Uncertainty relations play a crucial role in quantum mechanics [1]. On the one hand, we have shown that the locality of generalized uncertainty relations [2] gives rise to both known and hitherto unknown bounds on quantum correlations, e.g. [3-5]. On the other hand, in a recent work [6] and on-going research we have emphasized the relational aspects of position uncertainties, clock uncertainties and their influence on each other within the framework of quantum reference frames. In this talk I will address both local and relational aspects of uncertainty relations trying to reconcile them via a properly defined covariance matrix structure. As constructive examples of this approach I will discuss novel time-energy uncertainty relations [7], the appearance of non-Hermitian dynamics from the perspective of non-inertial quantum clocks [8] and more general consequences regarding entanglement and the relational flow of time.

 [1] E. Cohen and A. Carmi, Entropy 22 (2020) 302.

[2] A. Carmi, and E. Cohen, Sci. Adv. 5 (2019) eaav8370.

[3] A. Carmi, Y. Herasymenko, E. Cohen, and K. Snizhko, New J. Phys. 21 (2019) 073032.

[4] R. Lenny, A. Te’eni, B.Y. Peled, A. Carmi, and E. Cohen, Quantum Inf. Process. 22 (2023) 292.

[5] R. Lenny, D. Ben Porath, and E. Cohen,  arXiv:2406.16202.

[6] M. Suleymanov, I.L. Paiva, and E. Cohen, Phys. Rev. A 109 (2024) 032205.

[7] I.L. Paiva, A.C. Lobo, and E. Cohen, Quantum 6 (2022) 683.

[8] I.L. Paiva, A. Te’eni, B.Y. Peled, E. Cohen, and Y. Aharonov, Commun. Phys. 5 (2022) 298.