wootters approach has attracted much interest in recent years leading to major development, generalization and various applications [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].…”

Non-inertial quantum clock frames lead to non-Hermitian dynamics

“…With this scheme, which can be studied in the general context of quantum reference frames [14][15][16][17][18] , they showed that the usual unitary evolution given by the Schrödinger equation can be recovered. Their formalism has attracted much attention, especially during the last few years [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] . In particular, if an arbitrary interaction term between the clock and the remaining parts is considered, a generalized Schrödinger equation is obtained 23 .…”