Note that everything written here is about the movie, not the comics (which I haven’t read), so it’s possible that some of these speculations are explored in more detail in the comics. And I won’t give away any (major) spoilers!
As the Ancient One* tells Strange, our universe is one of many in an infinite multiverse. This idea is not peculiar to contemporary physics, but has its roots in Buddhism and other cultures. For example, the ancient Buddhist text called the Avatamsaka Sutra (A.S.) describes countless “Buddha-fields” of worlds, each maintained by different gods/bodhisattvas. Some of these worlds are similar to our own, and others are vastly different. These worlds can also be seen as jewels in the metaphorical Indra’s net. Regarding Indra’s net, the A.S. says:
“Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions…the artificer has hung a single glittering jewel in each "eye" of the net, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars…If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring.”
The multiverse is Indra’s net: all the worlds are connected and interdependent. There is no “source” of reality, but every world mirrors every other world in a fractalling pattern of worlds within worlds within worlds. This is the Buddhist concept of dependent origination (the lack of a source of reality, so all things are co-created with all other things) as well as emptiness (that physical worlds are just reflections of other worlds, which are all just reflections of other worlds…yet again, there is no source).
Thus, with all these worlds connected, if we can access their connections via portals, we can transfer energy between them. This was seen in the movie, with sorcerers channeling energy from other worlds in order to perform great feats of magic.
Other ideas about the multiverse crop up throughout history. Here are a few examples:
Again from the A.S.: “What worlds are there herein? I’ll tell you. In these seas of fragrant waters, numerous as atoms in unspeakably many buddha-fields, rest an equal number of world systems. Each world system also contains an equal number of worlds. Those world systems in the ocean of worlds have various resting places, various shapes and forms, various substances and essences, various locations, various entryways, various adornments, various boundaries, various alignments, various similarities, and various powers of maintenance.”
From the Greek philosopher Democritus (460 – 370 B.C.): “There are worlds infinite in number and different in size. In some there is neither sun nor moon, on others there are more than one sun and moon. The distances between the worlds are unequal…Their destruction comes about through collision with one another.”
From the Neoplatonic philosopher Plotinus (204 – 270): “The kosmos is like a net which takes all its life, as far as ever it stretches, from being wet in the water, and has no act of its own; the sea rolls away and the net with it, precisely to the full of its scope, for no mesh of it can strain beyond its set place: the soul is of so far-reaching a nature—a thing unbounded—as to embrace the entire body of the All in the one extension; so far as the universe extends, there soul is; and if the universe had no existence, the extent of soul would be the same; it is eternally what it is.”
From the Sufi poet Mahmoud Shabestari (1288 – 1340): “Know that the whole world is a mirror; in each atom are found a hundred blazing suns. If you split the center of a single drop of water, a hundred pure oceans spring forth. If you examine each particle of dust, a thousand Adams can be seen. A universe lies hidden in a grain of millet; everything is brought together at the point of the present.”
And one example (out of many) from current physics:
Another important idea explored is the power which people have to change the world. Not just changing it via macroscopic cause and effect, but by altering the microscopic nature of reality itself. From what scientists have learned about the subatomic world, where quantum mechanics reigns supreme (as opposed to the larger world where we live in, where gravity is the master), we know that consciousness influences matter. We don’t fully understand how this happens, but it has been experimentally proven. For example, the very act of observation causes a particle to take on a precise value for its position, whereas normally, it is in no defined place, instead acting like a wave spread over a large region. There have also been experiments performed where people have consciously directed the outcome of a random event generator (see this book).
In the movie, we see this power of consciousness in the magic wielded by the sorcerers, as well as when the Ancient One tells Strange that “At the root of existence, mind and matter meet. Thoughts form reality.” This is something common to Buddhism (A.S.: “Mind is like an artist able to paint the worlds”), and is coming to be accepted in physics as well. At the base of reality, there is just energy, which can vibrate and produce particles with mass (thanks to the equivalence of mass and energy: E = mc^2).
Yet what is different in the movie is that the power the sorcerers wield arises not just from the power of their minds and the energies from this world, but accessing energies from other worlds through certain portals. Regarding this, the Ancient One says, “Through the mystic arts, we harness energy and shape reality.”
We also saw the astral body explored in the movie. The astral body is a spiritual duplicate of the human body. It is usually contained within the body, but it’s possible for it to detach from the body and travel elsewhere, temporarily or permanently (if permanently, then death will result). For more about the astral body, see my previous post. Here's an example of the Ancient One jolting Strange's astral body out of him:
Astral projection is found in many different spiritual traditions (as well as Buddhism! e.g., the A.S. says about great sages, “To all lands in the cosmos, countless, they can travel by projection, their bodies most subtle, beyond comparison.”) and many people have been able to today (e.g., see this video). The trick, of course, is to control this skill, and it is only then that people can develop the powers shown rather simplistically in the movie.
Time is where the most confusion arises. I think it’s fair to say that Doctor Strange is a real Time Lord. By using a special device, he is able to manipulate time around particular objects and locations. For example, he experimented with bringing an apple backward and forward in time, causing it to be eaten and rot, then return to being whole. Likewise, he turned time back in an entire block of a city in Hong Kong, though he and a few other sorcerers are able to escape the effects of time.
Many issues arise from bending time in this manner. First, if you’re able to go forward or backward in time, what happens to your memories? It seems that the people who are subject to Strange’s time magic have no recollection of the future that Strange had “undone,” yet Strange and the other sorcerers are not subjected to this. They exist in a sort of temporal bubble where they physically go back in time with the rest of the people, but retain their memories and are not forced to “backtrack” whatever movements they have previously done.
This is either just some sort of magic, or, as I like to think, there are two sorts of time: the physical time, which is what our bodies are bound to as we progress through life, and which Strange can manipulate, as well as the mental time, which is the successive series of our thoughts, sensations, and memories that make us who we are. It could also be considered to be our “soul time”, since each soul has its own personal timeline that cannot be distorted by the physical events around it. So although most people, when subjected to a temporal back-track thanks to Doctor Strange, have their mental and physical times linked, meaning that their memories of the future are erased, sorcerers who can split their mental and physical timelines are able to physically turn back time without being affected by it mentally.
There is also the timeless world that the evil sorcerer Kaecilius wishes to find, where there is no death, etc. (typical promised land sort of thing), but if there really is no time whatsoever, then things can’t change. If there is no distinction between physical and mental time, then going to a timeless world would be the equivalent of entering an extreme coma: yes, your body is preserved, but you can’t think or sense anything. Thus, in order for Kaecilius’s wish to make sense (and maybe it just doesn’t: maybe he hasn’t thought it through), it has to be that he wants to go to a physically timeless world where his body will be preserved, but not a mentally timeless world, so that he will retain his sensations and consciousness and be able to interact with the world around him (albeit in a limited sense, since the physical objects can’t change).
Then there’s also the typical question of determinism and free will. If we travel to the future, is it to one of many possible futures, or is it to a certain future? And if you change the future, was that determined? Likewise, if you change the past, did that happen the “first time around”? We don’t really get any of these answers in the movie, but if the series continues (and it’s a Marvel movie, so of course it will), then hopefully we’ll see more about the effects of manipulating time and what it means for the conscious beings within it.
Well, there’s some food for thought. And that’s to say nothing about the dark dimension and Dormammu. To that end, I will end with a quote from the Ancient One:
“This universe is only one of an infinite number. Worlds without end; some benevolent and life-giving, others filled with malice and hunger. Dark places where powers older than time lie, ravenous and waiting.”