## 8 A Dual Universe

This sounds reasonable, so let’s look closer at spacetime quanta in their matrix and see what else quantized spacetime has to offer. These spheres with minimum dimensions are assumed to be tightly packed into a three-dimensional matrix in which spheres contact each other at five or six points, allowing particles to pass from quantum to quantum. Away from these contacts are spaces between the spheres that are interconnected and form a continuous medium outside of space and time. It has a zero-thickness interface with spacetime but has no spacetime dimensions. Those are in the spacetime quanta. The total space between quanta is a significant fraction of that of the spacetime universe, so it forms a second universe in contact with the spacetime universe, though a zero-thickness membrane

The examination of the properties of dual universes in contact like this is a branch of cosmology that expanded rapidly after a seminal paper by Juan Maldacena. In such universes the second may lack one space dimension and may be populated with various types of particles. Quantized spacetime gives rise to a second universe that I assume is full of energy. In its dimensionless bulk this energy would have no mass or gravity. Inside a black shell it would not change shell mass.

At the interface with spacetime, however, the second universe gains two space dimensions and one time dimension from a surface of spacetime lacking one spatial dimension, a situation similar to that investigated by Malcedona. With these surface dimensions the energy beyond spacetime would be able to function as potential energy and interact with the kinetic energy of particles in spacetime, giving rise to effects in quantum mechanics. In addition, the surface dimensions would also give the energy there the property of mass, which in aggregate over a region like a galaxy would affect the motion of stars in the manner attributed to dark matter.

One can say that this energy with no spacetime dimensions may have its own intensity dimension expressed by the work it can do when given specific dimensions. As such, it could also act as an honest broker when one form of energy turns into another. It might provide the number that Richard Feynman identified as remaining constant in a series of energy transformations: “a most abstract idea, because it is a mathematical principle . . . not a description of a mechanism or anything concrete.” Dimensionless energy might well be regarded as an abstract idea.

The action of surface energy would be like the activation of gravity when we throw an object skyward. Gravity minimizes this spacetime disturbance by slowing the object. The object loses kinetic energy continually (in quantum jumps) but it gains an equivalent amount of gravitational potential energy (in the absence of air friction). As its kinetic energy becomes zero, the object stops. Its potential energy then drives it back down to Earth, to arrive at its initial speed. Disturbance removed (and, possibly, the disturber).

When a region is beyond spacetime beyond spacetime it lacks spacetime dimensions, making it very different to the vacuum which has these dimensions. Being beyond the region of spacetime it can be referred to as hyperspacetime. It is an important region because it provides an essential service for particles within spacetime.

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