The issue though, is getting the "infinite mass" in the first place. There being no such thing as a free lunch, it basically takes infinite energy to get infinite mass; and the reverse is true as well. So, the only amount of "mass" that going to be available at CERN is that mass "created" by applying whatever energy they consume. And using E=mc^2, a whole lot of energy doesn't equal much mass at all.
However much energy these guys are using in say half an hour, to get a packet of 20 billion protons up to speed, is basically increasing the mass (at that location) to at most, a quarter of a microgram per half hour. And once the collision is done, the mass/energy storage is gone too.
Think of it as the reverse of an atom bomb, where mass is changed, quickly, to energy. Play that backwards to get an increase in mass (maybe a few grams), and you'll see that CERN has no chance of getting remotely close to the "point of infinite mass" situation.
I think I understand that.
You have been excellent at clarifying my confusion.
Greatly appreciated.
I think the key part that I didn’t appreciate fully enough was that even though one is at 99.9% of the speed of light . . . getting to
99.99%
and then
to 99.999%
and then to 99.9999% and then to 99.99999% etc.
each step takes a huge energy increase. I wasn’t appreciating that fact sufficiently.