Ah ha! We’ve tracked it down…
The answer is, of course, neither of them! If they are in inertial reference frames there is no problem. From my understanding, this was not really the issue here. Both of these trains can be going at whatever speed they please, for the purposes of our discussion it IS how they get there that matters. That is the ONLY way to get to the point where the event horizon is created. We see highly relativistic massive particles (cosmic rays) go whizzing by us all the time. We’re not exactly sure how they got to be that way, but there are any number of ways for us to get to a preposterously high relative velocity given enough spacetime. You could sit in a rocketship at 1 g acceleartion and get arbitarily near to the speed of light wrt Earth. It’ll just take a lot of spacetime. Just because you get arbitrarily close to c doesn’t mean you’re going to collapse into a black hole. Again, this goes back to our friend the stress-energy tensor and the relationship between energies and spacetime.
Here’s another way to think of the relationship: Black holes can have any mass they please, right? It just matters that the things are in the right concentration. I can have a whole lot of mass, but if it isn’t in a small amount of space there is no collapse. Likewise I can have a small amount of space, but if there isn’t enough mass there is no collapse. A semi-equivalent way of thinking about your thought experiment would be to ask why all these galaxies aren’t in black holes? After all, there masses are very large and in the intertial frame of a photon there doesn’t seem to be that much to them. The whole point of the matter is you have to take into account the energy as it relates to spacetime. Right now your trains’ relationships to their spacetime geometries aren’t changing because we are sitting on objects that are going at constant velocity.
That’s the whole thing. It DOES matter how the differences are arrived. Gravity deals in NON-inertial frames. That means we’re changing to a different inertial frame (in this case, a different speed). HOW the energy changes makes all the difference.
Maybe you are confused by what we are talking about. In your last post, we are talking about inertial frames, but I was more concerned about your thought experiment and the posts previous to it… this is what you say,
Herein lies the problem. You cannot add an infinite amount of energy and expect simply to not get any gravitation. The whole problem is we are CHANGING reference frames.
Let’s go back further in time. Here’s what bBlahMan** asks:
It’s that “leaving” bit that we are concerned with here. Forget the 99%C, all that does is tell us how much we are accelerating to. Once we arrive at that inertial frame, we’re home free. What we are concerned with here is the acceleration. So Achernar is technically on the ball when he talks about the increase in the gravity for the rocketship (assuming this weirdness about getting energy from some unknown source), though “mass” is a whole different matter.
You’re right as rain with this one. Bob’s your uncle.
Well, then, how are you EVER gonna get this rocketship off the ground? The whole point of the question we were responding to was that there was a reason to change inertial frames. If your initial conditions are two different frames, then you’re absolutely correct, you don’t ever have to worry about this problem. However, then you can only be in the same part of the universe once and only once over the lifetime of the universe (assuming the most basic of topologies and that the universe isn’t closed).
I hope this is nipped in the bud, but if not, we’ll have another go.