by Greg Ward

Our basic conjecture is that particle superpositions actually correspond to locations in a higher dimensional space. How does motion in these higher dimensions manifest in the 4 dimensions of space-time we normally perceive?

To take a specific example, let’s say the spin of an electron corresponds to its position in the 5^th dimension. Since this dimension is very small, we cannot directly measure the electron’s spin superposition, but see it only as one of two states at a particular point in 4D space-time where it enters our detector.

The question we wish to answer is this: Do higher dimensions, though they be small, allow for the existence of discrete space-time continua?

To answer this question, let us suppose we have signed a contract, stipulating that we will build our new particle accelerator in Des Moines if the spin we measure on our electron is "up," and will build the accelerator in Toronto if the spin we measure is "down." We know from quantum mechanics that it is not possible to predict which spin we will measure if the particle source allows for superposition; we can only assign probabilities to the two possible outcomes. Therefore, we cannot know in advance where we have committed to building our new accelerator.

From the particle’s viewpoint, the two universes it is heading towards are separated by a distance that is dwarfed by the Planck scale, yet they look very different. One space-time contains an accelerator in Iowa, and the other contains an accelerator in Ontario. At least in the time between the particle’s ejection from the source and its entry into the detector, the two universes are indeed very close together, and space-time is dramatically split along the 5^th dimension. Both universes are available to the particle up until the moment its state collapses in the detector, and during the electron’s flight, the two universes coexist, entangled with the electron’s spin in a binding contract.

This entanglement may last an arbitrary time, and may cross an arbitrary distance through "quantum teleportation." Extending our thought experiment, let us generate two electrons on Earth in such a way that their spin state is entangled and direct them to two of our remote space colonies. At some predictable future time, a receiver will detect one of the electrons at our remote outpost in the outer arm of Andromeda, and its state will be tied to the spin detected at about the same time on our other outpost in the M33 galaxy. From Earth, we also send a suggestion that the two colonies send emigrants to meet each other and establish a new colony together in Galaxy A if the entangled spin they detect is up/down and Galaxy B if the spin is down/up. (Diplomacy being what it is, the colonies have long since refused taking direct orders from us, but continue to accept coordinating help provided it comes in a form that is not subject to our direct control.)

During the millions of years it takes for both our message and our electrons to reach our two outposts, the two possible universes, one containing a future colony in Galaxy A and the other containing a future colony in Galaxy B, are separated by a infinitesimal distance in the 5^th dimension. When the two electrons finally arrive and are detected millions of light years apart, the distance that separates the two universes is still as small as when they split on Earth all those millions of years ago. This demonstrates that the discrete separation in a higher dimension may in fact span arbitrary distances and time over the entire universe, not just a small section of it. The two possible universes coexist with distinct futures, though their present looks much the same. To the entangled pair, the distance between the two universes is never greater than the length of the 5^th dimension, minute in size but not limited in its effect.