Time is a measure of change. Whether you use a sand glass, or a water clock, or the the years since the crowning of a king time measures a change of something. Hence I went to the beginning: I first read Aristotle's "Physica," especially his treatise on the nature of time. Next I read also his "De Generatione et Corruptione" to get Aristotle's picture of how change work. Finally I considered Bertrand Russell's "Principles of Mathematics" which includes the basis for the modern concept of time. What follows is a summary of my thoughts on the nature of time done as a critique of a book review.
Dr. Barr's review of Kitty Ferguson's "The Fire in the Equations: Science and Religion, and the Search for God" makes the same mistake of Hawking and Hartle and most other physicists concerning the nature of time. He assumes that when we talk of time that we must refer to the strictly increasing and differentiable time of physics that is related a change in motion, dx/dt. But time is a measure of change, and as such is not necessarily strictly increasing or differentiable. Indeed it may not even be monotonic.
For example a sculptor begins to change a block of marble into a statue. If I use as a "clock" the completeness of that statue, and the sculptor stops half way though his carving to take a vacation, time has "stood still" until he returns. If in addition the sculptor destroys a part of his statue to rework it, time by this "clock" can be said to reverse itself.
The above example is extreme and impracticable. But what of the time of physics? The special relativity theory tells us that if one of two identical twins goes to Mars he will return younger than the one who remains in the inertial frame. But this is true if, and only if, the biological clock of aging is identical with the clock of physics. The fact that in general the two clocks can be put in a one-to-one relation to each other does not make them identical. Furthermore, observations tell us that the aging process is not strictly increasing or differentiable, and in some instances may not even be monotonic.
In a word, the time of physics can not measure all change. The singularity of t = 0 at creation is a mathematical anomaly. It simply means that the clock of physics can not be put into a one-to-one relation with the clock of creation. It is the height of arrogance to assume, as does Hawking, that physics has the only clock that measures time. In fact there are as many clocks as there are of processes to be measured, and some of these have no relationship to the clock of physics whatsoever.
The Complexities of Time (by Lambert Dolphin)
my home page (http://www.mat.univie.ac.at/~neum)
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)