At the end of the first Back to the Future film, we see Doc Brown picking up Marty and Jennifer in 1985 to come rescue their kids in 2015.
I've always assumed him to be a 1985-ish Doc, who had traveled into the future and kept an eye on Marty and his family. But it occurred to me that we can't be sure, can we?
Could it have been Doc from 2015 who traveled back to 1985 to pick up Marty? Or a Doc from any other year? Is there any clue in any of the films or in any other canon materials?
There are quite a few indications that Doc is from 1985. For one thing, he consistently refers to 2015 as "the future", even when in 2015, although that could just be for Marty's benefit. Also:
Precisely! I already went further ahead into time to see what else happens. I backtracked everything to this one event, that's why we're here today to prevent this incident from ever happening. (His watch beeps.) Damn, I'm late!
This indicates that he went far into the future, saw that Marty's family got into trouble, and eventually worked his way back to 2015. Clearly he's not the 2015 version of Doc who went back in time immediately after seeing Marty Jr. being arrested.
I left him in a suspended animation kennel. Einstein never knew I was gone! (gets out of the car) Marty!
Einstein probably wouldn't survive until 2015. Doc could have gotten another dog and named in Einstein, but that seems unlikely.
My only regret is that I will never get a chance to visit my favorite historical era - the old west. But time travelling is just too dangerous. Better that I devote myself to study the other great mystery of the universe - women.
Surely over the course of 30 years he would have visited the Old West.
The official novelisation for the sequel indicates that the the Doc who arrives at the end of BTTF is the Doc Brown that is contemporaneous with 1985 Marty.
They would be very careful, Doc told himself, and there would be no mistakes. While he had been in the future, Doc had done some research into the nature of time paradoxes, and discovered their results could be far more devastating than he had ever imagined!
This line would make no sense if this was the Doc from the future. And
All that remained was a simple matter of logistics. Doc would pick up Marty and they would go back to the future . . . actually their own present, October 26 1985. And this time it would be the same 1985 they had left from on the morning of October 26 1985.
So it's their own shared present. His Doc is the Doc that he's been traveling with, not a future Doc (unless he's been very consistently lying to Marty).
Just looking at evidence from the movies, one really basic piece of evidence is the scene near the end of part I where Doc drops Marty off back at home, right after the scene at the mall where he showed Marty the bulletproof vest. From the transcript here, Doc says in the dialogue he's planning on making a trip "about 30 years" into the future:
Marty: About how far ahead are you going?
Doc: About 30 years, it's a nice round number.
Marty: Look me up when you get there, guess I'll be about 47.
Doc: I will.
Marty: Take care.
Doc: You too.
Marty: Alright, good-bye Einy. Oh, watch that re-entry, it's a little bumpy.
Doc: You bet.
And if you re-watch this scene you can see that after this dialogue, the DeLorean drives up the road in one direction and then Marty watches it speed by in the opposite direction, and right after it disappears from view there's a flash of bright light accompanied by the usual sounds of a time jump. So, it seems Doc immediately made his trip 30 years into the future after this dialogue, taking Einstein with him (which connects to the dialogue from part II quoted by @Acccumulation where Doc said he had left Einstein in a suspended animation clinic). And of course the next scene with Doc in part I is him coming to get Marty and Jennifer wearing futuristic clothes, so the implication is that he's just returned from the same trip to the future we saw him setting out on a few scenes earlier.
Then in part II, note that in 2015 when Doc saw that Jennifer was being taken by the police to her older self's home in Hilldale, he was extremely worried about the danger of time paradoxes, as shown in this dialogue (from the transcript here):
Doc: Great Scott! Jennifer could conceivably encounter her future self, the consequences of that could be disastrous.
Marty: Doc, what do you mean?
Doc: I foresee two possibilities. One - coming face-to-face with herself thirty years older could put her into shock and she could simply pass out. Or two - the encounter could create a time paradox, the results of which could cause a chain reaction that would unravel the very fabric of the space-time continuum and destroy the entire universe. Granted, that's the worse case scenario. The destruction might, in fact, be very localized, limited to merely our own galaxy.
After they got Jennifer back in 2015 and were about to return to 1985, Doc said "Lets get her back to 1985. And then I'm going to destroy the time machine!" When Marty asked why, he said "The risk is just too great, as this incident proves" (referring to Jennifer meeting her future self). After he dropped Marty off in 1985 (actually 1985-A, but they didn't know that), he said "If you need me, I'll be in my lab, dismantling this thing."
These scenes from part II give strong evidence that he was the Doc from 1985. If he was actually from 2015 (or any other year past 1985), and was so worried about the risk of time paradoxes, he wouldn't have wanted to dismantle the time machine in 1985, since that would leave him as a person from the future living out the next bunch of years in his own past (potentially changing things from the way he remembered 1985-2015 happening the first time around).
