Where is the information stored?

[Mister Agenda]

The reason smashing two electrons together gives you more mass in the form of particles then the two electrons themselves is because of mass energy equivalence. If you started with enough energy and just two electrons you could create enough particles to reconstruct anything.

Yes the outside energy for the smashing is magically derived through the magic of thought experiments. Stop being so nitty and have some fun with it.

Which brings us to the nit I was going to bring up: AFAIK, we can't do electron collisions. They're low mass and mutually repulsive, it would take so much energy tp produce an observable collision that I don't think we have anything yet that could do it.

I only have a layman's understanding, but my impression is that the outside energy is what could cause the electrons to produce anything more massive than photons...but maybe they would just produce more photons. Maybe someone else can speak with more knowledge about that.

Not attempting to contradict you, Heywood, more like expanding on your point, as I understand it.