Force Anomalies - A mathematical model of the most elusive phenomenon of the Force

Abstract

The term Force anomaly, colloquially better known as Force rupture, Force vortex, or hole or wound of the Force, describes a wide variety of phenomena related to unusual Force activity or concentration. As of yet, all recorded accounts of Force anomalies (such as [Sha7] and [An68]) presented as dominated by the Dark Side - consistent with the only known channels through which Force anomalies come to be -, but studies show no indication that a Light Side anomaly shouldn't be possible (see [Re102], [Ba114] or [Sha7]).

Shan and Bal in their famous work present a long list of proposed Force anomalies. The events listed there are without a doubt anomalous in nature, and it is now widely accepted that they were caused by a common mechanism of the Force. The details of this mechanism, meanwhile, are cause for a great deal of controversy (for an overview of this controversy, we refer to [Pu42], and for an extensive list of references and their discussion we refer to [Re102]). Shan and Bal themselves conclude their interpretation by noting that "the presented theory alone does not explain all [anomalies] to full satisfaction. Further factors must be at play." It is the goal of the present work to propose a selection of such "factors" in an attempt to fill the gaps left by Shan and Bal. Disregarding the controversy, which can be found elsewhere in the literature, section 1 presents a summarized account of the mechanism presented by Shan and Bal for the reader's convenience. Section 2 will present a theoretical analysis which addresses the main points of uncertainty in their hypotheses, and finally section 3 will describe the method of mending such a wound in the Force.

Section 1

The Force anomalies of Shan and Bal fall into two categories. The first group is localized to an astrographical location, such as a planet or occasionally a planetary system, but never larger than a few lightseconds. Even the ones which spread across a planetary system do not span the whole planetary system in size. Rather, they are confined into a volume no larger than a class 1 planet, but with the ability to wander and move around. Since they are not fixed in place, their "size" is considered to be the maximum area where its effects have ever been located. For the location of such a Force vortex, we use the definition of [Re102].

The second category describes anomalies which are tied to a living being, rather than a place. These beings are predominantly but not exclusively beings which already showed an increased affinity for the Force before the event of the anomaly. However, once the anomaly had formed and attached itself to these beings, their connection and sensitivity to the Force has been heightened near infinitely. It is this observation which lead Shan and Bal to hypothesize that all historical accounts of inexplicable Force abilities - both Light and Dark Side - are tied to an anomaly in one way or the other. However, as mentioned earlier, so far no definitive Light Side anomalies have been identified.

The two categories have in common that their first observation is preceded closely by a large-scale traumatic event, usually including the loss of many lives. Shan and Bal therefore theorize that the unnatural loss of life has a disturbing effect on the Living Force, and a sufficient amount of such can lead to a long-lasting anomaly, such as the ones described. Certainly, the accounts of numerous Jedi Masters confirm the effect that a loss of life has on the Living Force, but little is known towards the longevity of these disturbances. Generally, they are described as only lasting a few moments. Meanwhile, some of the anomalies on the list of Shan and Bal have persisted for several years.

The interpretation then is as follows. As is well known, when a living being comes to death, its life force is reunited with the Living Force, until eventually it is bestowed upon a new being. This cycle is well-understood. A comprehensive analysis can be found in "The Complete Handbook to the Force," first published in the year 237 after the Treaty of Coruscant.

When a being's life is ended unexpectedly and unnaturally, such as during a battle, its reunification with the Living Force is disorderly and chaotic, representative of its fear and pain. As long as such deaths do not occur with sufficient frequency, the Force can recover from it on its own, and the only evidence is what the Jedi call a disturbance. However, if the number of unnatural deaths exceeds a certain limit (the details of which are unknown) and occur in a short enough timespan, then their combined chaos in returning to the Living Force creates a vortex, preventing their life force from reuniting properly, and trapping them in a sort of limbo - separated from the physical world, but not yet fully merged with the Living Force.

Such is the interpretation given by Shan and Bal.

Section 2

In this section, we work to provide a rigorous framework for the interpretations by Shan and Bal, thereby resolving some of the main points of criticism.

