I can agree with Mr Barbour's banishment of time, for different reasons which I will get to, but not with his banishment of motion.
Firstly to time. I totally agree that time can only be understood in terms of change(constrained by entropy) which gives us the perception of temporal "direction", and unique configurations(as stored in the memory of conscious observers) which give us the perception of unique "times". These evolving, relative configurations of objects/observables, are the only physically measurable/recordable processes. "Time" in this sense, is at least as unprovable as the "fields" of QFT & GR.
Following this line of thought, can I refer back to part of Lawrence's earlier statement: "Ultimately physics is an empirical science, so we can only go with what we can measure and record. We record time with clocks. So if time does not exist on some deeper level, there would have to be some experiment or observation which could be conducted to ascertain whether that is the case." If we can only go with what we can measure & record, then surely we can obtain *no* evidence of "time" from clocks at all. Clocks only measure spacial displacement, in particular, cyclic processes, ie Earth's axial rotation, caesium atom oscillations. These cyclic processes themselves can only be "measured" or calibrated when referenced to some other external non cyclic process, again, of spacial displacement.
Lawrence: In relation to the existence of fields, could you please clarify your statement: "The graviton departs from the photon in having two directions of polarization, or helicity = 2". By this are you saying that it is the graviton or the photon that only has 2 polarisations? Also, how does the detection of gravitons prove the fields any more than the detection of other field excitations?
Now, to motion. This is where I depart from Mr Barbour, in that I think there is just too much evidence to support the reality of motion and that motion can exist without a "time" dimension. I think this could be "modelled" in a sort of "evolving block Universe", similar to that proposed by George Ellis (See last year's essay). If we take relativity as being correct & assume the photon to be 2 dimensional & "timeless", then consider the relevant symmetries at work which constrain the Universe's net charge and, in particular, it's net energy to be zero, then the "natural" state of the Universe(reality) is 2 dimensional & timeless. The 3rd spacial dimension & the "appearance" of time only emerge when mass (gravity) enters the scene. Within this state, light then "drives/defines" the spacial boundaries & matter moves in relative configurations with inertial frames from which the motion of light can be detacted. It is then the relative velocities of the massive objects that determine the perceived "time" differentials, so that, maximally, it is possible in principle for an observer in a frame accelerated to c or, equivalently, at the critical gravitational boundary of a black hole, to observe another frame relatively at rest to be "whizzing around" at the "future boundary".
To then derive the classical appearance of time in this "evolving block velocity space" purely in spacial terms, I guess we would need the equivalent of Lorentz transformations without the time coordinate? This reminds me of Richard Feynman's wish to "replace all time quantities with spacial quantities". He often did this to simplify his equations & there is some evidence already that most, if not all solutions & predictions of our physical laws may yet be derivable if reinterpreted using spacial dislacement.
This is of course all very sketchy, but I feel it contains the essence of where we should be heading if we are to progress much further in our understanding of reality. A convincing quantum gravity theory would probably give new insights to all of this. There is no doubt though that our lack of understanding of what we call "time" & how to treat it in QM & GR, hence the "problem of time", is a major barrier to progress.
Can any of the above help??
Cheers