Gamera
So if I go back to see dinosaurs and the time machine puts me in my ancestor instead of a shrew it would be a telephone sanitizer on Golgafringian Ark B???
Well, leaving aside relativity issues, and decidedly not being the brilliant, if late, Douglas Adams, I'd say it was possible.
Quantum probabliity (currently) holds that, if you found a way to create a time-space bubble, the interior of that bubble would tend to operate at your previous, 'native' time (the premise operates similarly to conservation of mass and energy). So, the you of the "now" would still be you in the "then." No regressing into protoplasm or dust or the like.
Now, sadly, current quantum theory posits that, if you went back in time, the "reality" you would experiece would not necessarily be the one in your own past. It would be the one where the quatum states resolved to where the coin toss comes up that your trip was successful (and not any of the times the coin toss was "tails" instead).
Next tricky part is that on your return trip to your previous "present," it, too has to be the one where all the coin flips equal your success. But, that might not (and probably wouldn't ) be the "present" you left to go to the past.
And, this stuff gets complicated, quick. A quantum decision tree always has three branches, decision made, positive; decision made, negative; and no decision.
Quantum states will admit to any possible combination of reality, and they resolve only in observation. So, in a given instant, there is a non-zero probability that you are a Llama. When you look in the mirror and you are not a 120kg 2m tall quadraped, then, either a quantum dcision occured, or inertia mooted the decision, and you did not transmogrify.
Now, the probablities of being a Golgafringian are significantly higher than a bowl of petunias, but either are non-zero, especially with quantum probabilities.
Then, it gets really deep