Perhaps the halting problem being solved would imply that a time machine, if possible, would be solved as well? EG.. Imagine a program that halts if a program t

Perhaps the halting problem being solved would imply that a time machine, if possible, would be solved as well? EG.. Imagine a program that halts if a program that iterates over every possible combination of a machines includes a time machine. Then devise a program that halts if the first step of building a time machine is to get a thimble, etc. Do some sort of binary search over the steps of building a time machine by constructing halting problems. What I'm getting at is that if the halting problem was solvable perhaps someone would travel back in time and tell us the solution to the halting problem. Or perhaps they wouldn't, but I wonder if they could.