It only accelerates to light speed, therefore it will need infinite time to complete the loops. Thus the risk is not the killing but getting stuck.
If the conjecture holds, naturally there is a small cycle so people can get on and off and use the train as a form of teleporting to the future.
If there are different loops, then still people can take turns.
Even if there are values that diverge, if it can be shown that at least one event of division occurs with a certain average frequency in the infinite divergence, then at any such point all previous guests can exit and the train can be ridden for one such span.
Only if there are no cases of division and endless steps of 3n+1 in the limit, would people be trapped on the train at no subjective time passing, and in essence time travel into the infinitely far future where they are killed.
It only accelerates to light speed, therefore it will need infinite time to complete the loops. Thus the risk is not the killing but getting stuck.
If the conjecture holds, naturally there is a small cycle so people can get on and off and use the train as a form of teleporting to the future.
If there are different loops, then still people can take turns.
Even if there are values that diverge, if it can be shown that at least one event of division occurs with a certain average frequency in the infinite divergence, then at any such point all previous guests can exit and the train can be ridden for one such span.
Only if there are no cases of division and endless steps of 3n+1 in the limit, would people be trapped on the train at no subjective time passing, and in essence time travel into the infinitely far future where they are killed.
That’s impossible because if n is an odd number, then 3n+1 is even. The number can never increase twice in a row.