Dear Andrew Walcott Beckwith,
Thank you for your very kind remarks. I'm very impressed with the work you do and generally attempt to read your papers. [I still pity your reviewers.]
The topic of cyclic cosmology is beyond a comment, so I will attempt to respond to your questions about Barbour's nature of time (an earlier FQXi essay).
He begins by noting that his mechanics books define neither time nor clocks. He further complains that the fundamental notions of duration and simultaneity are almost universally ignored, the latter due to Einstein's 'relativity of simultaneity'. In fact, Barbour states that only Newton discussed duration. Barbour hopes to persuade one that time as an independent concept has no place in physics.
In agreement with Einstein, ("There exists no space absent of field.") I view 'space' as contingent on 'field', where field is substantial in the sense it has energy, hence matter. Similarly, I view time as contingent on energy, essentially energy in the field (see Hertz's 'energy' quote, on my page 5). Barbour quotes Mach to the effect that 'time is an abstraction'. I would not go that far. I would agree with Newton that:
"Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration."
The nature of time, in my opinion, is universal simultaneity, and its property of 'duration' is almost certainly tied to local energy, and very likely to the constant of action.
In this sense I somewhat agree with Barbour that
"...intervals of time do not pre-exist, but are created by what the universe does."
The "intervals of time" are supposedly what clocks measure, as described in my essay as "counting frequency" or "measuring energy".
Ignoring his 'rotation of the earth', etc., I disagree with Barbour that "Newton was wrong... Mach was right, we do abstract time from motion." This is, if not duplicitous, at least confused; motion is no more fundamental than time, in my mind not as fundamental. Motion is essentially local, while time is universal simultaneity. Universal outranks local every time. Perhaps Barbour believes that Einstein's attachment of time dimensions to local moving objects make time also 'local' in nature. I do not.
The key to Barbour, as I see it, is his statement on page 4:
"Modern textbooks, leave us to fathom the meaning of t, say that all these quantities are functions of the time: phi(t), a(t), r(t)."
If this is true, one would expect that a clever approach could factor out t and this is what he does, ending on page 9 with an expression for delta-t in terms of energy.
I'm not impressed that Barbour has accomplished anything other than to support my arguments in my essay. I do not support all of his arguments.
My very best regards,
Edwin Eugene Klingman