The concept of entanglement is at the heart of quantum physics. It plays a central role in all quantum phenomena involving composite systems. Interestingly, there is an intriguing idea that has attracted considerable attention recently, according to which quantum entanglement may also be essential for understanding the very emergence of time and dynamical evolution. Within this point of view, sometimes referred to as the timeless picture of quantum dynamics, the Universe is regarded as consisting of a clock and a system (or “rest of the Universe”) that are jointly in a stationary quantum state, and time evolution arises as an emergent phenomenon rooted at the entanglement between the clock and the system. Here we provide a pedagogical and self-contained exposition, at the upper undergraduate level, of the role of entanglement in this timeless evolution approach to quantum mechanics. In particular, we give a detailed explanation of how the entanglement between the clock and the system is directly and quantitatively related to the average distinguishability between the states of the system at different times.

We derive the atomic radiative corrections predicted by QED using an alternative approach that offers the advantage of physical clarity and transparency. The element that gives rise to these corrections is the fluctuating zero-point radiation field (ZPF) of average energy per mode, which -in contrast with QED- is taken here as a primordial real entity in permanent interaction with matter and responsible for its quantization. After briefly recalling how quantum mechanics itself emerges as a result of the balance between the ZPF and radiation reaction, the most important higher-order effects of the radiative terms on the atom are studied. The nonrelativistic QED formulas for the lifetimes and the Lamb shift, as well as the corrections to the latter due to external factors that modify the vacuum field, are thus obtained in a self-consistent approach and without the need to resort to second quantization to the present order of approximation.