e.g. the machine is a big box. You can "start" the machine once and "end" it once. When you "start" the machine it instantaneously teleports everything inside it from when you "end" the machine.
If you "start" the machine and break it before "end"ing it, nothing gets sent through, or there's a giant explosion, or the universe collapses, etc.
Alternatively, you can "receive" and "send" any number of times on the machine. But every time you "receive" you get a unique ID, and you can only "send" to that ID once.
Doesn't any scenario of time travel imply an unlimited amount of entities?
If you go back in time to observe (but not interfere with) your younger self, your younger self will get old and go back to that exact time too. So there will be an infinite number of your old selves observing your younger self.
Not to mention that travelling back also means adding matter to the universe.
...and how would you actually do that if we assume that your travel has added matter to the universe, rather than completed an iteration of a time loop that was happening there already?
Yeah, "interfering with" is open to interpretation. One might argue that you don't have to say "hi" to yourself to interfere with, and it is sufficient to be within the same light cone.
