Memes

Well, I don't think time travel backwards in this manner is possible, but if it is, it would have to operate under the laws of thermodynamics which means the energy (and maybe even some of the atoms) that was "transported back in time" would represent a paradox.

The energy and/or some of the atoms in you and the time machine were already somewhere in the past when dinosaurs roamed the earth. Which presents a paradox (and this is probably not even the only paradox), so how does the universe conserve energy in that situation?

Somehow the "original" atoms and energy that became you and the machine would need to be reconciled with the duplicates that suddenly turned up.

So maybe there's a mysterious process that obliterates energy? What would it be and how would it work? Would that be equivalent to the false vacuum that could fundamentally destroy the universe as we currently know it?

Or maybe there's nothing to actually stop duplication of energy and atoms and it's entirely feasible to go back in time. You take the time machine back, see some dinos from space, and you managed to otherwise not change a thing. That means in some dozens of million years, you and that machine will be sent back to exactly the same time and location again because nothing has changed. Bam, now you and that time machine are in triplicate. But, with nothing really changing, the same process will occur again and again. Does it reach a point where there's so much duplicated energy / matter that something fundamentally different has to happen? Would all those duplicate yous and time machines coalesce into a giant cosmic object that comes crashing down to the Earth like a giant asteroid, thus killing off most dinosaurs and paving the way for human evolution? Hmmm.