Hi Garth, thanks for reading the paper and quoting from it, which, among other things, let's us have some common material to be looking at
Among the several points you raise, we could start here
Secondly Smolin's assumption
Almost every small change in the parameters of the standard models of particle physics and cosmology will either result in a universe that has less black holes than our present universe, or leaves that number unchanged.
does not take into account that a universe itself will be a significant black hole if it recycles quickly enough.
First, it is important to realize that what you call an assumption is NOT AN ASSUMPTION, but something he explicitly says is a PREDICTION of the model. that is it is something which can be used to test the model in the hope of falsifying it.
I hope you understand that a conjecture or theory like this is not something that Smolin believes or disbelieves, or that I or anybody else does, or that anyone is trying to persuade you of. It is offered to fellow scientists for
testing.
If you, Garth, can provide a solid objection to this prediction that actually shows it wrong then you will have had the honor of being the one to shoot down the CNS conjecture! I, for one, would congratulate you because I think that CNS is a very interesting idea and deserves to be carefully tested and shot down if its prediction (stated here) proves false.
Now you have offered an idea for falsifying this prediction, and thereby shooting CNS down. You have said that the prediction does not square with the possibility of a universe RECYCLING VERY FAST.
Smolin estimates that our universe creates roughly 100 black holes per second. So I would guess that you are imagining that a small (say one percent) change in the parameters of our observed universe might result in a universe that would experience a big bang-crunch-bounce-bang-crunch-bounce-bang...cycle at something faster than 100 times a second.
1. What one percent, or even 50 percent, change in any of the parameters do you think would produce this very rapidly cycling universe?
the idea in mathematics of a "small" change is left intentionally vague and depends on people being reasonable. In standard problems of optimization, of finding a local extremum (maximum or minimum) there is an idea of a small change being within an epsilon-neighborhood where the difference over such a change in the argument can be approximated by the derivative. It doesn't span two separate peaks in the payoff function. this should not be worrisome. I am quite comfortable with any reasonable idea of "small"----if you want think of a small change in the parameter as anything up to 95 percent change!
Anyway, to make your objection relevant to the prediction, you have to come up with a change in the parameters of our universe that you can reasonably call a SMALL change that would lead to a very rapidly cycling universe. If you can please say what it is.
2. I don't think you can come up with a proposed change like that, but even if you could it would still not validate your objection!
the reason is that the prediction is about the number of black holes produced by one iteration, one universe, in one 'generation'.
Smolin is predicting that no one can exhibit a small change in the parameters of THIS universe which would result in THIS universe having more black holes in IT.
I take it, because you want to compete by rapid cycling, your picture of a competing universe only has ONE gravitational collapse in it, the terminal one. Let us for the sake of argument call that a black hole. So it has one black hole. You think your universe can win by having that happen very quickly---no time for anything else, just expand a little and recollapse very quickly. But that does not offer any competition to our universe with its parameters.
the number that Smolin's prediction counts, and what you are competing with, is roughly 100 times the age of the universe expressed in seconds, or its estimated reproductive lifetime.
That is on the order of E18------ten to the 18th power---in american english we call it a "quintillion".
If you read Smolin's prediction carefully as you quoted it, you will see that you are offering ONE as competition for ONE QUINTILLION, so you see it does not work.
Too bad, please try again. It would be wonderful if one of us could shoot down this prediction made by CNS, effectively disposing of this interesting theory and clearing the way for the next falsifiable theory explaining the physical constants to be proposed and tested.