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The paper in question

Rovelli argues against both presentism and eternalism. Later he proposes third option in which the concept of "local present" is central. The problem is I cannot comprehend what this third option says about the universe. The way in which I understood it is that every point in spacetime has its own present. This sounds to me like "relativistic presentism", that is only present exists but the present is different for different points in spacetime. But this seems like very weird position to take and I have never seen anyone defend it so I doubt Rovelli would take it.

What is actually Rovelli's proposal?

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He is proposing a sort of localised presentism, in which at any particular point in space there is a 'now' but there is no suggestion that 'now' at one point can be simplistically extrapolated to equate it with a 'now' elsewhere, so the idea of simultaneity- in the sense in which we encounter it in Special Relativity, namely as a flat slice through spacetime- is abandoned.

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