We can state for certain that time travel will never be invented. The proof is right under our wheels.
If you ask someone what they would do if they could go back in time, you get the usual ideas: stop Hitler, tell the captain of the Titanic to slow down or, perhaps, figure out a way to get Hitler on the Titanic. Generic stuff.
We know time travel will never be invented because no one went back to talk to the people who designed the 35W-94 interchange. A time traveler could have saved them — and us — a lot of problems by showing them the plans for the current renovation.
Would they have believed him? That's another issue.
If I were to go back today and say, "I am from the year 2019!" they'd say, "Uh, you're wearing jeans and shoes my children wear."
"Well," I'd tell them, "this is how we dress. People still listen to the Beatles, too. Well, less and less. Would it help if I wore a silvery jumpsuit with big pointed shoulders and had a shaved head? Hold on, I'll be right back."
I'd return to 2019, get someone to sew me a costume, and then go back to 1966. "I come from the year 2020!"
"You said 2019 just a few minutes ago."