"Quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio.''

[Augustinus Hipponensis]

"...an infinite series of times, in a dizzily growing, ever spreading network of diverging, converging and parallel times. This web of time--the strands of which approach one another, bifurcate, intersect or ignore each other through the centuries--embraces every possibility.''

[Borges]

The "problem of time" in essence stems from the fact that a canonical quantization of general relativity yields the Wheeler-De Witt equation predicting a static state of the universe, contrary to obvious everyday evidence. A solution was proposed by Page and Wootters : thanks to quantum entanglement, a static system may describe an evolving "universe" from the point of view of the internal observers. Energy-entanglement between a "clock" system and the rest of the universe can yield a stationary state for an (hypothetical) external observer that is able to test the entanglement vs.  abstract coordinate time. The same state will be, instead, evolving for internal observers that test the correlations between the clock and the rest. Thus, time would be an emergent property of subsystems of the universe deriving from their entangled nature: an extremely elegant but controversial idea. Here we want to demystify it by showing experimentally that it can be naturally embedded into (small) subsystems of the universe, where Page and Wootters' mechanism (and Gambini et al. subsequent refinements) can be easily studied. We show how a  static, entangled state of two photons can be seen as evolving by an observer that uses one of the two photons as a clock to gauge the time-evolution of the other photon. However, an external observer can show that the global entangled state does not evolve.

 

"Time from quantum entanglement: an experimental illustration"
Ekaterina Moreva, Giorgio Brida, Marco Gramegna, Vittorio Giovannetti, Lorenzo Maccone, Marco Genovese
arXiv:1310.4691 (2013)