Please Note: This is a fringe hypothesis at best. The forces described here may or may not exist in real life. Don't get your heart set on finding them! Also note that the further into these articles you go, the sillier they'll sound. You were warned.
At first glance, Karma might seem a weird choice to add as a force into a story like Trigamon. In popular culture, Karma is usually a religious concept, often facilitated by a higher power. But unlike most concepts that come from religion, it's easy as a writer to replace the higher power with a set of physical laws. This is done by making good and evil aspects of a system that wants to maintain equilibrium, akin to positive and negative charges.
And Karma is extremely beneficial to a story in the plothole department. Karma helps explain why the "good guys" manage to win 99% of the time. (The fact that Trigamon bad guys tend to be dump and/or crazy helps too!) Karma also helps us explain all of the seemingly impossible coincidences that are required to drive the plot forwards. Of course by definition, true coincidences don't need any explanation, but add too many and believability of the story will go down, without a mechanism to explain the improbable statistics.
Some stories don't care about this factor, but many authors invent mechanisms to explain why the life of their main character(s) are more exiting than normal. Examples of this are the "Will of the D" from One Piece and the "Infinite Improbability Drive." from the Hitchhiker's Guide to the Galaxy. But giving characters a unique item or ability makes characters less relatable, as it tends to elevate them above the viewer, especially if they were just "born that way."
Of course this isn't all Karma does. Karma also is invaluable in resolving temporal paradoxes. Trigamon contains the world of Pokemon (in fact, it's the main target for parody) and the world of Pokemon contains timetravel (via Celebi, Dialga, et cetera) so temporal paradoxes can become a major concern. But I'll go into more detail about this a bit later.
Karma is a weak force, far weaker than Gravity. It's also unreliable by nature. Because of these factors, the full equation for the force that Karma exerts on an object isn't known, although scientists in the Trigamon universe are working on it. Any equation for Karma won't be simple, since it has to account for 108 different variables. But just because we haven't pinned down karma's exact equation (a quest that is comparable in difficulty to the Turing's Halting Problem) doesn't mean we don't know anything about it's workings. Quite the opposite in fact.
What we do know is that karma does not affect matter or energy directly: instead, it affects the probability that a certain event will occur. Note that karma does not actually cause events to occur (events are not guaranteed) just they become more likely under certain karmic conditions. And while in theory this should be easy to analyze statistically, there are problems with doing this in practice. Every action has a karmic value, and the action of measuring a karmic probability affects that probability.
Although we don't know how to measure karma, we can approximate it pretty well. The general rule is that the simpler the model the more likely it is to give useful results. (We don't know if this probability is influenced by Karma or not). Below is the simplest equation for karma, which also happens to be the most useful:
In the previous equation, the KQ, or Karma Quotient, is equal to how "good" an action or fortune was. (Or if the action or fortune was "bad," how bad). Like anything in nature, Karma wants to be at equilibrium. If you elevate your karma by doing "good" actions, good things will happen to you to reduce your karma back to equilibrium. Likewise if you do "bad" things, bad things will happen to you as your karma tries to go back to equilibrium. Well probably. Since Karma is probabilistic, rather than deterministic, bad things can still happen to good people. But is significantly less likely. Also bear in mind that karma probably doesn't share the same definitions of "good" and "bad" that you do, although its likely to be pretty close.
Karma of an object increases when:This is actually an oversimplification as karma is not one value, but really a vector of 108 different values. Since sets of objects each have their own karma, and every possible pairing of n objects has it's own karma, for a universe of n objects, has ∑i=1n (n choose i) variables. Since measuring something is an action, and karma changes every time an action occurs, measuring the karma of something changes it, and thus the true karma of any object changes the karma. And as stated earlier, karmic irregularities were how doesn't matter was detected.
With that stated, it's important to address what kinds of effects karma has on matter. At the most fundamental level, karma messes with probabilities in the subatomic realm, and everything else is just a manifestation of that. For example, karma can change the probability that a given photon will split into a particle-antiparticle pair at any specific moment. While this might seem too small to affect you, one of those particles might interact with a particle in your calculator to flip a bit and give you the wrong answer on your big exam. Alternatively (and more seriously), karma could cause a high energy particle to penetrate your sunscreen and give you skin cancer. Hypothetically, if you were evil enough, these quantum fluctuations could, over a long enough period, even send a meteor your way.
In talking about good and bad, it's often to overlook the fact that karma doesn't have just one kind of "good" or "bad", but 108 different kinds. Each of these 108 kinds of good/bad can be thought of as a axis, such that any action is really a vector in 108-dimensional space. And of course, karma also doesn't just affect one particle per action.
Although karma can cause some pretty crazy things, karma falls far short of controlling the universe. While there are many things that karma can do, there is a long list of things that it can't. Karma can't cause events that violate physical laws: i.e. conservation of energy. Karma won't give you the ability to fly, or even the ability to walk on water. This point should really be stressed, since Karma can't save you from your own stupidity. If your rocket explodes, no amount of karma will save you from a fiery death. Nor will karma enable to you to breathe on Mars. Karma won't materialize your soul-mate on your front porch Boltzmann-Brain style. While all of these are technically possible, the extreme unlikelihood is something far too great for karma to overcome. The more improbable something is, the more karma is needed to make it happen. If the chance is less than 1 in 1060, just forget about karma altogether.
Karmic Feedback Loops (KFLs) are few and far between, but are worth mentioning because of the role they played in making the Trigamon Universe the way it is. Karma is a bit like Gravity, in that things can get weird at extremely high levels of karma, to the point where KFLs occur, which is basically the karmic equivalent of a black hole. In a KFL, karma interacts with itself, modifying the "goodness" and "badness" of actions and causing the karma of a person or object to extend in one direction without limit.
KFLs are dangerous, not only because it can cause effects similar to an Infinite Improbability Drive[1], but also because it can override free will and turn people into puppets. KFLs are seen at the end of Madoka Magica[2], and while they are not depicted 100% accurately, they do have the effect of turning people into beings indistinguishable from gods.
Karmic information travels at nearly 1,000,000,000,000,000 (one quadrillion) times the speed of light. Karma can do this because karmic information is not exchanged with bosons, or a particle of any kind, which (unless supernatural and/or tachyonic) would be bound by the speed of light. Karma is neither a particle nor a wave, but rather a mathematical property that exists, at least at standard temperatures. Karmic bosons do appear at extremely high energy levels, in excess of a googol plex (1010100) degrees[3].
Next: Additions to the Standard Model[1] See Hitchhiker's Guide to the Galaxy
[2] In fact, the Karmic Feedback Loops (KFLs) in Madoka Magica (along with other KFLs happening to some of the same characters) actually helped shape the universe in which Trigamon takes place. These KFLs caused the universe itself to come alive and reset itself with a different karmic mechanism.
[3] Doesn't matter Fahrenheit or Celcius: do you have any idea of how big this number is?!