There are, historically speaking, only two concepts of time.
The first is the Space+Time vision of Kant, Newton, etc., with two small modifications. One is that of Einstein Time + Space are fused into the idea of Space-time. In Relativity theory Space-time can be 'cut' by a 'now'-plane in different ways, under different angles, so that simultaneity is no longer absolute, but dependent on the state of motion. But this vision is just a further mathematical elaboration of Space + Time, and does not contain any essential new insight into time itself.
The second minor modification is implicit in Quantum Mechanics. One of the four famous Heisenberg relations dE * dt > h implies, that 'now' is not 'absolute, and 'infinitely small', as commonly is believed, but has an extension that depends on the energy content of any existing objects. The more mass the object has, the more energy it has, (through E = mc2) and therefore the smaller its 'now'-interval is. This implies, that the 'now' of different objects is different; dependent on how much energy they consist of. From it you can explain how come that electrons that spin around these atoms do not radiate electromagnetic radiation. For if the time they need to revolve around the atom is equal to the 'now' interval, they essentially do not have the 'time' to complete that movement, so that, in a sense, you can say that they do not move. For if they do not move, they do not accelerate, and therefore do not radiate.
The second vision on time is the Leibniz vision. According to Leibniz, time is 'not really existing', but it is the conceptual order that our minds puts on existence. It is an ordering imposed on existence in terms of 'sooner and later'. In a philosophical sense this implies, that past, present, and future all 'really exist'.
All of physics is based on the Space + Time vision. Newton used it, Einstein used it, Quantum Mechanics is based on it. Therefore physics has not changed the understanding of time significantly.
Basically, what Julian Barbour does, is nothing less than a total reconstruction of the whole of physics, based on the Leibniz vision of time. He first shows how classical physics can then be understood. Then he moves on to do the same with the special and general theories of relativity of Einstein. After having done that, he even moves on to quantum mechanics.
Does he succeed? I think he does. As such the book is very interesting. Next to these attempts, the book contains some interesting insights that only indirectly relate to time. Barbour shows, for example, that it is possible to integrate the two different visions of Newton and Leibniz about space by using Mach's principle. I find this part of the book the most fascinating I have ever read on the subject.
The only objection about Julian Barbour's approach is, essentially, the same you can rise against the Leibniz view of time as such. Philosophically speaking, if you begin by assuming that there is no real change, and that all change is 'illusion', only 'existing in the mind', then you have to explain how this 'illusion' can arise, without introducing movement ANYWHERE. All such attempts have failed. To give an example: if we go to the cinema, to see 'a picture', then what we see on the screen definitely 'appears to move'. We all know, however, that the 'the picture' consist of a lot of pictures that are all static. The movie projector, so to speak, creates the 'illusion of movement' by showing all of these pictures 'in succession', i.e., in time. It is able to do this, because it 'operates in time'. In this way, change, and therefore time, is introduced 'through the back door' so to speak. Besides, the static pictures themselves are a recording made of movements that have actually taking place. Therefore you can say, that the pictures are the RESULT of movements in the past, and not themselves identical with these movements. I think that the whole Leibniz vision on time is based on an inability to make exactly this distinction between movement and the result(s) of movement.
Physics is about finding answers to our questions. Philosophy is about understanding the questions first. Sound physics should therefore be preceded by sound philosophy. Julian Barbour's book is very strong in its physics department, giving at times very original insights. However, it is very weak in its philosophy. In fact, a philosophical treatment of a clarification of what we mean by the question: 'what is time?' is almost missing in the book. The book goes straight to physics. Julian Barbour therefore fails to see, that the above 'projection example' is a basic flaw in every explanation of time that is based on Leibniz philosophy. In other words, if you believe that Leibniz vision on time makes sense, then Julian Barbour shows how physics can be understood in terms of it. But if you think, as I do, that the Leibniz vision on time itself contains a basic flaw, then Julian Barbour's book fails to address this. For the book is primarily about the physics of time, not the metaphysics of time.
Conclusion: Do not expect, to find an explanation in this book how, philosophically speaking, 'change' can be understood in terms of 'the non-changing'. For it barely touches on this question. The only part of some awareness of this more basic problem of time I found in the book is by the idea of what Julian Barbour calls: 'ephemeris time'. Essentially this idea of 'ephemeris time' starts with the insight, that to understand what time is no more is required than an understanding of change. Ephemeris time follows from this as the ultimate result of change comparisons, through the use of the laws of physics that connect all changes with each other. This 'program' is similar to an explanation whereby space can be seen as the ultimate result of length comparisons.
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