Although the Force has so far evaded any thorough mathematical description, including that of Midichlorians, which consistently fails to produce any reliable predictions, a number of models exist which describe the behaviour of the Force in many aspects.

For such readers, as are less mathematically inclined, we collect our results here. The Living Force behaves much like a liquid. Its response to absorbing the life force of a living being is not instantaneous. Small deformations are unstable, and return to the resting position quickly, but if the deformation is great enough, a new stable state can form: The Force separates into something that is best described as a bubble or a void that separates. These bubble, by their very nature, are stable and can therefore exist for many years. Furthermore, these bubbles are connected to both the Living Force and the real world, leading to an excessive concentration of Force Energy.

For the mathematical description, we provide a small extension onto the "Force tunnels" proposed by [Kun115]. Kun starts by noticing that all living beings are influenced by the Force, but the Jedi and Sith can equally influce the Force. He describes this mathematically as a tunnel whose diameter is representative of the individual's "strength" in influencing the Force. Note that once the diameter of the tunnel is allowed to vary, its time dependence must necessarily be decreasing.

Using his equations in the limit where the diameter of the tunnel vanishes, we obtain the equation of a cusp, whose degree of degeneracy depends on the exact sequence used to collapse the tunnel. We call this a collapsing equation.

For this study, we pick a collapsing equation which depends not only on the diameter but also the coordinate along the tunnel. In particular, one may collapse the "center" of the tunnel first, leaving the "ends" intact. In doing so, we observe that once the tunnel has collapsed fully in the center, the time dependence of the diameter vanishes, leading to a stationary configuration. What's more, the sensitivity of this configuration to perturbation also vanishes, making this not only a stationary but a stable configuration.

What remains to be shown is how the collapsing equation is derived from the events described by Shan and Bal. As noted above, the time dependence of the diameter of such a tunnel must necessarily be negative, leading to a tunnel which must eventually collapse, unless there is an opposing factor keeping it stable. Kun proposes the strength of the Force as this opposing factor, which resides in any force-sensitive being on one side and the Living Force on the other. As such, these tunnels are naturally least stable in their "center," giving rise to the collapsing equation described above.

Moreover, applying the time evolution not to the diameter of the tunnel but the position of the cusp once it has formed, we recover the anomaly location equation of [Re102]. In particular, its location will tend towards the place strongest in the Force, regardless of whether that be a moon, planet or a person. This provides a unified interpretation of the two categories presented in Shan and Bal's work.

We conclude that our cusp model follows naturally from Kun's tunnel model, by simply introducing time dependence. The behavior exhibited by these cusps aligns with the observations made by Shan and Bal, and it places tight lower bounds on the stability of a Force anomaly, depending primarily on the diameter of the initial tunnel, whose collapse lead to the anomaly in the first place.

Section 3

After understanding the origin and formation of Force anomalies, one may wish to understand, how to mend or correct an anomaly. As seen in section 2, the cusp model produces a configuration which is both stationary and stable, making it exceedingly robust against perturbations. Nonetheless, in principle the procedure to resolve an anomaly is straightforward. To resolve the cusp and thereby the anomaly, one must reconnect the cusp with either the Living Force or the real world, and then rebuild the tunnel, thereby allowing the trapped life force to escape. It is theorized what the effects of releasing unbound life force into the real world may be, but it is widely accepted that such unbound life force is unstable, and so any effects it may have are necessarily temporary, before the life force dissolves into the Living Force by itself.

As simple as the theory may be on the matter, there are no records anyone attempting to do so, and so no data exists towards the difficulty of the feat. It has been suggested to the authors that the energy required to resolve an anomaly is so great as to produce an anomaly of its own. Further data is required on this matter, but the nature of that data and the setup in acquiring this data is beyond the scope of this paper.

Acknowledgements

The authors are indebted to Jedi-Masters Shan and Bal, who inspired the discussion of anomalies over an afternoon caf. The authors are also thankful to the Coruscant Academy of Supernatural Sciences for providing housing, access to archives, as well as financial support for the authors. Finally, the first author is greatly thankful to his wife Tikk.

Chapters
Part I: Malachor V

Force Anomalies - A mathematical model of the most elusive phenomenon of the Force