Dear François-Xavier, Tom, Narendra and Matthew,
Thank you for your comments. In writing this essay one of my goal was the following. I have tried to show that the fact that the time-coordinate in GR has no physical significance and the relational understanding of evolution in GR that follows, both clarify in physics the relations between change and time. Moreover, I believe that Carlo Rovelli's ideas on time are not, as it has been very often claimed, the one of a Parmenidean. To the contrary.
The main dynamical equation of Canonical Quantum Gravity is an equation that does not factor evolution in time. This characteristic has led Julian Barbour to claim that at a fundamental level, reality is of a Parmenidean nature. Julian Barbour argues that the Wheeler-DeWitt equation pictures a timeless and changeless world "and simply gives relative probabilities for all the different possible three-dimensional configurations the universe could have".
Physicists like Karel Kuchaø have vigorously denied such theories and argued in favour of the Heraclitean nature of reality: "I do not want to see things evolving. I see things evolving, and I want to explain why I see them evolving."
Karel Kuchaø's claim is Heraclitean only on the surface since there is nothing Bergsonian or Heraclitean in trying to understand evolution by referring it to a variable t.
The fact that the time-coordinate in GR has no physical significance, the relational understanding of evolution in GR that follows, and the emergence of time in Loop Quantum Gravity from a timeless level are truly Bergsonian since for the French philosopher, time or duration's main attribute is change.
All the very best,
Alexis