Abstract
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.
Highlights
Modern physics recognizes quantum entanglement as one of the most intriguing and significant physical phenomena
A pedagogical discussion of entanglement within the timeless approach to quantum mechanics was presented. This is a scenario in which evolution and time are not primitive ingredients of the description of the physical world but, rather, emergent phenomena
The Universe is viewed as consisting of a clock C and a system R that are jointly in a stationary state
Summary
Modern physics recognizes quantum entanglement as one of the most intriguing and significant physical phenomena. The ‘evolution’ of R reflects the fact that for different states of C there correspond different states of R, while the whole U = R + C remains in a single static state In this sense, in the timeless approach both the dynamics and time emerge from non-local correlations, and contrary to Newtonian mechanics, motion is not assumed as a primitive, but secondary, concept [17]. For an observer in R, the notion of time (or temporal flux) emerges from this ‘frozen’ state as a result of the quantum entanglement between C and R, and the parameter t is identified with the values of an appropriate observable of the clock (the position of its hands).
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