This is a serious book about his own work, and Julian Barbour should be commended for reaching such a wide audience. He obviously shares the opinions of Einstein and Feynman that if you understand a new theory thoroughly you should be able to explain it to the layman.
If you want to combine Einstein's theory of gravity with quantum mechanics, it is well known that there are serious obstacles.
First obstacle: GR(General Relativity) is real and QM (quantum mechanics) is complex. (By complex, we mean z = x + iy, where i is the square root of -1.)
JB (Julian Barbour) attacks this problem using his two main weapons: History and Philosophy.
History: Schrodinger's first equation (I didn't know this) was real. It was also the one that he used to solve the problem of the hydrogen atom, which got him the Nobel prize.
But Schrodinger's first equation also was static--i.e. timeless. It was also a first order differential equation.
When Schrodinger later was developing his equation for the amplitude function that evolved with time, he was horrified to find that it turned into a second order differential equation, in which second derivatives appear. To bring it back down to a first order equation again, he used the trick that electrical engineers use: He introduced complex numbers. When they say that the impedance of a coil of wire is complex, it isn't really complex. This is just a mathematical trick based on the fact that AC current is sinusoidal and therefore satisfies a simple second order differential equation. By using complex numbers, they eliminate, in this case, differential equations altogether.
So Schrodinger eliminated second derivatives at the cost of making the amplitude complex.
Philosophy: JB's secoond weapon. He is an expert on Mach's two Principles. The second principle states essentially that inertia is an effect of the distant matter in the universe. JB uses this principle to produce a totally new geometry that he calls "Platonia," in which there is no time.
JB believes that GR and QM can be combined in Platonia into a timeless theory. In his view, we must unshackle QM from the confines of Euclidean geometry and its Lorenz variant.
Believe it or not, JB and others have shown that GR can be formulated in Platonia as is, and that Mach's principles are totally built into the fabric of GR (a fact that would have pleased Einstein). He even quotes results of others showing that GR is in a sense timeless despite earnest attempts to incorporate time into it.
JB has technical papers on his website backing up these claims, but he also goes on to speculate what a cosmological theory would look like.
By the way, he supports something like the "no collapse" view of Everett, but points out a serious flaw in Everett's view. In fact he points out a lot of things and is worth reading if only for that.
I would now like to add my own two cents worth.
Quantum Field theory is normally presented as if it lived in Minkowski space time, but it really doesn't. Consider the following:
1) A Fermion (e.g. an electron) must rotate twice (720 degrees) before it returns to its original state.
2) Feynman's virtual particles exist outside the light cone.
3) Feynman's method of summing over histories has a distinct "out of time" flavor to it. True it does tell how a particle can move from one place at one time to another place at another time, but the process takes place out of time. JB says (private communication) that it may be possible to model the Feynman propagator in Platonia.
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