#### Title

Emergence of Four Dimensions in the Causal Set Approach to Discrete Quantum Gravity

#### Document Type

Article

#### Publication Date

2014

#### Keywords

Causal sets, Discrete quantum gravity, Transition amplitudes, Four dimensions.

#### Abstract

One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a four-dimensional universe. Another approach would be to show that four-dimensions arise naturally from a reasonable model of the universe or multiverse. After reviewing the causal set approach to discrete quantum gravity in Section 1, we shall discuss the emergence of four-dimensions in Section 2. We shall see that certain patterns of four arise that suggest the introduction of a 4-dimensional discrete manifold. In the later sections we shall discuss some consequences of this introduced framework. In particular, we will show that quantum amplitudes can be employed to describe a multiverse dynamics. Moreover, a natural unitary operator together with energy, position and momentum operators will be introduced and their properties studied.

#### Recommended Citation

Gudder, S. (2014). Emergence of four dimensions in the causal set approach to discrete quantum gravity. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/6