No-paradox time travel is invented. Should it be shared with the world?

Only in whatever way it already did. That is the point of the Novikov principle. Going back in time will not change the timeline, because it already changed the timeline. You cannot change history. You already changed history.

But if you travelled back in time, you already were there.

Under the specified time travel model for this thread, it’s not about whether you can send back a bomb, it’s whether you did send back a bomb. If you did send back a bomb, then it appeared in the past. If you didn’t, you didn’t.

Look at it this way: in the specified time travel model, the future operates like the past, because it might actually be the past to somebody who just jumped back from there. And the way the past operates is that nobody can change how events played out in the past; they already happened and nobody can change that. If you planted a bomb somewhere yesterday, then that bomb was planted. If you didn’t plant a bomb, then no bomb was planted by you.

So, let’s consider Bomber Bob, who if he gets his hands on a time machine will most definitely use it send a bomb back and blow up Hitler. If no bomb blew up Hitler, what does this tell us? That Bob didn’t get his hands on a time machine. (And neither did anybody with similar ideas to him.) Everybody who gets their hands on a time machine won’t blow up Hitler. We know this because there’s documentary evidence that nobody did.

This isn’t a disproof of the Bill-and-Ted model of time travel, but it does strongly argue that time machines won’t be distributed to all and sundry in any universe with that model of time travel. Whoever makes a time machine will only give it to people who screw with the timeline in non-destructive ways.

So what happens if they try to give a machine to Bob anyway? Or they try to send a bomb back themselves? They’ll fail. At some point the plan to blow up Hitler will fail. Not because of divine intervention, but because they failed. It’s (quite literally) a foregone conclusion that they’ll fail, for one reason or another, in the same way that if you think back to a time you failed at something that failure was, after the fact, inevitable.

Or that he did, but that he had a bad plan. It’s quite plausible he did get his time machine but, apparently, his plan failed.

I mean, people AT THE TIME tried to blow up Hitler and failed. Hell, maybe Bob was helping out the July 1944 conspirators.

Which is why for example Baxter/Clarke propose in “Light of Other Days” for a passive viewer a type of anchored-wormhole effect that would alow you to look from your present into the past, so you can behold the events from your end. As the two ends of the wormhole are both “present” it does not involve sending anything into the past.