M-Theory Multiverse
"Extra dimensions" sounds as if it's straight out of science fiction, where you could be at the same location with another mass however you would not be able to see nor collide with that mass (superimposed). Well to everybody's surprise scientists have just confirmed the existence of Dark Matter. This mysterious Dark Matter is invisible however it provides the bulk of gravity that holds galaxies (not the regular matter that forms stars and planets). This invisible Dark Matter has weird collision properties (collisionless). Simply put: we cannot see Dark Matter nor collide with it but we can detect its gravity.
In this image, two huge clusters of invisible Dark Matter (in blue) clashed with each other. With each cluster having a mass of 10,000 galaxies (each cluster a quadrillion times the mass of the Sun, 1015!!!) (See: Universe Today). However upon impact, instead of disintegrating into smaller pieces, they passed through each other unscathed! This means that they did not collide with each other either! They simply passed through each other!!!
In order to explain why this invisible Dark Matter neither collided with each other, nor did it collide with us but still we detected its gravity, physicists and cosmologists are working on theories with extra dimensions. Traditionally scientists thought that we live in a four dimensional universe: Time and the usual three spatial dimensions of length, width and height (x,y,z). However today there is evidence for six extra spatial dimensions. So we cannot see nor collide with this Dark Matter because it is mass in the remaining six extra dimensions.
From a physics point of view, we are not living in a "Universe" but rather in a "Multiverse"; several universes superimposed above each other. Gravity is the only thing shared between these parallel universes:
The invisible Dark Matter is simply mass in other dimensions. In all 5 versions of String Theory there are 10 dimensions: "Time" plus the usual three spatial dimensions (x,y,z) plus six extra spatial dimensions making a total of ten dimensions (1 time + 9 spatial = 10 dimensions). Other competing theories like M-Theory has one extra spatial dimension (making the total 11 dimensions), however this extra spatial dimension is for Membranes (the Big Bang was a result of a collision of membranes...). Currently in all competing theories this Dark Matter is mass in other dimensions. Today we are sure that we are not living in a "Universe" but rather in a "Multiverse".
You might ask how does those six extra spatial dimensions look like:
Extra dimensions are tiny and curled up at each point in space. To envision a single extra dimension imagine the ant in the above video shrinking billions of times. Then this ant becomes small enough for transition to the extra circular dimension (like a roller coaster):
However instead of one extra circular dimension there are six dimensions and not necessarily circular; but they are all curled up at each point in space. The ant would encounter multiple routes like this:
As long as the ant remains in any of those extra dimensions we would not be able to see the ant nor collide with it but we would still detect its gravity. In M-Theory the Dark Mater is not only mass in other dimensions but they are in parallel universes (where the laws of physics might not be the same as ours). The only thing shared among those superimposed parallel universes is gravity. Add our universe to those parallel universes you get the Multiverse.