Sorry, Jim, for the laggard response to your article. You're always good in commenting on the postings of the rest of us on the forum - and always with an interesting and/or helpful observation. So you set a great example. On to my meager comment:

We live in a quantum universe where all aspects of it are discreet in nature (that we've been able to observe so far). Yet Einstein's maths are continuous maths. We can't deny the fundamental quantum aspects of reality so this must imply that Einstein's formulas describe emergent properties, and with all attempts of applying continuous maths to that which is discreet, it will do so imperfectly.

The big questions that arise with Einstein's maths is what happens when/where they produce infinities? Black holes are one case - matter continuously accelerating as the speed of light is approached is another, as presumably mass will infinitely increase.

I for one don't think a discreet universe will honor the infinities of continuous maths by allowing for so-called infinite conditions to arise.

So, Jim, you pose the very intriguing possibility of asking is this infinity condition a threshold barrier between two regimes - the latter becoming essentially unobservable to the first. The so-called infinity condition is then merely an observational artifact limit on the first regime.

Therefore does matter that's continuously accelerated simply go faster than light while the first frame observer sees it frozen in space/time? So far in particle accelerators we see increasing mass as particles are accelerated to near the speed of light. It may be that we have to approach Planck's unit granularity on resolving space/time before the forever frozen condition of perceiving increasing mass would arise.

The other possibility is we fling the particles out of the accelerator and measure transit time from A to B. Only neutrinos are capable of traveling through dense mass with low collision rate such that they can travel far enough distance for our current resolving technology to make useful measurements. Interestingly enough, two cases of FTL for said neutrinos have been experimentally alleged.