The movie depicts a vague time lapse where Doctor Strange undergoes lots of studying and training.
How much time has passed in his whole training arc of the movie?
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This supposes that the movie's end scene with Thor happens roughly around the time that Thor: Ragnarok is released (November 2017).
New information has come out, and according to the director of the film, the movie takes place in a single year.
Stephen Strange (Benedict Cumberbatch) spends about “three to six months” in recovery from his accident. (“There is a more precise answer, but I don't remember,” says Derrickson.) The entire film runs from one autumn to the following year’s autumn – though Derrickson adds the caveat: “Don't hold me to this, because I haven't thought about this in a long time.”
So if the whole film is about a year, and he's in recovery for 3-6 months, then the only time left to train is the 6-9 months. This is exactly in line with my original analysis.
Strange's accident happens on Tue Feb 2, 2016. I get this time from his watch when he's picking one out for the gala he's heading to:
When he's mugged, it's a Wednesday in January, 2017. This is about a full year later than anyone else has supposed, before. I assume it's 2017, because of the date previously established. To be January again, it has to be the following year. This makes sense considering the time he spent in the hospital, the number of surgeries he had performed, and the fact that he spent all of his money.
So, if we assume mid-late January 2017 to the Ancient One's death sometime before early November 2017, that's a max of 9 months (and a couple weeks, maybe). Given that we have no idea how long passes between her death and the scene with Thor, it could be shorter, but less than 6 months seems unlikely.
Although it's unclear, the day hand seems to be pointing to the upper left quadrant of the day section, somewhere between where we see the clear 17 and the unclear 7 from 27. The broken glass makes it hard to tell.
At the end of the movie, when Strange puts his watch back on, it appears to say Thursday, in January again. So, I'm not sure what's going on here. Everything else is in the same positions, included the day/night cycle, so I believe at this point weekday hand is probably just broken.
At the very most, Doctor Stephen Strange was in training for 3 and a half years.
It's virtually impossible to figure out the exact length of time that Stephen Strange was in training in Doctor Strange thanks to the lack of reference points for when he starts training and when he stops. However, we can safely assume that between the start of the movie and the first end credits scene, no more than 3 and a half years have elapsed.
The first thing we need to do is ignore a reference to an experimental armour that we hear before Stephen Strange crashes his car. Director Scott Derrickson recently confirmed that this is not meant to be Colonel James "Rhodey" Rhodes, meaning that we cannot use this as evidence for when the film is set.
This answer from @phantom42 includes a link to an interview with Kevin Feige that confirms that at the time of Captain America: The Winter Soldier, Stephen Strange is just a highly talented neurosurgeon.
"He is very well-known as a surgeon," Feige said during a recent visit to the set of Doctor Strange. "He has got various awards and plaques you're going to see over there; he attends various galas, might be driving at one point in this movie. He has name recognition and a talent and certain Hydra computers identified him as somebody that could cause trouble for their agendas."
So the answer is, Strange wasn't an immediate threat to Hydra in any meaningful way, but as a brilliant and famous person whose agenda didn't mesh with theirs, he stood a high probability of being a problem for them if they successfully took over government. Think of it like a politician targeting Bruce Springsteen or Ted Nugent because they might use their concerts as a platform to spread a message the politician in question didn't like.
This conclusively proves that as of spring 2014, Stephen Strange has not yet had his car crash. This means that we know for sure that he does not start his training until some point after spring 2014.
Our "end point" comes in the form of a post-credits scene in which;
Doctor Strange offers to help Thor and Loki find Odin on Earth.
This is a teaser for;
Thor Ragnarok, which is set to come out in Autumn 2017.
Assuming that the film above is set in roughly the same time period that it is released (as tends to be the case with most films set in the Marvel Cinematic Universe), then we know for sure that Doctor Strange ends by autumn 2017.
As such, his training has to take place between spring 2014 and autumn 2017, a period of 3 and a half years. Please note that this answer doesn't include the time required for him to recover from his car crash, as I have no idea what a reasonable recovery time for the types of injuries he sustained might be.
It's also worth noting that there are some people reporting that they saw trophies/awards in his apartment at the start of the movie dated 2016 (which would obviously severely reduce the period the film is set over to around about 18 months), but as I cannot verify those claims I have not taken them into account in this answer.
As for the word of God answer, when asked about this on Twitter, director Scott Derrickson simply replied;
"Time is relative"
Several articles reviewing the potential clues indicate the time between elements listed in the movie make the time from Strange's accident to the final battle took place in as little as a year.
From an interview with Director Scott Derrickson on Digital Spy:
Director Scott Derrickson spoke to Digital Spy and set us right on just when the events of Doctor Strange occur.
"That's not War Machine, actually," he said. "It sounds like it. And maybe in some other iteration we were even thinking it could be. The movie led up to present day.
"There's not that much of a time gap."
It is hard to believe Strange went from having multiple surgeries, went completely broke, traveled to Tibet, became proficient in magic, even with his photographic memory, and learned a martial art well enough to fight the Kaecilius' acolytes in a year to eighteen months even if he worked twenty hours a day.
