Brian Greene's another book,
The Fabric of the Cosmos
, has a very lucid clarification on how the so-called "arrow of time" emerges out of the Second Law of Thermomechanics.
When discussing about the concept of space-time, one have to specify the scale: On a macroscopic scale, most physicists subscribe to the Einsteinian picture: that although neither space nor time is absolute in itself, (and both are relative to the observer) the whole space-time metric
is absolute. However, on the minuscule scale of the quantum (the so-called Planck scale: the smallest of lengths and the briefest of times), space and time are believed to fluctuate in a haphazard manner, and concepts like "before" or "after" cease to have any meaning. How to reconcile the Plank-scale world (rife with turbulent "quantum foams") and the macroscopic picture (with its absolute space-time metric) is a challenge in theoretical physics.
As for "multiverse", be aware that the term has been used to refer to a number of different things: are we talking about new universes springing, from time to time, out of some ultra-special physical entities like black holes (the "bubble universes" type of theories)? or are we talking about how our present universe somehow "splits" whenever something happens, with different outcomes happening in different universes (Hugh Everett's Many-worlds Interpretation)? Some versions of Many-worlds Interpretation may indeed threaten the concept of time: people speculate that all "possible worlds" are already lying in wait, ready to be "picked up", and we are merely presented with different slices of "instances" that have always existed (e.g. as discussed in Julian Barbour's book
The End of Time
).