Well, I'm not sure that I am any more informed than I was before I read it. However, I will try a few comments. Just remember that my comments are strictly my thoughts, and may not have any relevance to the subject.
I can kind of see that if you look at any changing quantity at a single instant in time there will be no change in the quantity, since there is no time for the change to occur. I can see this, it is like looking at one frame of a motion picture. His idea seems to be that since there is no change in that instant there is no way for the quantity to change so that it can move to another instant, so if there is a quantum of time, as there is of energy, then there can be no change and the universe would be static and unchanging. I hope I have that right. Frankly the concepts he is talking about are not really easy to understand, which he admits in the last paragraph of Section 1.
Now to my thoughts on this, keeping in mind that I am not really qualified to do a deep analysis of the paper. An undergraduate degree in physics doesn't get you far enough to really qualify a person to get this deep.
Having made my disclaimer:
It seems to me that one of the problems with his idea is that he speaks of a single instant of time. I'm not sure that any of the hypotheses of quantum time really talk about an instant of time. They mostly assume that the quantum of time is closely related to the Plank Time, which has a definite "duration" if you can call it that. Basically this is just as short an interval as can be determined within the bounds of Quantum Theory (QT).
Another possible problem is that he isn't taking into consideration is the way QT handles state transitions. For example; take a hydrogen atom and consider the electron in the ground state. If a photon having sufficient energy strikes the atom the electron will immediately transition to the first (or higher) excited state. As far as I know there is no mention of time in this transition. If I am correct about this then there is a quantity that changes within an instant of time. So now the universe isn't static, it can move from one instant of time to another.
Of course there is always the view that there is no such thing as time. Scientific American had an article on it last year. I can't tell you what issue, I have already passed it on to my daughter. But here is a link
Forget time to an essay about that.
Bill Gill
