A curious feature of Barbour's timeless interpretation is that it entirely collapses the notion of the self as either an abiding entity or a being that undergoes change. Since only the "nows" are real, and there are as many nows as there are instantaneous configurations, each now contains a complete version of yourself at a unique instant -- some nearly identical, others differing wildly, but all equally timeless. This implies there are as many "selves" as there are different nows - many millions of them, an inconceivably large number! It isn't just that you never step into the same river twice, as Heraclitus is supposed to have said, but that both you and the river exist as features within the large-scale (physical) structure of innumerable individual nows. The appearance of change is a consequence of the structure, not of ontologically distinct things within the structures "changing" as a result of something called "time" having passed. So if time really is an illusion, as Barbour and others suspect, it almost certainly follows that the notion of the indissoluble self is also firmly an illusion.
But you don't have to disbelieve in the fundamental reality of time to have serious doubts about the idea of a singular, persisting self. As others have pointed out, the cells in your body are constantly being replaced, as well as the atoms they contain, although the rate at which this occurs varies greatly according to bodily location. There is evidence that certain cells, and presumably some atoms, do in fact persist throughout the lifespan of the body (particularly in the heart and the brain), and the rate of cell renewal among neurons is characteristically slow. Nevertheless, the vast majority of the body is entirely replaced, or "replicated" if you like, on a regular basis, on time scales ranging from just a few months for the skin and gut to about 10 years for the entire skeleton. Ultimately all of this regeneration and renewal is made possible through metabolic processes driven by the sun's energy stored in plants.
It seems natural to think about all these ongoing processes in terms of a certain amount of time passing for regeneration to occur, but this is precisely what the temporal skeptics are arguing against. In their alternative version of events all that really exists are the different configurations, or possible nows, that the molecules composing your body, along with the rest of the universe, can exist in as a complete unit. Some combinations are statistically more prevalent than others, and hence more likely to be experienced. Exactly how an instant comes to be perceived is as yet unknown, but the important thing to grasp is that the instant is not located "in" something called time, existing independently outside the universe of things and passing uniformly for everyone. Rather, the experience of time emerges as being one possible path, somewhat like a geodesic, between a series of "nows" or individual moments which can be thought of as occupying a region of timeless existence called configuration space. At least that is what Barbour's mathematical description suggests. And it is a description that he takes great pains to show is entirely compatible with the findings of both general relativity and quantum mechanics; unfortunately, most of us will probably have to take his word for it on that account.
What does seem is clear to me, at any rate, is that the question of time is deeply enmeshed with the question of subjectivity. Obviously there must be some significance to the fact that countless people have lived their entire lives before any of us were around, and countless people will presumably live similar lives long after we're completely out of the picture. And yet the same can be said from the perspective of those people, whose lives were no less real to them than ours are to us. That's the first clue, I suspect, that time is not one single thing silently chugging away the hours, minutes and centuries tucked somewhere underneath the fabric of some universal "arena" called reality. And even though we are fortunate (or unfortunate as the case may be) to share our existence with so many others who are part of the same material universe, in a very crucial sense "my time" can never be the same as "your time", even if we might decide to spend some of it together! After all, according to the principles of relativity worked out by Einstein in the early 20th century, every inertial frame is equivalent but, thanks to the Lorenz transformation, every observer will come to their own conclusion regarding simultaneity and the order of events. There is no absolute framework of space, and no absolute or universal time as Newton originally proposed. Time, then, must be something that exists in eye of the beholder, if it is not a property of the universe at large.
Many critical questions remain, which I feel have been inadequately addressed: First, precisely where does this configuration space exist, if all we can ever see or come to know are the configurations themselves? If the universe in fact consists of a near infinity of possible nows, it's not at all clear where we would ever find additional room for an utterly divergent realm (which Barbour discouragingly refers to as "Platonia") which somehow contains the "real" universe behind the appearance of change in things, save perhaps in the mind of the physicist. It almost seems a case of ushering one fictitious entity out the door while letting another one slip in through the window unnoticed! Then there is the question of just how the powerful illusion that time does exist and that things do change - something most of us take for granted - is generated from an arena consisting of a collection of static events. Barbour deals with this issue somewhat awkwardly, leaving it mainly to the neuroscientists to determine how configurations productive of such an illusion translate into actual experiences having all the hallmarks of temporality, not to mention why they exist in the first place. This is perhaps the weakest aspect of the proposal. It relies heavily on assumptions about the inner workings of the brain that may ultimately be disproved by subsequent discoveries. If, for instance, the appearance of motion (such as the Phi phenomenon) cannot be generated within discrete neurological states that are themselves static, then the problems of time and motion cannot so easily be explained away as being nothing more than psychological artifacts.
