# Rovelli's hierarchy of Time(s)

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## Main Question or Discussion Point

Rovelli's book "Quantum Gravity" (draft online) has an eight-page section---pages 53 to 60---called the meanings of time. As far as we know there is no one idea of time but he lists 9 properties that different ideas of time can have or lack-----some ideas of time have all 9 of these features, other ideas (like time in Newtonian physics) only have a subset

this is my abridged and annotated list, see Rovelli's online draft at his website for more about this

1. Linked to memory and expectation (these characterize time in common language)

2. Existence of a preferred instant, the present, the now.

3. Directionality (absent from Newtonian mechanics, where time can go in either direction)

4. Uniqueness (absent from relativity, where the timecoordinate can be changed)

5. Externality----independence from the dynamic process studied

6. Spatial globality---one time valid everywhere

7. Temporal globality---runs forever, the clock doesnt wear out or the definition reach a limit and break down

8. Metricity---like having numbers on the yardstick

9. One dimensionality---numbers erased: just a bare ordering of events

Common language time has the most features----all 9.

time in Newtonian mechanics is not directional and has no preferred present, so it only has properties 4-9

time in thermodynamics has direction so it has properties 3-9

proper time along a world-line in GR is one dimensional, metrical, and temporally global, but not spatially global or unique, so it has properties 7 -9

the time according to a material clock----an atomic clock or a planet's rotation for example----is one dimensional and metrical but not temporally global (material systems dont run forever) so it has properties 8 and 9, but not the others.

Rovelli identifies about ten different meanings of time or kinds of time and is able to arrange them in a kind of hierarchy depending on their incorporating more or less of these characteristics

there is no one pure, absolute, correct notion of time, it would seem, but the hierarchy is interesting, he has some table and list layout that I like

I also like it that he is able to identify 8 different meanings of Mach's principal and to say which ones are valid (born out by experiment) and which are not----that is on page 52-53