The Flux Capacitor collides heavy elements (in this case, Plutonium) along three spatial axes to create a mini-singularity into which the time machine
(DeLorean) implodes.
Because of the axial translation accomplished by the implosion, speed becomes equated with time (the faster you implode, the farther forward or
backward you travel in time), and the on-board computer compensates for spatial vectoring. If it didn't, you'd move in time, but Earth would not be
at the same point in space, so you'd end up either where the Earth used to be or will eventually be. The metal body of the DeLorean (as well as a
large steam locomotive), creates a protective bubble of isospace around the vehicle, keeping it from disintegrating from the shearing forces of the
singularity.
Imagine pushing a basketball or other inflatable object under the water in a pool. While the ball is underwater, it is essentially "outside" normal
space, and relativistic effects are not felt. How hard and in what direction you push the ball (using a magnetic "slingshot") will determine where
the ball explodes to the surface, reappearing again in "real" space. Remember, that while the DeLorean is "underwater" it's no longer in our
spacetime, so while there will be some time lag when we do the demonstration, in real life, the transition from one point to another will appear
instantaneous.
Reverse-exploding back into normal spacetime causes an accumulation of matter/energy at the singularity point, which results in the vehicle being
covered with ice from condensation.
The biggest technical problem with the Philadelphia Experiment was the failure to anticipate the need for a proper vectoring mechanism. As a result,
when the
USS Eldridge imploded into (subspace), it didn't "go" anywhere and flipped in and out of normal spacetime at random. Fortunately,
the ship was large enough that the gravitational field of the Earth, which has an effect in subspace, was able to keep it from exploding out into
space at the time and place the initial implosion happened, after the Earth moved on. It reappeared in normal spacetime outside Norfolk, Virginia for
a few seconds, then when the equipment was improperly turned off, not properly closing the singularity, it was pulled back into subspace,
"slingshotting" back to its original starting point.
Dr. Emmett Brown, thanks to his frequent contacts with Prof. Einstein, was able to duplicate the effect on a smaller scale and add a vectoring
mechanism, but he had to wait until the mid-1980s when computers had become sophisticated enough to calculate the necessary vectoring component to
ensure proper targeting and small enough to fit in an smaller vehicle (the DeLorean), thus reducing the power requirement to a functional level
(although admittedly still difficult to attain legally in 1985).
I hope this clarifies the theory a little, and clarifies the connection between the flux capacitor and the Philadelphia Experiment.