Quantum Spatial Dynamics

Barry Dalgarno

Originally published on 25 March 2011 under the title The Structure of a Black Hole.

Introduction

The prevailing view of a black hole is that of a gravitational singularity together with its associated event horizon. A gravitational singularity has been defined as an infinitely small point at the core, where the gravitational field is infinitely high. An event horizon is a region where the gravitational distortion of space is so high that nothing (neither matter nor electromagnetic radiation) can escape.

The Theory of Quantum Spatial Dynamics

The mysterious entity known as a black hole keeps within its core the secrets of our universe’s origin and destiny. The theory of quantum spatial dynamics (QSD) is introduced here as the basis for how the black hole structure was arrived at. In this communication, it is suggested that instead of a plurality of black hole cores of zero size and infinite density, there exists a single structure of two diametric halves consisting of matter and antimatter respectively, propagating through two dimensions. Our universe is split into two halves, each half connected to this single massive black hole core, through the event horizons at the matter propagation front and antimatter propagation front respectively. Density is extremely high with reference to the two-dimensional propagation plane, as is the strength of the gravitational field exerted by the two halves respectively. However, they are not infinitely high, and so the black hole core cannot be described as a gravitational singularity.

Transformation of Spatial Dimensionality

From the matter half of the universe, matter particles enter the event horizons connected to the matter half of the core. Similarly from the antimatter half of the universe, antimatter particles enter the event horizons connected to the antimatter half of the core. Each half of the core is the mirror image of the other, rotated by 180 degrees. Within the transformation space (the region between an event horizon and the core) at each half of the universe, the increased curvature of space does not proceed evenly for all three spatial dimensions. Gravitational distortion does not continue to contract space beyond that of the intrinsic size of a quantum of matter, and the abstract point of infinitely small space has no basis in physical reality. Instead, there is non-equivalent dimensional distortion as a direct result of the core’s unique geometry. For brevity, this paper will now only refer to that half of the core's structure that is populated by matter, as the other half is similar, differing with respect to population by antimatter as opposed to matter. For convenience, the core’s three spatial dimensions will be referred to simply as d₁, d₂ and d_3. Their overall relative magnitudes are as follows.

However, this simplified expression does not show the whole picture. The first dimension (d₁) is maximally contracted to the magnitude of the intrinsic size of a fundamental quantum of matter. This quantum mechanical limit precludes any freedom of structural propagation through the first dimension within the core, and so growth of the structure by quanta of matter is through two dimensions only. The second dimension (d₂) is prescribed by the primary propagation axis. Unlike d₁, it does not have a fixed value. Although it fluctuates along this axis, overall it increases as the core grows. The third dimension (d₃) also has no fixed value. It fluctuates along the propagation-front, and can have the maximal level of contraction. Overall its cumulative average magnitude increases with growth of the core. Its relationship with d₂ is a subtle one, and the rising and falling of d₃ is due to the ‘reverse fractal’ geometry of the core.

A Quantum Mechanical Operator for Space and Time

All energy (matter and radiation) that entered via an event horizon is converted to fundamental quanta of matter in the transformation space. Within the geometric framework at the core of a black hole, matter retains its quantum nature. On reaching the core, a quantum mechanical operator for space and time positions the quanta in the two-dimensional propagation plane according to a simple yet profound law. This is accompanied by a reversal of the familiar arrow of time. The geometry of the core has a structure of sequential triangular symmetry, and the potential for infinite propagation. The symmetry-directing operator maintains a state of almost zero entropy. In order for the state of zero entropy to be further approached, the supply of matter must continue, and quantum computational growth of the structure proceeds for as long as matter is added. The basis-set that is applied to the two-dimensional propagation is the infinite set of prime number intervals, and the operation determining the symmetry is referred to as geometric entanglement.¹

The Beginning of a New Universe

Quantum population of the core’s structure cannot continue without the co-existence of the universe, and this raises the question as to what will happen if our universe contains a finite amount of energy, matter and antimatter. Eventually all event horizons connected to the matter half of the core will merge, and all event horizons connected to the antimatter half of the core will also merge. The end of our universe is when all the remaining energy, matter and antimatter has been transferred to the structure via the single remaining event horizon on the matter and antimatter halves respectively. At that stage, the transformation of spatial dimensionality will be reversed, marking the beginning of time for a new universe.

Reference

1. B. Dalgarno (2009). A New Law of Prime Numbers Based on an Infinite Structure of Sequential Triangular Symmetry from Finely-Tuned Geometric Entanglement of the Prime Intervals.

https://sites.google.com/site/geometryoftheprimes/