On the other hand:
We don't know anything about how Kamar-Taj works in regard to the passage of time. Since more advanced magi have access to multiple dimensions and magi can train inside of the Mirror Dimension, there may be a temporal component involved giving a sorcerer more time to practice in. Thus he could have studied for years and to most people he may have only been gone for a year in the real world.
There is also the fact the Eye of Agammotto had control over temporal phenomena so it is possible the entire temple existed outside of time, altogether.
This is not just in the movie either. No exact period of time is ever listed for Strange's training in the comics either. We are only told he trains for what we presume will be several years. His ability is predicated upon his what the Ancient One deems Stephen Strange's innate potential.
From the first origin of Doctor Strange in Strange Tales #115 where we learn Stephen will study for years before he takes on the mantle of the Sorcerer Supreme.
Actually it's very easy to tell how much time passes over the course of the movie. Towards the beginning of the film when Strange is preparing for his speech in his flat the camera pans across an award on a shelf. It is difficult to see what the award is for, but it clearly says '2016' on it, implying that this moment in the film is at least in 2016. A short while later when Strange is searching for Kamar-Taj in Kathmandu he is mugged for his watch, during which the watch is damaged and stops on 1st February 2016. This implies that the entire opening section of the movie, from the moment we are introduced to Strange to the time he meets the Ancient One for the first time is within one month only. This means the recovery from his accident only takes just a few weeks - which I find surprising given the growth of his beard(!). A few scenes later Strange is allowed to begin his training and a clue of the time is given by blossom on a tree is Kamar-Taj telling the audience that we have now moved from late Winter to early-Spring 2016, and again after some scenes have passed time is once again implied to have passed by showing the same tree, now with brown leaves, clearly in Autumn. This is when the battles with the Zealots begin which take just a short time in late-October / early November 2016 (the approximate release date of the film). Thus to can surmise the entire film takes place within just 10 to 11 short months, and Strange's training, while intense, even shorter.
Though I enjoyed the movie I couldn't help but think my suspension of disbelief would have been aided by the time-frame being extended. Before I re-watched the film and stopped those 2016 dates at the beginning I believed that the opening could have taken place at any point after Stark Tower adopted the Avenger's 'A', i.e. after 2012 - a four year time frame would have made more sense!
I just saw the movie a second time and noticed one key detail I missed the first time. And apparently all of you did to. Before the accident when's putting on his watch you see a award dated 2016. So this 2014 theory is obviously wrong. That's the only thing in this movie that can hint towards its place in the timeline
With reference to the watch answer the dates must be 2014 and 2015. Firstly the years are obscured in all pictures of the watch. As we know from Iron Man 2 the days in the MCU do not correspond to those in our timeline. The newspaper showing the death of Howard Stark is dated Friday 17th December 1991 although in our timeline it was a Tuesday. We must therefore move the day back 3 for our timeline.
The first date is Tuesday 2nd February which would be Saturday 2nd February 2013 in our timeline. The second date a Wednesday in January would be a Sunday in our timeline. Some seem to think that the 17 is after the 19 but it is actually the 21 with the top obscured to look like 17 upside down. The needle does seem to be pointing to the top left which would be Sunday 26th January 2014.
Many think that the Lamborghini Huracan must date this 2014 or later due to the stated production date of 2014 to present but there were actually 76 produced in 2013. The watch was also released in 2013. The issue with this is that the watch was not launched until March 2013 (after February) and the 76 cars produced would surely have been later than February. Add to this that the award states 2016 and it gets even messier.
When Agent Sitwell mentions Stephen Strange in Winter Soldier you would like to think that this could occur after he has done some research into Kamar-Taj which HYDRA has used in the algorithm to identify Strange as a threat. This would fit the proposed dates above.
I would say it started in Spring and finished in Autumn (April/ May trees blossom in Nepal and autumn mid Sept/end Nov). So either about 6 months to conclude in 2015 or 18 months to conclude in 2016. The watch in Ultra HD does look like 2016 (maybe 2018 a t a push?) but as with the award stating 2016 and the x-ray of Pangborn dated 9th December 2014 https://screenrant.com/doctor-strange-mcu-timeline-year/ these are done by props people not the producer, writer or director so because of inconsistencies we need to sift the best and most commonly supported evidence from other films.
You may like to place it happening over 2015/16 or 2016/17 to fit with when it was released. I prefer to place the accident and recovery before Winter Soldier ;which must be at least 2 years before Civil War (Falcon says to Cap they have been looking for Bucky for 2 years) which is 2 years before Infinity War (Vision to Wanda, “For two years, we've stolen these moments...” Rhodey to Cap “Must've been a rough couple years.”) and Kamar-Taj after. When you date these will determine rest of MCU timeline but let us assume Winter Soldier 2014, Civil War 2016 and Infinity War 2018, so Doctor Strange 2014 to either 2015 or 2016 depending on how long we assume the training lasted, let us assume 2016 so that the end corresponds with the release date.