One of the dimensions that doesn't get mentioned a whole lot is that of Possibility. Yes, just like height, depth, width, and time, possibility is a dimension. This can be observed through quantum physics. The quintessential axiom describing this is referred to as "Schroedinger's Cat." Schroedinger suggested putting a hypothetical cat in a box. Along with the cat would go a device that, based on random quantum principles, would kill the cat at in an unknown amount of time. As long as you didn't observe the inside of the box the cat would exist both in a state of dead and not dead.
Sounds weird, but it can be demonstrated through other quantum oddities. One of the common quantum problems is light existing as either a wave or a particle. Light will behave as a wave until it is observed, at which point it behaves like a particle. That is because it exists as a wave of possibility. All subatomic particles exist as waves of possibility until the probable collapses the waveform into actual particles.
We as humans only observe the most probable of all possibilities. What is probable is defined by which possibility happens moment to moment, and the waveform continually collapses in front of us. Since the waveform collapses upon observation, the existence of the universe itself is dependent upon being observed. Other quantum experiments have shown a link between the will of the observer and what the waveform will collapse into.
In science fiction this phenomenon is typically described as "parallel universes" where a separate universe exists for every possibility, each universe being separate. Instead, there is one universe with the observer being as if he were on a jet boat. Without any extra input of effort or will, the boat will continually go in a straight line along a probability axis. With concentrated effort and force of will, a rudder can be applied which will shift the direction of movement of the observer's probability axis.
Now, what does this means in every day life? There are an infinite number of possibilities, yet possibilities are also very finite. To change what "parallel universe" you live in, you're best off deciding what universe you want to live in and steer in that direction. You won't arrive there immediately unless it is so very similar to the universe you are in to begin with that it won't matter, but a desired destiny (destination?) can be steered towards. And you don't even have to invent some science fiction-y portal, you just have to will each moment to change.