I got interested in this book after attending a seminar given by Barbour at the University of New Brunswick.
It's about Barbour's ideas in regard to the problem of quantum gravitation and motion in general. The basic thesis is that time is not a fundamental physical quantity or entity and that instead it arises from perception of motion. It's a sort of emergent property in the same way that pressure is an emergent property. He combines this with Mach's Principle which states, roughly speaking, that gravity is the effect of every mass in the universe on every other. This idea is almost incorporated in General Relativity.
Barbour is able to derive a formulation of Newton's Laws based on these ideas. He then goes on to develop a version that works for Special Relativity and then for General Relativity. The explanations get progressively harder to follow as the sophistication of the theories of motion increases, so that the Newtonian version was very convincing but the GR equivalent theory was not at all clear. But if you accept what he says, then you can formulate classical motion theory without time as a fundamental property.
Which is all very well, but it's been experimentally demonstrated that gravity is a quantum phenomenon. In tackling the notion of a quantum theory of gravity Barbour faces one of the most intractable problems in theoretical physics and he goes about it in a characteristically unique way. What if you take the same principles to be true; time is an emergent property, gravity is a consequence of Mach's Principle?
This immediately leads to dire problems. Time is a fundamental and separable quantity in the Schrodinger Equation, which explains how electrons behave if they are not going at relativistic velocity. Weirdly, that makes it harder to produce a theory in which it pops up as an emergent property than in the classical theories of motion where time and space are subtly different aspects of the same thing ("space-time"). Barbour's solution is to eliminate time altogether by saying that the solution to the equation must be static i.e. simply never changes. You might wonder how anything could change if this was true (and we see change everywhere) but the subtleties of quantum behaviour can get one through this problem. A fundamental fact of all quantum theories is that they can only ever tell you the probability of an outcome from an experiment. The Heisenberg Uncertainty Principle shows that even if the solution to the equation is static, the outcome of an experiment is not guaranteed to be always the same. Variation, change, can arise from a solution to the equation that itself does not change.
In this book Barbour is saying that the solution to the Schrodinger Equation for the entire universe is static. This is bringing in the idea of Mach's Principle, in a way: everything is affecting everything else in such a way that this one static solution explains what we observe.
Unlike the classical dynamical theories presented here, which make concrete predictions, these quantum notions are really on the level of hypothesis, because Barbour does not know what this solution to the SE looks like.
The book itself is aimed at a non-mathematical, non-physicist audience and tries to explain by analogy what the various standard theories say and what his own theories and hypotheses imply. It's a bit repetitive and I don't think that the more difficult topics are well handled but the main thrust of the ideas comes through well enough.
Towards the end Barbour goes off on an increasingly wild metaphysical whirl to do with consciousness of perception of change (i.e. motion) and woolly notions of how our sense of the past is formed from highly probable regions of the SE solution for the universe and how all these things inter-relate. These disfigure the book, especially coming at the end, leaving the author somewhat open to dismissal as a crackpot - which would be unfair, I think.
This book is already in a second edition that notes advances in Barbour's ideas that make the whole thing more plausible but it's still out of date; quite radically so, going by the seminar I mentioned at the top of the review.
In that talk, Barbour presented the same classical dynamical ideas as in this book but his quantum theoretical work has moved on a long way. He has ditched the Schrodinger Equation in favour of a modern formulation of a general Quantum Field Theory. What this means is that the theory now tackles all known particles and forces whether in a low energy or relativistic regime. This is a cutting edge game; people set up a "LaGrangian" with an "action" and examine the consequences. Basically this means a general equation, the solutions of which are another set of equations which represent all the forces and particles we see. One then compares these equations to what we know from experiment.
Barbour is still looking for his timeless Universe, so his LaGrangian and action need to produce solutions in which time does not feature anywhere. That was 2011. I wonder how he's getting on?